Bot-S: The Complete Works of Aristotle

'Yes. But, you see, evil is both evil and a
thing-to-learn, so that evil is an evil-thing-to-learn, although the knowledge of evils is good.' Again, 'Is it
true to say in the present moment that you are born?' Yes.' 'Then you are born in the present moment.' 'No;
the expression as divided has a different meaning: for it is true to say-in-the-present-moment that "you are
born", but not "You are born-in-the-present-moment".' Again, 'Could you do what you can, and as you
can?' Yes.' 'But when not harping, you have the power to harp: and therefore you could harp when not
harping.' 'No: he has not the power to harp- while-not-harping; merely, when he is not doing it, he has the
power to do it.' Some people solve this last refutation in another way as well. For, they say, if he has granted
that he can do anything in the way he can, still it does not follow that he can harp when not harping: for it has
not been granted that he will do anything in every way in which he can; and it is not the same thing' to do a

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thing in the way he can' and 'to do it in every way in which he can'. But evidently they do not solve it
properly: for of arguments that depend upon the same point the solution is the same, whereas this will not fit
all cases of the kind nor yet all ways of putting the questions: it is valid against the questioner, but not against
his argument.

Accentuation gives rise to no fallacious arguments, either as written or as spoken, except perhaps some few
that might be made up; e.g. the following argument. 'Is ou katalueis a house?' 'Yes.' 'Is then ou katalueis the
negation of katalueis?' 'Yes.' 'But you said that ou katalueis is a house: therefore the house is a negation.' How
one should solve this, is clear: for the word does not mean the same when spoken with an acuter and when
spoken with a graver accent.

It is clear also how one must meet those fallacies that depend on the identical expressions of things that are
not identical, seeing that we are in possession of the kinds of predications. For the one man, say, has granted,
when asked, that a term denoting a substance does not belong as an attribute, while the other has shown that
some attribute belongs which is in the Category of Relation or of Quantity, but is usually thought to denote a
substance because of its expression; e.g. in the following argument: 'Is it possible to be doing and to have
done the same thing at the same time?' 'No.' 'But, you see, it is surely possible to be seeing and to have seen
the same thing at the same time, and in the same aspect.' Again, 'Is any mode of passivity a mode of activity?'
'No.' 'Then "he is cut", "he is burnt", "he is struck by some sensible object" are alike in expression and all
denote some form of passivity, while again "to say", "to run", "to see" are like one like one another in
expression: but, you see, "to see" is surely a form of being struck by a sensible object; therefore it is at the
same time a form of passivity and of activity.' Suppose, however, that in that case any one, after granting that
it is not possible to do and to have done the same thing in the same time, were to say that it is possible to see
and to have seen it, still he has not yet been refuted, suppose him to say that 'to see' is not a form of 'doing'
(activity) but of 'passivity': for this question is required as well, though he is supposed by the listener to have
already granted it, when he granted that 'to cut' is a form of present, and 'to have cut' a form of past, activity,
and so on with the other things that have a like expression. For the listener adds the rest by himself, thinking
the meaning to be alike: whereas really the meaning is not alike, though it appears to be so because of the
expression. The same thing happens here as happens in cases of ambiguity: for in dealing with ambiguous
expressions the tyro in argument supposes the sophist to have negated the fact which he (the tyro) affirmed,
and not merely the name: whereas there still wants the question whether in using the ambiguous term he had
a single meaning in view: for if he grants that that was so, the refutation will be effected.

Like the above are also the following arguments. It is asked if a man has lost what he once had and
afterwards has not: for a man will no longer have ten dice even though he has only lost one die. No: rather it
is that he has lost what he had before and has not now; but there is no necessity for him to have lost as much
or as many things as he has not now. So then, he asks the questions as to what he has, and draws the
conclusion as to the whole number that he has: for ten is a number. If then he had asked to begin with,
whether a man no longer having the number of things he once had has lost the whole number, no one would
have granted it, but would have said 'Either the whole number or one of them'. Also there is the argument that
'a man may give what he has not got': for he has not got only one die. No: rather it is that he has given not
what he had not got, but in a manner in which he had not got it, viz. just the one. For the word 'only' does not
signify a particular substance or quality or number, but a manner relation, e.g. that it is not coupled with any
other. It is therefore just as if he had asked 'Could a man give what he has not got?' and, on being given the
answer 'No', were to ask if a man could give a thing quickly when he had not got it quickly, and, on this being
granted, were to conclude that 'a man could give what he had not got'. It is quite evident that he has not

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proved his point: for to 'give quickly' is not to give a thing, but to give in a certain manner; and a man could
certainly give a thing in a manner in which he has not got it, e.g. he might have got it with pleasure and give
it with pain.

Like these are also all arguments of the following kind: 'Could a man strike a blow with a hand which he has
not got, or see with an eye which he has not got?' For he has not got only one eye. Some people solve this
case, where a man has more than one eye, or more than one of anything else, by saying also that he has only
one. Others also solve it as they solve the refutation of the view that 'what a man has, he has received': for A
gave only one vote; and certainly B, they say, has only one vote from A. Others, again, proceed by
demolishing straight away the proposition asked, and admitting that it is quite possible to have what one has
not received; e.g. to have received sweet wine, but then, owing to its going bad in the course of receipt, to
have it sour. But, as was said also above,' all these persons direct their solutions against the man, not against
his argument. For if this were a genuine solution, then, suppose any one to grant the opposite, he could find
no solution, just as happens in other cases; e.g. suppose the true solution to be 'So-and-so is partly true and
partly not', then, if the answerer grants the expression without any qualification, the sophist's conclusion
follows. If, on the other hand, the conclusion does not follow, then that could not be the true solution: and
what we say in regard to the foregoing examples is that, even if all the sophist's premisses be granted, still no
proof is effected.

Moreover, the following too belong to this group of arguments. 'If something be in writing did some one
write it?' 'Yes.' 'But it is now in writing that you are seated-a false statement, though it was true at the time
when it was written: therefore the statement that was written is at the same time false and true.' But this is
fallacious, for the falsity or truth of a statement or opinion indicates not a substance but a quality: for the
same account applies to the case of an opinion as well. Again, 'Is what a learner learns what he learns?' 'Yes.'
'But suppose some one learns "slow" quick. Then his (the sophist's) words denote not what the learner learns
but how he learns it. Also, 'Does a man tread upon what he walks through? Yes.' 'But X walks through a
whole day.' No, rather the words denote not what he walks through, but when he walks; just as when any one
uses the words 'to drink the cup' he denotes not what he drinks, but the vessel out of which he drinks. Also, 'Is
it either by learning or by discovery that a man knows what he knows?' 'Yes.' 'But suppose that of a pair of
things he has discovered one and learned the other, the pair is not known to him by either method.' No: 'what'
he knows, means' every single thing' he knows, individually; but this does not mean 'all the things' he knows,
collectively. Again, there is the proof that there is a 'third man' distinct from Man and from individual men.
But that is a fallacy, for 'Man', and indeed every general predicate, denotes not an individual substance, but a
particular quality, or the being related to something in a particular manner, or something of that sort.
Likewise also in the case of 'Coriscus' and 'Coriscus the musician' there is the problem, Are they the same or
different?' For the one denotes an individual substance and the other a quality, so that it cannot be isolated;
though it is not the isolation which creates the 'third man', but the admission that it is an individual substance.
For 'Man' cannot be an individual substance, as Callias is. Nor is the case improved one whit even if one were
to call the clement he has isolated not an individual substance but a quality: for there will still be the one
beside the many, just as 'Man' was. It is evident then that one must not grant that what is a common predicate
applying to a class universally is an individual substance, but must say that denotes either a quality, or a
relation, or a quantity, or something of that kind.

It is a general rule in dealing with arguments that depend on language that the solution always follows the
opposite of the point on which the argument turns: e.g. if the argument depends upon combination, then the
solution consists in division; if upon division, then in combination. Again, if it depends on an acute accent,
the solution is a grave accent; if on a grave accent, it is an acute. If it depends on ambiguity, one can solve it
by using the opposite term; e.g. if you find yourself calling something inanimate, despite your previous denial

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that it was so, show in what sense it is alive: if, on the other hand, one has declared it to be inanimate and the
sophist has proved it to be animate, say how it is inanimate. Likewise also in a case of amphiboly. If the
argument depends on likeness of expression, the opposite will be the solution. 'Could a man give what he has
not got? 'No, not what he has not got; but he could give it in a way in which he has not got it, e.g. one die by
itself.' Does a man know either by learning or by discovery each thing that he knows, singly? but not the
things that he knows, collectively.' Also a man treads, perhaps, on any thing he walks through, but not on the
time he walks through. Likewise also in the case of the other examples.

In dealing with arguments that depend on Accident, one and the same solution meets all cases. For since it is
indeterminate when an attribute should be ascribed to a thing, in cases where it belongs to the accident of the
thing, and since in some cases it is generally agreed and people admit that it belongs, while in others they
deny that it need belong, we should therefore, as soon as the conclusion has been drawn, say in answer to
them all alike, that there is no need for such an attribute to belong. One must, however, be prepared to adduce
an example of the kind of attribute meant. All arguments such as the following depend upon Accident. 'Do
you know what I am going to ask you? you know the man who is approaching', or 'the man in the mask'? 'Is
the statue your work of art?' or 'Is the dog your father?' 'Is the product of a small number with a small number
a small number?' For it is evident in all these cases that there is no necessity for the attribute which is true of
the thing's accident to be true of the thing as well. For only to things that are indistinguishable and one in
essence is it generally agreed that all the same attributes belong; whereas in the case of a good thing, to be
good is not the same as to be going to be the subject of a question; nor in the case of a man approaching, or
wearing a mask, is 'to be approaching' the same thing as 'to be Coriscus', so that suppose I know Coriscus, but
do not know the man who is approaching, it still isn't the case that I both know and do not know the same
man; nor, again, if this is mine and is also a work of art, is it therefore my work of art, but my property or
thing or something else. (The solution is after the same manner in the other cases as well.)

Some solve these refutations by demolishing the original proposition asked: for they say that it is possible to
know and not to know the same thing, only not in the same respect: accordingly, when they don't know the
man who is coming towards them, but do know Corsicus, they assert that they do know and don't know the
same object, but not in the same respect. Yet, as we have already remarked, the correction of arguments that
depend upon the same point ought to be the same, whereas this one will not stand if one adopts the same
principle in regard not to knowing something, but to being, or to being is a in a certain state, e.g. suppose that
X is father, and is also yours: for if in some cases this is true and it is possible to know and not to know the
same thing, yet with that case the solution stated has nothing to do. Certainly there is nothing to prevent the
same argument from having a number of flaws; but it is not the exposition of any and every fault that
constitutes a solution: for it is possible for a man to show that a false conclusion has been proved, but not to
show on what it depends, e.g. in the case of Zeno's argument to prove that motion is impossible. So that even
if any one were to try to establish that this doctrine is an impossible one, he still is mistaken, and even if he
proved his case ten thousand times over, still this is no solution of Zeno's argument: for the solution was all
along an exposition of false reasoning, showing on what its falsity depends. If then he has not proved his
case, or is trying to establish even a true proposition, or a false one, in a false manner, to point this out is a
true solution. Possibly, indeed, the present suggestion may very well apply in some cases: but in these cases,
at any rate, not even this would be generally agreed: for he knows both that Coriscus is Coriscus and that the
approaching figure is approaching. To know and not to know the same thing is generally thought to be
possible, when e.g. one knows that X is white, but does not realize that he is musical: for in that way he does
know and not know the same thing, though not in the same respect. But as to the approaching figure and
Coriscus he knows both that it is approaching and that he is Coriscus.

A like mistake to that of those whom we have mentioned is that of those who solve the proof that every
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number is a small number: for if, when the conclusion is not proved, they pass this over and say that a
conclusion has been proved and is true, on the ground that every number is both great and small, they make a
mistake.

Some people also use the principle of ambiguity to solve the aforesaid reasonings, e.g. the proof that 'X is
your father', or 'son', or 'slave'. Yet it is evident that if the appearance a proof depends upon a plurality of
meanings, the term, or the expression in question, ought to bear a number of literal senses, whereas no one
speaks of A as being 'B's child' in the literal sense, if B is the child's master, but the combination depends
upon Accident. 'Is A yours?' 'Yes.' And is A a child?' Yes.' 'Then the child A is yours,' because he happens to
be both yours and a child; but he is not 'your child'.

There is also the proof that 'something "of evils" is good'; for wisdom is a 'knowledge "of evils'". But the
expression that this is 'of so and-so' (='so-and-so's') has not a number of meanings: it means that it is
'so-and-so's property'. We may suppose of course, on the other hand, that it has a number of meanings-for
we also say that man is 'of the animals', though not their property; and also that any term related to 'evils' in a
way expressed by a genitive case is on that account a so-and-so 'of evils', though it is not one of the
evils-but in that case the apparently different meanings seem to depend on whether the term is used relatively
or absolutely. 'Yet it is conceivably possible to find a real ambiguity in the phrase "Something of evils is
good".' Perhaps, but not with regard to the phrase in question. It would occur more nearly, suppose that A
servant is good of the wicked'; though perhaps it is not quite found even there: for a thing may be 'good' and
be 'X's' without being at the same time 'X's good'. Nor is the saying that 'Man is of the animals' a phrase with
a number of meanings: for a phrase does not become possessed of a number of meanings merely suppose we
express it elliptically: for we express 'Give me the Iliad' by quoting half a line of it, e.g. 'Give me "Sing,
goddess, of the wrath...'"

Those arguments which depend upon an expression that is valid of a particular thing, or in a particular
respect, or place, or manner, or relation, and not valid absolutely, should be solved by considering the
conclusion in relation to its contradictory, to see if any of these things can possibly have happened to it. For it
is impossible for contraries and opposites and an affirmative and a negative to belong to the same thing
absolutely; there is, however, nothing to prevent each from belonging in a particular respect or relation or
manner, or to prevent one of them from belonging in a particular respect and the other absolutely. So that if
this one belongs absolutely and that one in a particular respect, there is as yet no refutation. This is a feature
one has to find in the conclusion by examining it in comparison with its contradictory.

All arguments of the following kind have this feature: 'Is it possible for what is-not to be? "No." But, you
see, it is something, despite its not being.' Likewise also, Being will not be; for it will not he some particular
form of being. Is it possible for the same man at the same time to be a keeper and a breaker of his oath?' 'Can
the same man at the same time both obey and disobey the same man?' Or isn't it the case that being something
in particular and Being are not the same? On the other hand, Not-being, even if it be something, need not
also have absolute 'being' as well. Nor if a man keeps his oath in this particular instance or in this particular
respect, is he bound also to be a keeper of oaths absolutely, but he who swears that he will break his oath, and
then breaks it, keeps this particular oath only; he is not a keeper of his oath: nor is the disobedient man
'obedient', though he obeys one particular command. The argument is similar, also, as regards the problem
whether the same man can at the same time say what is both false and true: but it appears to be a troublesome
question because it is not easy to see in which of the two connexions the word 'absolutely' is to be
rendered-with 'true' or with 'false'. There is, however, nothing to prevent it from being false absolutely,
though true in some particular respect or relation, i.e. being true in some things, though not 'true' absolutely.
Likewise also in cases of some particular relation and place and time. For all arguments of the following kind

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depend upon this.' Is health, or wealth, a good thing?' 'Yes.' 'But to the fool who does not use it aright it is not
a good thing: therefore it is both good and not good.' 'Is health, or political power, a good thing?' 'Yes. "But
sometimes it is not particularly good: therefore the same thing is both good and not good to the same man.'
Or rather there is nothing to prevent a thing, though good absolutely, being not good to a particular man, or
being good to a particular man, and yet not good or here. 'Is that which the prudent man would not wish, an
evil?' 'Yes.' 'But to get rid of, he would not wish the good: therefore the good is an evil.' But that is a mistake;
for it is not the same thing to say 'The good is an evil' and 'to get rid of the good is an evil'. Likewise also the
argument of the thief is mistaken. For it is not the case that if the thief is an evil thing, acquiring things is also
evil: what he wishes, therefore, is not what is evil but what is good; for to acquire something good is good.
Also, disease is an evil thing, but not to get rid of disease. 'Is the just preferable to the unjust, and what takes
place justly to what takes place unjustly? 'Yes.' 'But to to be put to death unjustly is preferable.' 'Is it just that
each should have his own?' Yes.' 'But whatever decisions a man comes to on the strength of his personal
opinion, even if it be a false opinion, are valid in law: therefore the same result is both just and unjust.' Also,
should one decide in favour of him who says what is unjust?' 'The former.' 'But you see, it is just for the
injured party to say fully the things he has suffered; and these are fallacies. For because to suffer a thing
unjustly is preferable, unjust ways are not therefore preferable, though in this particular case the unjust may
very well be better than the just. Also, to have one's own is just, while to have what is another's is not just: all
the same, the decision in question may very well be a just decision, whatever it be that the opinion of the man
who gave the decision supports: for because it is just in this particular case or in this particular manner, it is
not also just absolutely. Likewise also, though things are unjust, there is nothing to prevent the speaking of
them being just: for because to speak of things is just, there is no necessity that the things should be just, any
more than because to speak of things be of use, the things need be of use. Likewise also in the case of what is
just. So that it is not the case that because the things spoken of are unjust, the victory goes to him who speaks
unjust things: for he speaks of things that are just to speak of, though absolutely, i.e. to suffer, they are unjust.

Refutations that depend on the definition of a refutation must, according to the plan sketched above, be met
by comparing together the conclusion with its contradictory, and seeing that it shall involve the same attribute
in the same respect and relation and manner and time. If this additional question be put at the start, you
should not admit that it is impossible for the same thing to be both double and not double, but grant that it is
possible, only not in such a way as was agreed to constitute a refutation of your case. All the following
arguments depend upon a point of that kind. 'Does a man who knows A to be A, know the thing called A?'
and in the same way, 'is one who is ignorant that A is A ignorant of the thing called A?' Yes.' 'But one who
knows that Coriscus is Coriscus might be ignorant of the fact that he is musical, so that he both knows and is
ignorant of the same thing.' Is a thing four cubits long greater than a thing three cubits long?' Yes.' 'But a
thing might grow from three to four cubits in length; 'now what is 'greater' is greater than a 'less': accordingly
the thing in question will be both greater and less than itself in the same respect.

As to refutations that depend on begging and assuming the original point to be proved, suppose the nature of
the question to be obvious, one should not grant it, even though it be a view generally held, but should tell
him the truth. Suppose, however, that it escapes one, then, thanks to the badness of arguments of that kind,
one should make one's error recoil upon the questioner, and say that he has brought no argument: for a
refutation must be proved independently of the original point. Secondly, one should say that the point was
granted under the impression that he intended not to use it as a premiss, but to reason against it, in the
opposite way from that adopted in refutations on side issues.

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Also, those refutations that bring one to their conclusion through the consequent you should show up in the
course of the argument itself. The mode in which consequences follow is twofold. For the argument either is
that as the universal follows on its particular-as (e.g.) 'animal' follows from 'man'-so does the particular on
its universal: for the claim is made that if A is always found with B, then B also is always found with A. Or
else it proceeds by way of the opposites of the terms involved: for if A follows B, it is claimed that A's
opposite will follow B's opposite. On this latter claim the argument of Melissus also depends: for he claims
that because that which has come to be has a beginning, that which has not come to be has none, so that if the
heaven has not come to be, it is also eternal. But that is not so; for the sequence is vice versa.

In the case of any refutations whose reasoning depends on some addition, look and see if upon its subtraction
the absurdity follows none the less: and then if so, the answerer should point this out, and say that he granted
the addition not because he really thought it, but for the sake of the argument, whereas the questioner has not
used it for the purpose of his argument at all.

To meet those refutations which make several questions into one, one should draw a distinction between them
straight away at the start. For a question must be single to which there is a single answer, so that one must not
affirm or deny several things of one thing, nor one thing of many, but one of one. But just as in the case of
ambiguous terms, an attribute belongs to a term sometimes in both its senses, and sometimes in neither, so
that a simple answer does one, as it happens, no harm despite the fact that the question is not simple, so it is
in these cases of double questions too. Whenever, then, the several attributes belong to the one subject, or the
one to the many, the man who gives a simple answer encounters no obstacle even though he has committed
this mistake: but whenever an attribute belongs to one subject but not to the other, or there is a question of a
number of attributes belonging to a number of subjects and in one sense both belong to both, while in another
sense, again, they do not, then there is trouble, so that one must beware of this. Thus (e.g.) in the following
arguments: Supposing to be good and B evil, you will, if you give a single answer about both, be compelled
to say that it is true to call these good, and that it is true to call them evil and likewise to call them neither
good nor evil (for each of them has not each character), so that the same thing will be both good and evil and
neither good nor evil. Also, since everything is the same as itself and different from anything else, inasmuch
as the man who answers double questions simply can be made to say that several things are 'the same' not as
other things but 'as themselves', and also that they are different from themselves, it follows that the same
things must be both the same as and different from themselves. Moreover, if what is good becomes evil while
what is evil is good, then they must both become two. So of two unequal things each being equal to itself, it
will follow that they are both equal and unequal to themselves.

Now these refutations fall into the province of other solutions as well: for 'both' and 'all' have more than one
meaning, so that the resulting affirmation and denial of the same thing does not occur, except verbally: and
this is not what we meant by a refutation. But it is clear that if there be not put a single question on a number
of points, but the answerer has affirmed or denied one attribute only of one subject only, the absurdity will
not come to pass.

With regard to those who draw one into repeating the same thing a number of times, it is clear that one must
not grant that predications of relative terms have any meaning in abstraction by themselves, e.g. that 'double'

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is a significant term apart from the whole phrase 'double of half merely on the ground that it figures in it. For
ten figures in 'ten minus one' and in 'not do', and generally the affirmation in the negation; but for all that,
suppose any one were to say, 'This is not white', he does not say that it is white. The bare word 'double', one
may perhaps say, has not even any meaning at all, any more than has 'the' in 'the half: and even if it has a
meaning, yet it has not the same meaning as in the combination. Nor is 'knowledge' the same thing in a
specific branch of it (suppose it, e.g. to be 'medical knowledge') as it is in general: for in general it was the
'knowledge of the knowable'. In the case of terms that are predicated of the terms through which they are
defined, you should say the same thing, that the term defined is not the same in abstraction as it is in the
whole phrase. For 'concave' has a general meaning which is the same in the case of a snub nose, and of a
bandy leg, but when added to either substantive nothing prevents it from differentiating its meaning; in fact it
bears one sense as applied to the nose, and another as applied to the leg: for in the former connexion it means
'snub' and in the latter 'bandy shaped'; i.e. it makes no difference whether you say 'a snub nose' or 'a concave
nose'. Moreover, the expression must not be granted in the nominative case: for it is a falsehood. For
snubness is not a concave nose but something (e.g. an affection) belonging to a nose: hence, there is no
absurdity in supposing that the snub nose is a nose possessing the concavity that belongs to a nose.

With regard to solecisms, we have previously said what it is that appears to bring them about; the method of
their solution will be clear in the course of the arguments themselves. Solecism is the result aimed at in all
arguments of the following kind: 'Is a thing truly that which you truly call it?' 'Yes'. 'But, speaking of a stone,
you call him real: therefore of a stone it follows that "him is real".' No: rather, talking of a stone means not
saying which' but 'whom', and not 'that' but 'him'. If, then, any one were to ask, 'Is a stone him whom you
truly call him?' he would be generally thought not to be speaking good Greek, any more than if he were to
ask, 'Is he what you call her?' Speak in this way of a 'stick' or any neuter word, and the difference does not
break out. For this reason, also, no solecism is incurred, suppose any one asks, 'Is a thing what you say it to
be?' 'Yes'. 'But, speaking of a stick, you call it real: therefore, of a stick it follows that it is real.' 'Stone',
however, and 'he' have masculine designations. Now suppose some one were to ask, 'Can "he" be a she" (a
female)?', and then again, 'Well, but is not he Coriscus?' and then were to say, 'Then he is a "she",' he has not
proved the solecism, even if the name 'Coriscus' does signify a 'she', if, on the other hand, the answerer does
not grant this: this point must be put as an additional question: while if neither is it the fact nor does he grant
it, then the sophist has not proved his case either in fact or as against the person he has been questioning. In
like manner, then, in the above instance as well it must be definitely put that 'he' means the stone. If,
however, this neither is so nor is granted, the conclusion must not be stated: though it follows apparently,
because the case (the accusative), that is really unlike, appears to be like the nominative. 'Is it true to say that
this object is what you call it by name?' Yes'. 'But you call it by the name of a shield: this object therefore is
"of a shield".' No: not necessarily, because the meaning of 'this object' is not 'of a shield' but 'a shield': 'of a
shield' would be the meaning of 'this object's'. Nor again if 'He is what you call him by name', while 'the name
you call him by is Cleon's', is he therefore 'Cleon's': for he is not 'Cleon's', for what was said was that 'He, not
his, is what I call him by name'. For the question, if put in the latter way, would not even be Greek. 'Do you
know this?' Yes.' 'But this is he: therefore you know he'. No: rather 'this' has not the same meaning in 'Do you
know this?' as in 'This is a stone'; in the first it stands for an accusative, in the second for a nominative case.
'When you have understanding of anything, do you understand it?' Yes.' 'But you have understanding of a
stone: therefore you understand of a stone.' No: the one phrase is in the genitive, 'of a stone', while the other
is in the accusative, 'a stone': and what was granted was that 'you understand that, not of that, of which you
have understanding', so that you understand not 'of a stone', but 'the stone'.

Thus that arguments of this kind do not prove solecism but merely appear to do so, and both why they so
appear and how you should meet them, is clear from what has been said.

32 27

ON SOPHISTICAL REFUTATIONS

We must also observe that of all the arguments aforesaid it is easier with some to see why and where the
reasoning leads the hearer astray, while with others it is more difficult, though often they are the same
arguments as the former. For we must call an argument the same if it depends upon the same point; but the
same argument is apt to be thought by some to depend on diction, by others on accident, and by others on
something else, because each of them, when worked with different terms, is not so clear as it was.
Accordingly, just as in fallacies that depend on ambiguity, which are generally thought to be the silliest form
of fallacy, some are clear even to the man in the street (for humorous phrases nearly all depend on diction;
e.g. 'The man got the cart down from the stand'; and 'Where are you bound?' 'To the yard arm'; and 'Which
cow will calve afore?' 'Neither, but both behind;' and 'Is the North wind clear?' 'No, indeed; for it has
murdered the beggar and the merchant." Is he a Good enough-King?' 'No, indeed; a Rob-son': and so with
the great majority of the rest as well), while others appear to elude the most expert (and it is a symptom of
this that they often fight about their terms, e.g. whether the meaning of 'Being' and 'One' is the same in all
their applications or different; for some think that 'Being' and 'One' mean the same; while others solve the
argument of Zeno and Parmenides by asserting that 'One' and 'Being' are used in a number of senses),
likewise also as regards fallacies of Accident and each of the other types, some of the arguments will be
easier to see while others are more difficult; also to grasp to which class a fallacy belongs, and whether it is a
refutation or not a refutation, is not equally easy in all cases.

An incisive argument is one which produces the greatest perplexity: for this is the one with the sharpest fang.
Now perplexity is twofold, one which occurs in reasoned arguments, respecting which of the propositions
asked one is to demolish, and the other in contentious arguments, respecting the manner in which one is to
assent to what is propounded. Therefore it is in syllogistic arguments that the more incisive ones produce the
keenest heart-searching. Now a syllogistic argument is most incisive if from premisses that are as generally
accepted as possible it demolishes a conclusion that is accepted as generally as possible. For the one
argument, if the contradictory is changed about, makes all the resulting syllogisms alike in character: for
always from premisses that are generally accepted it will prove a conclusion, negative or positive as the case
may be, that is just as generally accepted; and therefore one is bound to feel perplexed. An argument, then, of
this kind is the most incisive, viz. the one that puts its conclusion on all fours with the propositions asked; and
second comes the one that argues from premisses, all of which are equally convincing: for this will produce
an equal perplexity as to what kind of premiss, of those asked, one should demolish. Herein is a difficulty: for
one must demolish something, but what one must demolish is uncertain. Of contentious arguments, on the
other hand, the most incisive is the one which, in the first place, is characterized by an initial uncertainty
whether it has been properly reasoned or not; and also whether the solution depends on a false premiss or on
the drawing of a distinction; while, of the rest, the second place is held by that whose solution clearly depends
upon a distinction or a demolition, and yet it does not reveal clearly which it is of the premisses asked, whose
demolition, or the drawing of a distinction within it, will bring the solution about, but even leaves it vague
whether it is on the conclusion or on one of the premisses that the deception depends.

Now sometimes an argument which has not been properly reasoned is silly, supposing the assumptions
required to be extremely contrary to the general view or false; but sometimes it ought not to be held in
contempt. For whenever some question is left out, of the kind that concerns both the subject and the nerve of
the argument, the reasoning that has both failed to secure this as well, and also failed to reason properly, is
silly; but when what is omitted is some extraneous question, then it is by no means to be lightly despised, but
the argument is quite respectable, though the questioner has not put his questions well.

Just as it is possible to bring a solution sometimes against the argument, at others against the questioner and
his mode of questioning, and at others against neither of these, likewise also it is possible to marshal one's
questions and reasoning both against the thesis, and against the answerer and against the time, whenever the

33 28

ON SOPHISTICAL REFUTATIONS
solution requires a longer time to examine than the period available.

As to the number, then, and kind of sources whence fallacies arise in discussion, and how we are to show that
our opponent is committing a fallacy and make him utter paradoxes; moreover, by the use of what materials
solescism is brought about, and how to question and what is the way to arrange the questions; moreover, as to
the question what use is served by all arguments of this kind, and concerning the answerer's part, both as a
whole in general, and in particular how to solve arguments and solecisms-on all these things let the foregoing
discussion suffice. It remains to recall our original proposal and to bring our discussion to a close with a few
words upon it.

Our programme was, then, to discover some faculty of reasoning about any theme put before us from the
most generally accepted premisses that there are. For that is the essential task of the art of discussion
(dialectic) and of examination (peirastic). Inasmuch, however, as it is annexed to it, on account of the near
presence of the art of sophistry (sophistic), not only to be able to conduct an examination dialectically but
also with a show of knowledge, we therefore proposed for our treatise not only the aforesaid aim of being
able to exact an account of any view, but also the aim of ensuring that in standing up to an argument we shall
defend our thesis in the same manner by means of views as generally held as possible. The reason of this we
have explained; for this, too, was why Socrates used to ask questions and not to answer them; for he used to
confess that he did not know. We have made clear, in the course of what precedes, the number both of the
points with reference to which, and of the materials from which, this will be accomplished, and also from
what sources we can become well supplied with these: we have shown, moreover, how to question or arrange
the questioning as a whole, and the problems concerning the answers and solutions to be used against the
reasonings of the questioner. We have also cleared up the problems concerning all other matters that belong
to the same inquiry into arguments. In addition to this we have been through the subject of Fallacies, as we
have already stated above.

That our programme, then, has been adequately completed is clear. But we must not omit to notice what has
happened in regard to this inquiry. For in the case of all discoveries the results of previous labours that have
been handed down from others have been advanced bit by bit by those who have taken them on, whereas the
original discoveries generally make advance that is small at first though much more useful than the
development which later springs out of them. For it may be that in everything, as the saying is, 'the first start
is the main part': and for this reason also it is the most difficult; for in proportion as it is most potent in its
influence, so it is smallest in its compass and therefore most difficult to see: whereas when this is once
discovered, it is easier to add and develop the remainder in connexion with it. This is in fact what has
happened in regard to rhetorical speeches and to practically all the other arts: for those who discovered the
beginnings of them advanced them in all only a little way, whereas the celebrities of to-day are the heirs (so
to speak) of a long succession of men who have advanced them bit by bit, and so have developed them to
their present form, Tisias coming next after the first founders, then Thrasymachus after Tisias, and Theodorus
next to him, while several people have made their several contributions to it: and therefore it is not to be
wondered at that the art has attained considerable dimensions. Of this inquiry, on the other hand, it was not
the case that part of the work had been thoroughly done before, while part had not. Nothing existed at all. For
the training given by the paid professors of contentious arguments was like the treatment of the matter by
Gorgias. For they used to hand out speeches to be learned by heart, some rhetorical, others in the form of
question and answer, each side supposing that their arguments on either side generally fall among them. And
therefore the teaching they gave their pupils was ready but rough. For they used to suppose that they trained
people by imparting to them not the art but its products, as though any one professing that he would impart a
form of knowledge to obviate any pain in the feet, were then not to teach a man the art of shoe-making or the
sources whence he can acquire anything of the kind, but were to present him with several kinds of shoes of all

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ON SOPHISTICAL REFUTATIONS

sorts: for he has helped him to meet his need, but has not imparted an art to him. Moreover, on the subject of
Rhetoric there exists much that has been said long ago, whereas on the subject of reasoning we had nothing
else of an earlier date to speak of at all, but were kept at work for a long time in experimental researches. If,
then, it seems to you after inspection that, such being the situation as it existed at the start, our investigation is
in a satisfactory condition compared with the other inquiries that have been developed by tradition, there
must remain for all of you, or for our students, the task of extending us your pardon for the shortcomings of
the inquiry, and for the discoveries thereof your warm thanks.

-THE END-

34 30

ON THE HEAVENS

by Aristotle

ON THE HEAVENS

Table of Contents

ON THE HEAVENS 1

by Aristotle 1

Book 1 2

_1 2

2 2

3. 4

A 5

_5 5

_6 7

1 8

_8 10

_9 12

10 14

11 15

V2 16

Book II . 19

1 19

2 20

3. 21

A 21

_5 23

6. 23

1_ 24

3. 25

_9 26

10 27

H 27

12 27

13 29

11 32

Book III 34

1 34

2 36

1 37

A 38

1 39

_6 40

1_ 41

_8 42

Book IV 43

1 43

2 44

1 46

A 47

1 48

6 49

ON THE HEAVENS

by Aristotle

translated by J. L. Stocks

« Book I
1
2
3
4
5
6
7
8
9

10
11

12
• Book II

12
13
14
• Book III

• Book IV

• 1

ON THE HEAVENS

2
3
4
5
6

Book I

THE science which has to do with nature clearly concerns itself for the most part with bodies and magnitudes
and their properties and movements, but also with the principles of this sort of substance, as many as they
may be. For of things constituted by nature some are bodies and magnitudes, some possess body and
magnitude, and some are principles of things which possess these. Now a continuum is that which is divisible
into parts always capable of subdivision, and a body is that which is every way divisible. A magnitude if
divisible one way is a line, if two ways a surface, and if three a body. Beyond these there is no other
magnitude, because the three dimensions are all that there are, and that which is divisible in three directions is
divisible in all. For, as the Pythagoreans say, the world and all that is in it is determined by the number three,
since beginning and middle and end give the number of an 'all', and the number they give is the triad. And so,
having taken these three from nature as (so to speak) laws of it, we make further use of the number three in
the worship of the Gods. Further, we use the terms in practice in this way. Of two things, or men, we say
'both', but not 'all': three is the first number to which the term 'all' has been appropriated. And in this, as we
have said, we do but follow the lead which nature gives. Therefore, since 'every' and 'all' and 'complete' do
not differ from one another in respect of form, but only, if at all, in their matter and in that to which they are
applied, body alone among magnitudes can be complete. For it alone is determined by the three dimensions,
that is, is an 'all'. But if it is divisible in three dimensions it is every way divisible, while the other magnitudes
are divisible in one dimension or in two alone: for the divisibility and continuity of magnitudes depend upon
the number of the dimensions, one sort being continuous in one direction, another in two, another in all. All
magnitudes, then, which are divisible are also continuous. Whether we can also say that whatever is
continuous is divisible does not yet, on our present grounds, appear. One thing, however, is clear. We cannot
pass beyond body to a further kind, as we passed from length to surface, and from surface to body. For if we
could, it would cease to be true that body is complete magnitude. We could pass beyond it only in virtue of a
defect in it; and that which is complete cannot be defective, since it has being in every respect. Now bodies
which are classed as parts of the whole are each complete according to our formula, since each possesses
every dimension. But each is determined relatively to that part which is next to it by contact, for which reason
each of them is in a sense many bodies. But the whole of which they are parts must necessarily be complete,
and thus, in accordance with the meaning of the word, have being, not in some respect only, but in every
respect.

The question as to the nature of the whole, whether it is infinite in size or limited in its total mass, is a matter
for subsequent inquiry. We will now speak of those parts of the whole which are specifically distinct. Let us
take this as our starting-point. All natural bodies and magnitudes we hold to be, as such, capable of
locomotion; for nature, we say, is their principle of movement. But all movement that is in place, all
locomotion, as we term it, is either straight or circular or a combination of these two, which are the only

Book I 2

ON THE HEAVENS

simple movements. And the reason of this is that these two, the straight and the circular line, are the only
simple magnitudes. Now revolution about the centre is circular motion, while the upward and downward
movements are in a straight line, 'upward' meaning motion away from the centre, and 'downward' motion
towards it. All simple motion, then, must be motion either away from or towards or about the centre. This
seems to be in exact accord with what we said above: as body found its completion in three dimensions, so its
movement completes itself in three forms.

Bodies are either simple or compounded of such; and by simple bodies I mean those which possess a
principle of movement in their own nature, such as fire and earth with their kinds, and whatever is akin to
them. Necessarily, then, movements also will be either simple or in some sort compound-simple in the case
of the simple bodies, compound in that of the composite-and in the latter case the motion will be that of the
simple body which prevails in the composition. Supposing, then, that there is such a thing as simple
movement, and that circular movement is an instance of it, and that both movement of a simple body is
simple and simple movement is of a simple body (for if it is movement of a compound it will be in virtue of a
prevailing simple element), then there must necessarily be some simple body which revolves naturally and in
virtue of its own nature with a circular movement. By constraint, of course, it may be brought to move with
the motion of something else different from itself, but it cannot so move naturally, since there is one sort of
movement natural to each of the simple bodies. Again, if the unnatural movement is the contrary of the
natural and a thing can have no more than one contrary, it will follow that circular movement, being a simple
motion, must be unnatural, if it is not natural, to the body moved. If then (1) the body, whose movement is
circular, is fire or some other element, its natural motion must be the contrary of the circular motion. But a
single thing has a single contrary; and upward and downward motion are the contraries of one another. If, on
the other hand, (2) the body moving with this circular motion which is unnatural to it is something different
from the elements, there will be some other motion which is natural to it. But this cannot be. For if the natural
motion is upward, it will be fire or air, and if downward, water or earth. Further, this circular motion is
necessarily primary. For the perfect is naturally prior to the imperfect, and the circle is a perfect thing. This
cannot be said of any straight line:-not of an infinite line; for, if it were perfect, it would have a limit and an
end: nor of any finite line; for in every case there is something beyond it, since any finite line can be
extended. And so, since the prior movement belongs to the body which naturally prior, and circular
movement is prior to straight, and movement in a straight line belongs to simple bodies-fire moving straight
upward and earthy bodies straight downward towards the centre-since this is so, it follows that circular
movement also must be the movement of some simple body. For the movement of composite bodies is, as we
said, determined by that simple body which preponderates in the composition. These premises clearly give
the conclusion that there is in nature some bodily substance other than the formations we know, prior to them
all and more divine than they. But it may also be proved as follows. We may take it that all movement is
either natural or unnatural, and that the movement which is unnatural to one body is natural to another-as, for
instance, is the case with the upward and downward movements, which are natural and unnatural to fire and
earth respectively. It necessarily follows that circular movement, being unnatural to these bodies, is the
natural movement of some other. Further, if, on the one hand, circular movement is natural to something, it
must surely be some simple and primary body which is ordained to move with a natural circular motion, as
fire is ordained to fly up and earth down. If, on the other hand, the movement of the rotating bodies about the
centre is unnatural, it would be remarkable and indeed quite inconceivable that this movement alone should
be continuous and eternal, being nevertheless contrary to nature. At any rate the evidence of all other cases
goes to show that it is the unnatural which quickest passes away. And so, if, as some say, the body so moved
is fire, this movement is just as unnatural to it as downward movement; for any one can see that fire moves in
a straight line away from the centre. On all these grounds, therefore, we may infer with confidence that there
is something beyond the bodies that are about us on this earth, different and separate from them; and that the
superior glory of its nature is proportionate to its distance from this world of ours.

Book I

ON THE HEAVENS

In consequence of what has been said, in part by way of assumption and in part by way of proof, it is clear
that not every body either possesses lightness or heaviness. As a preliminary we must explain in what sense
we are using the words 'heavy' and 'light', sufficiently, at least, for our present purpose: we can examine the
terms more closely later, when we come to consider their essential nature. Let us then apply the term 'heavy'
to that which naturally moves towards the centre, and 'light' to that which moves naturally away from the
centre. The heaviest thing will be that which sinks to the bottom of all things that move downward, and the
lightest that which rises to the surface of everything that moves upward. Now, necessarily, everything which
moves either up or down possesses lightness or heaviness or both-but not both relatively to the same thing:
for things are heavy and light relatively to one another; air, for instance, is light relatively to water, and water
light relatively to earth. The body, then, which moves in a circle cannot possibly possess either heaviness or
lightness. For neither naturally nor unnaturally can it move either towards or away from the centre.
Movement in a straight line certainly does not belong to it naturally, since one sort of movement is, as we
saw, appropriate to each simple body, and so we should be compelled to identify it with one of the bodies
which move in this way. Suppose, then, that the movement is unnatural. In that case, if it is the downward
movement which is unnatural, the upward movement will be natural; and if it is the upward which is
unnatural, the downward will be natural. For we decided that of contrary movements, if the one is unnatural
to anything, the other will be natural to it. But since the natural movement of the whole and of its part of
earth, for instance, as a whole and of a small clod-have one and the same direction, it results, in the first
place, that this body can possess no lightness or heaviness at all (for that would mean that it could move by
its own nature either from or towards the centre, which, as we know, is impossible); and, secondly, that it
cannot possibly move in the way of locomotion by being forced violently aside in an upward or downward
direction. For neither naturally nor unnaturally can it move with any other motion but its own, either itself or
any part of it, since the reasoning which applies to the whole applies also to the part.

It is equally reasonable to assume that this body will be ungenerated and indestructible and exempt from
increase and alteration, since everything that comes to be comes into being from its contrary and in some
substrate, and passes away likewise in a substrate by the action of the contrary into the contrary, as we
explained in our opening discussions. Now the motions of contraries are contrary. If then this body can have
no contrary, because there can be no contrary motion to the circular, nature seems justly to have exempted
from contraries the body which was to be ungenerated and indestructible. For it is in contraries that
generation and decay subsist. Again, that which is subject to increase increases upon contact with a kindred
body, which is resolved into its matter. But there is nothing out of which this body can have been generated.
And if it is exempt from increase and diminution, the same reasoning leads us to suppose that it is also
unalterable. For alteration is movement in respect of quality; and qualitative states and dispositions, such as
health and disease, do not come into being without changes of properties. But all natural bodies which change
their properties we see to be subject without exception to increase and diminution. This is the case, for
instance, with the bodies of animals and their parts and with vegetable bodies, and similarly also with those
of the elements. And so, if the body which moves with a circular motion cannot admit of increase or
diminution, it is reasonable to suppose that it is also unalterable.

The reasons why the primary body is eternal and not subject to increase or diminution, but unaging and
unalterable and unmodified, will be clear from what has been said to any one who believes in our
assumptions. Our theory seems to confirm experience and to be confirmed by it. For all men have some
conception of the nature of the gods, and all who believe in the existence of gods at all, whether barbarian or
Greek, agree in allotting the highest place to the deity, surely because they suppose that immortal is linked
with immortal and regard any other supposition as inconceivable. If then there is, as there certainly is,
anything divine, what we have just said about the primary bodily substance was well said. The mere evidence
of the senses is enough to convince us of this, at least with human certainty. For in the whole range of time

ON THE HEAVENS

past, so far as our inherited records reach, no change appears to have taken place either in the whole scheme
of the outermost heaven or in any of its proper parts. The common name, too, which has been handed down
from our distant ancestors even to our own day, seems to show that they conceived of it in the fashion which
we have been expressing. The same ideas, one must believe, recur in men's minds not once or twice but again
and again. And so, implying that the primary body is something else beyond earth, fire, air, and water, they
gave the highest place a name of its own, aither, derived from the fact that it 'runs always' for an eternity of
time. Anaxagoras, however, scandalously misuses this name, taking aither as equivalent to fire.

It is also clear from what has been said why the number of what we call simple bodies cannot be greater than
it is. The motion of a simple body must itself be simple, and we assert that there are only these two simple
motions, the circular and the straight, the latter being subdivided into motion away from and motion towards
the centre.

That there is no other form of motion opposed as contrary to the circular may be proved in various ways. In
the first place, there is an obvious tendency to oppose the straight line to the circular. For concave and convex
are a not only regarded as opposed to one another, but they are also coupled together and treated as a unity in
opposition to the straight. And so, if there is a contrary to circular motion, motion in a straight line must be
recognized as having the best claim to that name. But the two forms of rectilinear motion are opposed to one
another by reason of their places; for up and down is a difference and a contrary opposition in place.
Secondly, it may be thought that the same reasoning which holds good of the rectilinear path applies also the
circular, movement from A to B being opposed as contrary to movement from B to A. But what is meant is
still rectilinear motion. For that is limited to a single path, while the circular paths which pass through the
same two points are infinite in number. Even if we are confined to the single semicircle and the opposition is
between movement from C to D and from D to C along that semicircle, the case is no better. For the motion
is the same as that along the diameter, since we invariably regard the distance between two points as the
length of the straight line which joins them. It is no more satisfactory to construct a circle and treat motion
'along one semicircle as contrary to motion along the other. For example, taking a complete circle, motion
from E to F on the semicircle G may be opposed to motion from F to E on the semicircle H. But even
supposing these are contraries, it in no way follows that the reverse motions on the complete circumference
contraries. Nor again can motion along the circle from A to B be regarded as the contrary of motion from A
to C: for the motion goes from the same point towards the same point, and contrary motion was distinguished
as motion from a contrary to its contrary. And even if the motion round a circle is the contrary of the reverse
motion, one of the two would be ineffective: for both move to the same point, because that which moves in a
circle, at whatever point it begins, must necessarily pass through all the contrary places alike. (By
contrarieties of place I mean up and down, back and front, and right and left; and the contrary oppositions of
movements are determined by those of places.) One of the motions, then, would be ineffective, for if the two
motions were of equal strength, there would be no movement either way, and if one of the two were
preponderant, the other would be inoperative. So that if both bodies were there, one of them, inasmuch as it
would not be moving with its own movement, would be useless, in the sense in which a shoe is useless when
it is not worn. But God and nature create nothing that has not its use.

This being clear, we must go on to consider the questions which remain. First, is there an infinite body, as the
majority of the ancient philosophers thought, or is this an impossibility? The decision of this question, either
way, is not unimportant, but rather all-important, to our search for the truth. It is this problem which has
practically always been the source of the differences of those who have written about nature as a whole. So it
has been and so it must be; since the least initial deviation from the truth is multiplied later a thousandfold.

ON THE HEAVENS

Admit, for instance, the existence of a minimum magnitude, and you will find that the minimum which you
have introduced, small as it is, causes the greatest truths of mathematics to totter. The reason is that a
principle is great rather in power than in extent; hence that which was small at the start turns out a giant at the
end. Now the conception of the infinite possesses this power of principles, and indeed in the sphere of
quantity possesses it in a higher degree than any other conception; so that it is in no way absurd or
unreasonable that the assumption that an infinite body exists should be of peculiar moment to our inquiry.
The infinite, then, we must now discuss, opening the whole matter from the beginning.

Every body is necessarily to be classed either as simple or as composite; the infinite body, therefore, will be
either simple or composite.

But it is clear, further, that if the simple bodies are finite, the composite must also be finite, since that which
is composed of bodies finite both in number and in magnitude is itself finite in respect of number and
magnitude: its quantity is in fact the same as that of the bodies which compose it. What remains for us to
consider, then, is whether any of the simple bodies can be infinite in magnitude, or whether this is impossible.
Let us try the primary body first, and then go on to consider the others.

The body which moves in a circle must necessarily be finite in every respect, for the following reasons. (1) If
the body so moving is infinite, the radii drawn from the centre will be infinite. But the space between infinite
radii is infinite: and by the space between the radii I mean the area outside which no magnitude which is in
contact with the two lines can be conceived as falling. This, I say, will be infinite: first, because in the case of
finite radii it is always finite; and secondly, because in it one can always go on to a width greater than any
given width; thus the reasoning which forces us to believe in infinite number, because there is no maximum,
applies also to the space between the radii. Now the infinite cannot be traversed, and if the body is infinite the
interval between the radii is necessarily infinite: circular motion therefore is an impossibility. Yet our eyes
tell us that the heavens revolve in a circle, and by argument also we have determined that there is something
to which circular movement belongs.

(2) Again, if from a finite time a finite time be subtracted, what remains must be finite and have a beginning.
And if the time of a journey has a beginning, there must be a beginning also of the movement, and
consequently also of the distance traversed. This applies universally. Take a line, ACE, infinite in one
direction, E, and another line, BB, infinite in both directions. Let ACE describe a circle, revolving upon C as
centre. In its movement it will cut BB continuously for a certain time. This will be a finite time, since the
total time is finite in which the heavens complete their circular orbit, and consequently the time subtracted
from it, during which the one line in its motion cuts the other, is also finite. Therefore there will be a point at
which ACE began for the first time to cut BB. This, however, is impossible. The infinite, then, cannot revolve
in a circle; nor could the world, if it were infinite.

(3) That the infinite cannot move may also be shown as follows. Let A be a finite line moving past the finite
line, B. Of necessity A will pass clear of B and B of A at the same moment; for each overlaps the other to
precisely the same extent. Now if the two were both moving, and moving in contrary directions, they would
pass clear of one another more rapidly; if one were still and the other moving past it, less rapidly; provided
that the speed of the latter were the same in both cases. This, however, is clear: that it is impossible to
traverse an infinite line in a finite time. Infinite time, then, would be required. (This we demonstrated above
in the discussion of movement.) And it makes no difference whether a finite is passing by an infinite or an
infinite by a finite. For when A is passing B, then B overlaps A and it makes no difference whether B is
moved or unmoved, except that, if both move, they pass clear of one another more quickly. It is, however,
quite possible that a moving line should in certain cases pass one which is stationary quicker than it passes
one moving in an opposite direction. One has only to imagine the movement to be slow where both move and
much faster where one is stationary. To suppose one line stationary, then, makes no difficulty for our
argument, since it is quite possible for A to pass B at a slower rate when both are moving than when only one

ON THE HEAVENS

is. If, therefore, the time which the finite moving line takes to pass the other is infinite, then necessarily the
time occupied by the motion of the infinite past the finite is also infinite. For the infinite to move at all is thus
absolutely impossible; since the very smallest movement conceivable must take an infinity of time. Moreover
the heavens certainly revolve, and they complete their circular orbit in a finite time; so that they pass round
the whole extent of any line within their orbit, such as the finite line AB. The revolving body, therefore,
cannot be infinite.

(4) Again, as a line which has a limit cannot be infinite, or, if it is infinite, is so only in length, so a surface
cannot be infinite in that respect in which it has a limit; or, indeed, if it is completely determinate, in any
respect whatever. Whether it be a square or a circle or a sphere, it cannot be infinite, any more than a
foot-rule can. There is then no such thing as an infinite sphere or square or circle, and where there is no
circle there can be no circular movement, and similarly where there is no infinite at all there can be no infinite
movement; and from this it follows that, an infinite circle being itself an impossibility, there can be no
circular motion of an infinite body.

(5) Again, take a centre C, an infinite line, AB, another infinite line at right angles to it, E, and a moving
radius, CD. CD will never cease contact with E, but the position will always be something like CE, CD
cutting E at F. The infinite line, therefore, refuses to complete the circle.

(6) Again, if the heaven is infinite and moves in a circle, we shall have to admit that in a finite time it has
traversed the infinite. For suppose the fixed heaven infinite, and that which moves within it equal to it. It
results that when the infinite body has completed its revolution, it has traversed an infinite equal to itself in a
finite time. But that we know to be impossible.

(7) It can also be shown, conversely, that if the time of revolution is finite, the area traversed must also be
finite; but the area traversed was equal to itself; therefore, it is itself finite.

We have now shown that the body which moves in a circle is not endless or infinite, but has its limit.

Further, neither that which moves towards nor that which moves away from the centre can be infinite. For the
upward and downward motions are contraries and are therefore motions towards contrary places. But if one
of a pair of contraries is determinate, the other must be determinate also. Now the centre is determined; for,
from whatever point the body which sinks to the bottom starts its downward motion, it cannot go farther than
the centre. The centre, therefore, being determinate, the upper place must also be determinate. But if these
two places are determined and finite, the corresponding bodies must also be finite. Further, if up and down
are determinate, the intermediate place is also necessarily determinate. For, if it is indeterminate, the
movement within it will be infinite; and that we have already shown to be an impossibility. The middle
region then is determinate, and consequently any body which either is in it, or might be in it, is determinate.
But the bodies which move up and down may be in it, since the one moves naturally away from the centre
and the other towards it.

From this alone it is clear that an infinite body is an impossibility; but there is a further point. If there is no
such thing as infinite weight, then it follows that none of these bodies can be infinite. For the supposed
infinite body would have to be infinite in weight. (The same argument applies to lightness: for as the one
supposition involves infinite weight, so the infinity of the body which rises to the surface involves infinite
lightness.) This is proved as follows. Assume the weight to be finite, and take an infinite body, AB, of the
weight C. Subtract from the infinite body a finite mass, BD, the weight of which shall be E. E then is less
than C, since it is the weight of a lesser mass. Suppose then that the smaller goes into the greater a certain

ON THE HEAVENS

number of times, and take BF bearing the same proportion to BD which the greater weight bears to the
smaller. For you may subtract as much as you please from an infinite. If now the masses are proportionate to
the weights, and the lesser weight is that of the lesser mass, the greater must be that of the greater. The
weights, therefore, of the finite and of the infinite body are equal. Again, if the weight of a greater body is
greater than that of a less, the weight of GB will be greater than that of FB ; and thus the weight of the finite
body is greater than that of the infinite. And, further, the weight of unequal masses will be the same, since the
infinite and the finite cannot be equal. It does not matter whether the weights are commensurable or not. If (a)
they are incommensurable the same reasoning holds. For instance, suppose E multiplied by three is rather
more than C: the weight of three masses of the full size of BD will be greater than C. We thus arrive at the
same impossibility as before. Again (b) we may assume weights which are commensurate; for it makes no
difference whether we begin with the weight or with the mass. For example, assume the weight E to be
commensurate with C, and take from the infinite mass a part BD of weight E. Then let a mass BF be taken
having the same proportion to BD which the two weights have to one another. (For the mass being infinite
you may subtract from it as much as you please.) These assumed bodies will be commensurate in mass and in
weight alike. Nor again does it make any difference to our demonstration whether the total mass has its
weight equally or unequally distributed. For it must always be Possible to take from the infinite mass a body
of equal weight to BD by diminishing or increasing the size of the section to the necessary extent.

From what we have said, then, it is clear that the weight of the infinite body cannot be finite. It must then be
infinite. We have therefore only to show this to be impossible in order to prove an infinite body impossible.
But the impossibility of infinite weight can be shown in the following way. A given weight moves a given
distance in a given time; a weight which is as great and more moves the same distance in a less time, the
times being in inverse proportion to the weights. For instance, if one weight is twice another, it will take half
as long over a given movement. Further, a finite weight traverses any finite distance in a finite time. It
necessarily follows from this that infinite weight, if there is such a thing, being, on the one hand, as great and
more than as great as the finite, will move accordingly, but being, on the other hand, compelled to move in a
time inversely proportionate to its greatness, cannot move at all. The time should be less in proportion as the
weight is greater. But there is no proportion between the infinite and the finite: proportion can only hold
between a less and a greater finite time. And though you may say that the time of the movement can be
continually diminished, yet there is no minimum. Nor, if there were, would it help us. For some finite body
could have been found greater than the given finite in the same proportion which is supposed to hold between
the infinite and the given finite; so that an infinite and a finite weight must have traversed an equal distance in
equal time. But that is impossible. Again, whatever the time, so long as it is finite, in which the infinite
performs the motion, a finite weight must necessarily move a certain finite distance in that same time. Infinite
weight is therefore impossible, and the same reasoning applies also to infinite lightness. Bodies then of
infinite weight and of infinite lightness are equally impossible.

That there is no infinite body may be shown, as we have shown it, by a detailed consideration of the various
cases. But it may also be shown universally, not only by such reasoning as we advanced in our discussion of
principles (though in that passage we have already determined universally the sense in which the existence of
an infinite is to be asserted or denied), but also suitably to our present purpose in the following way. That will
lead us to a further question. Even if the total mass is not infinite, it may yet be great enough to admit a
plurality of universes. The question might possibly be raised whether there is any obstacle to our believing
that there are other universes composed on the pattern of our own, more than one, though stopping short of
infinity. First, however, let us treat of the infinite universally.

Every body must necessarily be either finite or infinite, and if infinite, either of similar or of dissimilar parts.
If its parts are dissimilar, they must represent either a finite or an infinite number of kinds. That the kinds

ON THE HEAVENS

cannot be infinite is evident, if our original presuppositions remain unchallenged. For the primary movements
being finite in number, the kinds of simple body are necessarily also finite, since the movement of a simple
body is simple, and the simple movements are finite, and every natural body must always have its proper
motion. Now if the infinite body is to be composed of a finite number of kinds, then each of its parts must
necessarily be infinite in quantity, that is to say, the water, fire, which compose it. But this is impossible,
because, as we have already shown, infinite weight and lightness do not exist. Moreover it would be
necessary also that their places should be infinite in extent, so that the movements too of all these bodies
would be infinite. But this is not possible, if we are to hold to the truth of our original presuppositions and to
the view that neither that which moves downward, nor, by the same reasoning, that which moves upward, can
prolong its movement to infinity. For it is true in regard to quality, quantity, and place alike that any process
of change is impossible which can have no end. I mean that if it is impossible for a thing to have come to be
white, or a cubit long, or in Egypt, it is also impossible for it to be in process of coming to be any of these. It
is thus impossible for a thing to be moving to a place at which in its motion it can never by any possibility
arrive. Again, suppose the body to exist in dispersion, it may be maintained none the less that the total of all
these scattered particles, say, of fire, is infinite. But body we saw to be that which has extension every way.
How can there be several dissimilar elements, each infinite? Each would have to be infinitely extended every
way.

It is no more conceivable, again, that the infinite should exist as a whole of similar parts. For, in the first
place, there is no other (straight) movement beyond those mentioned: we must therefore give it one of them.
And if so, we shall have to admit either infinite weight or infinite lightness. Nor, secondly, could the body
whose movement is circular be infinite, since it is impossible for the infinite to move in a circle. This, indeed,
would be as good as saying that the heavens are infinite, which we have shown to be impossible.

Moreover, in general, it is impossible that the infinite should move at all. If it did, it would move either
naturally or by constraint: and if by constraint, it possesses also a natural motion, that is to say, there is
another place, infinite like itself, to which it will move. But that is impossible.

That in general it is impossible for the infinite to be acted upon by the finite or to act upon it may be shown as
follows.

(1. The infinite cannot be acted upon by the finite.) Let A be an infinite, B a finite, C the time of a given
movement produced by one in the other. Suppose, then, that A was heated, or impelled, or modified in any
way, or caused to undergo any sort of movement whatever, by in the time C. Let D be less than B; and,
assuming that a lesser agent moves a lesser patient in an equal time, call the quantity thus modified by D, E.
Then, as D is to B, so is E to some finite quantum. We assume that the alteration of equal by equal takes
equal time, and the alteration of less by less or of greater by greater takes the same time, if the quantity of the
patient is such as to keep the proportion which obtains between the agents, greater and less. If so, no
movement can be caused in the infinite by any finite agent in any time whatever. For a less agent will
produce that movement in a less patient in an equal time, and the proportionate equivalent of that patient will
be a finite quantity, since no proportion holds between finite and infinite.

(2. The infinite cannot act upon the finite.) Nor, again, can the infinite produce a movement in the finite in
any time whatever. Let A be an infinite, B a finite, C the time of action. In the time C, D will produce that
motion in a patient less than B, say F. Then take E, bearing the same proportion to D as the whole BF bears to
F. E will produce the motion in BF in the time C. Thus the finite and infinite effect the same alteration in
equal times. But this is impossible; for the assumption is that the greater effects it in a shorter time. It will be
the same with any time that can be taken, so that there will no time in which the infinite can effect this
movement. And, as to infinite time, in that nothing can move another or be moved by it. For such time has no
limit, while the action and reaction have.

ON THE HEAVENS

(3. There is no interaction between infinites.) Nor can infinite be acted upon in any way by infinite. Let A and
B be infinites, CD being the time of the action A of upon B. Now the whole B was modified in a certain time,
and the part of this infinite, E, cannot be so modified in the same time, since we assume that a less quantity
makes the movement in a less time. Let E then, when acted upon by A, complete the movement in the time
D. Then, as D is to CD, so is E to some finite part of B. This part will necessarily be moved by A in the time
CD. For we suppose that the same agent produces a given effect on a greater and a smaller mass in longer and
shorter times, the times and masses varying proportionately. There is thus no finite time in which infinites
can move one another. Is their time then infinite? No, for infinite time has no end, but the movement
communicated has.

If therefore every perceptible body possesses the power of acting or of being acted upon, or both of these, it is
impossible that an infinite body should be perceptible. All bodies, however, that occupy place are perceptible.
There is therefore no infinite body beyond the heaven. Nor again is there anything of limited extent beyond it.
And so beyond the heaven there is no body at all. For if you suppose it an object of intelligence, it will be in a
place-since place is what 'within' and 'beyond' denote-and therefore an object of perception. But nothing that
is not in a place is perceptible.

The question may also be examined in the light of more general considerations as follows. The infinite,
considered as a whole of similar parts, cannot, on the one hand, move in a circle. For there is no centre of the
infinite, and that which moves in a circle moves about the centre. Nor again can the infinite move in a straight
line. For there would have to be another place infinite like itself to be the goal of its natural movement and
another, equally great, for the goal of its unnatural movement. Moreover, whether its rectilinear movement is
natural or constrained, in either case the force which causes its motion will have to be infinite. For infinite
force is force of an infinite body, and of an infinite body the force is infinite. So the motive body also will be
infinite. (The proof of this is given in our discussion of movement, where it is shown that no finite thing
possesses infinite power, and no infinite thing finite power.) If then that which moves naturally can also move
unnaturally, there will be two infinites, one which causes, and another which exhibits the latter motion.
Again, what is it that moves the infinite? If it moves itself, it must be animate. But how can it possibly be
conceived as an infinite animal? And if there is something else that moves it, there will be two infinites, that
which moves and that which is moved, differing in their form and power.

If the whole is not continuous, but exists, as Democritus and Leucippus think, in the form of parts separated
by void, there must necessarily be one movement of all the multitude. They are distinguished, we are told,
from one another by their figures; but their nature is one, like many pieces of gold separated from one
another. But each piece must, as we assert, have the same motion. For a single clod moves to the same place
as the whole mass of earth, and a spark to the same place as the whole mass of fire. So that if it be weight that
all possess, no body is, strictly speaking, light: and if lightness be universal, none is heavy. Moreover,
whatever possesses weight or lightness will have its place either at one of the extremes or in the middle
region. But this is impossible while the world is conceived as infinite. And, generally, that which has no
centre or extreme limit, no up or down, gives the bodies no place for their motion; and without that
movement is impossible. A thing must move either naturally or unnaturally, and the two movements are
determined by the proper and alien places. Again, a place in which a thing rests or to which it moves
unnaturally, must be the natural place for some other body, as experience shows. Necessarily, therefore, not
everything possesses weight or lightness, but some things do and some do not. From these arguments then it
is clear that the body of the universe is not infinite.

We must now proceed to explain why there cannot be more than one heaven-the further question mentioned
above. For it may be thought that we have not proved universal of bodies that none whatever can exist

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ON THE HEAVENS

outside our universe, and that our argument applied only to those of indeterminate extent.

Now all things rest and move naturally and by constraint. A thing moves naturally to a place in which it rests
without constraint, and rests naturally in a place to which it moves without constraint. On the other hand, a
thing moves by constraint to a place in which it rests by constraint, and rests by constraint in a place to which
it moves by constraint. Further, if a given movement is due to constraint, its contrary is natural. If, then, it is
by constraint that earth moves from a certain place to the centre here, its movement from here to there will be
natural, and if earth from there rests here without constraint, its movement hither will be natural. And the
natural movement in each case is one. Further, these worlds, being similar in nature to ours, must all be
composed of the same bodies as it. Moreover each of the bodies, fire, I mean, and earth and their
intermediates, must have the same power as in our world. For if these names are used equivocally, if the
identity of name does not rest upon an identity of form in these elements and ours, then the whole to which
they belong can only be called a world by equivocation. Clearly, then, one of the bodies will move naturally
away from the centre and another towards the centre, since fire must be identical with fire, earth with earth,
and so on, as the fragments of each are identical in this world. That this must be the case is evident from the
principles laid down in our discussion of the movements, for these are limited in number, and the distinction
of the elements depends upon the distinction of the movements. Therefore, since the movements are the
same, the elements must also be the same everywhere. The particles of earth, then, in another world move
naturally also to our centre and its fire to our circumference. This, however, is impossible, since, if it were
true, earth must, in its own world, move upwards, and fire to the centre; in the same way the earth of our
world must move naturally away from the centre when it moves towards the centre of another universe. This
follows from the supposed juxtaposition of the worlds. For either we must refuse to admit the identical nature
of the simple bodies in the various universes, or, admitting this, we must make the centre and the extremity
one as suggested. This being so, it follows that there cannot be more worlds than one.

To postulate a difference of nature in the simple bodies according as they are more or less distant from their
proper places is unreasonable. For what difference can it make whether we say that a thing is this distance
away or that? One would have to suppose a difference proportionate to the distance and increasing with it, but
the form is in fact the same. Moreover, the bodies must have some movement, since the fact that they move is
quite evident. Are we to say then that all their movements, even those which are mutually contrary, are due to
constraint? No, for a body which has no natural movement at all cannot be moved by constraint. If then the
bodies have a natural movement, the movement of the particular instances of each form must necessarily
have for goal a place numerically one, i.e. a particular centre or a particular extremity. If it be suggested that
the goal in each case is one in form but numerically more than one, on the analogy of particulars which are
many though each undifferentiated in form, we reply that the variety of goal cannot be limited to this portion
or that but must extend to all alike. For all are equally undifferentiated in form, but any one is different
numerically from any other. What I mean is this: if the portions in this world behave similarly both to one
another and to those in another world, then the portion which is taken hence will not behave differently either
from the portions in another world or from those in the same world, but similarly to them, since in form no
portion differs from another. The result is that we must either abandon our present assumption or assert that
the centre and the extremity are each numerically one. But this being so, the heaven, by the same evidence
and the same necessary inferences, must be one only and no more.

A consideration of the other kinds of movement also makes it plain that there is some point to which earth
and fire move naturally. For in general that which is moved changes from something into something, the
starting-point and the goal being different in form, and always it is a finite change. For instance, to recover
health is to change from disease to health, to increase is to change from smallness to greatness. Locomotion
must be similar: for it also has its goal and starting-point — and therefore the starting-point and the goal of
the natural movement must differ in form-just as the movement of coming to health does not take any
direction which chance or the wishes of the mover may select. Thus, too, fire and earth move not to infinity
but to opposite points; and since the opposition in place is between above and below, these will be the limits

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ON THE HEAVENS

of their movement. (Even in circular movement there is a sort of opposition between the ends of the diameter,
though the movement as a whole has no contrary: so that here too the movement has in a sense an opposed
and finite goal.) There must therefore be some end to locomotion: it cannot continue to infinity.

This conclusion that local movement is not continued to infinity is corroborated by the fact that earth moves
more quickly the nearer it is to the centre, and fire the nearer it is to the upper place. But if movement were
infinite speed would be infinite also; and if speed then weight and lightness. For as superior speed in
downward movement implies superior weight, so infinite increase of weight necessitates infinite increase of
speed.

Further, it is not the action of another body that makes one of these bodies move up and the other down; nor
is it constraint, like the 'extrusion' of some writers. For in that case the larger the mass of fire or earth the
slower would be the upward or downward movement; but the fact is the reverse: the greater the mass of fire
or earth the quicker always is its movement towards its own place. Again, the speed of the movement would
not increase towards the end if it were due to constraint or extrusion; for a constrained movement always
diminishes in speed as the source of constraint becomes more distant, and a body moves without constraint to
the place whence it was moved by constraint.

A consideration of these points, then, gives adequate assurance of the truth of our contentions. The same
could also be shown with the aid of the discussions which fall under First Philosophy, as well as from the
nature of the circular movement, which must be eternal both here and in the other worlds. It is plain, too,
from the following considerations that the universe must be one.

The bodily elements are three, and therefore the places of the elements will be three also; the place, first, of
the body which sinks to the bottom, namely the region about the centre; the place, secondly, of the revolving
body, namely the outermost place, and thirdly, the intermediate place, belonging to the intermediate body.
Here in this third place will be the body which rises to the surface; since, if not here, it will be elsewhere, and
it cannot be elsewhere: for we have two bodies, one weightless, one endowed with weight, and below is place
of the body endowed with weight, since the region about the centre has been given to the heavy body. And its
position cannot be unnatural to it, for it would have to be natural to something else, and there is nothing else.
It must then occupy the intermediate place. What distinctions there are within the intermediate itself we will
explain later on.

We have now said enough to make plain the character and number of the bodily elements, the place of each,
and further, in general, how many in number the various places are.

We must show not only that the heaven is one, but also that more than one heaven is and, further, that, as
exempt from decay and generation, the heaven is eternal. We may begin by raising a difficulty. From one
point of view it might seem impossible that the heaven should be one and unique, since in all formations and
products whether of nature or of art we can distinguish the shape in itself and the shape in combination with
matter. For instance the form of the sphere is one thing and the gold or bronze sphere another; the shape of
the circle again is one thing, the bronze or wooden circle another. For when we state the essential nature of
the sphere or circle we do not include in the formula gold or bronze, because they do not belong to the
essence, but if we are speaking of the copper or gold sphere we do include them. We still make the distinction
even if we cannot conceive or apprehend any other example beside the particular thing. This may, of course,
sometimes be the case: it might be, for instance, that only one circle could be found; yet none the less the
difference will remain between the being of circle and of this particular circle, the one being form, the other
form in matter, i.e. a particular thing. Now since the universe is perceptible it must be regarded as a

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ON THE HEAVENS

particular; for everything that is perceptible subsists, as we know, in matter. But if it is a particular, there will
be a distinction between the being of 'this universe' and of 'universe' unqualified. There is a difference, then,
between 'this universe' and simple 'universe'; the second is form and shape, the first form in combination with
matter; and any shape or form has, or may have, more than one particular instance.

On the supposition of Forms such as some assert, this must be the case, and equally on the view that no such
entity has a separate existence. For in every case in which the essence is in matter it is a fact of observation
that the particulars of like form are several or infinite in number. Hence there either are, or may be, more
heavens than one. On these grounds, then, it might be inferred either that there are or that there might be
several heavens. We must, however, return and ask how much of this argument is correct and how much not.

Now it is quite right to say that the formula of the shape apart from the matter must be different from that of
the shape in the matter, and we may allow this to be true. We are not, however, therefore compelled to assert
a plurality of worlds. Such a plurality is in fact impossible if this world contains the entirety of matter, as in
fact it does. But perhaps our contention can be made clearer in this way. Suppose 'aquilinity' to be curvature
in the nose or flesh, and flesh to be the matter of aquilinity. Suppose further, that all flesh came together into
a single whole of flesh endowed with this aquiline quality. Then neither would there be, nor could there arise,
any other thing that was aquiline. Similarly, suppose flesh and bones to be the matter of man, and suppose a
man to be created of all flesh and all bones in indissoluble union. The possibility of another man would be
removed. Whatever case you took it would be the same. The general rule is this: a thing whose essence
resides in a substratum of matter can never come into being in the absence of all matter. Now the universe is
certainly a particular and a material thing: if however, it is composed not of a part but of the whole of matter,
then though the being of 'universe' and of 'this universe' are still distinct, yet there is no other universe, and no
possibility of others being made, because all the matter is already included in this. It remains, then, only to
prove that it is composed of all natural perceptible body.

First, however, we must explain what we mean by 'heaven' and in how many senses we use the word, in order
to make clearer the object of our inquiry, (a) In one sense, then, we call 'heaven' the substance of the extreme
circumference of the whole, or that natural body whose place is at the extreme circumference. We recognize
habitually a special right to the name 'heaven' in the extremity or upper region, which we take to be the seat
of all that is divine, (b) In another sense, we use this name for the body continuous with the extreme
circumference which contains the moon, the sun, and some of the stars; these we say are 'in the heaven', (c) In
yet another sense we give the name to all body included within extreme circumference, since we habitually
call the whole or totality 'the heaven'. The word, then, is used in three senses.

Now the whole included within the extreme circumference must be composed of all physical and sensible
body, because there neither is, nor can come into being, any body outside the heaven. For if there is a natural
body outside the extreme circumference it must be either a simple or a composite body, and its position must
be either natural or unnatural. But it cannot be any of the simple bodies. For, first, it has been shown that that
which moves in a circle cannot change its place. And, secondly, it cannot be that which moves from the
centre or that which lies lowest. Naturally they could not be there, since their proper places are elsewhere;
and if these are there unnaturally, the exterior place will be natural to some other body, since a place which is
unnatural to one body must be natural to another: but we saw that there is no other body besides these. Then
it is not possible that any simple body should be outside the heaven. But, if no simple body, neither can any
mixed body be there: for the presence of the simple body is involved in the presence of the mixture. Further
neither can any body come into that place: for it will do so either naturally or unnaturally, and will be either
simple or composite; so that the same argument will apply, since it makes no difference whether the question
is 'does A exist?' or 'could A come to exist?' From our arguments then it is evident not only that there is not,
but also that there could never come to be, any bodily mass whatever outside the circumference. The world as
a whole, therefore, includes all its appropriate matter, which is, as we saw, natural perceptible body. So that
neither are there now, nor have there ever been, nor can there ever be formed more heavens than one, but this

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ON THE HEAVENS

heaven of ours is one and unique and complete.

It is therefore evident that there is also no place or void or time outside the heaven. For in every place body
can be present; and void is said to be that in which the presence of body, though not actual, is possible; and
time is the number of movement. But in the absence of natural body there is no movement, and outside the
heaven, as we have shown, body neither exists nor can come to exist. It is clear then that there is neither
place, nor void, nor time, outside the heaven. Hence whatever is there, is of such a nature as not to occupy
any place, nor does time age it; nor is there any change in any of the things which lie beyond the outermost
motion; they continue through their entire duration unalterable and unmodified, living the best and most
selfsufficient of lives. As a matter of fact, this word 'duration' possessed a divine significance for the ancients,
for the fulfilment which includes the period of life of any creature, outside of which no natural development
can fall, has been called its duration. On the same principle the fulfilment of the whole heaven, the fulfilment
which includes all time and infinity, is 'duration'-a name based upon the fact that it is always-duration
immortal and divine. From it derive the being and life which other things, some more or less articulately but
others feebly, enjoy. So, too, in its discussions concerning the divine, popular philosophy often propounds the
view that whatever is divine, whatever is primary and supreme, is necessarily unchangeable. This fact
confirms what we have said. For there is nothing else stronger than it to move it-since that would mean more
divine-and it has no defect and lacks none of its proper excellences. Its unceasing movement, then, is also
reasonable, since everything ceases to move when it comes to its proper place, but the body whose path is the
circle has one and the same place for starting-point and goal.

Having established these distinctions, we may now proceed to the question whether the heaven is
ungenerated or generated, indestructible or destructible. Let us start with a review of the theories of other
thinkers; for the proofs of a theory are difficulties for the contrary theory. Besides, those who have first heard
the pleas of our adversaries will be more likely to credit the assertions which we are going to make. We shall
be less open to the charge of procuring judgement by default. To give a satisfactory decision as to the truth it
is necessary to be rather an arbitrator than a party to the dispute.

That the world was generated all are agreed, but, generation over, some say that it is eternal, others say that it
is destructible like any other natural formation. Others again, with Empedliocles of Acragas and Heraclitus of
Ephesus, believe that there is alternation in the destructive process, which takes now this direction, now that,
and continues without end.

Now to assert that it was generated and yet is eternal is to assert the impossible; for we cannot reasonably
attribute to anything any characteristics but those which observation detects in many or all instances. But in
this case the facts point the other way: generated things are seen always to be destroyed. Further, a thing
whose present state had no beginning and which could not have been other than it was at any previous
moment throughout its entire duration, cannot possibly be changed. For there will have to be some cause of
change, and if this had been present earlier it would have made possible another condition of that to which
any other condition was impossible. Suppose that the world was formed out of elements which were formerly
otherwise conditioned than as they are now. Then (1) if their condition was always so and could not have
been otherwise, the world could never have come into being. And (2) if the world did come into being, then,
clearly, their condition must have been capable of change and not eternal: after combination therefore they
will be dispersed, just as in the past after dispersion they came into combination, and this process either has
been, or could have been, indefinitely repeated. But if this is so, the world cannot be indestructible, and it
does not matter whether the change of condition has actually occurred or remains a possibility.

Some of those who hold that the world, though indestructible, was yet generated, try to support their case by
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a parallel which is illusory. They say that in their statements about its generation they are doing what
geometricians do when they construct their figures, not implying that the universe really had a beginning, but
for didactic reasons facilitating understanding by exhibiting the object, like the figure, as in course of
formation. The two cases, as we said, are not parallel; for, in the construction of the figure, when the various
steps are completed the required figure forthwith results; but in these other demonstrations what results is not
that which was required. Indeed it cannot be so; for antecedent and consequent, as assumed, are in
contradiction. The ordered, it is said, arose out of the unordered; and the same thing cannot be at the same
time both ordered and unordered; there must be a process and a lapse of time separating the two states. In the
figure, on the other hand, there is no temporal separation. It is clear then that the universe cannot be at once
eternal and generated.

To say that the universe alternately combines and dissolves is no more paradoxical than to make it eternal but
varying in shape. It is as if one were to think that there was now destruction and now existence when from a
child a man is generated, and from a man a child. For it is clear that when the elements come together the
result is not a chance system and combination, but the very same as before-especially on the view of those
who hold this theory, since they say that the contrary is the cause of each state. So that if the totality of body,
which is a continuum, is now in this order or disposition and now in that, and if the combination of the whole
is a world or heaven, then it will not be the world that comes into being and is destroyed, but only its
dispositions.

If the world is believed to be one, it is impossible to suppose that it should be, as a whole, first generated and
then destroyed, never to reappear; since before it came into being there was always present the combination
prior to it, and that, we hold, could never change if it was never generated. If, on the other hand, the worlds
are infinite in number the view is more plausible. But whether this is, or is not, impossible will be clear from
what follows. For there are some who think it possible both for the ungenerated to be destroyed and for the
generated to persist undestroyed. (This is held in the Timaeus, where Plato says that the heaven, though it was
generated, will none the less exist to eternity.) So far as the heaven is concerned we have answered this view
with arguments appropriate to the nature of the heaven: on the general question we shall attain clearness
when we examine the matter universally.

We must first distinguish the senses in which we use the words 'ungenerated' and 'generated', 'destructible'
and 'indestructible'. These have many meanings, and though it may make no difference to the argument, yet
some confusion of mind must result from treating as uniform in its use a word which has several distinct
applications. The character which is the ground of the predication will always remain obscure.

The word 'ungenerated' then is used (a) in one sense whenever something now is which formerly was not, no
process of becoming or change being involved. Such is the case, according to some, with contact and motion,
since there is no process of coming to be in contact or in motion, (b) It is used in another sense, when
something which is capable of coming to be, with or without process, does not exist; such a thing is
ungenerated in the sense that its generation is not a fact but a possibility, (c) It is also applied where there is
general impossibility of any generation such that the thing now is which then was not. And 'impossibility' has
two uses: first, where it is untrue to say that the thing can ever come into being, and secondly, where it cannot
do so easily, quickly, or well. In the same way the word 'generated' is used, (a) first, where what formerly was
not afterwards is, whether a process of becoming was or was not involved, so long as that which then was
not, now is; (b) secondly, of anything capable of existing, 'capable' being defined with reference either to
truth or to facility; (c) thirdly, of anything to which the passage from not being to being belongs, whether
already actual, if its existence is due to a past process of becoming, or not yet actual but only possible. The
uses of the words 'destructible' and 'indestructible' are similar. 'Destructible' is applied (a) to that which

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formerly was and afterwards either is not or might not be, whether a period of being destroyed and changed
intervenes or not; and (b) sometimes we apply the word to that which a process of destruction may cause not
to be; and also (c) in a third sense, to that which is easily destructible, to the 'easily destroyed', so to speak. Of
the indestructible the same account holds good. It is either (a) that which now is and now is not, without any
process of destruction, like contact, which without being destroyed afterwards is not, though formerly it was;
or (b) that which is but might not be, or which will at some time not be, though it now is. For you exist now
and so does the contact; yet both are destructible, because a time will come when it will not be true of you
that you exist, nor of these things that they are in contact. Thirdly (c) in its most proper use, it is that which is,
but is incapable of any destruction such that the thing which now is later ceases to be or might cease to be; or
again, that which has not yet been destroyed, but in the future may cease to be. For indestructible is also used
of that which is destroyed with difficulty.

This being so, we must ask what we mean by 'possible' and 'impossible'. For in its most proper use the
predicate 'indestructible' is given because it is impossible that the thing should be destroyed, i.e. exist at one
time and not at another. And 'ungenerated' also involves impossibility when used for that which cannot be
generated, in such fashion that, while formerly it was not, later it is. An instance is a commensurable
diagonal. Now when we speak of a power to move or to lift weights, we refer always to the maximum. We
speak, for instance, of a power to lift a hundred talents or walk a hundred stades-though a power to effect the
maximum is also a power to effect any part of the maximum-since we feel obliged in defining the power to
give the limit or maximum. A thing, then, which is within it. If, for example, a man can lift a hundred talents,
he can also lift two, and if he can walk a hundred stades, he can also walk two. But the power is of the
maximum, and a thing said, with reference to its maximum, to be incapable of so much is also incapable of
any greater amount. It is, for instance, clear that a person who cannot walk a thousand stades will also be
unable to walk a thousand and one. This point need not trouble us, for we may take it as settled that what is,
in the strict sense, possible is determined by a limiting maximum. Now perhaps the objection might be raised
that there is no necessity in this, since he who sees a stade need not see the smaller measures contained in it,
while, on the contrary, he who can see a dot or hear a small sound will perceive what is greater. This,
however, does not touch our argument. The maximum may be determined either in the power or in its object.
The application of this is plain. Superior sight is sight of the smaller body, but superior speed is that of the
greater body.

Having established these distinctions we car now proceed to the sequel. If there are thing! capable both of
being and of not being, there must be some definite maximum time of their being and not being; a time, I
mean, during which continued existence is possible to them and a time during which continued nonexistence
is possible. And this is true in every category, whether the thing is, for example, 'man', or 'white', or 'three
cubits long', or whatever it may be. For if the time is not definite in quantity, but longer than any that can be
suggested and shorter than none, then it will be possible for one and the same thing to exist for infinite time
and not to exist for another infinity. This, however, is impossible.

Let us take our start from this point. The impossible and the false have not the same significance. One use of
'impossible' and 'possible', and 'false' and 'true', is hypothetical. It is impossible, for instance, on a certain
hypothesis that the triangle should have its angles equal to two right angles, and on another the diagonal is
commensurable. But there are also things possible and impossible, false and true, absolutely. Now it is one
thing to be absolutely false, and another thing to be absolutely impossible. To say that you are standing when
you are not standing is to assert a falsehood, but not an impossibility. Similarly to say that a man who is
playing the harp, but not singing, is singing, is to say what is false but not impossible. To say, however, that
you are at once standing and sitting, or that the diagonal is commensurable, is to say what is not only false
but also impossible. Thus it is not the same thing to make a false and to make an impossible hypothesis, and

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from the impossible hypothesis impossible results follow. A man has, it is true, the capacity at once of sitting
and of standing, because when he possesses the one he also possesses the other; but it does not follow that he
can at once sit and stand, only that at another time he can do the other also. But if a thing has for infinite time
more than one capacity, another time is impossible and the times must coincide. Thus if a thing which exists
for infinite time is destructible, it will have the capacity of not being. Now if it exists for infinite time let this
capacity be actualized; and it will be in actuality at once existent and non-existent. Thus a false conclusion
would follow because a false assumption was made, but if what was assumed had not been impossible its
consequence would not have been impossible.

Anything then which always exists is absolutely imperishable. It is also ungenerated, since if it was generated
it will have the power for some time of not being. For as that which formerly was, but now is not, or is
capable at some future time of not being, is destructible, so that which is capable of formerly not having been
is generated. But in the case of that which always is, there is no time for such a capacity of not being, whether
the supposed time is finite or infinite; for its capacity of being must include the finite time since it covers
infinite time.

It is therefore impossible that one and the same thing should be capable of always existing and of always
not-existing. And 'not always existing', the contradictory, is also excluded. Thus it is impossible for a thing
always to exist and yet to be destructible. Nor, similarly, can it be generated. For of two attributes if B cannot
be present without A, the impossibility A of proves the impossibility of B. What always is, then, since it is
incapable of ever not being, cannot possibly be generated. But since the contradictory of 'that which is always
capable of being' 'that which is not always capable of being'; while 'that which is always capable of not being'
is the contrary, whose contradictory in turn is 'that which is not always capable of not being', it is necessary
that the contradictories of both terms should be predicable of one and the same thing, and thus that,
intermediate between what always is and what always is not, there should be that to which being and
not-being are both possible; for the contradictory of each will at times be true of it unless it always exists.
Hence that which not always is not will sometimes be and sometimes not be; and it is clear that this is true
also of that which cannot always be but sometimes is and therefore sometimes is not. One thing, then, will
have the power of being, and will thus be intermediate between the other two.

Expresed universally our argument is as follows. Let there be two attributes, A and B, not capable of being
present in any one thing together, while either A or C and either B or D are capable of being present in
everything. Then C and D must be predicated of everything of which neither A nor B is predicated. Let E lie
between A and B; for that which is neither of two contraries is a mean between them. In E both C and D must
be present, for either A or C is present everywhere and therefore in E. Since then A is impossible, C must be
present, and the same argument holds of D.

Neither that which always is, therefore, nor that which always is not is either generated or destructible. And
clearly whatever is generated or destructible is not eternal. If it were, it would be at once capable of always
being and capable of not always being, but it has already been shown that this is impossible. Surely then
whatever is ungenerated and in being must be eternal, and whatever is indestructible and in being must
equally be so. (I use the words 'ungenerated' and 'indestructible' in their proper sense, 'ungenerated' for that
which now is and could not at any previous time have been truly said not to be; 'indestructible' for that which
now is and cannot at any future time be truly said not to be.) If, again, the two terms are coincident, if the
ungenerated is indestructible, and the indestructible ungenearted, then each of them is coincident with
'eternal'; anything ungenerated is eternal and anything indestructible is eternal. This is clear too from the
definition of the terms, Whatever is destructible must be generated; for it is either ungenerated, or generated,
but, if ungenerated, it is by hypothesis indestructible. Whatever, further, is generated must be destructible.
For it is either destructible or indestructible, but, if indestructible, it is by hypothesis ungenerated.

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If, however, 'indestructible' and 'ungenerated' are not coincident, there is no necessity that either the
ungenerated or the indestructible should be eternal. But they must be coincident, for the following reasons.
The terms 'generated' and 'destructible' are coincident; this is obvious from our former remarks, since
between what always is and what always is not there is an intermediate which is neither, and that intermediate
is the generated and destructible. For whatever is either of these is capable both of being and of not being for
a definite time: in either case, I mean, there is a certain period of time during which the thing is and another
during which it is not. Anything therefore which is generated or destructible must be intermediate. Now let A
be that which always is and B that which always is not, C the generated, and D the destructible. Then C must
be intermediate between A and B. For in their case there is no time in the direction of either limit, in which
either A is not or B is. But for the generated there must be such a time either actually or potentially, though
not for A and B in either way. C then will be, and also not be, for a limited length of time, and this is true also
of D, the destructible. Therefore each is both generated and destructible. Therefore 'generated' and
'destructible' are coincident. Now let E stand for the ungenerated, F for the generated, G for the indestructible,
and H for the destructible. As for F and H, it has been shown that they are coincident. But when terms stand
to one another as these do, F and H coincident, E and F never predicated of the same thing but one or other of
everything, and G and H likewise, then E and G must needs be coincident. For suppose that E is not
coincident with G, then F will be, since either E or F is predictable of everything. But of that of which F is
predicated H will be predicable also. H will then be coincident with G, but this we saw to be impossible. And
the same argument shows that G is coincident with E.

Now the relation of the ungenerated (E) to the generated (F) is the same as that of the indestructible (G) to the
destructible (H). To say then that there is no reason why anything should not be generated and yet
indestructible or ungenerated and yet destroyed, to imagine that in the one case generation and in the other
case destruction occurs once for all, is to destroy part of the data. For (1) everything is capable of acting or
being acted upon, of being or not being, either for an infinite, or for a definitely limited space of time; and the
infinite time is only a possible alternative because it is after a fashion defined, as a length of time which
cannot be exceeded. But infinity in one direction is neither infinite or finite. (2) Further, why, after always
existing, was the thing destroyed, why, after an infinity of not being, was it generated, at one moment rather
than another? If every moment is alike and the moments are infinite in number, it is clear that a generated or
destructible thing existed for an infinite time. It has therefore for an infinite time the capacity of not being
(since the capacity of being and the capacity of not being will be present together), if destructible, in the time
before destruction, if generated, in the time after generation. If then we assume the two capacities to be
actualized, opposites will be present together. (3) Further, this second capacity will be present like the first at
every moment, so that the thing will have for an infinite time the capacity both of being and of not being; but
this has been shown to be impossible. (4) Again, if the capacity is present prior to the activity, it will be
present for all time, even while the thing was as yet ungenerated and non-existent, throughout the infinite
time in which it was capable of being generated. At that time, then, when it was not, at that same time it had
the capacity of being, both of being then and of being thereafter, and therefore for an infinity of time.

It is clear also on other grounds that it is impossible that the destructible should not at some time be
destroyed. For otherwise it will always be at once destructible and in actuality indestructible, so that it will be
at the same time capable of always existing and of not always existing. Thus the destructible is at some time
actually destroyed. The generable, similarly, has been generated, for it is capable of having been generated
and thus also of not always existing.

We may also see in the following way how impossible it is either for a thing which is generated to be
thenceforward indestructible, or for a thing which is ungenerated and has always hitherto existed to be
destroyed. Nothing that is by chance can be indestructible or ungenerated, since the products of chance and
fortune are opposed to what is, or comes to be, always or usually, while anything which exists for a time
infinite either absolutely or in one direction, is in existence either always or usually. That which is by chance,
then, is by nature such as to exist at one time and not at another. But in things of that character the

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ON THE HEAVENS

contradictory states proceed from one and the same capacity, the matter of the thing being the cause equally
of its existence and of its non-existence. Hence contradictories would be present together in actuality.

Further, it cannot truly be said of a thing now that it exists last year, nor could it be said last year that it exists
now. It is therefore impossible for what once did not exist later to be eternal. For in its later state it will
possess the capacity of not existing, only not of not existing at a time when it exists-since then it exists in
actuality-but of not existing last year or in the past. Now suppose it to be in actuality what it is capable of
being. It will then be true to say now that it does not exist last year. But this is impossible. No capacity relates
to being in the past, but always to being in the present or future. It is the same with the notion of an eternity
of existence followed later by non-existence. In the later state the capacity will be present for that which is
not there in actuality. Actualize, then, the capacity. It will be true to say now that this exists last year or in the
past generally.

Considerations also not general like these but proper to the subject show it to be impossible that what was
formerly eternal should later be destroyed or that what formerly was not should later be eternal. Whatever is
destructible or generated is always alterable. Now alteration is due to contraries, and the things which
compose the natural body are the very same that destroy it.

Book II

THAT the heaven as a whole neither came into being nor admits of destruction, as some assert, but is one and
eternal, with no end or beginning of its total duration, containing and embracing in itself the infinity of time,
we may convince ourselves not only by the arguments already set forth but also by a consideration of the
views of those who differ from us in providing for its generation. If our view is a possible one, and the
manner of generation which they assert is impossible, this fact will have great weight in convincing us of the
immortality and eternity of the world. Hence it is well to persuade oneself of the truth of the ancient and truly
traditional theories, that there is some immortal and divine thing which possesses movement, but movement
such as has no limit and is rather itself the limit of all other movement. A limit is a thing which contains; and
this motion, being perfect, contains those imperfect motions which have a limit and a goal, having itself no
beginning or end, but unceasing through the infinity of time, and of other movements, to some the cause of
their beginning, to others offering the goal. The ancients gave to the Gods the heaven or upper place, as being
alone immortal; and our present argument testifies that it is indestructible and ungenerated. Further, it is
unaffected by any mortal discomfort, and, in addition, effortless; for it needs no constraining necessity to
keep it to its path, and prevent it from moving with some other movement more natural to itself. Such a
constrained movement would necessarily involve effort the more so, the more eternal it were-and would be
inconsistent with perfection. Hence we must not believe the old tale which says that the world needs some
Atlas to keep it safe-a tale composed, it would seem, by men who, like later thinkers, conceived of all the
upper bodies as earthy and endowed with weight, and therefore supported it in their fabulous way upon
animate necessity. We must no more believe that than follow Empedocles when he says that the world, by
being whirled round, received a movement quick enough to overpower its own downward tendency, and thus
has been kept from destruction all this time. Nor, again, is it conceivable that it should persist eternally by the
necessitation of a soul. For a soul could not live in such conditions painlessly or happily, since the movement
involves constraint, being imposed on the first body, whose natural motion is different, and imposed
continuously. It must therefore be uneasy and devoid of all rational satisfaction; for it could not even, like the
soul of mortal animals, take recreation in the bodily relaxation of sleep. An Ixion's lot must needs possess it,
without end or respite. If then, as we said, the view already stated of the first motion is a possible one, it is
not only more appropriate so to conceive of its eternity, but also on this hypothesis alone are we able to
advance a theory consistent with popular divinations of the divine nature. But of this enough for the present.

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ON THE HEAVENS

Since there are some who say that there is a right and a left in the heaven, with those who are known as
Pythagoreans-to whom indeed the view really belongs-we must consider whether, if we are to apply these
principles to the body of the universe, we should follow their statement of the matter or find a better way. At
the start we may say that, if right and left are applicable, there are prior principles which must first be applied.
These principles have been analysed in the discussion of the movements of animals, for the reason that they
are proper to animal nature. For in some animals we find all such distinctions of parts as this of right and left
clearly present, and in others some; but in plants we find only above and below. Now if we are to apply to the
heaven such a distinction of parts, we must exect, as we have said, to find in it also the distinction which in
animals is found first of them all. The distinctions are three, namely, above and below, front and its opposite,
right and left-all these three oppositions we expect to find in the perfect body-and each may be called a
principle. Above is the principle of length, right of breadth, front of depth. Or again we may connect them
with the various movements, taking principle to mean that part, in a thing capable of movement, from which
movement first begins. Growth starts from above, locomotion from the right, sensemovement from in front
(for front is simply the part to which the senses are directed). Hence we must not look for above and below,
right and left, front and back, in every kind of body, but only in those which, being animate, have a principle
of movement within themselves. For in no inanimate thing do we observe a part from which movement
originates. Some do not move at all, some move, but not indifferently in any direction; fire, for example, only
upward, and earth only to the centre. It is true that we speak of above and below, right and left, in these
bodies relatively to ourselves. The reference may be to our own right hands, as with the diviner, or to some
similarity to our own members, such as the parts of a statue possess; or we may take the contrary spatial
order, calling right that which is to our left, and left that which is to our right. We observe, however, in the
things themselves none of these distinctions; indeed if they are turned round we proceed to speak of the
opposite parts as right and left, a boy land below, front and back. Hence it is remarkable that the
Pythagoreans should have spoken of these two principles, right and left, only, to the exclusion of the other
four, which have as good a title as they. There is no less difference between above and below or front and
back in animals generally than between right and left. The difference is sometimes only one of function,
sometimes also one of shape; and while the distinction of above and below is characteristic of all animate
things, whether plants or animals, that of right and left is not found in plants. Further, inasmuch as length is
prior to breadth, if above is the principle of length, right of breadth, and if the principle of that which is prior
is itself prior, then above will be prior to right, or let us say, since 'prior' is ambiguous, prior in order of
generation. If, in addition, above is the region from which movement originates, right the region in which it
starts, front the region to which it is directed, then on this ground too above has a certain original character as
compared with the other forms of position. On these two grounds, then, they may fairly be criticized, first, for
omitting the more fundamental principles, and secondly, for thinking that the two they mentioned were
attributable equally to everything.

Since we have already determined that functions of this kind belong to things which possess, a principle of
movement, and that the heaven is animate and possesses a principle of movement, clearly the heaven must
also exhibit above and below, right and left. We need not be troubled by the question, arising from the
spherical shape of the world, how there can be a distinction of right and left within it, all parts being alike and
all for ever in motion. We must think of the world as of something in which right differs from left in shape as
well as in other respects, which subsequently is included in a sphere. The difference of function will persist,
but will appear not to by reason of the regularity of shape. In the same fashion must we conceive of the
beginning of its movement. For even if it never began to move, yet it must possess a principle from which it
would have begun to move if it had begun, and from which it would begin again if it came to a stand. Now by
its length I mean the interval between its poles, one pole being above and the other below; for two
hemispheres are specially distinguished from all others by the immobility of the poles. Further, by 'transverse'
in the universe we commonly mean, not above and below, but a direction crossing the line of the poles,

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ON THE HEAVENS

which, by implication, is length: for transverse motion is motion crossing motion up and down. Of the poles,
that which we see above us is the lower region, and that which we do not see is the upper. For right in
anything is, as we say, the region in which locomotion originates, and the rotation of the heaven originates in
the region from which the stars rise. So this will be the right, and the region where they set the left. If then
they begin from the right and move round to the right, the upper must be the unseen pole. For if it is the pole
we see, the movement will be leftward, which we deny to be the fact. Clearly then the invisible pole is above.
And those who live in the other hemisphere are above and to the right, while we are below and to the left.
This is just the opposite of the view of the Pythagoreans, who make us above and on the right side and those
in the other hemisphere below and on the left side; the fact being the exact opposite. Relatively, however, to
the secondary revolution, I mean that of the planets, we are above and on the right and they are below and on
the left. For the principle of their movement has the reverse position, since the movement itself is the contrary
of the other: hence it follows that we are at its beginning and they at its end. Here we may end our discussion
of the distinctions of parts created by the three dimensions and of the consequent differences of position.

Since circular motion is not the contrary of the reverse circular motion, we must consider why there is more
than one motion, though we have to pursue our inquiries at a distance-a distance created not so much by our
spatial position as by the fact that our senses enable us to perceive very few of the attributes of the heavenly
bodies. But let not that deter us. The reason must be sought in the following facts. Everything which has a
function exists for its function. The activity of God is immortality, i.e. eternal life. Therefore the movement
of that which is divine must be eternal. But such is the heaven, viz. a divine body, and for that reason to it is
given the circular body whose nature it is to move always in a circle. Why, then, is not the whole body of the
heaven of the same character as that part? Because there must be something at rest at the centre of the
revolving body; and of that body no part can be at rest, either elsewhere or at the centre. It could do so only if
the body's natural movement were towards the centre. But the circular movement is natural, since otherwise it
could not be eternal: for nothing unnatural is eternal. The unnatural is subsequent to the natural, being a
derangement of the natural which occurs in the course of its generation. Earth then has to exist; for it is earth
which is at rest at the centre. (At present we may take this for granted: it shall be explained later.) But if earth
must exist, so must fire. For, if one of a pair of contraries naturally exists, the other, if it is really contrary,
exists also naturally. In some form it must be present, since the matter of contraries is the same. Also, the
positive is prior to its privation (warm, for instance, to cold), and rest and heaviness stand for the privation of
lightness and movement. But further, if fire and earth exist, the intermediate bodies must exist also: each
element stands in a contrary relation to every other. (This, again, we will here take for granted and try later to
explain.) these four elements generation clearly is involved, since none of them can be eternal: for contraries
interact with one another and destroy one another. Further, it is inconceivable that a movable body should be
eternal, if its movement cannot be regarded as naturally eternal: and these bodies we know to possess
movement. Thus we see that generation is necessarily involved. But if so, there must be at least one other
circular motion: for a single movement of the whole heaven would necessitate an identical relation of the
elements of bodies to one another. This matter also shall be cleared up in what follows: but for the present so
much is clear, that the reason why there is more than one circular body is the necessity of generation, which
follows on the presence of fire, which, with that of the other bodies, follows on that of earth; and earth is
required because eternal movement in one body necessitates eternal rest in another.

The shape of the heaven is of necessity spherical; for that is the shape most appropriate to its substance and
also by nature primary.

ON THE HEAVENS

First, let us consider generally which shape is primary among planes and solids alike. Every plane figure must
be either rectilinear or curvilinear. Now the rectilinear is bounded by more than one line, the curvilinear by
one only. But since in any kind the one is naturally prior to the many and the simple to the complex, the circle
will be the first of plane figures. Again, if by complete, as previously defined, we mean a thing outside which
no part of itself can be found, and if addition is always possible to the straight line but never to the circular,
clearly the line which embraces the circle is complete. If then the complete is prior to the incomplete, it
follows on this ground also that the circle is primary among figures. And the sphere holds the same position
among solids. For it alone is embraced by a single surface, while rectilinear solids have several. The sphere is
among solids what the circle is among plane figures. Further, those who divide bodies into planes and
generate them out of planes seem to bear witness to the truth of this. Alone among solids they leave the
sphere undivided, as not possessing more than one surface: for the division into surfaces is not just dividing a
whole by cutting it into its parts, but division of another fashion into parts different in form. It is clear, then,
that the sphere is first of solid figures.

If, again, one orders figures according to their numbers, it is most natural to arrange them in this way. The
circle corresponds to the number one, the triangle, being the sum of two right angles, to the number two. But
if one is assigned to the triangle, the circle will not be a figure at all.

Now the first figure belongs to the first body, and the first body is that at the farthest circumference. It
follows that the body which revolves with a circular movement must be spherical. The same then will be true
of the body continuous with it: for that which is continuous with the spherical is spherical. The same again
holds of the bodies between these and the centre. Bodies which are bounded by the spherical and in contact
with it must be, as wholes, spherical; and the bodies below the sphere of the planets are contiguous with the
sphere above them. The sphere then will be spherical throughout; for every body within it is contiguous and
continuous with spheres.

Again, since the whole revolves, palpably and by assumption, in a circle, and since it has been shown that
outside the farthest circumference there is neither void nor place, from these grounds also it will follow
necessarily that the heaven is spherical. For if it is to be rectilinear in shape, it will follow that there is place
and body and void without it. For a rectilinear figure as it revolves never continues in the same room, but
where formerly was body, is now none, and where now is none, body will be in a moment because of the
projection at the corners. Similarly, if the world had some other figure with unequal radii, if, for instance, it
were lentiform, or oviform, in every case we should have to admit space and void outside the moving body,
because the whole body would not always occupy the same room.

Again, if the motion of the heaven is the measure of all movements whatever in virtue of being alone
continuous and regular and eternal, and if, in each kind, the measure is the minimum, and the minimum
movement is the swiftest, then, clearly, the movement of the heaven must be the swiftest of all movements.
Now of lines which return upon themselves the line which bounds the circle is the shortest; and that
movement is the swiftest which follows the shortest line. Therefore, if the heaven moves in a circle and
moves more swiftly than anything else, it must necessarily be spherical.

Corroborative evidence may be drawn from the bodies whose position is about the centre. If earth is enclosed
by water, water by air, air by fire, and these similarly by the upper bodies-which while not continuous are yet
contiguous with them-and if the surface of water is spherical, and that which is continuous with or embraces
the spherical must itself be spherical, then on these grounds also it is clear that the heavens are spherical. But
the surface of water is seen to be spherical if we take as our starting-point the fact that water naturally tends
to collect in a hollow place-'hollow' meaning 'nearer the centre'. Draw from the centre the lines AB, AC, and
let their extremities be joined by the straight line BC. The line AD, drawn to the base of the triangle, will be
shorter than either of the radii. Therefore the place in which it terminates will be a hollow place. The water
then will collect there until equality is established, that is until the line AE is equal to the two radii. Thus

3 22

ON THE HEAVENS

water forces its way to the ends of the radii, and there only will it rest: but the line which connects the
extremities of the radii is circular: therefore the surface of the water BEC is spherical.

It is plain from the foregoing that the universe is spherical. It is plain, further, that it is turned (so to speak)
with a finish which no manufactured thing nor anything else within the range of our observation can even
approach. For the matter of which these are composed does not admit of anything like the same regularity and
finish as the substance of the enveloping body; since with each step away from earth the matter manifestly
becomes finer in the same proportion as water is finer than earth.

Now there are two ways of moving along a circle, from A to B or from A to C, and we have already
explained that these movements are not contrary to one another. But nothing which concerns the eternal can
be a matter of chance or spontaneity, and the heaven and its circular motion are eternal. We must therefore
ask why this motion takes one direction and not the other. Either this is itself an ultimate fact or there is an
ultimate fact behind it. It may seem evidence of excessive folly or excessive zeal to try to provide an
explanation of some things, or of everything, admitting no exception. The criticism, however, is not always
just: one should first consider what reason there is for speaking, and also what kind of certainty is looked for,
whether human merely or of a more cogent kind. When any one shall succeed in finding proofs of greater
precision, gratitude will be due to him for the discovery, but at present we must be content with a probable
solution. If nature always follows the best course possible, and, just as upward movement is the superior form
of rectilinear movement, since the upper region is more divine than the lower, so forward movement is
superior to backward, then front and back exhibits, like right and left, as we said before and as the difficulty
just stated itself suggests, the distinction of prior and posterior, which provides a reason and so solves our
difficulty. Supposing that nature is ordered in the best way possible, this may stand as the reason of the fact
mentioned. For it is best to move with a movement simple and unceasing, and, further, in the superior of two
possible directions.

We have next to show that the movement of the heaven is regular and not irregular. This applies only to the
first heaven and the first movement; for the lower spheres exhibit a composition of several movements into
one. If the movement is uneven, clearly there will be acceleration, maximum speed, and retardation, since
these appear in all irregular motions. The maximum may occur either at the starting-point or at the goal or
between the two; and we expect natural motion to reach its maximum at the goal, unnatural motion at the
starting-point, and missiles midway between the two. But circular movement, having no beginning or limit
or middle in the direct sense of the words, has neither whence nor whither nor middle: for in time it is eternal,
and in length it returns upon itself without a break. If then its movement has no maximum, it can have no
irregularity, since irregularity is produced by retardation and acceleration. Further, since everything that is
moved is moved by something, the cause of the irregularity of movement must lie either in the mover or in
the moved or both. For if the mover moved not always with the same force, or if the moved were altered and
did not remain the same, or if both were to change, the result might well be an irregular movement in the
moved. But none of these possibilities can be conceived as actual in the case of the heavens. As to that which
is moved, we have shown that it is primary and simple and ungenerated and indestructible and generally
unchanging; and the mover has an even better right to these attributes. It is the primary that moves the
primary, the simple the simple, the indestructible and ungenerated that which is indestructible and
ungenerated. Since then that which is moved, being a body, is nevertheless unchanging, how should the
mover, which is incorporeal, be changed?

ON THE HEAVENS

It follows then, further, that the motion cannot be irregular. For if irregularity occurs, there must be change
either in the movement as a whole, from fast to slow and slow to fast, or in its parts. That there is no
irregularity in the parts is obvious, since, if there were, some divergence of the stars would have taken place
before now in the infinity of time, as one moved slower and another faster: but no alteration of their intervals
is ever observed. Nor again is a change in the movement as a whole admissible. Retardation is always due to
incapacity, and incapacity is unnatural. The incapacities of animals, age, decay, and the like, are all unnatural,
due, it seems, to the fact that the whole animal complex is made up of materials which differ in respect of
their proper places, and no single part occupies its own place. If therefore that which is primary contains
nothing unnatural, being simple and unmixed and in its proper place and having no contrary, then it has no
place for incapacity, nor, consequently, for retardation or (since acceleration involves retardation) for
acceleration. Again, it is inconceivable that the mover should first show incapacity for an infinite time, and
capacity afterwards for another infinity. For clearly nothing which, like incapacity, unnatural ever continues
for an infinity of time; nor does the unnatural endure as long as the natural, or any form of incapacity as long
as the capacity. But if the movement is retarded it must necessarily be retarded for an infinite time. Equally
impossible is perpetual acceleration or perpetual retardation. For such movement would be infinite and
indefinite, but every movement, in our view, proceeds from one point to another and is definite in character.
Again, suppose one assumes a minimum time in less than which the heaven could not complete its
movement. For, as a given walk or a given exercise on the harp cannot take any and every time, but every
performance has its definite minimum time which is unsurpassable, so, one might suppose, the movement of
the heaven could not be completed in any and every time. But in that case perpetual acceleration is
impossible (and, equally, perpetual retardation: for the argument holds of both and each), if we may take
acceleration to proceed by identical or increasing additions of speed and for an infinite time. The remaining
alternative is to say that the movement exhibits an alternation of slower and faster: but this is a mere fiction
and quite inconceivable. Further, irregularity of this kind would be particularly unlikely to pass unobserved,
since contrast makes observation easy.

That there is one heaven, then, only, and that it is ungenerated and eternal, and further that its movement is
regular, has now been sufficiently explained.

We have next to speak of the stars, as they are called, of their composition, shape, and movements. It would
be most natural and consequent upon what has been said that each of the stars should be composed of that
substance in which their path lies, since, as we said, there is an element whose natural movement is circular.
In so saying we are only following the same line of thought as those who say that the stars are fiery because
they believe the upper body to be fire, the presumption being that a thing is composed of the same stuff as
that in which it is situated. The warmth and light which proceed from them are caused by the friction set up in
the air by their motion. Movement tends to create fire in wood, stone, and iron; and with even more reason
should it have that effect on air, a substance which is closer to fire than these. An example is that of missiles,
which as they move are themselves fired so strongly that leaden balls are melted; and if they are fired the
surrounding air must be similarly affected. Now while the missiles are heated by reason of their motion in air,
which is turned into fire by the agitation produced by their movement, the upper bodies are carried on a
moving sphere, so that, though they are not themselves fired, yet the air underneath the sphere of the
revolving body is necessarily heated by its motion, and particularly in that part where the sun is attached to it.
Hence warmth increases as the sun gets nearer or higher or overhead. Of the fact, then, that the stars are
neither fiery nor move in fire, enough has been said.

ON THE HEAVENS

Since changes evidently occur not only in the position of the stars but also in that of the whole heaven, there
are three possibilities. Either (1) both are at rest, or (2) both are in motion, or (3) the one is at rest and the
other in motion.

(1) That both should be at rest is impossible; for, if the earth is at rest, the hypothesis does not account for the
observations; and we take it as granted that the earth is at rest. It remains either that both are moved, or that
the one is moved and the other at rest.

(2) On the view, first, that both are in motion, we have the absurdity that the stars and the circles move with
the same speed, i.e. that the ace of every star is that of the circle in it moves. For star and circle are seen to
come back to the same place at the same moment; from which it follows that the star has traversed the circle
and the circle has completed its own movement, i.e. traversed its own circumference, at one and the same
moment. But it is difficult to conceive that the pace of each star should be exactly proportioned to the size of
its circle. That the pace of each circle should be proportionate to its size is not absurd but inevitable: but that
the same should be true of the movement of the stars contained in the circles is quite incredible. For if, on the
one and, we suppose that the star which moves on the greater circle is necessarily swifter, clearly we also
admit that if stars shifted their position so as to exchange circles, the slower would become swifter and the
swifter slower. But this would show that their movement was not their own, but due to the circles. If, on the
other hand, the arrangement was a chance combination, the coincidence in every case of a greater circle with
a swifter movement of the star contained in it is too much to believe. In one or two cases it might not
inconceivably fall out so, but to imagine it in every case alike is a mere fiction. Besides, chance has no place
in that which is natural, and what happens everywhere and in every case is no matter of chance.

(3) The same absurdity is equally plain if it is supposed that the circles stand still and that it is the stars
themselves which move. For it will follow that the outer stars are the swifter, and that the pace of the stars
corresponds to the size of their circles.

Since, then, we cannot reasonably suppose either that both are in motion or that the star alone moves, the
remaining alternative is that the circles should move, while the stars are at rest and move with the circles to
which they are attached. Only on this supposition are we involved in no absurd consequence. For, in the first
place, the quicker movement of the larger circle is natural when all the circles are attached to the same centre.
Whenever bodies are moving with their proper motion, the larger moves quicker. It is the same here with the
revolving bodies: for the are intercepted by two radii will be larger in the larger circle, and hence it is not
surprising that the revolution of the larger circle should take the same time as that of the smaller. And
secondly, the fact that the heavens do not break in pieces follows not only from this but also from the proof
already given of the continuity of the whole.

Again, since the stars are spherical, as our opponents assert and we may consistently admit, inasmuch as we
construct them out of the spherical body, and since the spherical body has two movements proper to itself,
namely rolling and spinning, it follows that if the stars have a movement of their own, it will be one of these.
But neither is observed. (1) Suppose them to spin. They would then stay where they were, and not change
their place, as, by observation and general consent, they do. Further, one would expect them all to exhibit the
same movement: but the only star which appears to possess this movement is the sun, at sunrise or sunset,
and this appearance is due not to the sun itself but to the distance from which we observe it. The visual ray
being excessively prolonged becomes weak and wavering. The same reason probably accounts for the
apparent twinkling of the fixed stars and the absence of twinkling in the planets. The planets are near, so that
the visual ray reaches them in its full vigour, but when it comes to the fixed stars it is quivering because of
the distance and its excessive extension; and its tremor produces an appearance of movement in the star: for it

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ON THE HEAVENS

makes no difference whether movement is set up in the ray or in the object of vision.

(2) On the other hand, it is also clear that the stars do not roll. For rolling involves rotation: but the 'face', as it
is called, of the moon is always seen. Therefore, since any movement of their own which the stars possessed
would presumably be one proper to themselves, and no such movement is observed in them, clearly they have
no movement of their own.

There is, further, the absurdity that nature has bestowed upon them no organ appropriate to such movement.
For nature leaves nothing to chance, and would not, while caring for animals, overlook things so precious.
Indeed, nature seems deliberately to have stripped them of everything which makes selforiginated
progression possible, and to have removed them as far as possible from things which have organs of
movement. This is just why it seems proper that the whole heaven and every star should be spherical. For
while of all shapes the sphere is the most convenient for movement in one place, making possible, as it does,
the swiftest and most selfcontained motion, for forward movement it is the most unsuitable, least of all
resembling shapes which are self-moved, in that it has no dependent or projecting part, as a rectilinear figure
has, and is in fact as far as possible removed in shape from ambulatory bodies. Since, therefore, the heavens
have to move in one lace, and the stars are not required to move themselves forward, it is natural that both
should be spherical-a shape which best suits the movement of the one and the immobility of the other.

From all this it is clear that the theory that the movement of the stars produces a harmony, i.e. that the sounds
they make are concordant, in spite of the grace and originality with which it has been stated, is nevertheless
untrue. Some thinkers suppose that the motion of bodies of that size must produce a noise, since on our earth
the motion of bodies far inferior in size and in speed of movement has that effect. Also, when the sun and the
moon, they say, and all the stars, so great in number and in size, are moving with so rapid a motion, how
should they not produce a sound immensely great? Starting from this argument and from the observation that
their speeds, as measured by their distances, are in the same ratios as musical concordances, they assert that
the sound given forth by the circular movement of the stars is a harmony. Since, however, it appears
unaccountable that we should not hear this music, they explain this by saying that the sound is in our ears
from the very moment of birth and is thus indistinguishable from its contrary silence, since sound and silence
are discriminated by mutual contrast. What happens to men, then, is just what happens to coppersmiths, who
are so accustomed to the noise of the smithy that it makes no difference to them. But, as we said before,
melodious and poetical as the theory is, it cannot be a true account of the facts. There is not only the absurdity
of our hearing nothing, the ground of which they try to remove, but also the fact that no effect other than
sensitive is produced upon us. Excessive noises, we know, shatter the solid bodies even of inanimate things:
the noise of thunder, for instance, splits rocks and the strongest of bodies. But if the moving bodies are so
great, and the sound which penetrates to us is proportionate to their size, that sound must needs reach us in an
intensity many times that of thunder, and the force of its action must be immense. Indeed the reason why we
do not hear, and show in our bodies none of the effects of violent force, is easily given: it is that there is no
noise. But not only is the explanation evident; it is also a corroboration of the truth of the views we have
advanced. For the very difficulty which made the Pythagoreans say that the motion of the stars produces a
concord corroborates our view. Bodies which are themselves in motion, produce noise and friction: but those
which are attached or fixed to a moving body, as the parts to a ship, can no more create noise, than a ship on a
river moving with the stream. Yet by the same argument one might say it was absurd that on a large vessel
the motion of mast and poop should not make a great noise, and the like might be said of the movement of
the vessel itself. But sound is caused when a moving body is enclosed in an unmoved body, and cannot be
caused by one enclosed in, and continuous with, a moving body which creates no friction. We may say, then,
in this matter that if the heavenly bodies moved in a generally diffused mass of air or fire, as every one
supposes, their motion would necessarily cause a noise of tremendous strength and such a noise would

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ON THE HEAVENS

necessarily reach and shatter us. Since, therefore, this effect is evidently not produced, it follows that none of
them can move with the motion either of animate nature or of constraint. It is as though nature had foreseen
the result, that if their movement were other than it is, nothing on this earth could maintain its character.

That the stars are spherical and are not selfmoved, has now been explained.

With their order-I mean the position of each, as involving the priority of some and the posteriority of others,
and their respective distances from the extremity-with this astronomy may be left to deal, since the
astronomical discussion is adequate. This discussion shows that the movements of the several stars depend,
as regards the varieties of speed which they exhibit, on the distance of each from the extremity. It is
established that the outermost revolution of the heavens is a simple movement and the swiftest of all, and that
the movement of all other bodies is composite and relatively slow, for the reason that each is moving on its
own circle with the reverse motion to that of the heavens. This at once leads us to expect that the body which
is nearest to that first simple revolution should take the longest time to complete its circle, and that which is
farthest from it the shortest, the others taking a longer time the nearer they are and a shorter time the farther
away they are. For it is the nearest body which is most strongly influenced, and the most remote, by reason of
its distance, which is least affected, the influence on the intermediate bodies varying, as the mathematicians
show, with their distance.

With regard to the shape of each star, the most reasonable view is that they are spherical. It has been shown
that it is not in their nature to move themselves, and, since nature is no wanton or random creator, clearly she
will have given things which possess no movement a shape particularly unadapted to movement. Such a
shape is the sphere, since it possesses no instrument of movement. Clearly then their mass will have the form
of a sphere. Again, what holds of one holds of all, and the evidence of our eyes shows us that the moon is
spherical. For how else should the moon as it waxes and wanes show for the most part a crescent-shaped or
gibbous figure, and only at one moment a half-moon? And astronomical arguments give further
confirmation; for no other hypothesis accounts for the crescent shape of the sun's eclipses. One, then, of the
heavenly bodies being spherical, clearly the rest will be spherical also.

There are two difficulties, which may very reasonably here be raised, of which we must now attempt to state
the probable solution: for we regard the zeal of one whose thirst after philosophy leads him to accept even
slight indications where it is very difficult to see one's way, as a proof rather of modesty than of
overconfidence.

Of many such problems one of the strangest is the problem why we find the greatest number of movements in
the intermediate bodies, and not, rather, in each successive body a variety of movement proportionate to its
distance from the primary motion. For we should expect, since the primary body shows one motion only, that
the body which is nearest to it should move with the fewest movements, say two, and the one next after that
with three, or some similar arrangement. But the opposite is the case. The movements of the sun and moon
are fewer than those of some of the planets. Yet these planets are farther from the centre and thus nearer to
the primary body than they, as observation has itself revealed. For we have seen the moon, half-full, pass
beneath the planet Mars, which vanished on its shadow side and came forth by the bright and shining part.
Similar accounts of other stars are given by the Egyptians and Babylonians, whose observations have been
kept for very many years past, and from whom much of our evidence about particular stars is derived. A

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ON THE HEAVENS

second difficulty which may with equal justice be raised is this. Why is it that the primary motion includes
such a multitude of stars that their whole array seems to defy counting, while of the other stars each one is
separated off, and in no case do we find two or more attached to the same motion?

On these questions, I say, it is well that we should seek to increase our understanding, though we have but
little to go upon, and are placed at so great a distance from the facts in question. Nevertheless there are
certain principles on which if we base our consideration we shall not find this difficulty by any means
insoluble. We may object that we have been thinking of the stars as mere bodies, and as units with a serial
order indeed but entirely inanimate; but should rather conceive them as enjoying life and action. On this view
the facts cease to appear surprising. For it is natural that the best-conditioned of all things should have its
good without action, that which is nearest to it should achieve it by little and simple action, and that which is
farther removed by a complexity of actions, just as with men's bodies one is in good condition without
exercise at all, another after a short walk, while another requires running and wrestling and hard training, and
there are yet others who however hard they worked themselves could never secure this good, but only some
substitute for it. To succeed often or in many things is difficult. For instance, to throw ten thousand Coan
throws with the dice would be impossible, but to throw one or two is comparatively easy. In action, again,
when A has to be done to get B, B to get C, and C to get D, one step or two present little difficulty, but as the
series extends the difficulty grows. We must, then, think of the action of the lower stars as similar to that of
animals and plants. For on our earth it is man that has the greatest variety of actions-for there are many
goods that man can secure; hence his actions are various and directed to ends beyond them-while the
perfectly conditioned has no need of action, since it is itself the end, and action always requires two terms,
end and means. The lower animals have less variety of action than man; and plants perhaps have little action
and of one kind only. For either they have but one attainable good (as indeed man has), or, if several, each
contributes directly to their ultimate good. One thing then has and enjoys the ultimate good, other things
attain to it, one immediately by few steps, another by many, while yet another does not even attempt to secure
it but is satisfied to reach a point not far removed from that consummation. Thus, taking health as the end,
there will be one thing that always possesses health, others that attain it, one by reducing flesh, another by
running and thus reducing flesh, another by taking steps to enable himself to run, thus further increasing the
number of movements, while another cannot attain health itself, but only running or reduction of flesh, so that
one or other of these is for such a being the end. For while it is clearly best for any being to attain the real
end, yet, if that cannot be, the nearer it is to the best the better will be its state. It is for this reason that the
earth moves not at all and the bodies near to it with few movements. For they do not attain the final end, but
only come as near to it as their share in the divine principle permits. But the first heaven finds it immediately
with a single movement, and the bodies intermediate between the first and last heavens attain it indeed, but at
the cost of a multiplicity of movement.

As to the difficulty that into the one primary motion is crowded a vast multitude of stars, while of the other
stars each has been separately given special movements of its own, there is in the first place this reason for
regarding the arrangement as a natural one. In thinking of the life and moving principle of the several heavens
one must regard the first as far superior to the others. Such a superiority would be reasonable. For this single
first motion has to move many of the divine bodies, while the numerous other motions move only one each,
since each single planet moves with a variety of motions. Thus, then, nature makes matters equal and
establishes a certain order, giving to the single motion many bodies and to the single body many motions.
And there is a second reason why the other motions have each only one body, in that each of them except the
last, i.e. that which contains the one star, is really moving many bodies. For this last sphere moves with many
others, to which it is fixed, each sphere being actually a body; so that its movement will be a joint product.
Each sphere, in fact, has its particular natural motion, to which the general movement is, as it were, added.
But the force of any limited body is only adequate to moving a limited body.

The characteristics of the stars which move with a circular motion, in respect of substance and shape,
movement and order, have now been sufficiently explained.

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ON THE HEAVENS

It remains to speak of the earth, of its position, of the question whether it is at rest or in motion, and of its
shape.

I. As to its position there is some difference of opinion. Most people-all, in fact, who regard the whole
heaven as finite-say it lies at the centre. But the Italian philosophers known as Pythagoreans take the contrary
view. At the centre, they say, is fire, and the earth is one of the stars, creating night and day by its circular
motion about the centre. They further construct another earth in opposition to ours to which they give the
name counterearth. In all this they are not seeking for theories and causes to account for observed facts, but
rather forcing their observations and trying to accommodate them to certain theories and opinions of their
own. But there are many others who would agree that it is wrong to give the earth the central position,
looking for confirmation rather to theory than to the facts of observation. Their view is that the most precious
place befits the most precious thing: but fire, they say, is more precious than earth, and the limit than the
intermediate, and the circumference and the centre are limits. Reasoning on this basis they take the view that
it is not earth that lies at the centre of the sphere, but rather fire. The Pythagoreans have a further reason.
They hold that the most important part of the world, which is the centre, should be most strictly guarded, and
name it, or rather the fire which occupies that place, the 'Guardhouse of Zeus', as if the word 'centre' were
quite unequivocal, and the centre of the mathematical figure were always the same with that of the thing or
the natural centre. But it is better to conceive of the case of the whole heaven as analogous to that of animals,
in which the centre of the animal and that of the body are different. For this reason they have no need to be so
disturbed about the world, or to call in a guard for its centre: rather let them look for the centre in the other
sense and tell us what it is like and where nature has set it. That centre will be something primary and
precious; but to the mere position we should give the last place rather than the first. For the middle is what is
defined, and what defines it is the limit, and that which contains or limits is more precious than that which is
limited, see ing that the latter is the matter and the former the essence of the system.

II. As to the position of the earth, then, this is the view which some advance, and the views advanced
concerning its rest or motion are similar. For here too there is no general agreement. All who deny that the
earth lies at the centre think that it revolves about the centre, and not the earth only but, as we said before, the
counter-earth as well. Some of them even consider it possible that there are several bodies so moving, which
are invisible to us owing to the interposition of the earth. This, they say, accounts for the fact that eclipses of
the moon are more frequent than eclipses of the sun: for in addition to the earth each of these moving bodies
can obstruct it. Indeed, as in any case the surface of the earth is not actually a centre but distant from it a full
hemisphere, there is no more difficulty, they think, in accounting for the observed facts on their view that we
do not dwell at the centre, than on the common view that the earth is in the middle. Even as it is, there is
nothing in the observations to suggest that we are removed from the centre by half the diameter of the earth.
Others, again, say that the earth, which lies at the centre, is 'rolled', and thus in motion, about the axis of the
whole heaven, So it stands written in the Timaeus.

III. There are similar disputes about the shape of the earth. Some think it is spherical, others that it is flat and
drum-shaped. For evidence they bring the fact that, as the sun rises and sets, the part concealed by the earth
shows a straight and not a curved edge, whereas if the earth were spherical the line of section would have to
be circular. In this they leave out of account the great distance of the sun from the earth and the great size of
the circumference, which, seen from a distance on these apparently small circles appears straight. Such an
appearance ought not to make them doubt the circular shape of the earth. But they have another argument.
They say that because it is at rest, the earth must necessarily have this shape. For there are many different
ways in which the movement or rest of the earth has been conceived.

The difficulty must have occurred to every one. It would indeed be a complacent mind that felt no surprise
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that, while a little bit of earth, let loose in mid-air moves and will not stay still, and more there is of it the
faster it moves, the whole earth, free in midair, should show no movement at all. Yet here is this great weight
of earth, and it is at rest. And again, from beneath one of these moving fragments of earth, before it falls, take
away the earth, and it will continue its downward movement with nothing to stop it. The difficulty then, has
naturally passed into a common place of philosophy; and one may well wonder that the solutions offered are
not seen to involve greater absurdities than the problem itself.

By these considerations some have been led to assert that the earth below us is infinite, saying, with
Xenophanes of Colophon, that it has 'pushed its roots to infinity',-in order to save the trouble of seeking for
the cause. Hence the sharp rebuke of Empedocles, in the words 'if the deeps of the earth are endless and
endless the ample ether-such is the vain tale told by many a tongue, poured from the mouths of those who
have seen but little of the whole. Others say the earth rests upon water. This, indeed, is the oldest theory that
has been preserved, and is attributed to Thales of Miletus. It was supposed to stay still because it floated like
wood and other similar substances, which are so constituted as to rest upon but not upon air. As if the same
account had not to be given of the water which carries the earth as of the earth itself! It is not the nature of
water, any more than of earth, to stay in mid-air: it must have something to rest upon. Again, as air is lighter
than water, so is water than earth: how then can they think that the naturally lighter substance lies below the
heavier? Again, if the earth as a whole is capable of floating upon water, that must obviously be the case with
any part of it. But observation shows that this is not the case. Any piece of earth goes to the bottom, the
quicker the larger it is. These thinkers seem to push their inquiries some way into the problem, but not so far
as they might. It is what we are all inclined to do, to direct our inquiry not by the matter itself, but by the
views of our opponents: and even when interrogating oneself one pushes the inquiry only to the point at
which one can no longer offer any opposition. Hence a good inquirer will be one who is ready in bringing
forward the objections proper to the genus, and that he will be when he has gained an understanding of all the
differences.

Anaximenes and Anaxagoras and Democritus give the flatness of the earth as the cause of its staying still.
Thus, they say, it does not cut, but covers like a lid, the air beneath it. This seems to be the way of
flat-shaped bodies: for even the wind can scarcely move them because of their power of resistance. The same
immobility, they say, is produced by the flatness of the surface which the earth presents to the air which
underlies it; while the air, not having room enough to change its place because it is underneath the earth, stays
there in a mass, like the water in the case of the water-clock. And they adduce an amount of evidence to
prove that air, when cut off and at rest, can bear a considerable weight.

Now, first, if the shape of the earth is not flat, its flatness cannot be the cause of its immobility. But in their
own account it is rather the size of the earth than its flatness that causes it to remain at rest. For the reason
why the air is so closely confined that it cannot find a passage, and therefore stays where it is, is its great
amount: and this amount great because the body which isolates it, the earth, is very large. This result, then,
will follow, even if the earth is spherical, so long as it retains its size. So far as their arguments go, the earth
will still be at rest.

In general, our quarrel with those who speak of movement in this way cannot be confined to the parts; it
concerns the whole universe. One must decide at the outset whether bodies have a natural movement or not,
whether there is no natural but only constrained movement. Seeing, however, that we have already decided
this matter to the best of our ability, we are entitled to treat our results as representing fact. Bodies, we say,
which have no natural movement, have no constrained movement; and where there is no natural and no
constrained movement there will be no movement at all. This is a conclusion, the necessity of which we have
already decided, and we have seen further that rest also will be inconceivable, since rest, like movement, is
either natural or constrained. But if there is any natural movement, constraint will not be the sole principle of
motion or of rest. If, then, it is by constraint that the earth now keeps its place, the so-called 'whirling'
movement by which its parts came together at the centre was also constrained. (The form of causation

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supposed they all borrow from observations of liquids and of air, in which the larger and heavier bodies
always move to the centre of the whirl. This is thought by all those who try to generate the heavens to explain
why the earth came together at the centre. They then seek a reason for its staying there; and some say, in the
manner explained, that the reason is its size and flatness, others, with Empedocles, that the motion of the
heavens, moving about it at a higher speed, prevents movement of the earth, as the water in a cup, when the
cup is given a circular motion, though it is often underneath the bronze, is for this same reason prevented
from moving with the downward movement which is natural to it.) But suppose both the 'whirl' and its
flatness (the air beneath being withdrawn) cease to prevent the earth's motion, where will the earth move to
then? Its movement to the centre was constrained, and its rest at the centre is due to constraint; but there must
be some motion which is natural to it. Will this be upward motion or downward or what? It must have some
motion; and if upward and downward motion are alike to it, and the air above the earth does not prevent
upward movement, then no more could air below it prevent downward movement. For the same cause must
necessarily have the same effect on the same thing.

Further, against Empedocles there is another point which might be made. When the elements were separated
off by Hate, what caused the earth to keep its place? Surely the 'whirl' cannot have been then also the cause. It
is absurd too not to perceive that, while the whirling movement may have been responsible for the original
coming together of the art of earth at the centre, the question remains, why now do all heavy bodies move to
the earth. For the whirl surely does not come near us. Why, again, does fire move upward? Not, surely,
because of the whirl. But if fire is naturally such as to move in a certain direction, clearly the same may be
supposed to hold of earth. Again, it cannot be the whirl which determines the heavy and the light. Rather that
movement caused the pre-existent heavy and light things to go to the middle and stay on the surface
respectively. Thus, before ever the whirl began, heavy and light existed; and what can have been the ground
of their distinction, or the manner and direction of their natural movements? In the infinite chaos there can
have been neither above nor below, and it is by these that heavy and light are determined.

It is to these causes that most writers pay attention: but there are some, Anaximander, for instance, among the
ancients, who say that the earth keeps its place because of its indifference. Motion upward and downward and
sideways were all, they thought, equally inappropriate to that which is set at the centre and indifferently
related to every extreme point; and to move in contrary directions at the same time was impossible: so it must
needs remain still. This view is ingenious but not true. The argument would prove that everything, whatever
it be, which is put at the centre, must stay there. Fire, then, will rest at the centre: for the proof turns on no
peculiar property of earth. But this does not follow. The observed facts about earth are not only that it
remains at the centre, but also that it moves to the centre. The place to which any fragment of earth moves
must necessarily be the place to which the whole moves; and in the place to which a thing naturally moves, it
will naturally rest. The reason then is not in the fact that the earth is indifferently related to every extreme
point: for this would apply to any body, whereas movement to the centre is peculiar to earth. Again it is
absurd to look for a reason why the earth remains at the centre and not for a reason why fire remains at the
extremity. If the extremity is the natural place of fire, clearly earth must also have a natural place. But
suppose that the centre is not its place, and that the reason of its remaining there is this necessity of
indifference-on the analogy of the hair which, it is said, however great the tension, will not break under it, if
it be evenly distributed, or of the men who, though exceedingly hungry and thirsty, and both equally, yet
being equidistant from food and drink, is therefore bound to stay where he is-even so, it still remains to
explain why fire stays at the extremities. It is strange, too, to ask about things staying still but not about their
motion,-why, I mean, one thing, if nothing stops it, moves up, and another thing to the centre. Again, their
statements are not true. It happens, indeed, to be the case that a thing to which movement this way and that is
equally inappropriate is obliged to remain at the centre. But so far as their argument goes, instead of
remaining there, it will move, only not as a mass but in fragments. For the argument applies equally to fire.
Fire, if set at the centre, should stay there, like earth, since it will be indifferently related to every point on the
extremity. Nevertheless it will move, as in fact it always does move when nothing stops it, away from the
centre to the extremity. It will not, however, move in a mass to a single point on the circumference-the only

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possible result on the lines of the indifference theory-but rather each corresponding portion of fire to the
corresponding part of the extremity, each fourth part, for instance, to a fourth part of the circumference. For
since no body is a point, it will have parts. The expansion, when the body increased the place occupied,
would be on the same principle as the contraction, in which the place was diminished. Thus, for all the
indifference theory shows to the contrary, earth also would have moved in this manner away from the centre,
unless the centre had been its natural place.

We have now outlined the views held as to the shape, position, and rest or movement of the earth.

Let us first decide the question whether the earth moves or is at rest. For, as we said, there are some who
make it one of the stars, and others who, setting it at the centre, suppose it to be 'rolled' and in motion about
the pole as axis. That both views are untenable will be clear if we take as our starting-point the fact that the
earth's motion, whether the earth be at the centre or away from it, must needs be a constrained motion. It
cannot be the movement of the earth itself. If it were, any portion of it would have this movement; but in fact
every part moves in a straight line to the centre. Being, then, constrained and unnatural, the movement could
not be eternal. But the order of the universe is eternal. Again, everything that moves with the circular
movement, except the first sphere, is observed to be passed, and to move with more than one motion. The
earth, then, also, whether it move about the centre or as stationary at it, must necessarily move with two
motions. But if this were so, there would have to be passings and turnings of the fixed stars. Yet no such
thing is observed. The same stars always rise and set in the same parts of the earth.

Further, the natural movement of the earth, part and whole alike, is the centre of the whole-whence the fact
that it is now actually situated at the centre-but it might be questioned since both centres are the same, which
centre it is that portions of earth and other heavy things move to. Is this their goal because it is the centre of
the earth or because it is the centre of the whole? The goal, surely, must be the centre of the whole. For fire
and other light things move to the extremity of the area which contains the centre. It happens, however, that
the centre of the earth and of the whole is the same. Thus they do move to the centre of the earth, but
accidentally, in virtue of the fact that the earth's centre lies at the centre of the whole. That the centre of the
earth is the goal of their movement is indicated by the fact that heavy bodies moving towards the earth do not
parallel but so as to make equal angles, and thus to a single centre, that of the earth. It is clear, then, that the
earth must be at the centre and immovable, not only for the reasons already given, but also because heavy
bodies forcibly thrown quite straight upward return to the point from which they started, even if they are
thrown to an infinite distance. From these considerations then it is clear that the earth does not move and does
not lie elsewhere than at the centre.

From what we have said the explanation of the earth's immobility is also apparent. If it is the nature of earth,
as observation shows, to move from any point to the centre, as of fire contrariwise to move from the centre to
the extremity, it is impossible that any portion of earth should move away from the centre except by
constraint. For a single thing has a single movement, and a simple thing a simple: contrary movements cannot
belong to the same thing, and movement away from the centre is the contrary of movement to it. If then no
portion of earth can move away from the centre, obviously still less can the earth as a whole so move. For it
is the nature of the whole to move to the point to which the part naturally moves. Since, then, it would require
a force greater than itself to move it, it must needs stay at the centre. This view is further supported by the
contributions of mathematicians to astronomy, since the observations made as the shapes change by which
the order of the stars is determined, are fully accounted for on the hypothesis that the earth lies at the centre.
Of the position of the earth and of the manner of its rest or movement, our discussion may here end.

Its shape must necessarily be spherical. For every portion of earth has weight until it reaches the centre, and
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the jostling of parts greater and smaller would bring about not a waved surface, but rather compression and
convergence of part and part until the centre is reached. The process should be conceived by supposing the
earth to come into being in the way that some of the natural philosophers describe. Only they attribute the
downward movement to constraint, and it is better to keep to the truth and say that the reason of this motion
is that a thing which possesses weight is naturally endowed with a centripetal movement. When the mixture,
then, was merely potential, the things that were separated off moved similarly from every side towards the
centre. Whether the parts which came together at the centre were distributed at the extremities evenly, or in
some other way, makes no difference. If, on the one hand, there were a similar movement from each quarter
of the extremity to the single centre, it is obvious that the resulting mass would be similar on every side. For
if an equal amount is added on every side the extremity of the mass will be everywhere equidistant from its
centre, i.e. the figure will be spherical. But neither will it in any way affect the argument if there is not a
similar accession of concurrent fragments from every side. For the greater quantity, finding a lesser in front
of it, must necessarily drive it on, both having an impulse whose goal is the centre, and the greater weight
driving the lesser forward till this goal is reached. In this we have also the solution of a possible difficulty.
The earth, it might be argued, is at the centre and spherical in shape: if, then, a weight many times that of the
earth were added to one hemisphere, the centre of the earth and of the whole will no longer be coincident. So
that either the earth will not stay still at the centre, or if it does, it will be at rest without having its centre at
the place to which it is still its nature to move. Such is the difficulty. A short consideration will give us an
easy answer, if we first give precision to our postulate that any body endowed with weight, of whatever size,
moves towards the centre. Clearly it will not stop when its edge touches the centre. The greater quantity must
prevail until the body's centre occupies the centre. For that is the goal of its impulse. Now it makes no
difference whether we apply this to a clod or common fragment of earth or to the earth as a whole. The fact
indicated does not depend upon degrees of size but applies universally to everything that has the centripetal
impulse. Therefore earth in motion, whether in a mass or in fragments, necessarily continues to move until it
occupies the centre equally every way, the less being forced to equalize itself by the greater owing to the
forward drive of the impulse.

If the earth was generated, then, it must have been formed in this way, and so clearly its generation was
spherical; and if it is ungenerated and has remained so always, its character must be that which the initial
generation, if it had occurred, would have given it. But the spherical shape, necessitated by this argument,
follows also from the fact that the motions of heavy bodies always make equal angles, and are not parallel.
This would be the natural form of movement towards what is naturally spherical. Either then the earth is
spherical or it is at least naturally spherical. And it is right to call anything that which nature intends it to be,
and which belongs to it, rather than that which it is by constraint and contrary to nature. The evidence of the
senses further corroborates this. How else would eclipses of the moon show segments shaped as we see
them? As it is, the shapes which the moon itself each month shows are of every kind straight, gibbous, and
concave-but in eclipses the outline is always curved: and, since it is the interposition of the earth that makes
the eclipse, the form of this line will be caused by the form of the earth's surface, which is therefore spherical.
Again, our observations of the stars make it evident, not only that the earth is circular, but also that it is a
circle of no great size. For quite a small change of position to south or north causes a manifest alteration of
the horizon. There is much change, I mean, in the stars which are overhead, and the stars seen are different, as
one moves northward or southward. Indeed there are some stars seen in Egypt and in the neighbourhood of
Cyprus which are not seen in the northerly regions; and stars, which in the north are never beyond the range
of observation, in those regions rise and set. All of which goes to show not only that the earth is circular in
shape, but also that it is a sphere of no great size: for otherwise the effect of so slight a change of place would
not be quickly apparent. Hence one should not be too sure of the incredibility of the view of those who
conceive that there is continuity between the parts about the pillars of Hercules and the parts about India, and
that in this way the ocean is one. As further evidence in favour of this they quote the case of elephants, a
species occurring in each of these extreme regions, suggesting that the common characteristic of these
extremes is explained by their continuity. Also, those mathematicians who try to calculate the size of the
earth's circumference arrive at the figure 400,000 stades. This indicates not only that the earth's mass is

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spherical in shape, but also that as compared with the stars it is not of great size.

Book III

WE have already discussed the first heaven and its parts, the moving stars within it, the matter of which these
are composed and their bodily constitution, and we have also shown that they are ungenerated and
indestructible. Now things that we call natural are either substances or functions and attributes of substances.
As substances I class the simple bodies-fire, earth, and the other terms of the series-and all things composed
of them; for example, the heaven as a whole and its parts, animals, again, and plants and their parts. By
attributes and functions I mean the movements of these and of all other things in which they have power in
themselves to cause movement, and also their alterations and reciprocal transformations. It is obvious, then,
that the greater part of the inquiry into nature concerns bodies: for a natural substance is either a body or a
thing which cannot come into existence without body and magnitude. This appears plainly from an analysis
of the character of natural things, and equally from an inspection of the instances of inquiry into nature.
Since, then, we have spoken of the primary element, of its bodily constitution, and of its freedom from
destruction and generation, it remains to speak of the other two. In speaking of them we shall be obliged also
to inquire into generation and destruction. For if there is generation anywhere, it must be in these elements
and things composed of them.

This is indeed the first question we have to ask: is generation a fact or not? Earlier speculation was at
variance both with itself and with the views here put forward as to the true answer to this question. Some
removed generation and destruction from the world altogether. Nothing that is, they said, is generated or
destroyed, and our conviction to the contrary is an illusion. So maintained the school of Melissus and
Parmenides. But however excellent their theories may otherwise be, anyhow they cannot be held to speak as
students of nature. There may be things not subject to generation or any kind of movement, but if so they
belong to another and a higher inquiry than the study of nature. They, however, had no idea of any form of
being other than the substance of things perceived; and when they saw, what no one previously had seen, that
there could be no knowledge or wisdom without some such unchanging entities, they naturally transferred
what was true of them to things perceived. Others, perhaps intentionally, maintain precisely the contrary
opinion to this. It has been asserted that everything in the world was subject to generation and nothing was
ungenerated, but that after being generated some things remained indestructible while the rest were again
destroyed. This had been asserted in the first instance by Hesiod and his followers, but afterwards outside his
circle by the earliest natural philosophers. But what these thinkers maintained was that all else has been
generated and, as they said, 'is flowing away, nothing having any solidity, except one single thing which
persists as the basis of all these transformations. So we may interpret the statements of Heraclitus of Ephesus
and many others. And some subject all bodies whatever to generation, by means of the composition and
separation of planes.

Discussion of the other views may be postponed. But this last theory which composes every body of planes
is, as the most superficial observation shows, in many respects in plain contradiction with mathematics. It is,
however, wrong to remove the foundations of a science unless you can replace them with others more
convincing. And, secondly, the same theory which composes solids of planes clearly composes planes of
lines and lines of points, so that a part of a line need not be a line. This matter has been already considered in
our discussion of movement, where we have shown that an indivisible length is impossible. But with respect
to natural bodies there are impossibilities involved in the view which asserts indivisible lines, which we may
briefly consider at this point. For the impossible consequences which result from this view in the
mathematical sphere will reproduce themselves when it is applied to physical bodies, but there will be
difficulties in physics which are not present in mathematics; for mathematics deals with an abstract and

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physics with a more concrete object. There are many attributes necessarily present in physical bodies which
are necessarily excluded by indivisibility; all attributes, in fact, which are divisible. There can be nothing
divisible in an indivisible thing, but the attributes of bodies are all divisible in one of two ways. They are
divisible into kinds, as colour is divided into white and black, and they are divisible per accidens when that
which has them is divisible. In this latter sense attributes which are simple are nevertheless divisible.
Attributes of this kind will serve, therefore, to illustrate the impossibility of the view. It is impossible, if two
parts of a thing have no weight, that the two together should have weight. But either all perceptible bodies or
some, such as earth and water, have weight, as these thinkers would themselves admit. Now if the point has
no weight, clearly the lines have not either, and, if they have not, neither have the planes. Therefore no body
has weight. It is, further, manifest that their point cannot have weight. For while a heavy thing may always be
heavier than something and a light thing lighter than something, a thing which is heavier or lighter than
something need not be itself heavy or light, just as a large thing is larger than others, but what is larger is not
always large. A thing which, judged absolutely, is small may none the less be larger than other things.
Whatever, then, is heavy and also heavier than something else, must exceed this by something which is
heavy. A heavy thing therefore is always divisible. But it is common ground that a point is indivisible. Again,
suppose that what is heavy or weight is a dense body, and what is light rare. Dense differs from rare in
containing more matter in the same cubic area. A point, then, if it may be heavy or light, may be dense or
rare. But the dense is divisible while a point is indivisible. And if what is heavy must be either hard or soft,
an impossible consequence is easy to draw. For a thing is soft if its surface can be pressed in, hard if it
cannot; and if it can be pressed in it is divisible.

Moreover, no weight can consist of parts not possessing weight. For how, except by the merest fiction, can
they specify the number and character of the parts which will produce weight? And, further, when one weight
is greater than another, the difference is a third weight; from which it will follow that every indivisible part
possesses weight. For suppose that a body of four points possesses weight. A body composed of more than
four points will superior in weight to it, a thing which has weight. But the difference between weight and
weight must be a weight, as the difference between white and whiter is white. Here the difference which
makes the superior weight heavier is the single point which remains when the common number, four, is
subtracted. A single point, therefore, has weight.

Further, to assume, on the one hand, that the planes can only be put in linear contact would be ridiculous. For
just as there are two ways of putting lines together, namely, end to and side by side, so there must be two
ways of putting planes together. Lines can be put together so that contact is linear by laying one along the
other, though not by putting them end to end. But if, similarly, in putting the lanes together, superficial
contact is allowed as an alternative to linear, that method will give them bodies which are not any element
nor composed of elements. Again, if it is the number of planes in a body that makes one heavier than another,
as the Timaeus explains, clearly the line and the point will have weight. For the three cases are, as we said
before, analogous. But if the reason of differences of weight is not this, but rather the heaviness of earth and
the lightness of fire, then some of the planes will be light and others heavy (which involves a similar
distinction in the lines and the points); the earthplane, I mean, will be heavier than the fire-plane. In general,
the result is either that there is no magnitude at all, or that all magnitude could be done away with. For a point
is to a line as a line is to a plane and as a plane is to a body. Now the various forms in passing into one
another will each be resolved into its ultimate constituents. It might happen therefore that nothing existed
except points, and that there was no body at all. A further consideration is that if time is similarly constituted,
there would be, or might be, a time at which it was done away with. For the indivisible now is like a point in
a line. The same consequences follow from composing the heaven of numbers, as some of the Pythagoreans
do who make all nature out of numbers. For natural bodies are manifestly endowed with weight and lightness,
but an assemblage of units can neither be composed to form a body nor possess weight.

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The necessity that each of the simple bodies should have a natural movement may be shown as follows. They
manifestly move, and if they have no proper movement they must move by constraint: and the constrained is
the same as the unnatural. Now an unnatural movement presupposes a natural movement which it
contravenes, and which, however many the unnatural movements, is always one. For naturally a thing moves
in one way, while its unnatural movements are manifold. The same may be shown, from the fact of rest. Rest,
also, must either be constrained or natural, constrained in a place to which movement was constrained,
natural in a place movement to which was natural. Now manifestly there is a body which is at rest at the
centre. If then this rest is natural to it, clearly motion to this place is natural to it. If, on the other hand, its rest
is constrained, what is hindering its motion? Something, which is at rest: but if so, we shall simply repeat the
same argument; and either we shall come to an ultimate something to which rest where it is or we shall have
an infinite process, which is impossible. The hindrance to its movement, then, we will suppose, is a moving
thing-as Empedocles says that it is the vortex which keeps the earth still-: but in that case we ask, where
would it have moved to but for the vortex? It could not move infinitely; for to traverse an infinite is
impossible, and impossibilities do not happen. So the moving thing must stop somewhere, and there rest not
by constraint but naturally. But a natural rest proves a natural movement to the place of rest. Hence
Leucippus and Democritus, who say that the primary bodies are in perpetual movement in the void or infinite,
may be asked to explain the manner of their motion and the kind of movement which is natural to them. For
if the various elements are constrained by one another to move as they do, each must still have a natural
movement which the constrained contravenes, and the prime mover must cause motion not by constraint but
naturally. If there is no ultimate natural cause of movement and each preceding term in the series is always
moved by constraint, we shall have an infinite process. The same difficulty is involved even if it is supposed,
as we read in the Timaeus, that before the ordered world was made the elements moved without order. Their
movement must have been due either to constraint or to their nature. And if their movement was natural, a
moment's consideration shows that there was already an ordered world. For the prime mover must cause
motion in virtue of its own natural movement, and the other bodies, moving without constraint, as they came
to rest in their proper places, would fall into the order in which they now stand, the heavy bodies moving
towards the centre and the light bodies away from it. But that is the order of their distribution in our world.
There is a further question, too, which might be asked. Is it possible or impossible that bodies in unordered
movement should combine in some cases into combinations like those of which bodies of nature's composing
are composed, such, I mean, as bones and flesh? Yet this is what Empedocles asserts to have occurred under
Love. 'Many a head', says he, 'came to birth without a neck.' The answer to the view that there are infinite
bodies moving in an infinite is that, if the cause of movement is single, they must move with a single motion,
and therefore not without order; and if, on the other hand, the causes are of infinite variety, their motions too
must be infinitely varied. For a finite number of causes would produce a kind of order, since absence of order
is not proved by diversity of direction in motions: indeed, in the world we know, not all bodies, but only
bodies of the same kind, have a common goal of movement. Again, disorderly movement means in reality
unnatural movement, since the order proper to perceptible things is their nature. And there is also absurdity
and impossibility in the notion that the disorderly movement is infinitely continued. For the nature of things
is the nature which most of them possess for most of the time. Thus their view brings them into the contrary
position that disorder is natural, and order or system unnatural. But no natural fact can originate in chance.
This is a point which Anaxagoras seems to have thoroughly grasped; for he starts his cosmogony from
unmoved things. The others, it is true, make things collect together somehow before they try to produce
motion and separation. But there is no sense in starting generation from an original state in which bodies are
separated and in movement. Hence Empedocles begins after the process ruled by Love: for he could not have
constructed the heaven by building it up out of bodies in separation, making them to combine by the power of
Love, since our world has its constituent elements in separation, and therefore presupposes a previous state of
unity and combination.

ON THE HEAVENS

These arguments make it plain that every body has its natural movement, which is not constrained or contrary
to its nature. We go on to show that there are certain bodies whose necessary impetus is that of weight and
lightness. Of necessity, we assert, they must move, and a moved thing which has no natural impetus cannot
move either towards or away from the centre. Suppose a body A without weight, and a body B endowed with
weight. Suppose the weightless body to move the distance CD, while B in the same time moves the distance
CE, which will be greater since the heavy thing must move further. Let the heavy body then be divided in the
proportion CE: CD (for there is no reason why a part of B should not stand in this relation to the whole). Now
if the whole moves the whole distance CE, the part must in the same time move the distance CD. A
weightless body, therefore, and one which has weight will move the same distance, which is impossible. And
the same argument would fit the case of lightness. Again, a body which is in motion but has neither weight
nor lightness, must be moved by constraint, and must continue its constrained movement infinitely. For there
will be a force which moves it, and the smaller and lighter a body is the further will a given force move it.
Now let A, the weightless body, be moved the distance CE, and B, which has weight, be moved in the same
time the distance CD. Dividing the heavy body in the proportion CE:CD, we subtract from the heavy body a
part which will in the same time move the distance CE, since the whole moved CD: for the relative speeds of
the two bodies will be in inverse ratio to their respective sizes. Thus the weightless body will move the same
distance as the heavy in the same time. But this is impossible. Hence, since the motion of the weightless body
will cover a greater distance than any that is suggested, it will continue infinitely. It is therefore obvious that
every body must have a definite weight or lightness. But since 'nature' means a source of movement within
the thing itself, while a force is a source of movement in something other than it or in itself qua other, and
since movement is always due either to nature or to constraint, movement which is natural, as downward
movement is to a stone, will be merely accelerated by an external force, while an unnatural movement will be
due to the force alone. In either case the air is as it were instrumental to the force. For air is both light and
heavy, and thus qua light produces upward motion, being propelled and set in motion by the force, and qua
heavy produces a downward motion. In either case the force transmits the movement to the body by first, as it
were, impregnating the air. That is why a body moved by constraint continues to move when that which gave
the impulse ceases to accompany it. Otherwise, i.e. if the air were not endowed with this function,
constrained movement would be impossible. And the natural movement of a body may be helped on in the
same way. This discussion suffices to show (1) that all bodies are either light or heavy, and (2) how unnatural
movement takes place.

From what has been said earlier it is plain that there cannot be generation either of everything or in an
absolute sense of anything. It is impossible that everything should be generated, unless an extra-corporeal
void is possible. For, assuming generation, the place which is to be occupied by that which is coming to be,
must have been previously occupied by void in which no body was. Now it is quite possible for one body to
be generated out of another, air for instance out of fire, but in the absence of any pre-existing mass
generation is impossible. That which is potentially a certain kind of body may, it is true, become such in
actuality, But if the potential body was not already in actuality some other kind of body, the existence of an
extra-corporeal void must be admitted.

It remains to say what bodies are subject to generation, and why. Since in every case knowledge depends on
what is primary, and the elements are the primary constituents of bodies, we must ask which of such bodies
are elements, and why; and after that what is their number and character. The answer will be plain if we first
explain what kind of substance an element is. An element, we take it, is a body into which other bodies may
be analysed, present in them potentially or in actuality (which of these, is still disputable), and not itself
divisible into bodies different in form. That, or something like it, is what all men in every case mean by
element. Now if what we have described is an element, clearly there must be such bodies. For flesh and wood
and all other similar bodies contain potentially fire and earth, since one sees these elements exuded from

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them; and, on the other hand, neither in potentiality nor in actuality does fire contain flesh or wood, or it
would exude them. Similarly, even if there were only one elementary body, it would not contain them. For
though it will be either flesh or bone or something else, that does not at once show that it contained these in
potentiality: the further question remains, in what manner it becomes them. Now Anaxagoras opposes
Empedocles' view of the elements. Empedocles says that fire and earth and the related bodies are elementary
bodies of which all things are composed; but this Anaxagoras denies. His elements are the homoeomerous
things, viz. flesh, bone, and the like. Earth and fire are mixtures, composed of them and all the other seeds,
each consisting of a collection of all the homoeomerous bodies, separately invisible; and that explains why
from these two bodies all others are generated. (To him fire and aither are the same thing.) But since every
natural body has it proper movement, and movements are either simple or mixed, mixed in mixed bodies and
simple in simple, there must obviously be simple bodies; for there are simple movements. It is plain, then,
that there are elements, and why.

The next question to consider is whether the elements are finite or infinite in number, and, if finite, what their
number is. Let us first show reason or denying that their number is infinite, as some suppose. We begin with
the view of Anaxagoras that all the homoeomerous bodies are elements. Any one who adopts this view
misapprehends the meaning of element. Observation shows that even mixed bodies are often divisible into
homoeomerous parts; examples are flesh, bone, wood, and stone. Since then the composite cannot be an
element, not every homoeomerous body can be an element; only, as we said before, that which is not
divisible into bodies different in form. But even taking 'element' as they do, they need not assert an infinity of
elements, since the hypothesis of a finite number will give identical results. Indeed even two or three such
bodies serve the purpose as well, as Empedocles' attempt shows. Again, even on their view it turns out that all
things are not composed of homoeomerous bodies. They do not pretend that a face is composed of faces, or
that any other natural conformation is composed of parts like itself. Obviously then it would be better to
assume a finite number of principles. They should, in fact, be as few as possible, consistently with proving
what has to be proved. This is the common demand of mathematicians, who always assume as principles
things finite either in kind or in number. Again, if body is distinguished from body by the appropriate
qualitative difference, and there is a limit to the number of differences (for the difference lies in qualities
apprehended by sense, which are in fact finite in number, though this requires proof), then manifestly there is
necessarily a limit to the number of elements.

There is, further, another view-that of Leucippus and Democritus of Abdera-the implications of which are
also unacceptable. The primary masses, according to them, are infinite in number and indivisible in mass: one
cannot turn into many nor many into one; and all things are generated by their combination and involution.
Now this view in a sense makes things out to be numbers or composed of numbers. The exposition is not
clear, but this is its real meaning. And further, they say that since the atomic bodies differ in shape, and there
is an infinity of shapes, there is an infinity of simple bodies. But they have never explained in detail the
shapes of the various elements, except so far to allot the sphere to fire. Air, water, and the rest they
distinguished by the relative size of the atom, assuming that the atomic substance was a sort of master-seed
for each and every element. Now, in the first place, they make the mistake already noticed. The principles
which they assume are not limited in number, though such limitation would necessitate no other alteration in
their theory. Further, if the differences of bodies are not infinite, plainly the elements will not be an infinity.
Besides, a view which asserts atomic bodies must needs come into conflict with the mathematical sciences, in
addition to invalidating many common opinions and apparent data of sense perception. But of these things we
have already spoken in our discussion of time and movement. They are also bound to contradict themselves.
For if the elements are atomic, air, earth, and water cannot be differentiated by the relative sizes of their
atoms, since then they could not be generated out of one another. The extrusion of the largest atoms is a
process that will in time exhaust the supply; and it is by such a process that they account for the generation of

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water, air, and earth from one another. Again, even on their own presuppositions it does not seem as if the
elements would be infinite in number. The atoms differ in figure, and all figures are composed of pyramids,
rectilinear the case of rectilinear figures, while the sphere has eight pyramidal parts. The figures must have
their principles, and, whether these are one or two or more, the simple bodies must be the same in number as
they. Again, if every element has its proper movement, and a simple body has a simple movement, and the
number of simple movements is not infinite, because the simple motions are only two and the number of
places is not infinite, on these grounds also we should have to deny that the number of elements is infinite.

Since the number of the elements must be limited, it remains to inquire whether there is more than one
element. Some assume one only, which is according to some water, to others air, to others fire, to others
again something finer than water and denser than air, an infinite body-so they say-bracing all the heavens.

Now those who decide for a single element, which is either water or air or a body finer than water and denser
than air, and proceed to generate other things out of it by use of the attributes density and rarity, all alike fail
to observe the fact that they are depriving the element of its priority. Generation out of the elements is, as
they say, synthesis, and generation into the elements is analysis, so that the body with the finer parts must
have priority in the order of nature. But they say that fire is of all bodies the finest. Hence fire will be first in
the natural order. And whether the finest body is fire or not makes no difference; anyhow it must be one of
the other bodies that is primary and not that which is intermediate. Again, density and rarity, as instruments
of generation, are equivalent to fineness and coarseness, since the fine is rare, and coarse in their use means
dense. But fineness and coarseness, again, are equivalent to greatness and smallness, since a thing with small
parts is fine and a thing with large parts coarse. For that which spreads itself out widely is fine, and a thing
composed of small parts is so spread out. In the end, then, they distinguish the various other substances from
the element by the greatness and smallness of their parts. This method of distinction makes all judgement
relative. There will be no absolute distinction between fire, water, and air, but one and the same body will be
relatively to this fire, relatively to something else air. The same difficulty is involved equally in the view
elements and distinguishes them by their greatness and smallness. The principle of distinction between bodies
being quantity, the various sizes will be in a definite ratio, and whatever bodies are in this ratio to one another
must be air, fire, earth, and water respectively. For the ratios of smaller bodies may be repeated among
greater bodies.

Those who start from fire as the single element, while avoiding this difficulty, involve themselves in many
others. Some of them give fire a particular shape, like those who make it a pyramid, and this on one of two
grounds. The reason given may be-more crudely-that the pyramid is the most piercing of figures as fire is of
bodies, or-more ingeniously-the position may be supported by the following argument. As all bodies are
composed of that which has the finest parts, so all solid figures are composed of pryamids: but the finest body
is fire, while among figures the pyramid is primary and has the smallest parts; and the primary body must
have the primary figure: therefore fire will be a pyramid. Others, again, express no opinion on the subject of
its figure, but simply regard it as the of the finest parts, which in combination will form other bodies, as the
fusing of gold-dust produces solid gold. Both of these views involve the same difficulties. For (1) if, on the
one hand, they make the primary body an atom, the view will be open to the objections already advanced
against the atomic theory. And further the theory is inconsistent with a regard for the facts of nature. For if all
bodies are quantitatively commensurable, and the relative size of the various homoeomerous masses and of
their several elements are in the same ratio, so that the total mass of water, for instance, is related to the total
mass of air as the elements of each are to one another, and so on, and if there is more air than water and,
generally, more of the finer body than of the coarser, obviously the element of water will be smaller than that
of air. But the lesser quantity is contained in the greater. Therefore the air element is divisible. And the same
could be shown of fire and of all bodies whose parts are relatively fine. (2) If, on the other hand, the primary

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body is divisible, then (a) those who give fire a special shape will have to say that a part of fire is not fire,
because a pyramid is not composed of pyramids, and also that not every body is either an element or
composed of elements, since a part of fire will be neither fire nor any other element. And (b) those whose
ground of distinction is size will have to recognize an element prior to the element, a regress which continues
infinitely, since every body is divisible and that which has the smallest parts is the element. Further, they too
will have to say that the same body is relatively to this fire and relatively to that air, to others again water and
earth.

The common error of all views which assume a single element is that they allow only one natural movement,
which is the same for every body. For it is a matter of observation that a natural body possesses a principle of
movement. If then all bodies are one, all will have one movement. With this motion the greater their quantity
the more they will move, just as fire, in proportion as its quantity is greater, moves faster with the upward
motion which belongs to it. But the fact is that increase of quantity makes many things move the faster
downward. For these reasons, then, as well as from the distinction already established of a plurality of natural
movements, it is impossible that there should be only one element. But if the elements are not an infinity and
not reducible to one, they must be several and finite in number.

First we must inquire whether the elements are eternal or subject to generation and destruction; for when this
question has been answered their number and character will be manifest. In the first place, they cannot be
eternal. It is a matter of observation that fire, water, and every simple body undergo a process of analysis,
which must either continue infinitely or stop somewhere. (1) Suppose it infinite. Then the time occupied by
the process will be infinite, and also that occupied by the reverse process of synthesis. For the processes of
analysis and synthesis succeed one another in the various parts. It will follow that there are two infinite times
which are mutually exclusive, the time occupied by the synthesis, which is infinite, being preceded by the
period of analysis. There are thus two mutually exclusive infinites, which is impossible. (2) Suppose, on the
other hand, that the analysis stops somewhere. Then the body at which it stops will be either atomic or, as
Empedocles seems to have intended, a divisible body which will yet never be divided. The foregoing
arguments show that it cannot be an atom; but neither can it be a divisible body which analysis will never
reach. For a smaller body is more easily destroyed than a larger; and a destructive process which succeeds in
destroying, that is, in resolving into smaller bodies, a body of some size, cannot reasonably be expected to
fail with the smaller body. Now in fire we observe a destruction of two kinds: it is destroyed by its contrary
when it is quenched, and by itself when it dies out. But the effect is produced by a greater quantity upon a
lesser, and the more quickly the smaller it is. The elements of bodies must therefore be subject to destruction
and generation.

Since they are generated, they must be generated either from something incorporeal or from a body, and if
from a body, either from one another or from something else. The theory which generates them from
something incorporeal requires an extra-corporeal void. For everything that comes to be comes to be in
something, and that in which the generation takes place must either be incorporeal or possess body; and if it
has body, there will be two bodies in the same place at the same time, viz. that which is coming to be and that
which was previously there, while if it is incorporeal, there must be an extra-corporeal void. But we have
already shown that this is impossible. But, on the other hand, it is equally impossible that the elements should
be generated from some kind of body. That would involve a body distinct from the elements and prior to
them. But if this body possesses weight or lightness, it will be one of the elements; and if it has no tendency
to movement, it will be an immovable or mathematical entity, and therefore not in a place at all. A place in
which a thing is at rest is a place in which it might move, either by constraint, i.e. unnaturally, or in the
absence of constraint, i.e. naturally. If, then, it is in a place and somewhere, it will be one of the elements; and
if it is not in a place, nothing can come from it, since that which comes into being and that out of which it

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comes must needs be together. The elements therefore cannot be generated from something incorporeal nor
from a body which is not an element, and the only remaining alternative is that they are generated from one
another.

We must, therefore, turn to the question, what is the manner of their generation from one another? Is it as
Empedocles and Democritus say, or as those who resolve bodies into planes say, or is there yet another
possibility? (1) What the followers of Empedocles do, though without observing it themselves, is to reduce
the generation of elements out of one another to an illusion. They make it a process of excretion from a body
of what was in it all the time-as though generation required a vessel rather than a material-so that it involves
no change of anything. And even if this were accepted, there are other implications equally unsatisfactory.
We do not expect a mass of matter to be made heavier by compression. But they will be bound to maintain
this, if they say that water is a body present in air and excreted from air, since air becomes heavier when it
turns into water. Again, when the mixed body is divided, they can show no reason why one of the
constituents must by itself take up more room than the body did: but when water turns into air, the room
occupied is increased. The fact is that the finer body takes up more room, as is obvious in any case of
transformation. As the liquid is converted into vapour or air the vessel which contains it is often burst because
it does not contain room enough. Now, if there is no void at all, and if, as those who take this view say, there
is no expansion of bodies, the impossibility of this is manifest: and if there is void and expansion, there is no
accounting for the fact that the body which results from division cfpies of necessity a greater space. It is
inevitable, too, that generation of one out of another should come to a stop, since a finite quantum cannot
contain an infinity of finite quanta. When earth produces water something is taken away from the earth, for
the process is one of excretion. The same thing happens again when the residue produces water. But this can
only go on for ever, if the finite body contains an infinity, which is impossible. Therefore the generation of
elements out of one another will not always continue.

(2) We have now explained that the mutual transformations of the elements cannot take place by means of
excretion. The remaining alternative is that they should be generated by changing into one another. And this
in one of two ways, either by change of shape, as the same wax takes the shape both of a sphere and of a
cube, or, as some assert, by resolution into planes, (a) Generation by change of shape would necessarily
involve the assertion of atomic bodies. For if the particles were divisible there would be a part of fire which
was not fire and a part of earth which was not earth, for the reason that not every part of a pyramid is a
pyramid nor of a cube a cube. But if (b) the process is resolution into planes, the first difficulty is that the
elements cannot all be generated out of one another. This they are obliged to assert, and do assert. It is
absurd, because it is unreasonable that one element alone should have no part in the transformations, and also
contrary to the observed data of sense, according to which all alike change into one another. In fact their
explanation of the observations is not consistent with the observations. And the reason is that their ultimate
principles are wrongly assumed: they had certain predetermined views, and were resolved to bring everything
into line with them. It seems that perceptible things require perceptible principles, eternal things eternal
principles, corruptible things corruptible principles; and, in general, every subject matter principles
homogeneous with itself. But they, owing to their love for their principles, fall into the attitude of men who
undertake the defence of a position in argument. In the confidence that the principles are true they are ready
to accept any consequence of their application. As though some principles did not require to be judged from
their results, and particularly from their final issue! And that issue, which in the case of productive
knowledge is the product, in the knowledge of nature is the unimpeachable evidence of the senses as to each
fact.

The result of their view is that earth has the best right to the name element, and is alone indestructible; for
that which is indissoluble is indestructible and elementary, and earth alone cannot be dissolved into any body

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but itself. Again, in the case of those elements which do suffer dissolution, the 'suspension' of the triangles is
unsatisfactory. But this takes place whenever one is dissolved into another, because of the numerical
inequality of the triangles which compose them. Further, those who hold these views must needs suppose that
generation does not start from a body. For what is generated out of planes cannot be said to have been
generated from a body. And they must also assert that not all bodies are divisible, coming thus into conflict
with our most accurate sciences, namely the mathematical, which assume that even the intelligible is
divisible, while they, in their anxiety to save their hypothesis, cannot even admit this of every perceptible
thing. For any one who gives each element a shape of its own, and makes this the ground of distinction
between the substances, has to attribute to them indivisibility; since division of a pyramid or a sphere must
leave somewhere at least a residue which is not sphere or a pyramid. Either, then, a part of fire is not fire, so
that there is a body prior to the element-for every body is either an element or composed of elements-or not
every body is divisible.

In general, the attempt to give a shape to each of the simple bodies is unsound, for the reason, first, that they
will not succeed in filling the whole. It is agreed that there are only three plane figures which can fill a space,
the triangle, the square, and the hexagon, and only two solids, the pyramid and the cube. But the theory needs
more than these because the elements which it recognizes are more in number. Secondly, it is manifest that
the simple bodies are often given a shape by the place in which they are included, particularly water and air.
In such a case the shape of the element cannot persist; for, if it did, the contained mass would not be in
continuous contact with the containing body; while, if its shape is changed, it will cease to be water, since the
distinctive quality is shape. Clearly, then, their shapes are not fixed. Indeed, nature itself seems to offer
corroboration of this theoretical conclusion. Just as in other cases the substratum must be formless and
unshapen-for thus the 'all-receptive', as we read in the Timaeus, will be best for modelling-so the elements
should be conceived as a material for composite things; and that is why they can put off their qualitative
distinctions and pass into one another. Further, how can they account for the generation of flesh and bone or
any other continuous body? The elements alone cannot produce them because their collocation cannot
produce a continuum. Nor can the composition of planes; for this produces the elements themselves, not
bodies made up of them. Any one then who insists upon an exact statement of this kind of theory, instead of
assenting after a passing glance at it, will see that it removes generation from the world.

Further, the very properties, powers, and motions, to which they paid particular attention in allotting shapes,
show the shapes not to be in accord with the bodies. Because fire is mobile and productive of heat and
combustion, some made it a sphere, others a pyramid. These shapes, they thought, were the most mobile
because they offer the fewest points of contact and are the least stable of any; they were also the most apt to
produce warmth and combustion, because the one is angular throughout while the other has the most acute
angles, and the angles, they say, produce warmth and combustion. Now, in the first place, with regard to
movement both are in error. These may be the figures best adapted to movement; they are not, however, well
adapted to the movement of fire, which is an upward and rectilinear movement, but rather to that form of
circular movement which we call rolling. Earth, again, they call a cube because it is stable and at rest. But it
rests only in its own place, not anywhere; from any other it moves if nothing hinders, and fire and the other
bodies do the same. The obvious inference, therefore, is that fire and each several element is in a foreign
place a sphere or a pyramid, but in its own a cube. Again, if the possession of angles makes a body produce
heat and combustion, every element produces heat, though one may do so more than another. For they all
possess angles, the octahedron and dodecahedron as well as the pyramid; and Democritus makes even the
sphere a kind of angle, which cuts things because of its mobility. The difference, then, will be one of degree:
and this is plainly false. They must also accept the inference that the mathematical produce heat and
combustion, since they too possess angles and contain atomic spheres and pyramids, especially if there are, as
they allege, atomic figures. Anyhow if these functions belong to some of these things and not to others, they

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should explain the difference, instead of speaking in quite general terms as they do. Again, combustion of a
body produces fire, and fire is a sphere or a pyramid. The body, then, is turned into spheres or pyramids. Let
us grant that these figures may reasonably be supposed to cut and break up bodies as fire does; still it remains
quite inexplicable that a pyramid must needs produce pyramids or a sphere spheres. One might as well
postulate that a knife or a saw divides things into knives or saws. It is also ridiculous to think only of division
when allotting fire its shape. Fire is generally thought of as combining and connecting rather than as
separating. For though it separates bodies different in kind, it combines those which are the same; and the
combining is essential to it, the functions of connecting and uniting being a mark of fire, while the separating
is incidental. For the expulsion of the foreign body is an incident in the compacting of the homogeneous. In
choosing the shape, then, they should have thought either of both functions or preferably of the combining
function. In addition, since hot and cold are contrary powers, it is impossible to allot any shape to the cold.
For the shape given must be the contrary of that given to the hot, but there is no contrariety between figures.
That is why they have all left the cold out, though properly either all or none should have their distinguishing
figures. Some of them, however, do attempt to explain this power, and they contradict themselves. A body of
large particles, they say, is cold because instead of penetrating through the passages it crushes. Clearly, then,
that which is hot is that which penetrates these passages, or in other words that which has fine particles. It
results that hot and cold are distinguished not by the figure but by the size of the particles. Again, if the
pyramids are unequal in size, the large ones will not be fire, and that figure will produce not combustion but
its contrary.

From what has been said it is clear that the difference of the elements does not depend upon their shape. Now
their most important differences are those of property, function, and power; for every natural body has, we
maintain, its own functions, properties, and powers. Our first business, then, will be to speak of these, and
that inquiry will enable us to explain the differences of each from each.

Book IV

WE have now to consider the terms 'heavy' and 'light'. We must ask what the bodies so called are, how they
are constituted, and what is the reason of their possessing these powers. The consideration of these questions
is a proper part of the theory of movement, since we call things heavy and light because they have the power
of being moved naturally in a certain way. The activities corresponding to these powers have not been given
any name, unless it is thought that 'impetus' is such a name. But because the inquiry into nature is concerned
with movement, and these things have in themselves some spark (as it were) of movement, all inquirers avail
themselves of these powers, though in all but a few cases without exact discrimination. We must then first
look at whatever others have said, and formulate the questions which require settlement in the interests of this
inquiry, before we go on to state our own view of the matter.

Language recognizes (a) an absolute, (b) a relative heavy and light. Of two heavy things, such as wood and
bronze, we say that the one is relatively light, the other relatively heavy. Our predecessors have not dealt at
all with the absolute use, of the terms, but only with the relative. I mean, they do not explain what the heavy
is or what the light is, but only the relative heaviness and lightness of things possessing weight. This can be
made clearer as follows. There are things whose constant nature it is to move away from the centre, while
others move constantly towards the centre; and of these movements that which is away from the centre I call
upward movement and that which is towards it I call downward movement. (The view, urged by some, that
there is no up and no down in the heaven, is absurd. There can be, they say, no up and no down, since the
universe is similar every way, and from any point on the earth's surface a man by advancing far enough will
come to stand foot to foot with himself. But the extremity of the whole, which we call 'above', is in position
above and in nature primary. And since the universe has an extremity and a centre, it must clearly have an up

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and down. Common usage is thus correct, though inadequate. And the reason of its inadequacy is that men
think that the universe is not similar every way. They recognize only the hemisphere which is over us. But if
they went on to think of the world as formed on this pattern all round, with a centre identically related to each
point on the extremity, they would have to admit that the extremity was above and the centre below.) By
absolutely light, then, we mean that which moves upward or to the extremity, and by absolutely heavy that
which moves downward or to the centre. By lighter or relatively light we mean that one, of two bodies
endowed with weight and equal in bulk, which is exceeded by the other in the speed of its natural downward
movement.

Those of our predecessors who have entered upon this inquiry have for the most part spoken of light and
heavy things only in the sense in which one of two things both endowed with weight is said to be the lighter.
And this treatment they consider a sufficient analysis also of the notions of absolute heaviness, to which their
account does not apply. This, however, will become clearer as we advance. One use of the terms 'lighter' and
'heavier' is that which is set forth in writing in the Timaeus, that the body which is composed of the greater
number of identical parts is relatively heavy, while that which is composed of a smaller number is relatively
light. As a larger quantity of lead or of bronze is heavier than a smaller-and this holds good of all
homogeneous masses, the superior weight always depending upon a numerical superiority of equal parts-in
precisely the same way, they assert, lead is heavier than wood. For all bodies, in spite of the general opinion
to the contrary, are composed of identical parts and of a single material. But this analysis says nothing of the
absolutely heavy and light. The facts are that fire is always light and moves upward, while earth and all
earthy things move downwards or towards the centre. It cannot then be the fewness of the triangles (of which,
in their view, all these bodies are composed) which disposes fire to move upward. If it were, the greater the
quantity of fire the slower it would move, owing to the increase of weight due to the increased number of
triangles. But the palpable fact, on the contrary, is that the greater the quantity, the lighter the mass is and the
quicker its upward movement: and, similarly, in the reverse movement from above downward, the small mass
will move quicker and the large slower. Further, since to be lighter is to have fewer of these homogeneous
parts and to be heavier is to have more, and air, water, and fire are composed of the same triangles, the only
difference being in the number of such parts, which must therefore explain any distinction of relatively light
and heavy between these bodies, it follows that there must be a certain quantum of air which is heavier than
water. But the facts are directly opposed to this. The larger the quantity of air the more readily it moves
upward, and any portion of air without exception will rise up out of the water.

So much for one view of the distinction between light and heavy. To others the analysis seems insufficient;
and their views on the subject, though they belong to an older generation than ours, have an air of novelty. It
is apparent that there are bodies which, when smaller in bulk than others, yet exceed them in weight. It is
therefore obviously insufficient to say that bodies of equal weight are composed of an equal number of
primary parts: for that would give equality of bulk. Those who maintain that the primary or atomic parts, of
which bodies endowed with weight are composed, are planes, cannot so speak without absurdity; but those
who regard them as solids are in a better position to assert that of such bodies the larger is the heavier. But
since in composite bodies the weight obviously does not correspond in this way to the bulk, the lesser bulk
being often superior in weight (as, for instance, if one be wool and the other bronze), there are some who
think and say that the cause is to be found elsewhere. The void, they say, which is imprisoned in bodies,
lightens them and sometimes makes the larger body the lighter. The reason is that there is more void. And
this would also account for the fact that a body composed of a number of solid parts equal to, or even smaller
than, that of another is sometimes larger in bulk than it. In short, generally and in every case a body is
relatively light when it contains a relatively large amount of void. This is the way they put it themselves, but
their account requires an addition. Relative lightness must depend not only on an excess of void, but also an a
defect of solid: for if the ratio of solid to void exceeds a certain proportion, the relative lightness will

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ON THE HEAVENS

disappear. Thus fire, they say, is the lightest of things just for this reason that it has the most void. But it
would follow that a large mass of gold, as containing more void than a small mass of fire, is lighter than it,
unless it also contains many times as much solid. The addition is therefore necessary.

Of those who deny the existence of a void some, like Anaxagoras and Empedocles, have not tried to analyse
the notions of light and heavy at all; and those who, while still denying the existence of a void, have
attempted this, have failed to explain why there are bodies which are absolutely heavy and light, or in other
words why some move upward and others downward. The fact, again, that the body of greater bulk is
sometimes lighter than smaller bodies is one which they have passed over in silence, and what they have said
gives no obvious suggestion for reconciling their views with the observed facts.

But those who attribute the lightness of fire to its containing so much void are necessarily involved in
practically the same difficulties. For though fire be supposed to contain less solid than any other body, as well
as more void, yet there will be a certain quantum of fire in which the amount of solid or plenum is in excess
of the solids contained in some small quantity of earth. They may reply that there is an excess of void also.
But the question is, how will they discriminate the absolutely heavy? Presumably, either by its excess of solid
or by its defect of void. On the former view there could be an amount of earth so small as to contain less solid
than a large mass of fire. And similarly, if the distinction rests on the amount of void, there will be a body,
lighter than the absolutely light, which nevertheless moves downward as constantly as the other moves
upward. But that cannot be so, since the absolutely light is always lighter than bodies which have weight and
move downward, while, on the other hand, that which is lighter need not be light, because in common speech
we distinguish a lighter and a heavier (viz. water and earth) among bodies endowed with weight. Again, the
suggestion of a certain ratio between the void and the solid in a body is no more equal to solving the problem
before us. The manner of speaking will issue in a similar impossibility. For any two portions of fire, small or
great, will exhibit the same ratio of solid to void, but the upward movement of the greater is quicker than that
of the less, just as the downward movement of a mass of gold or lead, or of any other body endowed with
weight, is quicker in proportion to its size. This, however, should not be the case if the ratio is the ground of
distinction between heavy things and light. There is also an absurdity in attributing the upward movement of
bodies to a void which does not itself move. If, however, it is the nature of a void to move upward and of a
plenum to move downward, and therefore each causes a like movement in other things, there was no need to
raise the question why composite bodies are some light and some heavy; they had only to explain why these
two things are themselves light and heavy respectively, and to give, further, the reason why the plenum and
the void are not eternally separated. It is also unreasonable to imagine a place for the void, as if the void were
not itself a kind of place. But if the void is to move, it must have a place out of which and into which the
change carries it. Also what is the cause of its movement? Not, surely, its voidness: for it is not the void only
which is moved, but also the solid.

Similar difficulties are involved in all other methods of distinction, whether they account for the relative
lightness and heaviness of bodies by distinctions of size, or proceed on any other principle, so long as they
attribute to each the same matter, or even if they recognize more than one matter, so long as that means only a
pair of contraries. If there is a single matter, as with those who compose things of triangles, nothing can be
absolutely heavy or light: and if there is one matter and its contrary-the void, for instance, and the
plenum-no reason can be given for the relative lightness and heaviness of the bodies intermediate between
the absolutely light and heavy when compared either with one another or with these themselves. The view
which bases the distinction upon differences of size is more like a mere fiction than those previously
mentioned, but, in that it is able to make distinctions between the four elements, it is in a stronger position for
meeting the foregoing difficulties. Since, however, it imagines that these bodies which differ in size are all
made of one substance, it implies, equally with the view that there is but one matter, that there is nothing
absolutely light and nothing which moves upward (except as being passed by other things or forced up by
them); and since a multitude of small atoms are heavier than a few large ones, it will follow that much air or
fire is heavier than a little water or earth, which is impossible.

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ON THE HEAVENS

These, then, are the views which have been advanced by others and the terms in which they state them. We
may begin our own statement by settling a question which to some has been the main difficulty-the question
why some bodies move always and naturally upward and others downward, while others again move both
upward and downward. After that we will inquire into light and heavy and of the various phenomena
connected with them. The local movement of each body into its own place must be regarded as similar to
what happens in connexion with other forms of generation and change. There are, in fact, three kinds of
movement, affecting respectively the size, the form, and the place of a thing, and in each it is observable that
change proceeds from a contrary to a contrary or to something intermediate: it is never the change of any
chance subject in any chance direction, nor, similarly, is the relation of the mover to its object fortuitous: the
thing altered is different from the thing increased, and precisely the same difference holds between that which
produces alteration and that which produces increase. In the same manner it must be thought that produces
local motion and that which is so moved are not fortuitously related. Now, that which produces upward and
downward movement is that which produces weight and lightness, and that which is moved is that which is
potentially heavy or light, and the movement of each body to its own place is motion towards its own form.
(It is best to interpret in this sense the common statement of the older writers that 'like moves to like'. For the
words are not in every sense true to fact. If one were to remove the earth to where the moon now is, the
various fragments of earth would each move not towards it but to the place in which it now is. In general,
when a number of similar and undifferentiated bodies are moved with the same motion this result is
necessarily produced, viz. that the place which is the natural goal of the movement of each single part is also
that of the whole. But since the place of a thing is the boundary of that which contains it, and the continent of
all things that move upward or downward is the extremity and the centre, and this boundary comes to be, in a
sense, the form of that which is contained, it is to its like that a body moves when it moves to its own place.
For the successive members of the scries are like one another: water, I mean, is like air and air like fire, and
between intermediates the relation may be converted, though not between them and the extremes; thus air is
like water, but water is like earth: for the relation of each outer body to that which is next within it is that of
form to matter.) Thus to ask why fire moves upward and earth downward is the same as to ask why the
healable, when moved and changed qua healable, attains health and not whiteness; and similar questions
might be asked concerning any other subject of aletion. Of course the subject of increase, when changed qua
increasable, attains not health but a superior size. The same applies in the other cases. One thing changes in
quality, another in quantity: and so in place, a light thing goes upward, a heavy thing downward. The only
difference is that in the last case, viz. that of the heavy and the light, the bodies are thought to have a spring
of change within themselves, while the subjects of healing and increase are thought to be moved purely from
without. Sometimes, however, even they change of themselves, ie. in response to a slight external movement
reach health or increase, as the case may be. And since the same thing which is healable is also receptive of
disease, it depends on whether it is moved qua healable or qua liable to disease whether the motion is towards
health or towards disease. But the reason why the heavy and the light appear more than these things to
contain within themselves the source of their movements is that their matter is nearest to being. This is
indicated by the fact that locomotion belongs to bodies only when isolated from other bodies, and is
generated last of the several kinds of movement; in order of being then it will be first. Now whenever air
comes into being out of water, light out of heavy, it goes to the upper place. It is forthwith light: becoming is
at an end, and in that place it has being. Obviously, then, it is a potentiality, which, in its passage to actuality,
comes into that place and quantity and quality which belong to its actuality. And the same fact explains why
what is already actually fire or earth moves, when nothing obstructs it, towards its own place. For motion is
equally immediate in the case of nutriment, when nothing hinders, and in the case of the thing healed, when
nothing stays the healing. But the movement is also due to the original creative force and to that which
removes the hindrance or off which the moving thing rebounded, as was explained in our opening
discussions, where we tried to show how none of these things moves itself. The reason of the various motions
of the various bodies, and the meaning of the motion of a body to its own place, have now been explained.

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ON THE HEAVENS

We have now to speak of the distinctive properties of these bodies and of the various phenomena connected
with them. In accordance with general conviction we may distinguish the absolutely heavy, as that which
sinks to the bottom of all things, from the absolutely light, which is that which rises to the surface of all
things. I use the term 'absolutely', in view of the generic character of 'light' and 'heavy', in order to confine the
application to bodies which do not combine lightness and heaviness. It is apparent, I mean, that fire, in
whatever quantity, so long as there is no external obstacle moves upward, and earth downward; and, if the
quantity is increased, the movement is the same, though swifter. But the heaviness and lightness of bodies
which combine these qualities is different from this, since while they rise to the surface of some bodies they
sink to the bottom of others. Such are air and water. Neither of them is absolutely either light or heavy. Both
are lighter than earth-for any portion of either rises to the surface of it-but heavier than fire, since a portion
of either, whatever its quantity, sinks to the bottom of fire; compared together, however, the one has absolute
weight, the other absolute lightness, since air in any quantity rises to the surface of water, while water in any
quantity sinks to the bottom of air. Now other bodies are severally light and heavy, and evidently in them the
attributes are due to the difference of their uncompounded parts: that is to say, according as the one or the
other happens to preponderate the bodies will be heavy and light respectively. Therefore we need only speak
of these parts, since they are primary and all else consequential: and in so doing we shall be following the
advice which we gave to those whose attribute heaviness to the presence of plenum and lightness to that of
void. It is due to the properties of the elementary bodies that a body which is regarded as light in one place is
regarded as heavy in another, and vice versa. In air, for instance, a talent's weight of wood is heavier than a
mina of lead, but in water the wood is the lighter. The reason is that all the elements except fire have weight
and all but earth lightness. Earth, then, and bodies in which earth preponderates, must needs have weight
everywhere, while water is heavy anywhere but in earth, and air is heavy when not in water or earth. In its
own place each of these bodies has weight except fire, even air. Of this we have evidence in the fact that a
bladder when inflated weighs more than when empty. A body, then, in which air preponderates over earth
and water, may well be lighter than something in water and yet heavier than it in air, since such a body does
not rise in air but rises to the surface in water.

The following account will make it plain that there is an absolutely light and an absolutely heavy body. And
by absolutely light I mean one which of its own nature always moves upward, by absolutely heavy one which
of its own nature always moves downward, if no obstacle is in the way. There are, I say, these two kinds of
body, and it is not the case, as some maintain, that all bodies have weight. Different views are in fact agreed
that there is a heavy body, which moves uniformly towards the centre. But is also similarly a light body. For
we see with our eyes, as we said before, that earthy things sink to the bottom of all things and move towards
the centre. But the centre is a fixed point. If therefore there is some body which rises to the surface of all
things-and we observe fire to move upward even in air itself, while the air remains at rest-clearly this body
is moving towards the extremity. It cannot then have any weight. If it had, there would be another body in
which it sank: and if that had weight, there would be yet another which moved to the extremity and thus rose
to the surface of all moving things. In fact, however, we have no evidence of such a body. Fire, then, has no
weight. Neither has earth any lightness, since it sinks to the bottom of all things, and that which sinks moves
to the centre. That there is a centre towards which the motion of heavy things, and away from which that of
light things is directed, is manifest in many ways. First, because no movement can continue to infinity. For
what cannot be can no more come-to-be than be, and movement is a coming to-be in one place from
another. Secondly, like the upward movement of fire, the downward movement of earth and all heavy things
makes equal angles on every side with the earth's surface: it must therefore be directed towards the centre.
Whether it is really the centre of the earth and not rather that of the whole to which it moves, may be left to
another inquiry, since these are coincident. But since that which sinks to the bottom of all things moves to the
centre, necessarily that which rises to the surface moves to the extremity of the region in which the movement
of these bodies takes place. For the centre is opposed as contrary to the extremity, as that which sinks is

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ON THE HEAVENS

opposed to that which rises to the surface. This also gives a reasonable ground for the duality of heavy and
light in the spatial duality centre and extremity. Now there is also the intermediate region to which each name
is given in opposition to the other extreme. For that which is intermediate between the two is in a sense both
extremity and centre. For this reason there is another heavy and light; namely, water and air. But in our view
the continent pertains to form and the contained to matter: and this distinction is present in every genus. Alike
in the sphere of quality and in that of quantity there is that which corresponds rather to form and that which
corresponds to matter. In the same way, among spatial distinctions, the above belongs to the determinate, the
below to matter. The same holds, consequently, also of the matter itself of that which is heavy and light: as
potentially possessing the one character, it is matter for the heavy, and as potentially possessing the other, for
the light. It is the same matter, but its being is different, as that which is receptive of disease is the same as
that which is receptive of health, though in being different from it, and therefore diseasedness is different
from healthiness.

A thing then which has the one kind of matter is light and always moves upward, while a thing which has the
opposite matter is heavy and always moves downward. Bodies composed of kinds of matter different from
these but having relatively to each other the character which these have absolutely, possess both the upward
and the downward motion. Hence air and water each have both lightness and weight, and water sinks to the
bottom of all things except earth, while air rises to the surface of all things except fire. But since there is one
body only which rises to the surface of all things and one only which sinks to the bottom of all things, there
must needs be two other bodies which sink in some bodies and rise to the surface of others. The kinds of
matter, then, must be as numerous as these bodies, i.e. four, but though they are four there must be a common
matter of ail-particularly if they pass into one another-which in each is in being different. There is no reason
why there should not be one or more intermediates between the contraries, as in the case of colour; for
'intermediate' and 'mean' are capable of more than one application.

Now in its own place every body endowed with both weight and lightness has weightwhereas earth has
weight everywhere-but they only have lightness among bodies to whose surface they rise. Hence when a
support is withdrawn such a body moves downward until it reaches the body next below it, air to the place of
water and water to that of earth. But if the fire above air is removed, it will not move upward to the place of
fire, except by constraint; and in that way water also may be drawn up, when the upward movement of air
which has had a common surface with it is swift enough to overpower the downward impulse of the water.
Nor does water move upward to the place of air, except in the manner just described. Earth is not so affected
at all, because a common surface is not possible to it. Hence water is drawn up into the vessel to which fire is
applied, but not earth. As earth fails to move upward, so fire fails to move downward when air is withdrawn
from beneath it: for fire has no weight even in its own place, as earth has no lightness. The other two move
downward when the body beneath is withdrawn because, while the absolutely heavy is that which sinks to the
bottom of all things, the relatively heavy sinks to its own place or to the surface of the body in which it rises,
since it is similar in matter to it.

It is plain that one must suppose as many distinct species of matter as there are bodies. For if, first, there is a
single matter of all things, as, for instance, the void or the plenum or extension or the triangles, either all
things will move upward or all things will move downward, and the second motion will be abolished. And so,
either there will be no absolutely light body, if superiority of weight is due to superior size or number of the
constituent bodies or to the fullness of the body: but the contrary is a matter of observation, and it has been
shown that the downward and upward movements are equally constant and universal: or, if the matter in
question is the void or something similar, which moves uniformly upward, there will be nothing to move
uniformly downward. Further, it will follow that the intermediate bodies move downward in some cases
quicker than earth: for air in sufficiently large quantity will contain a larger number of triangles or solids or

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ON THE HEAVENS

particles. It is, however, manifest that no portion of air whatever moves downward. And the same reasoning
applies to lightness, if that is supposed to depend on superiority of quantity of matter. But if, secondly, the
kinds of matter are two, it will be difficult to make the intermediate bodies behave as air and water behave.
Suppose, for example, that the two asserted are void and plenum. Fire, then, as moving upward, will be void,
earth, as moving downward, plenum; and in air, it will be said, fire preponderates, in water, earth. There will
then be a quantity of water containing more fire than a little air, and a large amount of air will contain more
earth than a little water: consequently we shall have to say that air in a certain quantity moves downward
more quickly than a little water. But such a thing has never been observed anywhere. Necessarily, then, as
fire goes up because it has something, e.g. void, which other things do not have, and earth goes downward
because it has plenum, so air goes to its own place above water because it has something else, and water goes
downward because of some special kind of body. But if the two bodies are one matter, or two matters both
present in each, there will be a certain quantity of each at which water will excel a little air in the upward
movement and air excel water in the downward movement, as we have already often said.

The shape of bodies will not account for their moving upward or downward in general, though it will account
for their moving faster or slower. The reasons for this are not difficult to see. For the problem thus raised is
why a flat piece of iron or lead floats upon water, while smaller and less heavy things, so long as they are
round or long-a needle, for instance-sink down; and sometimes a thing floats because it is small, as with
gold dust and the various earthy and dusty materials which throng the air. With regard to these questions, it is
wrong to accept the explanation offered by Democritus. He says that the warm bodies moving up out of the
water hold up heavy bodies which are broad, while the narrow ones fall through, because the bodies which
offer this resistance are not numerous. But this would be even more likely to happen in air-an objection
which he himself raises. His reply to the objection is feeble. In the air, he says, the 'drive' (meaning by drive
the movement of the upward moving bodies) is not uniform in direction. But since some continua are easily
divided and others less easily, and things which produce division differ similarly in the case with which they
produce it, the explanation must be found in this fact. It is the easily bounded, in proportion as it is easily
bounded, which is easily divided; and air is more so than water, water than earth. Further, the smaller the
quantity in each kind, the more easily it is divided and disrupted. Thus the reason why broad things keep their
place is because they cover so wide a surface and the greater quantity is less easily disrupted. Bodies of the
opposite shape sink down because they occupy so little of the surface, which is therefore easily parted. And
these considerations apply with far greater force to air, since it is so much more easily divided than water. But
since there are two factors, the force responsible for the downward motion of the heavy body and the
disruption-resisting force of the continuous surface, there must be some ratio between the two. For in
proportion as the force applied by the heavy thing towards disruption and division exceeds that which resides
in the continuum, the quicker will it force its way down; only if the force of the heavy thing is the weaker,
will it ride upon the surface.

We have now finished our examination of the heavy and the light and of the phenomena connected with
them.

THE END

ON THE SOUL

by Aristotle

ON THE SOUL

Table of Contents

ON THE SOUL. 1

by Aristotle 1

Book 1 1

Book IL 13

Book III 28

ON THE SOUL

by Aristotle

translated by J. A. Smith

« Book I
• Book II
« Book III

Book I

HOLDING as we do that, while knowledge of any kind is a thing to be honoured and prized, one kind of it
may, either by reason of its greater exactness or of a higher dignity and greater wonderfulness in its objects,
be more honourable and precious than another, on both accounts we should naturally be led to place in the
front rank the study of the soul. The knowledge of the soul admittedly contributes greatly to the advance of
truth in general, and, above all, to our understanding of Nature, for the soul is in some sense the principle of
animal life. Our aim is to grasp and understand, first its essential nature, and secondly its properties; of these
some are taught to be affections proper to the soul itself, while others are considered to attach to the animal
owing to the presence within it of soul.

To attain any assured knowledge about the soul is one of the most difficult things in the world. As the form of
question which here presents itself, viz. the question 'What is it?', recurs in other fields, it might be supposed
that there was some single method of inquiry applicable to all objects whose essential nature (as we are
endeavouring to ascertain there is for derived properties the single method of demonstration); in that case
what we should have to seek for would be this unique method. But if there is no such single and general
method for solving the question of essence, our task becomes still more difficult; in the case of each different
subject we shall have to determine the appropriate process of investigation. If to this there be a clear answer,
e.g. that the process is demonstration or division, or some known method, difficulties and hesitations still
beset us-with what facts shall we begin the inquiry? For the facts which form the starting-points in different
subjects must be different, as e.g. in the case of numbers and surfaces.

First, no doubt, it is necessary to determine in which of the summa genera soul lies, what it is; is it 'a
this-somewhat, 'a substance, or is it a quale or a quantum, or some other of the remaining kinds of predicates
which we have distinguished? Further, does soul belong to the class of potential existents, or is it not rather
an actuality? Our answer to this question is of the greatest importance.

We must consider also whether soul is divisible or is without parts, and whether it is everywhere
homogeneous or not; and if not homogeneous, whether its various forms are different specifically or
generically: up to the present time those who have discussed and investigated soul seem to have confined

ON THE SOUL 1

ON THE SOUL

themselves to the human soul. We must be careful not to ignore the question whether soul can be defined in a
single unambiguous formula, as is the case with animal, or whether we must not give a separate formula for
each of it, as we do for horse, dog, man, god (in the latter case the 'universal' animal-and so too every other
'common predicate'-being treated either as nothing at all or as a later product). Further, if what exists is not a
plurality of souls, but a plurality of parts of one soul, which ought we to investigate first, the whole soul or its
parts? (It is also a difficult problem to decide which of these parts are in nature distinct from one another.)
Again, which ought we to investigate first, these parts or their functions, mind or thinking, the faculty or the
act of sensation, and so on? If the investigation of the functions precedes that of the parts, the further question
suggests itself: ought we not before either to consider the correlative objects, e.g. of sense or thought? It
seems not only useful for the discovery of the causes of the derived properties of substances to be acquainted
with the essential nature of those substances (as in mathematics it is useful for the understanding of the
property of the equality of the interior angles of a triangle to two right angles to know the essential nature of
the straight and the curved or of the line and the plane) but also conversely, for the knowledge of the essential
nature of a substance is largely promoted by an acquaintance with its properties: for, when we are able to give
an account conformable to experience of all or most of the properties of a substance, we shall be in the most
favourable position to say something worth saying about the essential nature of that subject; in all
demonstration a definition of the essence is required as a starting-point, so that definitions which do not
enable us to discover the derived properties, or which fail to facilitate even a conjecture about them, must
obviously, one and all, be dialectical and futile.

A further problem presented by the affections of soul is this: are they all affections of the complex of body
and soul, or is there any one among them peculiar to the soul by itself? To determine this is indispensable but
difficult. If we consider the majority of them, there seems to be no case in which the soul can act or be acted
upon without involving the body; e.g. anger, courage, appetite, and sensation generally. Thinking seems the
most probable exception; but if this too proves to be a form of imagination or to be impossible without
imagination, it too requires a body as a condition of its existence. If there is any way of acting or being acted
upon proper to soul, soul will be capable of separate existence; if there is none, its separate existence is
impossible. In the latter case, it will be like what is straight, which has many properties arising from the
straightness in it, e.g. that of touching a bronze sphere at a point, though straightness divorced from the other
constituents of the straight thing cannot touch it in this way; it cannot be so divorced at all, since it is always
found in a body. It therefore seems that all the affections of soul involve a body-passion, gentleness, fear,
pity, courage, joy, loving, and hating; in all these there is a concurrent affection of the body. In support of this
we may point to the fact that, while sometimes on the occasion of violent and striking occurrences there is no
excitement or fear felt, on others faint and feeble stimulations produce these emotions, viz. when the body is
already in a state of tension resembling its condition when we are angry. Here is a still clearer case: in the
absence of any external cause of terror we find ourselves experiencing the feelings of a man in terror. From
all this it is obvious that the affections of soul are enmattered formulable essences.

Consequently their definitions ought to correspond, e.g. anger should be defined as a certain mode of
movement of such and such a body (or part or faculty of a body) by this or that cause and for this or that end.
That is precisely why the study of the soul must fall within the science of Nature, at least so far as in its
affections it manifests this double character. Hence a physicist would define an affection of soul differently
from a dialectician; the latter would define e.g. anger as the appetite for returning pain for pain, or something
like that, while the former would define it as a boiling of the blood or warm substance surround the heart. The
latter assigns the material conditions, the former the form or formulable essence; for what he states is the
formulable essence of the fact, though for its actual existence there must be embodiment of it in a material
such as is described by the other. Thus the essence of a house is assigned in such a formula as 'a shelter
against destruction by wind, rain, and heat'; the physicist would describe it as 'stones, bricks, and timbers'; but
there is a third possible description which would say that it was that form in that material with that purpose or
end. Which, then, among these is entitled to be regarded as the genuine physicist? The one who confines
himself to the material, or the one who restricts himself to the formulable essence alone? Is it not rather the

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one who combines both in a single formula? If this is so, how are we to characterize the other two? Must we
not say that there is no type of thinker who concerns himself with those qualities or attributes of the material
which are in fact inseparable from the material, and without attempting even in thought to separate them? The
physicist is he who concerns himself with all the properties active and passive of bodies or materials thus or
thus defined; attributes not considered as being of this character he leaves to others, in certain cases it may be
to a specialist, e.g. a carpenter or a physician, in others (a) where they are inseparable in fact, but are
separable from any particular kind of body by an effort of abstraction, to the mathematician, (b) where they
are separate both in fact and in thought from body altogether, to the First Philosopher or metaphysician. But
we must return from this digression, and repeat that the affections of soul are inseparable from the material
substratum of animal life, to which we have seen that such affections, e.g. passion and fear, attach, and have
not the same mode of being as a line or a plane.

For our study of soul it is necessary, while formulating the problems of which in our further advance we are
to find the solutions, to call into council the views of those of our predecessors who have declared any
opinion on this subject, in order that we may profit by whatever is sound in their suggestions and avoid their
errors.

The starting-point of our inquiry is an exposition of those characteristics which have chiefly been held to
belong to soul in its very nature. Two characteristic marks have above all others been recognized as
distinguishing that which has soul in it from that which has not-movement and sensation. It may be said that
these two are what our predecessors have fixed upon as characteristic of soul.

Some say that what originates movement is both pre-eminently and primarily soul; believing that what is not
itself moved cannot originate movement in another, they arrived at the view that soul belongs to the class of
things in movement. This is what led Democritus to say that soul is a sort of fire or hot substance; his 'forms'
or atoms are infinite in number; those which are spherical he calls fire and soul, and compares them to the
motes in the air which we see in shafts of light coming through windows; the mixture of seeds of all sorts he
calls the elements of the whole of Nature (Leucippus gives a similar account); the spherical atoms are
identified with soul because atoms of that shape are most adapted to permeate everywhere, and to set all the
others moving by being themselves in movement. This implies the view that soul is identical with what
produces movement in animals. That is why, further, they regard respiration as the characteristic mark of life;
as the environment compresses the bodies of animals, and tends to extrude those atoms which impart
movement to them, because they themselves are never at rest, there must be a reinforcement of these by
similar atoms coming in from without in the act of respiration; for they prevent the extrusion of those which
are already within by counteracting the compressing and consolidating force of the environment; and animals
continue to live only so long as they are able to maintain this resistance.

The doctrine of the Pythagoreans seems to rest upon the same ideas; some of them declared the motes in air,
others what moved them, to be soul. These motes were referred to because they are seen always in
movement, even in a complete calm.

The same tendency is shown by those who define soul as that which moves itself; all seem to hold the view
that movement is what is closest to the nature of soul, and that while all else is moved by soul, it alone moves
itself. This belief arises from their never seeing anything originating movement which is not first itself
moved.

Similarly also Anaxagoras (and whoever agrees with him in saying that mind set the whole in movement)
declares the moving cause of things to be soul. His position must, however, be distinguished from that of
Democritus. Democritus roundly identifies soul and mind, for he identifies what appears with what is

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true-that is why he commends Homer for the phrase 'Hector lay with thought distraught'; he does not employ
mind as a special faculty dealing with truth, but identifies soul and mind. What Anaxagoras says about them
is more obscure; in many places he tells us that the cause of beauty and order is mind, elsewhere that it is
soul; it is found, he says, in all animals, great and small, high and low, but mind (in the sense of intelligence)
appears not to belong alike to all animals, and indeed not even to all human beings.

All those, then, who had special regard to the fact that what has soul in it is moved, adopted the view that
soul is to be identified with what is eminently originative of movement. All, on the other hand, who looked to
the fact that what has soul in it knows or perceives what is, identify soul with the principle or principles of
Nature, according as they admit several such principles or one only. Thus Empedocles declares that it is
formed out of all his elements, each of them also being soul; his words are:

For 'tis by Earth we see Earth, by Water Water,

By Ether Ether divine, by Fire destructive Fire,

By Love Love, and Hate by cruel Hate.

In the same way Plato in the Timaeus fashions soul out of his elements; for like, he holds, is known by like,
and things are formed out of the principles or elements, so that soul must be so too. Similarly also in his
lectures 'On Philosophy' it was set forth that the Animal-itself is compounded of the Idea itself of the One
together with the primary length, breadth, and depth, everything else, the objects of its perception, being
similarly constituted. Again he puts his view in yet other terms: Mind is the monad, science or knowledge the
dyad (because it goes undeviatingly from one point to another), opinion the number of the plane, sensation
the number of the solid; the numbers are by him expressly identified with the Forms themselves or principles,
and are formed out of the elements; now things are apprehended either by mind or science or opinion or
sensation, and these same numbers are the Forms of things.

Some thinkers, accepting both premisses, viz. that the soul is both originative of movement and cognitive,
have compounded it of both and declared the soul to be a self-moving number.

As to the nature and number of the first principles opinions differ. The difference is greatest between those
who regard them as corporeal and those who regard them as incorporeal, and from both dissent those who
make a blend and draw their principles from both sources. The number of principles is also in dispute; some
admit one only, others assert several. There is a consequent diversity in their several accounts of soul; they
assume, naturally enough, that what is in its own nature originative of movement must be among what is
primordial. That has led some to regard it as fire, for fire is the subtlest of the elements and nearest to
incorporeality; further, in the most primary sense, fire both is moved and originates movement in all the
others.

Democritus has expressed himself more ingeniously than the rest on the grounds for ascribing each of these
two characters to soul; soul and mind are, he says, one and the same thing, and this thing must be one of the
primary and indivisible bodies, and its power of originating movement must be due to its fineness of grain
and the shape of its atoms; he says that of all the shapes the spherical is the most mobile, and that this is the
shape of the particles of fire and mind.

Anaxagoras, as we said above, seems to distinguish between soul and mind, but in practice he treats them as a
single substance, except that it is mind that he specially posits as the principle of all things; at any rate what
he says is that mind alone of all that is simple, unmixed, and pure. He assigns both characteristics, knowing
and origination of movement, to the same principle, when he says that it was mind that set the whole in
movement.

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Thales, too, to judge from what is recorded about him, seems to have held soul to be a motive force, since he
said that the magnet has a soul in it because it moves the iron.

Diogenes (and others) held the soul to be air because he believed air to be finest in grain and a first principle;
therein lay the grounds of the soul's powers of knowing and originating movement. As the primordial
principle from which all other things are derived, it is cognitive; as finest in grain, it has the power to
originate movement.

Heraclitus too says that the first principle-the 'warm exhalation' of which, according to him, everything else
is composed-is soul; further, that this exhalation is most incorporeal and in ceaseless flux; that what is in
movement requires that what knows it should be in movement; and that all that is has its being essentially in
movement (herein agreeing with the majority).

Alcmaeon also seems to have held a similar view about soul; he says that it is immortal because it resembles
'the immortals,' and that this immortality belongs to it in virtue of its ceaseless movement; for all the 'things
divine,' moon, sun, the planets, and the whole heavens, are in perpetual movement.

of More superficial writers, some, e.g. Hippo, have pronounced it to be water; they seem to have argued from
the fact that the seed of all animals is fluid, for Hippo tries to refute those who say that the soul is blood, on
the ground that the seed, which is the primordial soul, is not blood.

Another group (Critias, for example) did hold it to be blood; they take perception to be the most characteristic
attribute of soul, and hold that perceptiveness is due to the nature of blood.

Each of the elements has thus found its partisan, except earth-earth has found no supporter unless we count
as such those who have declared soul to be, or to be compounded of, all the elements. All, then, it may be
said, characterize the soul by three marks, Movement, Sensation, Incorporeality, and each of these is traced
back to the first principles. That is why (with one exception) all those who define the soul by its power of
knowing make it either an element or constructed out of the elements. The language they all use is similar;
like, they say, is known by like; as the soul knows everything, they construct it out of all the principles.
Hence all those who admit but one cause or element, make the soul also one (e.g. fire or air), while those who
admit a multiplicity of principles make the soul also multiple. The exception is Anaxagoras; he alone says
that mind is impassible and has nothing in common with anything else. But, if this is so, how or in virtue of
what cause can it know? That Anaxagoras has not explained, nor can any answer be inferred from his words.
All who acknowledge pairs of opposites among their principles, construct the soul also out of these
contraries, while those who admit as principles only one contrary of each pair, e.g. either hot or cold, likewise
make the soul some one of these. That is why, also, they allow themselves to be guided by the names; those
who identify soul with the hot argue that sen (to live) is derived from sein (to boil), while those who identify
it with the cold say that soul (psuche) is so called from the process of respiration and (katapsuxis). Such are
the traditional opinions concerning soul, together with the grounds on which they are maintained.

We must begin our examination with movement; for doubtless, not only is it false that the essence of soul is
correctly described by those who say that it is what moves (or is capable of moving) itself, but it is an
impossibility that movement should be even an attribute of it.

We have already pointed out that there is no necessity that what originates movement should itself be moved.
There are two senses in which anything may be moved-either (a) indirectly, owing to something other than
itself, or (b) directly, owing to itself. Things are 'indirectly moved' which are moved as being contained in
something which is moved, e.g. sailors in a ship, for they are moved in a different sense from that in which

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the ship is moved; the ship is 'directly moved', they are 'indirectly moved', because they are in a moving
vessel. This is clear if we consider their limbs; the movement proper to the legs (and so to man) is walking,
and in this case the sailors tare not walking. Recognizing the double sense of 'being moved', what we have to
consider now is whether the soul is 'directly moved' and participates in such direct movement.

There are four species of movement-locomotion, alteration, diminution, growth; consequently if the soul is
moved, it must be moved with one or several or all of these species of movement. Now if its movement is not
incidental, there must be a movement natural to it, and, if so, as all the species enumerated involve place,
place must be natural to it. But if the essence of soul be to move itself, its being moved cannot be incidental
to-as it is to what is white or three cubits long; they too can be moved, but only incidentally-what is moved
is that of which 'white' and 'three cubits long' are the attributes, the body in which they inhere; hence they
have no place: but if the soul naturally partakes in movement, it follows that it must have a place.

Further, if there be a movement natural to the soul, there must be a counter-movement unnatural to it, and
conversely. The same applies to rest as well as to movement; for the terminus ad quem of a thing's natural
movement is the place of its natural rest, and similarly the terminus ad quem of its enforced movement is the
place of its enforced rest. But what meaning can be attached to enforced movements or rests of the soul, it is
difficult even to imagine.

Further, if the natural movement of the soul be upward, the soul must be fire; if downward, it must be earth;
for upward and downward movements are the definitory characteristics of these bodies. The same reasoning
applies to the intermediate movements, termini, and bodies. Further, since the soul is observed to originate
movement in the body, it is reasonable to suppose that it transmits to the body the movements by which it
itself is moved, and so, reversing the order, we may infer from the movements of the body back to similar
movements of the soul. Now the body is moved from place to place with movements of locomotion. Hence it
would follow that the soul too must in accordance with the body change either its place as a whole or the
relative places of its parts. This carries with it the possibility that the soul might even quit its body and
re-enter it, and with this would be involved the possibility of a resurrection of animals from the dead. But, it
may be contended, the soul can be moved indirectly by something else; for an animal can be pushed out of its
course. Yes, but that to whose essence belongs the power of being moved by itself, cannot be moved by
something else except incidentally, just as what is good by or in itself cannot owe its goodness to something
external to it or to some end to which it is a means.

If the soul is moved, the most probable view is that what moves it is sensible things.

We must note also that, if the soul moves itself, it must be the mover itself that is moved, so that it follows
that if movement is in every case a displacement of that which is in movement, in that respect in which it is
said to be moved, the movement of the soul must be a departure from its essential nature, at least if its
self-movement is essential to it, not incidental.

Some go so far as to hold that the movements which the soul imparts to the body in which it is are the same
in kind as those with which it itself is moved. An example of this is Democritus, who uses language like that
of the comic dramatist Philippus, who accounts for the movements that Daedalus imparted to his wooden
Aphrodite by saying that he poured quicksilver into it; similarly Democritus says that the spherical atoms
which according to him constitute soul, owing to their own ceaseless movements draw the whole body after
them and so produce its movements. We must urge the question whether it is these very same atoms which
produce rest also-how they could do so, it is difficult and even impossible to say. And, in general, we may
object that it is not in this way that the soul appears to originate movement in animals-it is through intention
or process of thinking.

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It is in the same fashion that the Timaeus also tries to give a physical account of how the soul moves its body;
the soul, it is there said, is in movement, and so owing to their mutual implication moves the body also. After
compounding the soul-substance out of the elements and dividing it in accordance with the harmonic
numbers, in order that it may possess a connate sensibility for 'harmony' and that the whole may move in
movements well attuned, the Demiurge bent the straight line into a circle; this single circle he divided into
two circles united at two common points; one of these he subdivided into seven circles. All this implies that
the movements of the soul are identified with the local movements of the heavens.

Now, in the first place, it is a mistake to say that the soul is a spatial magnitude. It is evident that Plato means
the soul of the whole to be like the sort of soul which is called mind not like the sensitive or the desiderative
soul, for the movements of neither of these are circular. Now mind is one and continuous in the sense in
which the process of thinking is so, and thinking is identical with the thoughts which are its parts; these have
a serial unity like that of number, not a unity like that of a spatial magnitude. Hence mind cannot have that
kind of unity either; mind is either without parts or is continuous in some other way than that which
characterizes a spatial magnitude. How, indeed, if it were a spatial magnitude, could mind possibly think?
Will it think with any one indifferently of its parts? In this case, the 'part' must be understood either in the
sense of a spatial magnitude or in the sense of a point (if a point can be called a part of a spatial magnitude).
If we accept the latter alternative, the points being infinite in number, obviously the mind can never
exhaustively traverse them; if the former, the mind must think the same thing over and over again, indeed an
infinite number of times (whereas it is manifestly possible to think a thing once only). If contact of any part
whatsoever of itself with the object is all that is required, why need mind move in a circle, or indeed possess
magnitude at all? On the other hand, if contact with the whole circle is necessary, what meaning can be given
to the contact of the parts? Further, how could what has no parts think what has parts, or what has parts think
what has none? We must identify the circle referred to with mind; for it is mind whose movement is thinking,
and it is the circle whose movement is revolution, so that if thinking is a movement of revolution, the circle
which has this characteristic movement must be mind.

If the circular movement is eternal, there must be something which mind is always thinking-what can this
be? For all practical processes of thinking have limits-they all go on for the sake of something outside the
process, and all theoretical processes come to a close in the same way as the phrases in speech which express
processes and results of thinking. Every such linguistic phrase is either definitory or demonstrative.
Demonstration has both a starting-point and may be said to end in a conclusion or inferred result; even if the
process never reaches final completion, at any rate it never returns upon itself again to its starting-point, it
goes on assuming a fresh middle term or a fresh extreme, and moves straight forward, but circular movement
returns to its starting-point. Definitions, too, are closed groups of terms.

Further, if the same revolution is repeated, mind must repeatedly think the same object.

Further, thinking has more resemblance to a coming to rest or arrest than to a movement; the same may be
said of inferring.

It might also be urged that what is difficult and enforced is incompatible with blessedness; if the movement
of the soul is not of its essence, movement of the soul must be contrary to its nature. It must also be painful
for the soul to be inextricably bound up with the body; nay more, if, as is frequently said and widely
accepted, it is better for mind not to be embodied, the union must be for it undesirable.

Further, the cause of the revolution of the heavens is left obscure. It is not the essence of soul which is the
cause of this circular movement-that movement is only incidental to soul-nor is, a fortiori, the body its
cause. Again, it is not even asserted that it is better that soul should be so moved; and yet the reason for
which God caused the soul to move in a circle can only have been that movement was better for it than rest,
and movement of this kind better than any other. But since this sort of consideration is more appropriate to

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another field of speculation, let us dismiss it for the present.

The view we have just been examining, in company with most theories about the soul, involves the following
absurdity: they all join the soul to a body, or place it in a body, without adding any specification of the reason
of their union, or of the bodily conditions required for it. Yet such explanation can scarcely be omitted; for
some community of nature is presupposed by the fact that the one acts and the other is acted upon, the one
moves and the other is moved; interaction always implies a special nature in the two interagents. All,
however, that these thinkers do is to describe the specific characteristics of the soul; they do not try to
determine anything about the body which is to contain it, as if it were possible, as in the Pythagorean myths,
that any soul could be clothed upon with any body-an absurd view, for each body seems to have a form and
shape of its own. It is as absurd as to say that the art of carpentry could embody itself in flutes; each art must
use its tools, each soul its body.

There is yet another theory about soul, which has commended itself to many as no less probable than any of
those we have hitherto mentioned, and has rendered public account of itself in the court of popular
discussion. Its supporters say that the soul is a kind of harmony, for (a) harmony is a blend or composition of
contraries, and (b) the body is compounded out of contraries. Harmony, however, is a certain proportion or
composition of the constituents blended, and soul can be neither the one nor the other of these. Further, the
power of originating movement cannot belong to a harmony, while almost all concur in regarding this as a
principal attribute of soul. It is more appropriate to call health (or generally one of the good states of the
body) a harmony than to predicate it of the soul. The absurdity becomes most apparent when we try to
attribute the active and passive affections of the soul to a harmony; the necessary readjustment of their
conceptions is difficult. Further, in using the word 'harmony' we have one or other of two cases in our mind;
the most proper sense is in relation to spatial magnitudes which have motion and position, where harmony
means the disposition and cohesion of their parts in such a manner as to prevent the introduction into the
whole of anything homogeneous with it, and the secondary sense, derived from the former, is that in which it
means the ratio between the constituents so blended; in neither of these senses is it plausible to predicate it of
soul. That soul is a harmony in the sense of the mode of composition of the parts of the body is a view easily
refutable; for there are many composite parts and those variously compounded; of what bodily part is mind or
the sensitive or the appetitive faculty the mode of composition? And what is the mode of composition which
constitutes each of them? It is equally absurd to identify the soul with the ratio of the mixture; for the mixture
which makes flesh has a different ratio between the elements from that which makes bone. The consequence
of this view will therefore be that distributed throughout the whole body there will be many souls, since every
one of the bodily parts is a different mixture of the elements, and the ratio of mixture is in each case a
harmony, i.e. a soul.

From Empedocles at any rate we might demand an answer to the following question for he says that each of
the parts of the body is what it is in virtue of a ratio between the elements: is the soul identical with this ratio,
or is it not rather something over and above this which is formed in the parts? Is love the cause of any and
every mixture, or only of those that are in the right ratio? Is love this ratio itself, or is love something over
and above this? Such are the problems raised by this account. But, on the other hand, if the soul is different
from the mixture, why does it disappear at one and the same moment with that relation between the elements
which constitutes flesh or the other parts of the animal body? Further, if the soul is not identical with the ratio
of mixture, and it is consequently not the case that each of the parts has a soul, what is that which perishes
when the soul quits the body?

That the soul cannot either be a harmony, or be moved in a circle, is clear from what we have said. Yet that it
can be moved incidentally is, as we said above, possible, and even that in a sense it can move itself, i.e. in the
sense that the vehicle in which it is can be moved, and moved by it; in no other sense can the soul be moved

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in space.

More legitimate doubts might remain as to its movement in view of the following facts. We speak of the soul
as being pained or pleased, being bold or fearful, being angry, perceiving, thinking. All these are regarded as
modes of movement, and hence it might be inferred that the soul is moved. This, however, does not
necessarily follow. We may admit to the full that being pained or pleased, or thinking, are movements (each
of them a 'being moved'), and that the movement is originated by the soul. For example we may regard anger
or fear as such and such movements of the heart, and thinking as such and such another movement of that
organ, or of some other; these modifications may arise either from changes of place in certain parts or from
qualitative alterations (the special nature of the parts and the special modes of their changes being for our
present purpose irrelevant). Yet to say that it is the soul which is angry is as inexact as it would be to say that
it is the soul that weaves webs or builds houses. It is doubtless better to avoid saying that the soul pities or
learns or thinks and rather to say that it is the man who does this with his soul. What we mean is not that the
movement is in the soul, but that sometimes it terminates in the soul and sometimes starts from it, sensation
e.g. coming from without inwards, and reminiscence starting from the soul and terminating with the
movements, actual or residual, in the sense organs.

The case of mind is different; it seems to be an independent substance implanted within the soul and to be
incapable of being destroyed. If it could be destroyed at all, it would be under the blunting influence of old
age. What really happens in respect of mind in old age is, however, exactly parallel to what happens in the
case of the sense organs; if the old man could recover the proper kind of eye, he would see just as well as the
young man. The incapacity of old age is due to an affection not of the soul but of its vehicle, as occurs in
drunkenness or disease. Thus it is that in old age the activity of mind or intellectual apprehension declines
only through the decay of some other inward part; mind itself is impassible. Thinking, loving, and hating are
affections not of mind, but of that which has mind, so far as it has it. That is why, when this vehicle decays,
memory and love cease; they were activities not of mind, but of the composite which has perished; mind is,
no doubt, something more divine and impassible. That the soul cannot be moved is therefore clear from what
we have said, and if it cannot be moved at all, manifestly it cannot be moved by itself.

Of all the opinions we have enumerated, by far the most unreasonable is that which declares the soul to be a
self-moving number; it involves in the first place all the impossibilities which follow from regarding the soul
as moved, and in the second special absurdities which follow from calling it a number. How we to imagine a
unit being moved? By what agency? What sort of movement can be attributed to what is without parts or
internal differences? If the unit is both originative of movement and itself capable of being moved, it must
contain difference.

Further, since they say a moving line generates a surface and a moving point a line, the movements of the
psychic units must be lines (for a point is a unit having position, and the number of the soul is, of course,
somewhere and has position).

Again, if from a number a number or a unit is subtracted, the remainder is another number; but plants and
many animals when divided continue to live, and each segment is thought to retain the same kind of soul.

It must be all the same whether we speak of units or corpuscles; for if the spherical atoms of Democritus
became points, nothing being retained but their being a quantum, there must remain in each a moving and a
moved part, just as there is in what is continuous; what happens has nothing to do with the size of the atoms,
it depends solely upon their being a quantum. That is why there must be something to originate movement in
the units. If in the animal what originates movement is the soul, so also must it be in the case of the number,
so that not the mover and the moved together, but the mover only, will be the soul. But how is it possible for
one of the units to fulfil this function of originating movement? There must be some difference between such
a unit and all the other units, and what difference can there be between one placed unit and another except a

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ON THE SOUL

difference of position? If then, on the other hand, these psychic units within the body are different from the
points of the body, there will be two sets of units both occupying the same place; for each unit will occupy a
point. And yet, if there can be two, why cannot there be an infinite number? For if things can occupy an
indivisible lace, they must themselves be indivisible. If, on the other hand, the points of the body are identical
with the units whose number is the soul, or if the number of the points in the body is the soul, why have not
all bodies souls? For all bodies contain points or an infinity of points.

Further, how is it possible for these points to be isolated or separated from their bodies, seeing that lines
cannot be resolved into points?

The result is, as we have said, that this view, while on the one side identical with that of those who maintain
that soul is a subtle kind of body, is on the other entangled in the absurdity peculiar to Democritus' way of
describing the manner in which movement is originated by soul. For if the soul is present throughout the
whole percipient body, there must, if the soul be a kind of body, be two bodies in the same place; and for
those who call it a number, there must be many points at one point, or every body must have a soul, unless
the soul be a different sort of number-other, that is, than the sum of the points existing in a body. Another
consequence that follows is that the animal must be moved by its number precisely in the way that
Democritus explained its being moved by his spherical psychic atoms. What difference does it make whether
we speak of small spheres or of large units, or, quite simply, of units in movement? One way or another, the
movements of the animal must be due to their movements. Hence those who combine movement and number
in the same subject lay themselves open to these and many other similar absurdities. It is impossible not only
that these characters should give the definition of soul-it is impossible that they should even be attributes of
it. The point is clear if the attempt be made to start from this as the account of soul and explain from it the
affections and actions of the soul, e.g. reasoning, sensation, pleasure, pain, For, to repeat what we have said
earlier, movement and number do not facilitate even conjecture about the derivative properties of soul.

Such are the three ways in which soul has traditionally been defined; one group of thinkers declared it to be
that which is most originative of movement because it moves itself, another group to be the subtlest and most
nearly incorporeal of all kinds of body. We have now sufficiently set forth the difficulties and inconsistencies
to which these theories are exposed. It remains now to examine the doctrine that soul is composed of the
elements.

The reason assigned for this doctrine is that thus the soul may perceive or come to know everything that is,
but the theory necessarily involves itself in many impossibilities. Its upholders assume that like is known
only by like, and imagine that by declaring the soul to be composed of the elements they succeed in
identifying the soul with all the things it is capable of apprehending. But the elements are not the only things
it knows; there are many others, or, more exactly, an infinite number of others, formed out of the elements.
Let us admit that the soul knows or perceives the elements out of which each of these composites is made up;
but by what means will it know or perceive the composite whole, e.g. what God, man, flesh, bone (or any
other compound) is? For each is, not merely the elements of which it is composed, but those elements
combined in a determinate mode or ratio, as Empedocles himself says of bone,

The kindly Earth in its broad-bosomed moulds

Won of clear Water two parts out of eight,

And four of Fire; and so white bones were formed.

ON THE SOUL 10

ON THE SOUL

Nothing, therefore, will be gained by the presence of the elements in the soul, unless there be also present
there the various formulae of proportion and the various compositions in accordance with them. Each element
will indeed know its fellow outside, but there will be no knowledge of bone or man, unless they too are
present in the constitution of the soul. The impossibility of this needs no pointing out; for who would suggest
that stone or man could enter into the constitution of the soul? The same applies to 'the good' and 'the
not-good', and so on.

Further, the word 'is' has many meanings: it may be used of a 'this' or substance, or of a quantum, or of a
quale, or of any other of the kinds of predicates we have distinguished. Does the soul consist of all of these or
not? It does not appear that all have common elements. Is the soul formed out of those elements alone which
enter into substances? so how will it be able to know each of the other kinds of thing? Will it be said that each
kind of thing has elements or principles of its own, and that the soul is formed out of the whole of these? In
that case, the soul must be a quantum and a quale and a substance. But all that can be made out of the
elements of a quantum is a quantum, not a substance. These (and others like them) are the consequences of
the view that the soul is composed of all the elements.

It is absurd, also, to say both (a) that like is not capable of being affected by like, and (b) that like is perceived
or known by like, for perceiving, and also both thinking and knowing, are, on their own assumption, ways of
being affected or moved.

There are many puzzles and difficulties raised by saying, as Empedocles does, that each set of things is
known by means of its corporeal elements and by reference to something in soul which is like them, and
additional testimony is furnished by this new consideration; for all the parts of the animal body which consist
wholly of earth such as bones, sinews, and hair seem to be wholly insensitive and consequently not
perceptive even of objects earthy like themselves, as they ought to have been.

Further, each of the principles will have far more ignorance than knowledge, for though each of them will
know one thing, there will be many of which it will be ignorant. Empedocles at any rate must conclude that
his God is the least intelligent of all beings, for of him alone is it true that there is one thing, Strife, which he
does not know, while there is nothing which mortal beings do not know, for ere is nothing which does not
enter into their composition.

In general, we may ask, Why has not everything a soul, since everything either is an element, or is formed out
of one or several or all of the elements? Each must certainly know one or several or all.

The problem might also be raised, What is that which unifies the elements into a soul? The elements
correspond, it would appear, to the matter; what unites them, whatever it is, is the supremely important factor.
But it is impossible that there should be something superior to, and dominant over, the soul (and a fortiori
over the mind); it is reasonable to hold that mind is by nature most primordial and dominant, while their
statement that it is the elements which are first of all that is.

All, both those who assert that the soul, because of its knowledge or perception of what is compounded out of
the elements, and is those who assert that it is of all things the most originative of movement, fail to take into
consideration all kinds of soul. In fact (1) not all beings that perceive can originate movement; there appear to
be certain animals which stationary, and yet local movement is the only one, so it seems, which the soul
originates in animals. And (2) the same object-on holds against all those who construct mind and the
perceptive faculty out of the elements; for it appears that plants live, and yet are not endowed with
locomotion or perception, while a large number of animals are without discourse of reason. Even if these
points were waived and mind admitted to be a part of the soul (and so too the perceptive faculty), still, even
so, there would be kinds and parts of soul of which they had failed to give any account.

ON THE SOUL 11

ON THE SOUL

The same objection lies against the view expressed in the 'Orphic' poems: there it is said that the soul comes
in from the whole when breathing takes place, being borne in upon the winds. Now this cannot take place in
the case of plants, nor indeed in the case of certain classes of animal, for not all classes of animal breathe.
This fact has escaped the notice of the holders of this view.

If we must construct the soul out of the elements, there is no necessity to suppose that all the elements enter
into its construction; one element in each pair of contraries will suffice to enable it to know both that element
itself and its contrary. By means of the straight line we know both itself and the curved-the carpenter's rule
enables us to test both-but what is curved does not enable us to distinguish either itself or the straight.
Certain thinkers say that soul is intermingled in the whole universe, and it is perhaps for that reason that
Thales came to the opinion that all things are full of gods. This presents some difficulties: Why does the soul
when it resides in air or fire not form an animal, while it does so when it resides in mixtures of the elements,
and that although it is held to be of higher quality when contained in the former? (One might add the
question, why the soul in air is maintained to be higher and more immortal than that in animals.) Both
possible ways of replying to the former question lead to absurdity or paradox; for it is beyond paradox to say
that fire or air is an animal, and it is absurd to refuse the name of animal to what has soul in it. The opinion
that the elements have soul in them seems to have arisen from the doctrine that a whole must be
homogeneous with its parts. If it is true that animals become animate by drawing into themselves a portion of
what surrounds them, the partisans of this view are bound to say that the soul of the Whole too is
homogeneous with all its parts. If the air sucked in is homogeneous, but soul heterogeneous, clearly while
some part of soul will exist in the inbreathed air, some other part will not. The soul must either be
homogeneous, or such that there are some parts of the Whole in which it is not to be found.

From what has been said it is now clear that knowing as an attribute of soul cannot be explained by soul's
being composed of the elements, and that it is neither sound nor true to speak of soul as moved. But since (a)
knowing, perceiving, opining, and further (b) desiring, wishing, and generally all other modes of appetition,
belong to soul, and (c) the local movements of animals, and (d) growth, maturity, and decay are produced by
the soul, we must ask whether each of these is an attribute of the soul as a whole, i.e. whether it is with the
whole soul we think, perceive, move ourselves, act or are acted upon, or whether each of them requires a
different part of the soul? So too with regard to life. Does it depend on one of the parts of soul? Or is it
dependent on more than one? Or on all? Or has it some quite other cause?

Some hold that the soul is divisible, and that one part thinks, another desires. If, then, its nature admits of its
being divided, what can it be that holds the parts together? Surely not the body; on the contrary it seems
rather to be the soul that holds the body together; at any rate when the soul departs the body disintegrates and
decays. If, then, there is something else which makes the soul one, this unifying agency would have the best
right to the name of soul, and we shall have to repeat for it the question: Is it one or multipartite? If it is one,
why not at once admit that 'the soul' is one? If it has parts, once more the question must be put: What holds its
parts together, and so ad infinitum?

The question might also be raised about the parts of the soul: What is the separate role of each in relation to
the body? For, if the whole soul holds together the whole body, we should expect each part of the soul to hold
together a part of the body. But this seems an impossibility; it is difficult even to imagine what sort of bodily
part mind will hold together, or how it will do this.

It is a fact of observation that plants and certain insects go on living when divided into segments; this means
that each of the segments has a soul in it identical in species, though not numerically identical in the different
segments, for both of the segments for a time possess the power of sensation and local movement. That this
does not last is not surprising, for they no longer possess the organs necessary for self-maintenance. But, all
the same, in each of the bodily parts there are present all the parts of soul, and the souls so present are
homogeneous with one another and with the whole; this means that the several parts of the soul are

ON THE SOUL 12

ON THE SOUL

indisseverable from one another, although the whole soul is divisible. It seems also that the principle found in
plants is also a kind of soul; for this is the only principle which is common to both animals and plants; and
this exists in isolation from the principle of sensation, though there nothing which has the latter without the
former.

Book II

LET the foregoing suffice as our account of the views concerning the soul which have been handed on by our
predecessors; let us now dismiss them and make as it were a completely fresh start, endeavouring to give a
precise answer to the question, What is soul? i.e. to formulate the most general possible definition of it.

We are in the habit of recognizing, as one determinate kind of what is, substance, and that in several senses,
(a) in the sense of matter or that which in itself is not 'a this', and (b) in the sense of form or essence, which is
that precisely in virtue of which a thing is called 'a this', and thirdly (c) in the sense of that which is
compounded of both (a) and (b). Now matter is potentiality, form actuality; of the latter there are two grades
related to one another as e.g. knowledge to the exercise of knowledge.

Among substances are by general consent reckoned bodies and especially natural bodies; for they are the
principles of all other bodies. Of natural bodies some have life in them, others not; by life we mean
self-nutrition and growth (with its correlative decay). It follows that every natural body which has life in it is
a substance in the sense of a composite.

But since it is also a body of such and such a kind, viz. having life, the body cannot be soul; the body is the
subject or matter, not what is attributed to it. Hence the soul must be a substance in the sense of the form of a
natural body having life potentially within it. But substance is actuality, and thus soul is the actuality of a
body as above characterized. Now the word actuality has two senses corresponding respectively to the
possession of knowledge and the actual exercise of knowledge. It is obvious that the soul is actuality in the
first sense, viz. that of knowledge as possessed, for both sleeping and waking presuppose the existence of
soul, and of these waking corresponds to actual knowing, sleeping to knowledge possessed but not employed,
and, in the history of the individual, knowledge comes before its employment or exercise.

That is why the soul is the first grade of actuality of a natural body having life potentially in it. The body so
described is a body which is organized. The parts of plants in spite of their extreme simplicity are 'organs';
e.g. the leaf serves to shelter the pericarp, the pericarp to shelter the fruit, while the roots of plants are
analogous to the mouth of animals, both serving for the absorption of food. If, then, we have to give a general
formula applicable to all kinds of soul, we must describe it as the first grade of actuality of a natural
organized body. That is why we can wholly dismiss as unnecessary the question whether the soul and the
body are one: it is as meaningless as to ask whether the wax and the shape given to it by the stamp are one, or
generally the matter of a thing and that of which it is the matter. Unity has many senses (as many as 'is' has),
but the most proper and fundamental sense of both is the relation of an actuality to that of which it is the
actuality. We have now given an answer to the question, What is soul?-an answer which applies to it in its
full extent. It is substance in the sense which corresponds to the definitive formula of a thing's essence. That
means that it is 'the essential whatness' of a body of the character just assigned. Suppose that what is literally
an 'organ', like an axe, were a natural body, its 'essential whatness', would have been its essence, and so its
soul; if this disappeared from it, it would have ceased to be an axe, except in name. As it is, it is just an axe; it
wants the character which is required to make its whatness or formulable essence a soul; for that, it would
have had to be a natural body of a particular kind, viz. one having in itself the power of setting itself in
movement and arresting itself. Next, apply this doctrine in the case of the 'parts' of the living body. Suppose

Book II 13

ON THE SOUL

that the eye were an animal-sight would have been its soul, for sight is the substance or essence of the eye
which corresponds to the formula, the eye being merely the matter of seeing; when seeing is removed the eye
is no longer an eye, except in name-it is no more a real eye than the eye of a statue or of a painted figure. We
must now extend our consideration from the 'parts' to the whole living body; for what the departmental sense
is to the bodily part which is its organ, that the whole faculty of sense is to the whole sensitive body as such.

We must not understand by that which is 'potentially capable of living' what has lost the soul it had, but only
what still retains it; but seeds and fruits are bodies which possess the qualification. Consequently, while
waking is actuality in a sense corresponding to the cutting and the seeing, the soul is actuality in the sense
corresponding to the power of sight and the power in the tool; the body corresponds to what exists in
potentiality; as the pupil plus the power of sight constitutes the eye, so the soul plus the body constitutes the
animal.

From this it indubitably follows that the soul is inseparable from its body, or at any rate that certain parts of it
are (if it has parts) for the actuality of some of them is nothing but the actualities of their bodily parts. Yet
some may be separable because they are not the actualities of any body at all. Further, we have no light on the
problem whether the soul may not be the actuality of its body in the sense in which the sailor is the actuality
of the ship.

This must suffice as our sketch or outline determination of the nature of soul.

Since what is clear or logically more evident emerges from what in itself is confused but more observable by
us, we must reconsider our results from this point of view. For it is not enough for a definitive formula to
express as most now do the mere fact; it must include and exhibit the ground also. At present definitions are
given in a form analogous to the conclusion of a syllogism; e.g. What is squaring? The construction of an
equilateral rectangle equal to a given oblong rectangle. Such a definition is in form equivalent to a
conclusion. One that tells us that squaring is the discovery of a line which is a mean proportional between the
two unequal sides of the given rectangle discloses the ground of what is defined.

We resume our inquiry from a fresh starting-point by calling attention to the fact that what has soul in it
differs from what has not, in that the former displays life. Now this word has more than one sense, and
provided any one alone of these is found in a thing we say that thing is living. Living, that is, may mean
thinking or perception or local movement and rest, or movement in the sense of nutrition, decay and growth.
Hence we think of plants also as living, for they are observed to possess in themselves an originative power
through which they increase or decrease in all spatial directions; they grow up and down, and everything that
grows increases its bulk alike in both directions or indeed in all, and continues to live so long as it can absorb
nutriment.

This power of self-nutrition can be isolated from the other powers mentioned, but not they from it-in mortal
beings at least. The fact is obvious in plants; for it is the only psychic power they possess.

This is the originative power the possession of which leads us to speak of things as living at all, but it is the
possession of sensation that leads us for the first time to speak of living things as animals; for even those
beings which possess no power of local movement but do possess the power of sensation we call animals and
not merely living things.

The primary form of sense is touch, which belongs to all animals, just as the power of self-nutrition can be
isolated from touch and sensation generally, so touch can be isolated from all other forms of sense. (By the
power of self-nutrition we mean that departmental power of the soul which is common to plants and animals:

Book II 14

ON THE SOUL

all animals whatsoever are observed to have the sense of touch.) What the explanation of these two facts is,
we must discuss later. At present we must confine ourselves to saying that soul is the source of these
phenomena and is characterized by them, viz. by the powers of self-nutrition, sensation, thinking, and
motivity.

Is each of these a soul or a part of a soul? And if a part, a part in what sense? A part merely distinguishable
by definition or a part distinct in local situation as well? In the case of certain of these powers, the answers to
these questions are easy, in the case of others we are puzzled what to say. just as in the case of plants which
when divided are observed to continue to live though removed to a distance from one another (thus showing
that in their case the soul of each individual plant before division was actually one, potentially many), so we
notice a similar result in other varieties of soul, i.e. in insects which have been cut in two; each of the
segments possesses both sensation and local movement; and if sensation, necessarily also imagination and
appetition; for, where there is sensation, there is also pleasure and pain, and, where these, necessarily also
desire.

We have no evidence as yet about mind or the power to think; it seems to be a widely different kind of soul,
differing as what is eternal from what is perishable; it alone is capable of existence in isolation from all other
psychic powers. All the other parts of soul, it is evident from what we have said, are, in spite of certain
statements to the contrary, incapable of separate existence though, of course, distinguishable by definition. If
opining is distinct from perceiving, to be capable of opining and to be capable of perceiving must be distinct,
and so with all the other forms of living above enumerated. Further, some animals possess all these parts of
soul, some certain of them only, others one only (this is what enables us to classify animals); the cause must
be considered later.' A similar arrangement is found also within the field of the senses; some classes of
animals have all the senses, some only certain of them, others only one, the most indispensable, touch.

Since the expression 'that whereby we live and perceive' has two meanings, just like the expression 'that
whereby we know'-that may mean either (a) knowledge or (b) the soul, for we can speak of knowing by or
with either, and similarly that whereby we are in health may be either (a) health or (b) the body or some part
of the body; and since of the two terms thus contrasted knowledge or health is the name of a form, essence, or
ratio, or if we so express it an actuality of a recipient matter-knowledge of what is capable of knowing,
health of what is capable of being made healthy (for the operation of that which is capable of originating
change terminates and has its seat in what is changed or altered); further, since it is the soul by or with which
primarily we live, perceive, and think:-it follows that the soul must be a ratio or formulable essence, not a
matter or subject. For, as we said, word substance has three meanings form, matter, and the complex of both
and of these three what is called matter is potentiality, what is called form actuality. Since then the complex
here is the living thing, the body cannot be the actuality of the soul; it is the soul which is the actuality of a
certain kind of body. Hence the rightness of the view that the soul cannot be without a body, while it csnnot
he a body; it is not a body but something relative to a body. That is why it is in a body, and a body of a
definite kind. It was a mistake, therefore, to do as former thinkers did, merely to fit it into a body without
adding a definite specification of the kind or character of that body. Reflection confirms the observed fact;
the actuality of any given thing can only be realized in what is already potentially that thing, i.e. in a matter of
its own appropriate to it. From all this it follows that soul is an actuality or formulable essence of something
that possesses a potentiality of being besouled.

Of the psychic powers above enumerated some kinds of living things, as we have said, possess all, some less
than all, others one only. Those we have mentioned are the nutritive, the appetitive, the sensory, the
locomotive, and the power of thinking. Plants have none but the first, the nutritive, while another order of
living things has this plus the sensory. If any order of living things has the sensory, it must also have the
appetitive; for appetite is the genus of which desire, passion, and wish are the species; now all animals have

Book II 15

ON THE SOUL

one sense at least, viz. touch, and whatever has a sense has the capacity for pleasure and pain and therefore
has pleasant and painful objects present to it, and wherever these are present, there is desire, for desire is just
appetition of what is pleasant. Further, all animals have the sense for food (for touch is the sense for food);
the food of all living things consists of what is dry, moist, hot, cold, and these are the qualities apprehended
by touch; all other sensible qualities are apprehended by touch only indirectly. Sounds, colours, and odours
contribute nothing to nutriment; flavours fall within the field of tangible qualities. Hunger and thirst are
forms of desire, hunger a desire for what is dry and hot, thirst a desire for what is cold and moist; flavour is a
sort of seasoning added to both. We must later clear up these points, but at present it may be enough to say
that all animals that possess the sense of touch have also appetition. The case of imagination is obscure; we
must examine it later. Certain kinds of animals possess in addition the power of locomotion, and still another
order of animate beings, i.e. man and possibly another order like man or superior to him, the power of
thinking, i.e. mind. It is now evident that a single definition can be given of soul only in the same sense as
one can be given of figure. For, as in that case there is no figure distinguishable and apart from triangle, so
here there is no soul apart from the forms of soul just enumerated. It is true that a highly general definition
can be given for figure which will fit all figures without expressing the peculiar nature of any figure. So here
in the case of soul and its specific forms. Hence it is absurd in this and similar cases to demand an absolutely
general definition which will fail to express the peculiar nature of anything that is, or again, omitting this, to
look for separate definitions corresponding to each infima species. The cases of figure and soul are exactly
parallel; for the particulars subsumed under the common name in both cases-figures and living
beings-constitute a series, each successive term of which potentially contains its predecessor, e.g. the square
the triangle, the sensory power the self-nutritive. Hence we must ask in the case of each order of living
things, What is its soul, i.e. What is the soul of plant, animal, man? Why the terms are related in this serial
way must form the subject of later examination. But the facts are that the power of perception is never found
apart from the power of self-nutrition, while-in plants-the latter is found isolated from the former. Again, no
sense is found apart from that of touch, while touch is found by itself; many animals have neither sight,
hearing, nor smell. Again, among living things that possess sense some have the power of locomotion, some
not. Lastly, certain living beings-a small minority-possess calculation and thought, for (among mortal
beings) those which possess calculation have all the other powers above mentioned, while the converse does
not hold-indeed some live by imagination alone, while others have not even imagination. The mind that
knows with immediate intuition presents a different problem.

It is evident that the way to give the most adequate definition of soul is to seek in the case of each of its forms
for the most appropriate definition.

It is necessary for the student of these forms of soul first to find a definition of each, expressive of what it is,
and then to investigate its derivative properties, But if we are to express what each is, viz. what the thinking
power is, or the perceptive, or the nutritive, we must go farther back and first give an account of thinking or
perceiving, for in the order of investigation the question of what an agent does precedes the question, what
enables it to do what it does. If this is correct, we must on the same ground go yet another step farther back
and have some clear view of the objects of each; thus we must start with these objects, e.g. with food, with
what is perceptible, or with what is intelligible.

It follows that first of all we must treat of nutrition and reproduction, for the nutritive soul is found along with
all the others and is the most primitive and widely distributed power of soul, being indeed that one in virtue
of which all are said to have life. The acts in which it manifests itself are reproduction and the use of
food-reproduction, I say, because for any living thing that has reached its normal development and which is
unmutilated, and whose mode of generation is not spontaneous, the most natural act is the production of
another like itself, an animal producing an animal, a plant a plant, in order that, as far as its nature allows, it
may partake in the eternal and divine. That is the goal towards which all things strive, that for the sake of

Book II 16

ON THE SOUL

which they do whatsoever their nature renders possible. The phrase 'for the sake of which' is ambiguous; it
may mean either (a) the end to achieve which, or (b) the being in whose interest, the act is done. Since then
no living thing is able to partake in what is eternal and divine by uninterrupted continuance (for nothing
perishable can for ever remain one and the same), it tries to achieve that end in the only way possible to it,
and success is possible in varying degrees; so it remains not indeed as the self-same individual but continues
its existence in something like itself-not numerically but specifically one.

The soul is the cause or source of the living body. The terms cause and source have many senses. But the soul
is the cause of its body alike in all three senses which we explicitly recognize. It is (a) the source or origin of
movement, it is (b) the end, it is (c) the essence of the whole living body.

That it is the last, is clear; for in everything the essence is identical with the ground of its being, and here, in
the case of living things, their being is to live, and of their being and their living the soul in them is the cause
or source. Further, the actuality of whatever is potential is identical with its formulable essence.

It is manifest that the soul is also the final cause of its body. For Nature, like mind, always does whatever it
does for the sake of something, which something is its end. To that something corresponds in the case of
animals the soul and in this it follows the order of nature; all natural bodies are organs of the soul. This is true
of those that enter into the constitution of plants as well as of those which enter into that of animals. This
shows that that the sake of which they are is soul. We must here recall the two senses of 'that for the sake of
which', viz. (a) the end to achieve which, and (b) the being in whose interest, anything is or is done.

We must maintain, further, that the soul is also the cause of the living body as the original source of local
movement. The power of locomotion is not found, however, in all living things. But change of quality and
change of quantity are also due to the soul. Sensation is held to be a qualitative alteration, and nothing except
what has soul in it is capable of sensation. The same holds of the quantitative changes which constitute
growth and decay; nothing grows or decays naturally except what feeds itself, and nothing feeds itself except
what has a share of soul in it.

Empedocles is wrong in adding that growth in plants is to be explained, the downward rooting by the natural
tendency of earth to travel downwards, and the upward branching by the similar natural tendency of fire to
travel upwards. For he misinterprets up and down; up and down are not for all things what they are for the
whole Cosmos: if we are to distinguish and identify organs according to their functions, the roots of plants
are analogous to the head in animals. Further, we must ask what is the force that holds together the earth and
the fire which tend to travel in contrary directions; if there is no counteracting force, they will be torn
asunder; if there is, this must be the soul and the cause of nutrition and growth. By some the element of fire is
held to be the cause of nutrition and growth, for it alone of the primary bodies or elements is observed to feed
and increase itself. Hence the suggestion that in both plants and animals it is it which is the operative force. A
concurrent cause in a sense it certainly is, but not the principal cause, that is rather the soul; for while the
growth of fire goes on without limit so long as there is a supply of fuel, in the case of all complex wholes
formed in the course of nature there is a limit or ratio which determines their size and increase, and limit and
ratio are marks of soul but not of fire, and belong to the side of formulable essence rather than that of matter.

Nutrition and reproduction are due to one and the same psychic power. It is necessary first to give precision
to our account of food, for it is by this function of absorbing food that this psychic power is distinguished
from all the others. The current view is that what serves as food to a living thing is what is contrary to it-not
that in every pair of contraries each is food to the other: to be food a contrary must not only be transformable
into the other and vice versa, it must also in so doing increase the bulk of the other. Many a contrary is
transformed into its other and vice versa, where neither is even a quantum and so cannot increase in bulk, e.g.
an invalid into a healthy subject. It is clear that not even those contraries which satisfy both the conditions
mentioned above are food to one another in precisely the same sense; water may be said to feed fire, but not

Book II 17

ON THE SOUL

fire water. Where the members of the pair are elementary bodies only one of the contraries, it would appear,
can be said to feed the other. But there is a difficulty here. One set of thinkers assert that like fed, as well as
increased in amount, by like. Another set, as we have said, maintain the very reverse, viz. that what feeds and
what is fed are contrary to one another; like, they argue, is incapable of being affected by like; but food is
changed in the process of digestion, and change is always to what is opposite or to what is intermediate.
Further, food is acted upon by what is nourished by it, not the other way round, as timber is worked by a
carpenter and not conversely; there is a change in the carpenter but it is merely a change from not-working to
working. In answering this problem it makes all the difference whether we mean by 'the food' the 'finished' or
the 'raw' product. If we use the word food of both, viz. of the completely undigested and the completely
digested matter, we can justify both the rival accounts of it; taking food in the sense of undigested matter, it is
the contrary of what is fed by it, taking it as digested it is like what is fed by it. Consequently it is clear that in
a certain sense we may say that both parties are right, both wrong.

Since nothing except what is alive can be fed, what is fed is the besouled body and just because it has soul in
it. Hence food is essentially related to what has soul in it. Food has a power which is other than the power to
increase the bulk of what is fed by it; so far forth as what has soul in it is a quantum, food may increase its
quantity, but it is only so far as what has soul in it is a 'this-somewhat' or substance that food acts as food; in
that case it maintains the being of what is fed, and that continues to be what it is so long as the process of
nutrition continues. Further, it is the agent in generation, i.e. not the generation of the individual fed but the
reproduction of another like it; the substance of the individual fed is already in existence; the existence of no
substance is a self-generation but only a self-maintenance.

Hence the psychic power which we are now studying may be described as that which tends to maintain
whatever has this power in it of continuing such as it was, and food helps it to do its work. That is why, if
deprived of food, it must cease to be.

The process of nutrition involves three factors, (a) what is fed, (b) that wherewith it is fed, (c) what does the
feeding; of these (c) is the first soul, (a) the body which has that soul in it, (b) the food. But since it is right to
call things after the ends they realize, and the end of this soul is to generate another being like that in which it
is, the first soul ought to be named the reproductive soul. The expression (b) 'wherewith it is fed' is
ambiguous just as is the expression 'wherewith the ship is steered'; that may mean either (i) the hand or (ii)
the rudder, i.e. either (i) what is moved and sets in movement, or (ii) what is merely moved. We can apply
this analogy here if we recall that all food must be capable of being digested, and that what produces
digestion is warmth; that is why everything that has soul in it possesses warmth.

We have now given an outline account of the nature of food; further details must be given in the appropriate
place.

Having made these distinctions let us now speak of sensation in the widest sense. Sensation depends, as we
have said, on a process of movement or affection from without, for it is held to be some sort of change of
quality. Now some thinkers assert that like is affected only by like; in what sense this is possible and in what
sense impossible, we have explained in our general discussion of acting and being acted upon.

Here arises a problem: why do we not perceive the senses themselves as well as the external objects of sense,
or why without the stimulation of external objects do they not produce sensation, seeing that they contain in
themselves fire, earth, and all the other elements, which are the direct or indirect objects is so of sense? It is
clear that what is sensitive is only potentially, not actually. The power of sense is parallel to what is
combustible, for that never ignites itself spontaneously, but requires an agent which has the power of starting
ignition; otherwise it could have set itself on fire, and would not have needed actual fire to set it ablaze.

Book II 18

ON THE SOUL

In reply we must recall that we use the word 'perceive' in two ways, for we say (a) that what has the power to
hear or see, 'sees' or 'hears', even though it is at the moment asleep, and also (b) that what is actually seeing or
hearing, 'sees' or 'hears'. Hence 'sense' too must have two meanings, sense potential, and sense actual.
Similarly 'to be a sentient' means either (a) to have a certain power or (b) to manifest a certain activity. To
begin with, for a time, let us speak as if there were no difference between (i) being moved or affected, and (ii)
being active, for movement is a kind of activity-an imperfect kind, as has elsewhere been explained.
Everything that is acted upon or moved is acted upon by an agent which is actually at work. Hence it is that in
one sense, as has already been stated, what acts and what is acted upon are like, in another unlike, i.e. prior to
and during the change the two factors are unlike, after it like.

But we must now distinguish not only between what is potential and what is actual but also different senses
in which things can be said to be potential or actual; up to now we have been speaking as if each of these
phrases had only one sense. We can speak of something as 'a knower' either (a) as when we say that man is a
knower, meaning that man falls within the class of beings that know or have knowledge, or (b) as when we
are speaking of a man who possesses a knowledge of grammar; each of these is so called as having in him a
certain potentiality, but there is a difference between their respective potentialities, the one (a) being a
potential knower, because his kind or matter is such and such, the other (b), because he can in the absence of
any external counteracting cause realize his knowledge in actual knowing at will. This implies a third
meaning of 'a knower' (c), one who is already realizing his knowledge-he is a knower in actuality and in the
most proper sense is knowing, e.g. this A. Both the former are potential knowers, who realize their respective
potentialities, the one (a) by change of quality, i.e. repeated transitions from one state to its opposite under
instruction, the other (b) by the transition from the inactive possession of sense or grammar to their active
exercise. The two kinds of transition are distinct.

Also the expression 'to be acted upon' has more than one meaning; it may mean either (a) the extinction of
one of two contraries by the other, or (b) the maintenance of what is potential by the agency of what is actual
and already like what is acted upon, with such likeness as is compatible with one's being actual and the other
potential. For what possesses knowledge becomes an actual knower by a transition which is either not an
alteration of it at all (being in reality a development into its true self or actuality) or at least an alteration in a
quite different sense from the usual meaning.

Hence it is wrong to speak of a wise man as being 'altered' when he uses his wisdom, just as it would be
absurd to speak of a builder as being altered when he is using his skill in building a house.

What in the case of knowing or understanding leads from potentiality to actuality ought not to be called
teaching but something else. That which starting with the power to know learns or acquires knowledge
through the agency of one who actually knows and has the power of teaching either (a) ought not to be said
'to be acted upon' at all or (b) we must recognize two senses of alteration, viz. (i) the substitution of one
quality for another, the first being the contrary of the second, or (ii) the development of an existent quality
from potentiality in the direction of fixity or nature.

In the case of what is to possess sense, the first transition is due to the action of the male parent and takes
place before birth so that at birth the living thing is, in respect of sensation, at the stage which corresponds to
the possession of knowledge. Actual sensation corresponds to the stage of the exercise of knowledge. But
between the two cases compared there is a difference; the objects that excite the sensory powers to activity,
the seen, the heard, are outside. The ground of this difference is that what actual sensation apprehends is
individuals, while what knowledge apprehends is universals, and these are in a sense within the soul. That is
why a man can exercise his knowledge when he wishes, but his sensation does not depend upon himself a
sensible object must be there. A similar statement must be made about our knowledge of what is sensible-on
the same ground, viz. that the sensible objects are individual and external.

Book II 19

ON THE SOUL

A later more appropriate occasion may be found thoroughly to clear up all this. At present it must be enough
to recognize the distinctions already drawn; a thing may be said to be potential in either of two senses, (a) in
the sense in which we might say of a boy that he may become a general or (b) in the sense in which we might
say the same of an adult, and there are two corresponding senses of the term 'a potential sentient'. There are
no separate names for the two stages of potentiality; we have pointed out that they are different and how they
are different. We cannot help using the incorrect terms 'being acted upon or altered' of the two transitions
involved. As we have said, has the power of sensation is potentially like what the perceived object is actually;
that is, while at the beginning of the process of its being acted upon the two interacting factors are dissimilar,
at the end the one acted upon is assimilated to the other and is identical in quality with it.

In dealing with each of the senses we shall have first to speak of the objects which are perceptible by each.
The term 'object of sense' covers three kinds of objects, two kinds of which are, in our language, directly
perceptible, while the remaining one is only incidentally perceptible. Of the first two kinds one (a) consists of
what is perceptible by a single sense, the other (b) of what is perceptible by any and all of the senses. I call by
the name of special object of this or that sense that which cannot be perceived by any other sense than that
one and in respect of which no error is possible; in this sense colour is the special object of sight, sound of
hearing, flavour of taste. Touch, indeed, discriminates more than one set of different qualities. Each sense has
one kind of object which it discerns, and never errs in reporting that what is before it is colour or sound
(though it may err as to what it is that is coloured or where that is, or what it is that is sounding or where that
is.) Such objects are what we propose to call the special objects of this or that sense.

'Common sensibles' are movement, rest, number, figure, magnitude; these are not peculiar to any one sense,
but are common to all. There are at any rate certain kinds of movement which are perceptible both by touch
and by sight.

We speak of an incidental object of sense where e.g. the white object which we see is the son of Diares; here
because 'being the son of Diares' is incidental to the directly visible white patch we speak of the son of Diares
as being (incidentally) perceived or seen by us. Because this is only incidentally an object of sense, it in no
way as such affects the senses. Of the two former kinds, both of which are in their own nature perceptible by
sense, the first kind-that of special objects of the several senses-constitute the objects of sense in the strictest
sense of the term and it is to them that in the nature of things the structure of each several sense is adapted.

The object of sight is the visible, and what is visible is (a) colour and (b) a certain kind of object which can be
described in words but which has no single name; what we mean by (b) will be abundantly clear as we
proceed. Whatever is visible is colour and colour is what lies upon what is in its own nature visible; 'in its
own nature' here means not that visibility is involved in the definition of what thus underlies colour, but that
that substratum contains in itself the cause of visibility. Every colour has in it the power to set in movement
what is actually transparent; that power constitutes its very nature. That is why it is not visible except with the
help of light; it is only in light that the colour of a thing is seen. Hence our first task is to explain what light
is.

Now there clearly is something which is transparent, and by 'transparent' I mean what is visible, and yet not
visible in itself, but rather owing its visibility to the colour of something else; of this character are air, water,
and many solid bodies. Neither air nor water is transparent because it is air or water; they are transparent
because each of them has contained in it a certain substance which is the same in both and is also found in the
eternal body which constitutes the uppermost shell of the physical Cosmos. Of this substance light is the
activity-the activity of what is transparent so far forth as it has in it the determinate power of becoming

Book II 20

ON THE SOUL

transparent; where this power is present, there is also the potentiality of the contrary, viz. darkness. Light is as
it were the proper colour of what is transparent, and exists whenever the potentially transparent is excited to
actuality by the influence of fire or something resembling 'the uppermost body'; for fire too contains
something which is one and the same with the substance in question.

We have now explained what the transparent is and what light is; light is neither fire nor any kind whatsoever
of body nor an efflux from any kind of body (if it were, it would again itself be a kind of body)-it is the
presence of fire or something resembling fire in what is transparent. It is certainly not a body, for two bodies
cannot be present in the same place. The opposite of light is darkness; darkness is the absence from what is
transparent of the corresponding positive state above characterized; clearly therefore, light is just the presence
of that.

Empedocles (and with him all others who used the same forms of expression) was wrong in speaking of light
as 'travelling' or being at a given moment between the earth and its envelope, its movement being
unobservable by us; that view is contrary both to the clear evidence of argument and to the observed facts; if
the distance traversed were short, the movement might have been unobservable, but where the distance is
from extreme East to extreme West, the draught upon our powers of belief is too great.

What is capable of taking on colour is what in itself is colourless, as what can take on sound is what is
soundless; what is colourless includes (a) what is transparent and (b) what is invisible or scarcely visible, i.e.
what is 'dark'. The latter (b) is the same as what is transparent, when it is potentially, not of course when it is
actually transparent; it is the same substance which is now darkness, now light.

Not everything that is visible depends upon light for its visibility. This is only true of the 'proper' colour of
things. Some objects of sight which in light are invisible, in darkness stimulate the sense; that is, things that
appear fiery or shining. This class of objects has no simple common name, but instances of it are fungi, flesh,
heads, scales, and eyes of fish. In none of these is what is seen their own proper' colour. Why we see these at
all is another question. At present what is obvious is that what is seen in light is always colour. That is why
without the help of light colour remains invisible. Its being colour at all means precisely its having in it the
power to set in movement what is already actually transparent, and, as we have seen, the actuality of what is
transparent is just light.

The following experiment makes the necessity of a medium clear. If what has colour is placed in immediate
contact with the eye, it cannot be seen. Colour sets in movement not the sense organ but what is transparent,
e.g. the air, and that, extending continuously from the object to the organ, sets the latter in movement.
Democritus misrepresents the facts when he expresses the opinion that if the interspace were empty one could
distinctly see an ant on the vault of the sky; that is an impossibility. Seeing is due to an affection or change of
what has the perceptive faculty, and it cannot be affected by the seen colour itself; it remains that it must be
affected by what comes between. Hence it is indispensable that there be something in between-if there were
nothing, so far from seeing with greater distinctness, we should see nothing at all.

We have now explained the cause why colour cannot be seen otherwise than in light. Fire on the other hand is
seen both in darkness and in light; this double possibility follows necessarily from our theory, for it is just fire
that makes what is potentially transparent actually transparent.

The same account holds also of sound and smell; if the object of either of these senses is in immediate contact
with the organ no sensation is produced. In both cases the object sets in movement only what lies between,
and this in turn sets the organ in movement: if what sounds or smells is brought into immediate contact with
the organ, no sensation will be produced. The same, in spite of all appearances, applies also to touch and
taste; why there is this apparent difference will be clear later. What comes between in the case of sounds is
air; the corresponding medium in the case of smell has no name. But, corresponding to what is transparent in

Book II 21

ON THE SOUL

the case of colour, there is a quality found both in air and water, which serves as a medium for what has
smell-I say 'in water' because animals that live in water as well as those that live on land seem to possess the
sense of smell, and 'in air' because man and all other land animals that breathe, perceive smells only when
they breathe air in. The explanation of this too will be given later.

Now let us, to begin with, make certain distinctions about sound and hearing.

Sound may mean either of two things (a) actual, and (b) potential, sound. There are certain things which, as
we say, 'have no sound', e.g. sponges or wool, others which have, e.g. bronze and in general all things which
are smooth and solid-the latter are said to have a sound because they can make a sound, i.e. can generate
actual sound between themselves and the organ of hearing.

Actual sound requires for its occurrence (i, ii) two such bodies and (iii) a space between them; for it is
generated by an impact. Hence it is impossible for one body only to generate a sound-there must be a body
impinging and a body impinged upon; what sounds does so by striking against something else, and this is
impossible without a movement from place to place.

As we have said, not all bodies can by impact on one another produce sound; impact on wool makes no
sound, while the impact on bronze or any body which is smooth and hollow does. Bronze gives out a sound
when struck because it is smooth; bodies which are hollow owing to reflection repeat the original impact over
and over again, the body originally set in movement being unable to escape from the concavity.

Further, we must remark that sound is heard both in air and in water, though less distinctly in the latter. Yet
neither air nor water is the principal cause of sound. What is required for the production of sound is an impact
of two solids against one another and against the air. The latter condition is satisfied when the air impinged
upon does not retreat before the blow, i.e. is not dissipated by it.

That is why it must be struck with a sudden sharp blow, if it is to sound-the movement of the whip must
outrun the dispersion of the air, just as one might get in a stroke at a heap or whirl of sand as it was traveling
rapidly past.

An echo occurs, when, a mass of air having been unified, bounded, and prevented from dissipation by the
containing walls of a vessel, the air originally struck by the impinging body and set in movement by it
rebounds from this mass of air like a ball from a wall. It is probable that in all generation of sound echo takes
place, though it is frequently only indistinctly heard. What happens here must be analogous to what happens
in the case of light; light is always reflected-otherwise it would not be diffused and outside what was directly
illuminated by the sun there would be blank darkness; but this reflected light is not always strong enough, as
it is when it is reflected from water, bronze, and other smooth bodies, to cast a shadow, which is the
distinguishing mark by which we recognize light.

It is rightly said that an empty space plays the chief part in the production of hearing, for what people mean
by 'the vacuum' is the air, which is what causes hearing, when that air is set in movement as one continuous
mass; but owing to its friability it emits no sound, being dissipated by impinging upon any surface which is
not smooth. When the surface on which it impinges is quite smooth, what is produced by the original impact
is a united mass, a result due to the smoothness of the surface with which the air is in contact at the other end.

What has the power of producing sound is what has the power of setting in movement a single mass of air
which is continuous from the impinging body up to the organ of hearing. The organ of hearing is physically
united with air, and because it is in air, the air inside is moved concurrently with the air outside. Hence

Book II 22

ON THE SOUL

animals do not hear with all parts of their bodies, nor do all parts admit of the entrance of air; for even the
part which can be moved and can sound has not air everywhere in it. Air in itself is, owing to its friability,
quite soundless; only when its dissipation is prevented is its movement sound. The air in the ear is built into a
chamber just to prevent this dissipating movement, in order that the animal may accurately apprehend all
varieties of the movements of the air outside. That is why we hear also in water, viz. because the water cannot
get into the air chamber or even, owing to the spirals, into the outer ear. If this does happen, hearing ceases,
as it also does if the tympanic membrane is damaged, just as sight ceases if the membrane covering the pupil
is damaged. It is also a test of deafness whether the ear does or does not reverberate like a horn; the air inside
the ear has always a movement of its own, but the sound we hear is always the sounding of something else,
not of the organ itself. That is why we say that we hear with what is empty and echoes, viz. because what we
hear with is a chamber which contains a bounded mass of air.

Which is it that 'sounds', the striking body or the struck? Is not the answer 'it is both, but each in a different
way'? Sound is a movement of what can rebound from a smooth surface when struck against it. As we have
explained' not everything sounds when it strikes or is struck, e.g. if one needle is struck against another,
neither emits any sound. In order, therefore, that sound may be generated, what is struck must be smooth, to
enable the air to rebound and be shaken off from it in one piece.

The distinctions between different sounding bodies show themselves only in actual sound; as without the help
of light colours remain invisible, so without the help of actual sound the distinctions between acute and grave
sounds remain inaudible. Acute and grave are here metaphors, transferred from their proper sphere, viz. that
of touch, where they mean respectively (a) what moves the sense much in a short time, (b) what moves the
sense little in a long time. Not that what is sharp really moves fast, and what is grave, slowly, but that the
difference in the qualities of the one and the other movement is due to their respective speeds. There seems to
be a sort of parallelism between what is acute or grave to hearing and what is sharp or blunt to touch; what is
sharp as it were stabs, while what is blunt pushes, the one producing its effect in a short, the other in a long
time, so that the one is quick, the other slow.

Let the foregoing suffice as an analysis of sound. Voice is a kind of sound characteristic of what has soul in
it; nothing that is without soul utters voice, it being only by a metaphor that we speak of the voice of the flute
or the lyre or generally of what (being without soul) possesses the power of producing a succession of notes
which differ in length and pitch and timbre. The metaphor is based on the fact that all these differences are
found also in voice. Many animals are voiceless, e.g. all non-sanuineous animals and among sanguineous
animals fish. This is just what we should expect, since voice is a certain movement of air. The fish, like those
in the Achelous, which are said to have voice, really make the sounds with their gills or some similar organ.
Voice is the sound made by an animal, and that with a special organ. As we saw, everything that makes a
sound does so by the impact of something (a) against something else, (b) across a space, (c) filled with air;
hence it is only to be expected that no animals utter voice except those which take in air. Once air is
inbreathed, Nature uses it for two different purposes, as the tongue is used both for tasting and for
articulating; in that case of the two functions tasting is necessary for the animal's existence (hence it is found
more widely distributed), while articulate speech is a luxury subserving its possessor's well-being; similarly
in the former case Nature employs the breath both as an indispensable means to the regulation of the inner
temperature of the living body and also as the matter of articulate voice, in the interests of its possessor's
well-being. Why its former use is indispensable must be discussed elsewhere.

The organ of respiration is the windpipe, and the organ to which this is related as means to end is the lungs.
The latter is the part of the body by which the temperature of land animals is raised above that of all others.
But what primarily requires the air drawn in by respiration is not only this but the region surrounding the
heart. That is why when animals breathe the air must penetrate inwards.

Book II 23

ON THE SOUL

Voice then is the impact of the inbreathed air against the 'windpipe', and the agent that produces the impact is
the soul resident in these parts of the body. Not every sound, as we said, made by an animal is voice (even
with the tongue we may merely make a sound which is not voice, or without the tongue as in coughing); what
produces the impact must have soul in it and must be accompanied by an act of imagination, for voice is a
sound with a meaning, and is not merely the result of any impact of the breath as in coughing; in voice the
breath in the windpipe is used as an instrument to knock with against the walls of the windpipe. This is
confirmed by our inability to speak when we are breathing either out or in-we can only do so by holding our
breath; we make the movements with the breath so checked. It is clear also why fish are voiceless; they have
no windpipe. And they have no windpipe because they do not breathe or take in air. Why they do not is a
question belonging to another inquiry.

Smell and its object are much less easy to determine than what we have hitherto discussed; the distinguishing
characteristic of the object of smell is less obvious than those of sound or colour. The ground of this is that
our power of smell is less discriminating and in general inferior to that of many species of animals; men have
a poor sense of smell and our apprehension of its proper objects is inseparably bound up with and so confused
by pleasure and pain, which shows that in us the organ is inaccurate. It is probable that there is a parallel
failure in the perception of colour by animals that have hard eyes: probably they discriminate differences of
colour only by the presence or absence of what excites fear, and that it is thus that human beings distinguish
smells. It seems that there is an analogy between smell and taste, and that the species of tastes run parallel to
those of smells-the only difference being that our sense of taste is more discriminating than our sense of
smell, because the former is a modification of touch, which reaches in man the maximum of discriminative
accuracy. While in respect of all the other senses we fall below many species of animals, in respect of touch
we far excel all other species in exactness of discrimination. That is why man is the most intelligent of all
animals. This is confirmed by the fact that it is to differences in the organ of touch and to nothing else that the
differences between man and man in respect of natural endowment are due; men whose flesh is hard are
ill-endowed by nature, men whose flesh is soft, wellendowed.

As flavours may be divided into (a) sweet, (b) bitter, so with smells. In some things the flavour and the smell
have the same quality, i.e. both are sweet or both bitter, in others they diverge. Similarly a smell, like a
flavour, may be pungent, astringent, acid, or succulent. But, as we said, because smells are much less easy to
discriminate than flavours, the names of these varieties are applied to smells only metaphorically; for
example 'sweet' is extended from the taste to the smell of saffron or honey, 'pungent' to that of thyme, and so
on.

In the same sense in which hearing has for its object both the audible and the inaudible, sight both the visible
and the invisible, smell has for its object both the odorous and the inodorous. 'Inodorous' may be either (a)
what has no smell at all, or (b) what has a small or feeble smell. The same ambiguity lurks in the word
'tasteless'.

Smelling, like the operation of the senses previously examined, takes place through a medium, i.e. through air
or water-I add water, because water-animals too (both sanguineous and non-sanguineous) seem to smell just
as much as land-animals; at any rate some of them make directly for their food from a distance if it has any
scent. That is why the following facts constitute a problem for us. All animals smell in the same way, but
man smells only when he inhales; if he exhales or holds his breath, he ceases to smell, no difference being
made whether the odorous object is distant or near, or even placed inside the nose and actually on the wall of
the nostril; it is a disability common to all the senses not to perceive what is in immediate contact with the
organ of sense, but our failure to apprehend what is odorous without the help of inhalation is peculiar (the
fact is obvious on making the experiment). Now since bloodless animals do not breathe, they must, it might
be argued, have some novel sense not reckoned among the usual five. Our reply must be that this is

Book II 24

ON THE SOUL

impossible, since it is scent that is perceived; a sense that apprehends what is odorous and what has a good or
bad odour cannot be anything but smell. Further, they are observed to be deleteriously effected by the same
strong odours as man is, e.g. bitumen, sulphur, and the like. These animals must be able to smell without
being able to breathe. The probable explanation is that in man the organ of smell has a certain superiority
over that in all other animals just as his eyes have over those of hard-eyed animals. Man's eyes have in the
eyelids a kind of shelter or envelope, which must be shifted or drawn back in order that we may see, while
hardeyed animals have nothing of the kind, but at once see whatever presents itself in the transparent
medium. Similarly in certain species of animals the organ of smell is like the eye of hard-eyed animals,
uncurtained, while in others which take in air it probably has a curtain over it, which is drawn back in
inhalation, owing to the dilating of the veins or pores. That explains also why such animals cannot smell
under water; to smell they must first inhale, and that they cannot do under water.

Smells come from what is dry as flavours from what is moist. Consequently the organ of smell is potentially
dry.

What can be tasted is always something that can be touched, and just for that reason it cannot be perceived
through an interposed foreign body, for touch means the absence of any intervening body. Further, the
flavoured and tasteable body is suspended in a liquid matter, and this is tangible. Hence, if we lived in water,
we should perceive a sweet object introduced into the water, but the water would not be the medium through
which we perceived; our perception would be due to the solution of the sweet substance in what we imbibed,
just as if it were mixed with some drink. There is no parallel here to the perception of colour, which is due
neither to any blending of anything with anything, nor to any efflux of anything from anything. In the case of
taste, there is nothing corresponding to the medium in the case of the senses previously discussed; but as the
object of sight is colour, so the object of taste is flavour. But nothing excites a perception of flavour without
the help of liquid; what acts upon the sense of taste must be either actually or potentially liquid like what is
saline; it must be both (a) itself easily dissolved, and (b) capable of dissolving along with itself the tongue.
Taste apprehends both (a) what has taste and (b) what has no taste, if we mean by (b) what has only a slight
or feeble flavour or what tends to destroy the sense of taste. In this it is exactly parallel to sight, which
apprehends both what is visible and what is invisible (for darkness is invisible and yet is discriminated by
sight; so is, in a different way, what is over brilliant), and to hearing, which apprehends both sound and
silence, of which the one is audible and the other inaudible, and also over-loud sound. This corresponds in
the case of hearing to over-bright light in the case of sight. As a faint sound is 'inaudible', so in a sense is a
loud or violent sound. The word 'invisible' and similar privative terms cover not only (a) what is simply
without some power, but also (b) what is adapted by nature to have it but has not it or has it only in a very
low degree, as when we say that a species of swallow is 'footless' or that a variety of fruit is 'stoneless'. So too
taste has as its object both what can be tasted and the tasteless-the latter in the sense of what has little flavour
or a bad flavour or one destructive of taste. The difference between what is tasteless and what is not seems to
rest ultimately on that between what is drinkable and what is undrinkable both are tasteable, but the latter is
bad and tends to destroy taste, while the former is the normal stimulus of taste. What is drinkable is the
common object of both touch and taste.

Since what can be tasted is liquid, the organ for its perception cannot be either (a) actually liquid or (b)
incapable of becoming liquid. Tasting means a being affected by what can be tasted as such; hence the organ
of taste must be liquefied, and so to start with must be non-liquid but capable of liquefaction without loss of
its distinctive nature. This is confirmed by the fact that the tongue cannot taste either when it is too dry or
when it is too moist; in the latter case what occurs is due to a contact with the pre-existent moisture in the
tongue itself, when after a foretaste of some strong flavour we try to taste another flavour; it is in this way
that sick persons find everything they taste bitter, viz. because, when they taste, their tongues are overflowing
with bitter moisture.

Book II 25

ON THE SOUL

The species of flavour are, as in the case of colour, (a) simple, i.e. the two contraries, the sweet and the bitter,
(b) secondary, viz. (i) on the side of the sweet, the succulent, (ii) on the side of the bitter, the saline, (iii)
between these come the pungent, the harsh, the astringent, and the acid; these pretty well exhaust the varieties
of flavour. It follows that what has the power of tasting is what is potentially of that kind, and that what is
tasteable is what has the power of making it actually what it itself already is.

Whatever can be said of what is tangible, can be said of touch, and vice versa; if touch is not a single sense
but a group of senses, there must be several kinds of what is tangible. It is a problem whether touch is a single
sense or a group of senses. It is also a problem, what is the organ of touch; is it or is it not the flesh (including
what in certain animals is homologous with flesh)? On the second view, flesh is 'the medium' of touch, the
real organ being situated farther inward. The problem arises because the field of each sense is according to
the accepted view determined as the range between a single pair of contraries, white and black for sight, acute
and grave for hearing, bitter and sweet for taste; but in the field of what is tangible we find several such pairs,
hot cold, dry moist, hard soft, This problem finds a partial solution, when it is recalled that in the case of the
other senses more than one pair of contraries are to be met with, e.g. in sound not only acute and grave but
loud and soft, smooth and rough, there are similar contrasts in the field of colour. Nevertheless we are unable
clearly to detect in the case of touch what the single subject is which underlies the contrasted qualities and
corresponds to sound in the case of hearing.

To the question whether the organ of touch lies inward or not (i.e. whether we need look any farther than the
flesh), no indication in favour of the second answer can be drawn from the fact that if the object comes into
contact with the flesh it is at once perceived. For even under present conditions if the experiment is made of
making a web and stretching it tight over the flesh, as soon as this web is touched the sensation is reported in
the same manner as before, yet it is clear that the or is gan is not in this membrane. If the membrane could be
grown on to the flesh, the report would travel still quicker. The flesh plays in touch very much the same part
as would be played in the other senses by an air-envelope growing round our body; had we such an envelope
attached to us we should have supposed that it was by a single organ that we perceived sounds, colours, and
smells, and we should have taken sight, hearing, and smell to be a single sense. But as it is, because that
through which the different movements are transmitted is not naturally attached to our bodies, the difference
of the various sense-organs is too plain to miss. But in the case of touch the obscurity remains.

There must be such a naturally attached 'medium' as flesh, for no living body could be constructed of air or
water; it must be something solid. Consequently it must be composed of earth along with these, which is just
what flesh and its analogue in animals which have no true flesh tend to be. Hence of necessity the medium
through which are transmitted the manifoldly contrasted tactual qualities must be a body naturally attached to
the organism. That they are manifold is clear when we consider touching with the tongue; we apprehend at
the tongue all tangible qualities as well as flavour. Suppose all the rest of our flesh was, like the tongue,
sensitive to flavour, we should have identified the sense of taste and the sense of touch; what saves us from
this identification is the fact that touch and taste are not always found together in the same part of the body.
The following problem might be raised. Let us assume that every body has depth, i.e. has three dimensions,
and that if two bodies have a third body between them they cannot be in contact with one another; let us
remember that what is liquid is a body and must be or contain water, and that if two bodies touch one another
under water, their touching surfaces cannot be dry, but must have water between, viz. the water which wets
their bounding surfaces; from all this it follows that in water two bodies cannot be in contact with one
another. The same holds of two bodies in air-air being to bodies in air precisely what water is to bodies in
water-but the facts are not so evident to our observation, because we live in air, just as animals that live in
water would not notice that the things which touch one another in water have wet surfaces. The problem,
then, is: does the perception of all objects of sense take place in the same way, or does it not, e.g. taste and
touch requiring contact (as they are commonly thought to do), while all other senses perceive over a distance?

Book II 26

ON THE SOUL

The distinction is unsound; we perceive what is hard or soft, as well as the objects of hearing, sight, and
smell, through a 'medium', only that the latter are perceived over a greater distance than the former; that is
why the facts escape our notice. For we do perceive everything through a medium; but in these cases the fact
escapes us. Yet, to repeat what we said before, if the medium for touch were a membrane separating us from
the object without our observing its existence, we should be relatively to it in the same condition as we are
now to air or water in which we are immersed; in their case we fancy we can touch objects, nothing coming
in between us and them. But there remains this difference between what can be touched and what can be seen
or can sound; in the latter two cases we perceive because the medium produces a certain effect upon us,
whereas in the perception of objects of touch we are affected not by but along with the medium; it is as if a
man were struck through his shield, where the shock is not first given to the shield and passed on to the man,
but the concussion of both is simultaneous.

In general, flesh and the tongue are related to the real organs of touch and taste, as air and water are to those
of sight, hearing, and smell. Hence in neither the one case nor the other can there be any perception of an
object if it is placed immediately upon the organ, e.g. if a white object is placed on the surface of the eye.
This again shows that what has the power of perceiving the tangible is seated inside. Only so would there be a
complete analogy with all the other senses. In their case if you place the object on the organ it is not
perceived, here if you place it on the flesh it is perceived; therefore flesh is not the organ but the medium of
touch.

What can be touched are distinctive qualities of body as body; by such differences I mean those which
characterize the elements, viz, hot cold, dry moist, of which we have spoken earlier in our treatise on the
elements. The organ for the perception of these is that of touch-that part of the body in which primarily the
sense of touch resides. This is that part which is potentially such as its object is actually: for all
sense-perception is a process of being so affected; so that that which makes something such as it itself
actually is makes the other such because the other is already potentially such. That is why when an object of
touch is equally hot and cold or hard and soft we cannot perceive; what we perceive must have a degree of
the sensible quality lying beyond the neutral point. This implies that the sense itself is a 'mean' between any
two opposite qualities which determine the field of that sense. It is to this that it owes its power of discerning
the objects in that field. What is 'in the middle' is fitted to discern; relatively to either extreme it can put itself
in the place of the other. As what is to perceive both white and black must, to begin with, be actually neither
but potentially either (and so with all the other sense-organs), so the organ of touch must be neither hot nor
cold.

Further, as in a sense sight had for its object both what was visible and what was invisible (and there was a
parallel truth about all the other senses discussed), so touch has for its object both what is tangible and what
is intangible. Here by 'intangible' is meant (a) what like air possesses some quality of tangible things in a very
slight degree and (b) what possesses it in an excessive degree, as destructive things do.

We have now given an outline account of each of the several senses.

The following results applying to any and every sense may now be formulated.

(A) By a 'sense' is meant what has the power of receiving into itself the sensible forms of things without the
matter. This must be conceived of as taking place in the way in which a piece of wax takes on the impress of
a signet-ring without the iron or gold; we say that what produces the impression is a signet of bronze or gold,
but its particular metallic constitution makes no difference: in a similar way the sense is affected by what is
coloured or flavoured or sounding, but it is indifferent what in each case the substance is; what alone matters
is what quality it has, i.e. in what ratio its constituents are combined.

Book II 27

ON THE SOUL

(B) By 'an organ of sense' is meant that in which ultimately such a power is seated.

The sense and its organ are the same in fact, but their essence is not the same. What perceives is, of course, a
spatial magnitude, but we must not admit that either the having the power to perceive or the sense itself is a
magnitude; what they are is a certain ratio or power in a magnitude. This enables us to explain why objects of
sense which possess one of two opposite sensible qualities in a degree largely in excess of the other opposite
destroy the organs of sense; if the movement set up by an object is too strong for the organ, the equipoise of
contrary qualities in the organ, which just is its sensory power, is disturbed; it is precisely as concord and
tone are destroyed by too violently twanging the strings of a lyre. This explains also why plants cannot
perceive, in spite of their having a portion of soul in them and obviously being affected by tangible objects
themselves; for undoubtedly their temperature can be lowered or raised. The explanation is that they have no
mean of contrary qualities, and so no principle in them capable of taking on the forms of sensible objects
without their matter; in the case of plants the affection is an affection by form-and-matter together. The
problem might be raised: Can what cannot smell be said to be affected by smells or what cannot see by
colours, and so on? It might be said that a smell is just what can be smelt, and if it produces any effect it can
only be so as to make something smell it, and it might be argued that what cannot smell cannot be affected by
smells and further that what can smell can be affected by it only in so far as it has in it the power to smell
(similarly with the proper objects of all the other senses). Indeed that this is so is made quite evident as
follows. Light or darkness, sounds and smells leave bodies quite unaffected; what does affect bodies is not
these but the bodies which are their vehicles, e.g. what splits the trunk of a tree is not the sound of the thunder
but the air which accompanies thunder. Yes, but, it may be objected, bodies are affected by what is tangible
and by flavours. If not, by what are things that are without soul affected, i.e. altered in quality? Must we not,
then, admit that the objects of the other senses also may affect them? Is not the true account this, that all
bodies are capable of being affected by smells and sounds, but that some on being acted upon, having no
boundaries of their own, disintegrate, as in the instance of air, which does become odorous, showing that
some effect is produced on it by what is odorous? But smelling is more than such an affection by what is
odorous-what more? Is not the answer that, while the air owing to the momentary duration of the action upon
it of what is odorous does itself become perceptible to the sense of smell, smelling is an observing of the
result produced?

Book III

THAT there is no sixth sense in addition to the five enumerated-sight, hearing, smell, taste, touch-may be
established by the following considerations:

If we have actually sensation of everything of which touch can give us sensation (for all the qualities of the
tangible qua tangible are perceived by us through touch); and if absence of a sense necessarily involves
absence of a sense-organ; and if (1) all objects that we perceive by immediate contact with them are
perceptible by touch, which sense we actually possess, and (2) all objects that we perceive through media, i.e.
without immediate contact, are perceptible by or through the simple elements, e.g. air and water (and this is
so arranged that (a) if more than one kind of sensible object is perceivable through a single medium, the
possessor of a sense-organ homogeneous with that medium has the power of perceiving both kinds of
objects; for example, if the sense-organ is made of air, and air is a medium both for sound and for colour;
and that (b) if more than one medium can transmit the same kind of sensible objects, as e.g. water as well as
air can transmit colour, both being transparent, then the possessor of either alone will be able to perceive the
kind of objects transmissible through both); and if of the simple elements two only, air and water, go to form
sense-organs (for the pupil is made of water, the organ of hearing is made of air, and the organ of smell of
one or other of these two, while fire is found either in none or in all-warmth being an essential condition of

Book III 28

ON THE SOUL

all sensibility-and earth either in none or, if anywhere, specially mingled with the components of the organ
of touch; wherefore it would remain that there can be no sense-organ formed of anything except water and
air); and if these sense-organs are actually found in certain animals ;-then all the possible senses are
possessed by those animals that are not imperfect or mutilated (for even the mole is observed to have eyes
beneath its skin); so that, if there is no fifth element and no property other than those which belong to the four
elements of our world, no sense can be wanting to such animals.

Further, there cannot be a special sense-organ for the common sensibles either, i.e. the objects which we
perceive incidentally through this or that special sense, e.g. movement, rest, figure, magnitude, number,
unity; for all these we perceive by movement, e.g. magnitude by movement, and therefore also figure (for
figure is a species of magnitude), what is at rest by the absence of movement: number is perceived by the
negation of continuity, and by the special sensibles; for each sense perceives one class of sensible objects. So
that it is clearly impossible that there should be a special sense for any one of the common sensibles, e.g.
movement; for, if that were so, our perception of it would be exactly parallel to our present perception of
what is sweet by vision. That is so because we have a sense for each of the two qualities, in virtue of which
when they happen to meet in one sensible object we are aware of both contemporaneously. If it were not like
this our perception of the common qualities would always be incidental, i.e. as is the perception of Cleon's
son, where we perceive him not as Cleon's son but as white, and the white thing which we really perceive
happens to be Cleon's son.

But in the case of the common sensibles there is already in us a general sensibility which enables us to
perceive them directly; there is therefore no special sense required for their perception: if there were, our
perception of them would have been exactly like what has been above described.

The senses perceive each other's special objects incidentally; not because the percipient sense is this or that
special sense, but because all form a unity: this incidental perception takes place whenever sense is directed
at one and the same moment to two disparate qualities in one and the same object, e.g. to the bitterness and
the yellowness of bile, the assertion of the identity of both cannot be the act of either of the senses; hence the
illusion of sense, e.g. the belief that if a thing is yellow it is bile.

It might be asked why we have more senses than one. Is it to prevent a failure to apprehend the common
sensibles, e.g. movement, magnitude, and number, which go along with the special sensibles? Had we no
sense but sight, and that sense no object but white, they would have tended to escape our notice and
everything would have merged for us into an indistinguishable identity because of the concomitance of colour
and magnitude. As it is, the fact that the common sensibles are given in the objects of more than one sense
reveals their distinction from each and all of the special sensibles.

Since it is through sense that we are aware that we are seeing or hearing, it must be either by sight that we are
aware of seeing, or by some sense other than sight. But the sense that gives us this new sensation must
perceive both sight and its object, viz. colour: so that either (1) there will be two senses both percipient of the
same sensible object, or (2) the sense must be percipient of itself. Further, even if the sense which perceives
sight were different from sight, we must either fall into an infinite regress, or we must somewhere assume a
sense which is aware of itself. If so, we ought to do this in the first case.

This presents a difficulty: if to perceive by sight is just to see, and what is seen is colour (or the coloured),
then if we are to see that which sees, that which sees originally must be coloured. It is clear therefore that 'to
perceive by sight' has more than one meaning; for even when we are not seeing, it is by sight that we
discriminate darkness from light, though not in the same way as we distinguish one colour from another.
Further, in a sense even that which sees is coloured; for in each case the sense-organ is capable of receiving

Book III 29

ON THE SOUL

the sensible object without its matter. That is why even when the sensible objects are gone the sensings and
imaginings continue to exist in the sense-organs.

The activity of the sensible object and that of the percipient sense is one and the same activity, and yet the
distinction between their being remains. Take as illustration actual sound and actual hearing: a man may have
hearing and yet not be hearing, and that which has a sound is not always sounding. But when that which can
hear is actively hearing and which can sound is sounding, then the actual hearing and the actual sound are
merged in one (these one might call respectively hearkening and sounding).

If it is true that the movement, both the acting and the being acted upon, is to be found in that which is acted
upon, both the sound and the hearing so far as it is actual must be found in that which has the faculty of
hearing; for it is in the passive factor that the actuality of the active or motive factor is realized; that is why
that which causes movement may be at rest. Now the actuality of that which can sound is just sound or
sounding, and the actuality of that which can hear is hearing or hearkening; 'sound' and 'hearing' are both
ambiguous. The same account applies to the other senses and their objects. For as

the-acting-and-being-acted-upon is to be found in the passive, not in the active factor, so also the actuality
of the sensible object and that of the sensitive subject are both realized in the latter. But while in some cases
each aspect of the total actuality has a distinct name, e.g. sounding and hearkening, in some one or other is
nameless, e.g. the actuality of sight is called seeing, but the actuality of colour has no name: the actuality of
the faculty of taste is called tasting, but the actuality of flavour has no name. Since the actualities of the
sensible object and of the sensitive faculty are one actuality in spite of the difference between their modes of
being, actual hearing and actual sounding appear and disappear from existence at one and the same moment,
and so actual savour and actual tasting, while as potentialities one of them may exist without the other. The
earlier students of nature were mistaken in their view that without sight there was no white or black, without
taste no savour. This statement of theirs is partly true, partly false: 'sense' and 'the sensible object' are
ambiguous terms, i.e. may denote either potentialities or actualities: the statement is true of the latter, false of
the former. This ambiguity they wholly failed to notice.

If voice always implies a concord, and if the voice and the hearing of it are in one sense one and the same,
and if concord always implies a ratio, hearing as well as what is heard must be a ratio. That is why the excess
of either the sharp or the flat destroys the hearing. (So also in the case of savours excess destroys the sense of
taste, and in the case of colours excessive brightness or darkness destroys the sight, and in the case of smell
excess of strength whether in the direction of sweetness or bitterness is destructive.) This shows that the sense
is a ratio.

That is also why the objects of sense are (1) pleasant when the sensible extremes such as acid or sweet or salt
being pure and unmixed are brought into the proper ratio; then they are pleasant: and in general what is
blended is more pleasant than the sharp or the flat alone; or, to touch, that which is capable of being either
warmed or chilled: the sense and the ratio are identical: while (2) in excess the sensible extremes are painful
or destructive.

Each sense then is relative to its particular group of sensible qualities: it is found in a sense-organ as such
and discriminates the differences which exist within that group; e.g. sight discriminates white and black, taste
sweet and bitter, and so in all cases. Since we also discriminate white from sweet, and indeed each sensible
quality from every other, with what do we perceive that they are different? It must be by sense; for what is
before us is sensible objects. (Hence it is also obvious that the flesh cannot be the ultimate sense-organ: if it
were, the discriminating power could not do its work without immediate contact with the object.)

Therefore (1) discrimination between white and sweet cannot be effected by two agencies which remain
separate; both the qualities discriminated must be present to something that is one and single. On any other
supposition even if I perceived sweet and you perceived white, the difference between them would be

Book III 30

ON THE SOUL

apparent. What says that two things are different must be one; for sweet is different from white. Therefore
what asserts this difference must be self-identical, and as what asserts, so also what thinks or perceives. That
it is not possible by means of two agencies which remain separate to discriminate two objects which are
separate, is therefore obvious; and that (it is not possible to do this in separate movements of time may be
seen' if we look at it as follows. For as what asserts the difference between the good and the bad is one and
the same, so also the time at which it asserts the one to be different and the other to be different is not
accidental to the assertion (as it is for instance when I now assert a difference but do not assert that there is
now a difference); it asserts thus-both now and that the objects are different now; the objects therefore must
be present at one and the same moment. Both the discriminating power and the time of its exercise must be
one and undivided.

But, it may be objected, it is impossible that what is self-identical should be moved at me and the same time
with contrary movements in so far as it is undivided, and in an undivided moment of time. For if what is
sweet be the quality perceived, it moves the sense or thought in this determinate way, while what is bitter
moves it in a contrary way, and what is white in a different way. Is it the case then that what discriminates,
though both numerically one and indivisible, is at the same time divided in its being? In one sense, it is what
is divided that perceives two separate objects at once, but in another sense it does so qua undivided; for it is
divisible in its being but spatially and numerically undivided, is not this impossible? For while it is true that
what is self-identical and undivided may be both contraries at once potentially, it cannot be self-identical in
its being-it must lose its unity by being put into activity. It is not possible to be at once white and black, and
therefore it must also be impossible for a thing to be affected at one and the same moment by the forms of
both, assuming it to be the case that sensation and thinking are properly so described.

The answer is that just as what is called a 'point' is, as being at once one and two, properly said to be
divisible, so here, that which discriminates is qua undivided one, and active in a single moment of time, while
so far forth as it is divisible it twice over uses the same dot at one and the same time. So far forth then as it
takes the limit as two' it discriminates two separate objects with what in a sense is divided: while so far as it
takes it as one, it does so with what is one and occupies in its activity a single moment of time.

About the principle in virtue of which we say that animals are percipient, let this discussion suffice.

There are two distinctive peculiarities by reference to which we characterize the soul (1) local movement and
(2) thinking, discriminating, and perceiving. Thinking both speculative and practical is regarded as akin to a
form of perceiving; for in the one as well as the other the soul discriminates and is cognizant of something
which is. Indeed the ancients go so far as to identify thinking and perceiving; e.g. Empedocles says 'For 'tis in
respect of what is present that man's wit is increased', and again 'Whence it befalls them from time to time to
think diverse thoughts', and Homer's phrase 'For suchlike is man's mind' means the same. They all look upon
thinking as a bodily process like perceiving, and hold that like is known as well as perceived by like, as I
explained at the beginning of our discussion. Yet they ought at the same time to have accounted for error
also; for it is more intimately connected with animal existence and the soul continues longer in the state of
error than in that of truth. They cannot escape the dilemma: either (1) whatever seems is true (and there are
some who accept this) or (2) error is contact with the unlike; for that is the opposite of the knowing of like by
like.

But it is a received principle that error as well as knowledge in respect to contraries is one and the same.

That perceiving and practical thinking are not identical is therefore obvious; for the former is universal in the
animal world, the latter is found in only a small division of it. Further, speculative thinking is also distinct
from perceiving-I mean that in which we find Tightness and wrongness-rightness in prudence, knowledge,

Book III 31

ON THE SOUL

true opinion, wrongness in their opposites; for perception of the special objects of sense is always free from
error, and is found in all animals, while it is possible to think falsely as well as truly, and thought is found
only where there is discourse of reason as well as sensibility. For imagination is different from either
perceiving or discursive thinking, though it is not found without sensation, or judgement without it. That this
activity is not the same kind of thinking as judgement is obvious. For imagining lies within our own power
whenever we wish (e.g. we can call up a picture, as in the practice of mnemonics by the use of mental
images), but in forming opinions we are not free: we cannot escape the alternative of falsehood or truth.
Further, when we think something to be fearful or threatening, emotion is immediately produced, and so too
with what is encouraging; but when we merely imagine we remain as unaffected as persons who are looking
at a painting of some dreadful or encouraging scene. Again within the field of judgement itself we find
varieties, knowledge, opinion, prudence, and their opposites; of the differences between these I must speak
elsewhere.

Thinking is different from perceiving and is held to be in part imagination, in part judgement: we must
therefore first mark off the sphere of imagination and then speak of judgement. If then imagination is that in
virtue of which an image arises for us, excluding metaphorical uses of the term, is it a single faculty or
disposition relative to images, in virtue of which we discriminate and are either in error or not? The faculties
in virtue of which we do this are sense, opinion, science, intelligence.

That imagination is not sense is clear from the following considerations: Sense is either a faculty or an
activity, e.g. sight or seeing: imagination takes place in the absence of both, as e.g. in dreams. (Again, sense
is always present, imagination not. If actual imagination and actual sensation were the same, imagination
would be found in all the brutes: this is held not to be the case; e.g. it is not found in ants or bees or grubs.
(Again, sensations are always true, imaginations are for the most part false. (Once more, even in ordinary
speech, we do not, when sense functions precisely with regard to its object, say that we imagine it to be a
man, but rather when there is some failure of accuracy in its exercise. And as we were saying before, visions
appear to us even when our eyes are shut. Neither is imagination any of the things that are never in error: e.g.
knowledge or intelligence; for imagination may be false.

It remains therefore to see if it is opinion, for opinion may be either true or false.

But opinion involves belief (for without belief in what we opine we cannot have an opinion), and in the
brutes though we often find imagination we never find belief. Further, every opinion is accompanied by
belief, belief by conviction, and conviction by discourse of reason: while there are some of the brutes in
which we find imagination, without discourse of reason. It is clear then that imagination cannot, again, be (1)
opinion plus sensation, or (2) opinion mediated by sensation, or (3) a blend of opinion and sensation; this is
impossible both for these reasons and because the content of the supposed opinion cannot be different from
that of the sensation (I mean that imagination must be the blending of the perception of white with the
opinion that it is white: it could scarcely be a blend of the opinion that it is good with the perception that it is
white): to imagine is therefore (on this view) identical with the thinking of exactly the same as what one in
the strictest sense perceives. But what we imagine is sometimes false though our contemporaneous judgement
about it is true; e.g. we imagine the sun to be a foot in diameter though we are convinced that it is larger than
the inhabited part of the earth, and the following dilemma presents itself. Either (a while the fact has not
changed and the (observer has neither forgotten nor lost belief in the true opinion which he had, that opinion
has disappeared, or (b) if he retains it then his opinion is at once true and false. A true opinion, however,
becomes false only when the fact alters without being noticed.

Imagination is therefore neither any one of the states enumerated, nor compounded out of them.

But since when one thing has been set in motion another thing may be moved by it, and imagination is held to
be a movement and to be impossible without sensation, i.e. to occur in beings that are percipient and to have

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ON THE SOUL

for its content what can be perceived, and since movement may be produced by actual sensation and that
movement is necessarily similar in character to the sensation itself, this movement must be (1) necessarily (a)
incapable of existing apart from sensation, (b) incapable of existing except when we perceive, (such that in
virtue of its possession that in which it is found may present various phenomena both active and passive, and
(such that it may be either true or false.

The reason of the last characteristic is as follows. Perception (1) of the special objects of sense is never in
error or admits the least possible amount of falsehood. (2) That of the concomitance of the objects
concomitant with the sensible qualities comes next: in this case certainly we may be deceived; for while the
perception that there is white before us cannot be false, the perception that what is white is this or that may be
false. (3) Third comes the perception of the universal attributes which accompany the concomitant objects to
which the special sensibles attach (I mean e.g. of movement and magnitude); it is in respect of these that the
greatest amount of sense-illusion is possible.

The motion which is due to the activity of sense in these three modes of its exercise will differ from the
activity of sense; (1) the first kind of derived motion is free from error while the sensation is present; (2) and
(3) the others may be erroneous whether it is present or absent, especially when the object of perception is far
off. If then imagination presents no other features than those enumerated and is what we have described, then
imagination must be a movement resulting from an actual exercise of a power of sense.

As sight is the most highly developed sense, the name Phantasia (imagination) has been formed from Phaos
(light) because it is not possible to see without light.

And because imaginations remain in the organs of sense and resemble sensations, animals in their actions are
largely guided by them, some (i.e. the brutes) because of the non-existence in them of mind, others (i.e. men)
because of the temporary eclipse in them of mind by feeling or disease or sleep.

About imagination, what it is and why it exists, let so much suffice.

Turning now to the part of the soul with which the soul knows and thinks (whether this is separable from the
others in definition only, or spatially as well) we have to inquire (1) what differentiates this part, and (2) how
thinking can take place.

If thinking is like perceiving, it must be either a process in which the soul is acted upon by what is capable of
being thought, or a process different from but analogous to that. The thinking part of the soul must therefore
be, while impassible, capable of receiving the form of an object; that is, must be potentially identical in
character with its object without being the object. Mind must be related to what is thinkable, as sense is to
what is sensible.

Therefore, since everything is a possible object of thought, mind in order, as Anaxagoras says, to dominate,
that is, to know, must be pure from all admixture; for the co-presence of what is alien to its nature is a
hindrance and a block: it follows that it too, like the sensitive part, can have no nature of its own, other than
that of having a certain capacity. Thus that in the soul which is called mind (by mind I mean that whereby the
soul thinks and judges) is, before it thinks, not actually any real thing. For this reason it cannot reasonably be
regarded as blended with the body: if so, it would acquire some quality, e.g. warmth or cold, or even have an
organ like the sensitive faculty: as it is, it has none. It was a good idea to call the soul 'the place of forms',
though (1) this description holds only of the intellective soul, and (2) even this is the forms only potentially,
not actually.

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ON THE SOUL

Observation of the sense-organs and their employment reveals a distinction between the impassibility of the
sensitive and that of the intellective faculty. After strong stimulation of a sense we are less able to exercise it
than before, as e.g. in the case of a loud sound we cannot hear easily immediately after, or in the case of a
bright colour or a powerful odour we cannot see or smell, but in the case of mind thought about an object that
is highly intelligible renders it more and not less able afterwards to think objects that are less intelligible: the
reason is that while the faculty of sensation is dependent upon the body, mind is separable from it.

Once the mind has become each set of its possible objects, as a man of science has, when this phrase is used
of one who is actually a man of science (this happens when he is now able to exercise the power on his own
initiative), its condition is still one of potentiality, but in a different sense from the potentiality which
preceded the acquisition of knowledge by learning or discovery: the mind too is then able to think itself.

Since we can distinguish between a spatial magnitude and what it is to be such, and between water and what
it is to be water, and so in many other cases (though not in all; for in certain cases the thing and its form are
identical), flesh and what it is to be flesh are discriminated either by different faculties, or by the same faculty
in two different states: for flesh necessarily involves matter and is like what is snub-nosed, a this in a this.
Now it is by means of the sensitive faculty that we discriminate the hot and the cold, i.e. the factors which
combined in a certain ratio constitute flesh: the essential character of flesh is apprehended by something
different either wholly separate from the sensitive faculty or related to it as a bent line to the same line when
it has been straightened out.

Again in the case of abstract objects what is straight is analogous to what is snub-nosed; for it necessarily
implies a continuum as its matter: its constitutive essence is different, if we may distinguish between
straightness and what is straight: let us take it to be two-ness. It must be apprehended, therefore, by a
different power or by the same power in a different state. To sum up, in so far as the realities it knows are
capable of being separated from their matter, so it is also with the powers of mind.

The problem might be suggested: if thinking is a passive affection, then if mind is simple and impassible and
has nothing in common with anything else, as Anaxagoras says, how can it come to think at all? For
interaction between two factors is held to require a precedent community of nature between the factors. Again
it might be asked, is mind a possible object of thought to itself? For if mind is thinkable per se and what is
thinkable is in kind one and the same, then either (a) mind will belong to everything, or (b) mind will contain
some element common to it with all other realities which makes them all thinkable.

(1) Have not we already disposed of the difficulty about interaction involving a common element, when we
said that mind is in a sense potentially whatever is thinkable, though actually it is nothing until it has thought?
What it thinks must be in it just as characters may be said to be on a writingtablet on which as yet nothing
actually stands written: this is exactly what happens with mind.

(Mind is itself thinkable in exactly the same way as its objects are. For (a) in the case of objects which
involve no matter, what thinks and what is thought are identical; for speculative knowledge and its object are
identical. (Why mind is not always thinking we must consider later.) (b) In the case of those which contain
matter each of the objects of thought is only potentially present. It follows that while they will not have mind
in them (for mind is a potentiality of them only in so far as they are capable of being disengaged from matter)
mind may yet be thinkable.

Since in every class of things, as in nature as a whole, we find two factors involved, (1) a matter which is
potentially all the particulars included in the class, (2) a cause which is productive in the sense that it makes
them all (the latter standing to the former, as e.g. an art to its material), these distinct elements must likewise

Book III 34

ON THE SOUL

be found within the soul.

And in fact mind as we have described it is what it is what it is by virtue of becoming all things, while there
is another which is what it is by virtue of making all things: this is a sort of positive state like light; for in a
sense light makes potential colours into actual colours.

Mind in this sense of it is separable, impassible, unmixed, since it is in its essential nature activity (for always
the active is superior to the passive factor, the originating force to the matter which it forms).

Actual knowledge is identical with its object: in the individual, potential knowledge is in time prior to actual
knowledge, but in the universe as a whole it is not prior even in time. Mind is not at one time knowing and at
another not. When mind is set free from its present conditions it appears as just what it is and nothing more:
this alone is immortal and eternal (we do not, however, remember its former activity because, while mind in
this sense is impassible, mind as passive is destructible), and without it nothing thinks.

The thinking then of the simple objects of thought is found in those cases where falsehood is impossible:
where the alternative of true or false applies, there we always find a putting together of objects of thought in a
quasi-unity. As Empedocles said that 'where heads of many a creature sprouted without necks' they
afterwards by Love's power were combined, so here too objects of thought which were given separate are
combined, e.g. 'incommensurate' and 'diagonal': if the combination be of objects past or future the
combination of thought includes in its content the date. For falsehood always involves a synthesis; for even if
you assert that what is white is not white you have included not white in a synthesis. It is possible also to call
all these cases division as well as combination. However that may be, there is not only the true or false
assertion that Cleon is white but also the true or false assertion that he was or will he white. In each and every
case that which unifies is mind.

Since the word 'simple' has two senses, i.e. may mean either (a) 'not capable of being divided' or (b) 'not
actually divided', there is nothing to prevent mind from knowing what is undivided, e.g. when it apprehends a
length (which is actually undivided) and that in an undivided time; for the time is divided or undivided in the
same manner as the line. It is not possible, then, to tell what part of the line it was apprehending in each half
of the time: the object has no actual parts until it has been divided: if in thought you think each half
separately, then by the same act you divide the time also, the half-lines becoming as it were new wholes of
length. But if you think it as a whole consisting of these two possible parts, then also you think it in a time
which corresponds to both parts together. (But what is not quantitatively but qualitatively simple is thought in
a simple time and by a simple act of the soul.)

But that which mind thinks and the time in which it thinks are in this case divisible only incidentally and not
as such. For in them too there is something indivisible (though, it may be, not isolable) which gives unity to
the time and the whole of length; and this is found equally in every continuum whether temporal or spatial.

Points and similar instances of things that divide, themselves being indivisible, are realized in consciousness
in the same manner as privations.

A similar account may be given of all other cases, e.g. how evil or black is cognized; they are cognized, in a
sense, by means of their contraries. That which cognizes must have an element of potentiality in its being,
and one of the contraries must be in it. But if there is anything that has no contrary, then it knows itself and is
actually and possesses independent existence.

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ON THE SOUL

Assertion is the saying of something concerning something, e.g. affirmation, and is in every case either true
or false: this is not always the case with mind: the thinking of the definition in the sense of the constitutive
essence is never in error nor is it the assertion of something concerning something, but, just as while the
seeing of the special object of sight can never be in error, the belief that the white object seen is a man may
be mistaken, so too in the case of objects which are without matter.

Actual knowledge is identical with its object: potential knowledge in the individual is in time prior to actual
knowledge but in the universe it has no priority even in time; for all things that come into being arise from
what actually is. In the case of sense clearly the sensitive faculty already was potentially what the object
makes it to be actually; the faculty is not affected or altered. This must therefore be a different kind from
movement; for movement is, as we saw, an activity of what is imperfect, activity in the unqualified sense, i.e.
that of what has been perfected, is different from movement.

To perceive then is like bare asserting or knowing; but when the object is pleasant or painful, the soul makes
a quasi-affirmation or negation, and pursues or avoids the object. To feel pleasure or pain is to act with the
sensitive mean towards what is good or bad as such. Both avoidance and appetite when actual are identical
with this: the faculty of appetite and avoidance are not different, either from one another or from the faculty
of sense-perception; but their being is different.

To the thinking soul images serve as if they were contents of perception (and when it asserts or denies them
to be good or bad it avoids or pursues them). That is why the soul never thinks without an image. The process
is like that in which the air modifies the pupil in this or that way and the pupil transmits the modification to
some third thing (and similarly in hearing), while the ultimate point of arrival is one, a single mean, with
different manners of being.

With what part of itself the soul discriminates sweet from hot I have explained before and must now describe
again as follows: That with which it does so is a sort of unity, but in the way just mentioned, i.e. as a
connecting term. And the two faculties it connects, being one by analogy and numerically, are each to each as
the qualities discerned are to one another (for what difference does it make whether we raise the problem of
discrimination between disparates or between contraries, e.g. white and black?). Let then C be to D as is to B:
it follows alternando that C: A:: D: B. If then C and D belong to one subject, the case will be the same with
them as with and B; and B form a single identity with different modes of being; so too will the former pair.
The same reasoning holds if be sweet and B white.

The faculty of thinking then thinks the forms in the images, and as in the former case what is to be pursued or
avoided is marked out for it, so where there is no sensation and it is engaged upon the images it is moved to
pursuit or avoidance. E.g.. perceiving by sense that the beacon is fire, it recognizes in virtue of the general
faculty of sense that it signifies an enemy, because it sees it moving; but sometimes by means of the images
or thoughts which are within the soul, just as if it were seeing, it calculates and deliberates what is to come by
reference to what is present; and when it makes a pronouncement, as in the case of sensation it pronounces
the object to be pleasant or painful, in this case it avoids or persues and so generally in cases of action.

That too which involves no action, i.e. that which is true or false, is in the same province with what is good or
bad: yet they differ in this, that the one set imply and the other do not a reference to a particular person.

The so-called abstract objects the mind thinks just as, if one had thought of the snubnosed not as snub-nosed
but as hollow, one would have thought of an actuality without the flesh in which it is embodied: it is thus that
the mind when it is thinking the objects of Mathematics thinks as separate elements which do not exist
separate. In every case the mind which is actively thinking is the objects which it thinks. Whether it is

Book III 36

ON THE SOUL

possible for it while not existing separate from spatial conditions to think anything that is separate, or not, we
must consider later.

Let us now summarize our results about soul, and repeat that the soul is in a way all existing things; for
existing things are either sensible or thinkable, and knowledge is in a way what is knowable, and sensation is
in a way what is sensible: in what way we must inquire.

Knowledge and sensation are divided to correspond with the realities, potential knowledge and sensation
answering to potentialities, actual knowledge and sensation to actualities. Within the soul the faculties of
knowledge and sensation are potentially these objects, the one what is knowable, the other what is sensible.
They must be either the things themselves or their forms. The former alternative is of course impossible: it is
not the stone which is present in the soul but its form.

It follows that the soul is analogous to the hand; for as the hand is a tool of tools, so the mind is the form of
forms and sense the form of sensible things.

Since according to common agreement there is nothing outside and separate in existence from sensible spatial
magnitudes, the objects of thought are in the sensible forms, viz. both the abstract objects and all the states
and affections of sensible things. Hence (1) no one can learn or understand anything in the absence of sense,
and (when the mind is actively aware of anything it is necessarily aware of it along with an image; for images
are like sensuous contents except in that they contain no matter.

Imagination is different from assertion and denial; for what is true or false involves a synthesis of concepts.
In what will the primary concepts differ from images? Must we not say that neither these nor even our other
concepts are images, though they necessarily involve them?

The soul of animals is characterized by two faculties, (a) the faculty of discrimination which is the work of
thought and sense, and (b) the faculty of originating local movement. Sense and mind we have now
sufficiently examined. Let us next consider what it is in the soul which originates movement. Is it a single
part of the soul separate either spatially or in definition? Or is it the soul as a whole? If it is a part, is that part
different from those usually distinguished or already mentioned by us, or is it one of them? The problem at
once presents itself, in what sense we are to speak of parts of the soul, or how many we should distinguish.
For in a sense there is an infinity of parts: it is not enough to distinguish, with some thinkers, the calculative,
the passionate, and the desiderative, or with others the rational and the irrational; for if we take the dividing
lines followed by these thinkers we shall find parts far more distinctly separated from one another than these,
namely those we have just mentioned: (1) the nutritive, which belongs both to plants and to all animals, and
(2) the sensitive, which cannot easily be classed as either irrational or rational; further (3) the imaginative,
which is, in its being, different from all, while it is very hard to say with which of the others it is the same or
not the same, supposing we determine to posit separate parts in the soul; and lastly (4) the appetitive, which
would seem to be distinct both in definition and in power from all hitherto enumerated.

It is absurd to break up the last-mentioned faculty: as these thinkers do, for wish is found in the calculative
part and desire and passion in the irrational; and if the soul is tripartite appetite will be found in all three
parts. Turning our attention to the present object of discussion, let us ask what that is which originates local
movement of the animal.

Book III 37

ON THE SOUL

The movement of growth and decay, being found in all living things, must be attributed to the faculty of
reproduction and nutrition, which is common to all: inspiration and expiration, sleep and waking, we must
consider later: these too present much difficulty: at present we must consider local movement, asking what it
is that originates forward movement in the animal.

That it is not the nutritive faculty is obvious; for this kind of movement is always for an end and is
accompanied either by imagination or by appetite; for no animal moves except by compulsion unless it has an
impulse towards or away from an object. Further, if it were the nutritive faculty, even plants would have been
capable of originating such movement and would have possessed the organs necessary to carry it out.
Similarly it cannot be the sensitive faculty either; for there are many animals which have sensibility but
remain fast and immovable throughout their lives.

If then Nature never makes anything without a purpose and never leaves out what is necessary (except in the
case of mutilated or imperfect growths; and that here we have neither mutilation nor imperfection may be
argued from the facts that such animals (a) can reproduce their species and (b) rise to completeness of nature
and decay to an end), it follows that, had they been capable of originating forward movement, they would
have possessed the organs necessary for that purpose. Further, neither can the calculative faculty or what is
called 'mind' be the cause of such movement; for mind as speculative never thinks what is practicable, it
never says anything about an object to be avoided or pursued, while this movement is always in something
which is avoiding or pursuing an object. No, not even when it is aware of such an object does it at once
enjoin pursuit or avoidance of it; e.g. the mind often thinks of something terrifying or pleasant without
enjoining the emotion of fear. It is the heart that is moved (or in the case of a pleasant object some other part).
Further, even when the mind does command and thought bids us pursue or avoid something, sometimes no
movement is produced; we act in accordance with desire, as in the case of moral weakness. And, generally,
we observe that the possessor of medical knowledge is not necessarily healing, which shows that something
else is required to produce action in accordance with knowledge; the knowledge alone is not the cause.
Lastly, appetite too is incompetent to account fully for movement; for those who successfully resist
temptation have appetite and desire and yet follow mind and refuse to enact that for which they have appetite.

These two at all events appear to be sources of movement: appetite and mind (if one may venture to regard
imagination as a kind of thinking; for many men follow their imaginations contrary to knowledge, and in all
animals other than man there is no thinking or calculation but only imagination).

Both of these then are capable of originating local movement, mind and appetite: (1) mind, that is, which
calculates means to an end, i.e. mind practical (it differs from mind speculative in the character of its end);
while (2) appetite is in every form of it relative to an end: for that which is the object of appetite is the
stimulant of mind practical; and that which is last in the process of thinking is the beginning of the action. It
follows that there is a justification for regarding these two as the sources of movement, i.e. appetite and
practical thought; for the object of appetite starts a movement and as a result of that thought gives rise to
movement, the object of appetite being it a source of stimulation. So too when imagination originates
movement, it necessarily involves appetite.

That which moves therefore is a single faculty and the faculty of appetite; for if there had been two sources of
movement-mind and appetite-they would have produced movement in virtue of some common character. As
it is, mind is never found producing movement without appetite (for wish is a form of appetite; and when
movement is produced according to calculation it is also according to wish), but appetite can originate
movement contrary to calculation, for desire is a form of appetite. Now mind is always right, but appetite and
imagination may be either right or wrong. That is why, though in any case it is the object of appetite which
originates movement, this object may be either the real or the apparent good. To produce movement the

Book III 38

ON THE SOUL

object must be more than this: it must be good that can be brought into being by action; and only what can be
otherwise than as it is can thus be brought into being. That then such a power in the soul as has been
described, i.e. that called appetite, originates movement is clear. Those who distinguish parts in the soul, if
they distinguish and divide in accordance with differences of power, find themselves with a very large
number of parts, a nutritive, a sensitive, an intellective, a deliberative, and now an appetitive part; for these
are more different from one another than the faculties of desire and passion.

Since appetites run counter to one another, which happens when a principle of reason and a desire are
contrary and is possible only in beings with a sense of time (for while mind bids us hold back because of
what is future, desire is influenced by what is just at hand: a pleasant object which is just at hand presents
itself as both pleasant and good, without condition in either case, because of want of foresight into what is
farther away in time), it follows that while that which originates movement must be specifically one, viz. the
faculty of appetite as such (or rather farthest back of all the object of that faculty; for it is it that itself
remaining unmoved originates the movement by being apprehended in thought or imagination), the things
that originate movement are numerically many.

All movement involves three factors, (1) that which originates the movement, (2) that by means of which it
originates it, and (3) that which is moved. The expression 'that which originates the movement' is ambiguous:
it may mean either (a) something which itself is unmoved or (b) that which at once moves and is moved. Here
that which moves without itself being moved is the realizable good, that which at once moves and is moved is
the faculty of appetite (for that which is influenced by appetite so far as it is actually so influenced is set in
movement, and appetite in the sense of actual appetite is a kind of movement), while that which is in motion
is the animal. The instrument which appetite employs to produce movement is no longer psychical but
bodily: hence the examination of it falls within the province of the functions common to body and soul. To
state the matter summarily at present, that which is the instrument in the production of movement is to be
found where a beginning and an end coincide as e.g. in a ball and socket joint; for there the convex and the
concave sides are respectively an end and a beginning (that is why while the one remains at rest, the other is
moved): they are separate in definition but not separable spatially. For everything is moved by pushing and
pulling. Hence just as in the case of a wheel, so here there must be a point which remains at rest, and from
that point the movement must originate.

To sum up, then, and repeat what I have said, inasmuch as an animal is capable of appetite it is capable of
self-movement; it is not capable of appetite without possessing imagination; and all imagination is either (1)
calculative or (2) sensitive. In the latter an animals, and not only man, partake.

We must consider also in the case of imperfect animals, sc. those which have no sense but touch, what it is
that in them originates movement. Can they have imagination or not? or desire? Clearly they have feelings of
pleasure and pain, and if they have these they must have desire. But how can they have imagination? Must
not we say that, as their movements are indefinite, they have imagination and desire, but indefinitely?

Sensitive imagination, as we have said, is found in all animals, deliberative imagination only in those that are
calculative: for whether this or that shall be enacted is already a task requiring calculation; and there must be
a single standard to measure by, for that is pursued which is greater. It follows that what acts in this way must
be able to make a unity out of several images.

This is the reason why imagination is held not to involve opinion, in that it does not involve opinion based on
inference, though opinion involves imagination. Hence appetite contains no deliberative element. Sometimes
it overpowers wish and sets it in movement: at times wish acts thus upon appetite, like one sphere imparting
its movement to another, or appetite acts thus upon appetite, i.e. in the condition of moral weakness (though

Book III 39

ON THE SOUL

by nature the higher faculty is always more authoritative and gives rise to movement). Thus three modes of
movement are possible.

The faculty of knowing is never moved but remains at rest. Since the one premiss or judgement is universal
and the other deals with the particular (for the first tells us that such and such a kind of man should do such
and such a kind of act, and the second that this is an act of the kind meant, and I a person of the type
intended), it is the latter opinion that really originates movement, not the universal; or rather it is both, but the
one does so while it remains in a state more like rest, while the other partakes in movement.

The nutritive soul then must be possessed by everything that is alive, and every such thing is endowed with
soul from its birth to its death. For what has been born must grow, reach maturity, and decay-all of which are
impossible without nutrition. Therefore the nutritive faculty must be found in everything that grows and
decays.

But sensation need not be found in all things that live. For it is impossible for touch to belong either (1) to
those whose body is uncompounded or (2) to those which are incapable of taking in the forms without their
matter.

But animals must be endowed with sensation, since Nature does nothing in vain. For all things that exist by
Nature are means to an end, or will be concomitants of means to an end. Every body capable of forward
movement would, if unendowed with sensation, perish and fail to reach its end, which is the aim of Nature;
for how could it obtain nutriment? Stationary living things, it is true, have as their nutriment that from which
they have arisen; but it is not possible that a body which is not stationary but produced by generation should
have a soul and a discerning mind without also having sensation. (Nor yet even if it were not produced by
generation. Why should it not have sensation? Because it were better so either for the body or for the soul?
But clearly it would not be better for either: the absence of sensation will not enable the one to think better or
the other to exist better.) Therefore no body which is not stationary has soul without sensation.

But if a body has sensation, it must be either simple or compound. And simple it cannot be; for then it could
not have touch, which is indispensable. This is clear from what follows. An animal is a body with soul in it:
every body is tangible, i.e. perceptible by touch; hence necessarily, if an animal is to survive, its body must
have tactual sensation. All the other senses, e.g. smell, sight, hearing, apprehend through media; but where
there is immediate contact the animal, if it has no sensation, will be unable to avoid some things and take
others, and so will find it impossible to survive. That is why taste also is a sort of touch; it is relative to
nutriment, which is just tangible body; whereas sound, colour, and odour are innutritious, and further neither
grow nor decay. Hence it is that taste also must be a sort of touch, because it is the sense for what is tangible
and nutritious.

Both these senses, then, are indispensable to the animal, and it is clear that without touch it is impossible for
an animal to be. All the other senses subserve well-being and for that very reason belong not to any and
every kind of animal, but only to some, e.g. those capable of forward movement must have them; for, if they
are to survive, they must perceive not only by immediate contact but also at a distance from the object. This
will be possible if they can perceive through a medium, the medium being affected and moved by the
perceptible object, and the animal by the medium, just as that which produces local movement causes a
change extending to a certain point, and that which gave an impulse causes another to produce a new impulse
so that the movement traverses a medium the first mover impelling without being impelled, the last moved
being impelled without impelling, while the medium (or media, for there are many) is both-so is it also in the
case of alteration, except that the agent produces produces it without the patient's changing its place. Thus if
an object is dipped into wax, the movement goes on until submersion has taken place, and in stone it goes no

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ON THE SOUL

distance at all, while in water the disturbance goes far beyond the object dipped: in air the disturbance is
propagated farthest of all, the air acting and being acted upon, so long as it maintains an unbroken unity. That
is why in the case of reflection it is better, instead of saying that the sight issues from the eye and is reflected,
to say that the air, so long as it remains one, is affected by the shape and colour. On a smooth surface the air
possesses unity; hence it is that it in turn sets the sight in motion, just as if the impression on the wax were
transmitted as far as the wax extends.

It is clear that the body of an animal cannot be simple, i.e. consist of one element such as fire or air. For
without touch it is impossible to have any other sense; for every body that has soul in it must, as we have
said, be capable of touch. All the other elements with the exception of earth can constitute organs of sense,
but all of them bring about perception only through something else, viz. through the media. Touch takes place
by direct contact with its objects, whence also its name. All the other organs of sense, no doubt, perceive by
contact, only the contact is mediate: touch alone perceives by immediate contact. Consequently no animal
body can consist of these other elements.

Nor can it consist solely of earth. For touch is as it were a mean between all tangible qualities, and its organ is
capable of receiving not only all the specific qualities which characterize earth, but also the hot and the cold
and all other tangible qualities whatsoever. That is why we have no sensation by means of bones, hair,
because they consist of earth. So too plants, because they consist of earth, have no sensation. Without touch
there can be no other sense, and the organ of touch cannot consist of earth or of any other single element.

It is evident, therefore, that the loss of this one sense alone must bring about the death of an animal. For as on
the one hand nothing which is not an animal can have this sense, so on the other it is the only one which is
indispensably necessary to what is an animal. This explains, further, the following difference between the
other senses and touch. In the case of all the others excess of intensity in the qualities which they apprehend,
i.e. excess of intensity in colour, sound, and smell, destroys not the but only the organs of the sense (except
incidentally, as when the sound is accompanied by an impact or shock, or where through the objects of sight
or of smell certain other things are set in motion, which destroy by contact); flavour also destroys only in so
far as it is at the same time tangible. But excess of intensity in tangible qualities, e.g. heat, cold, or hardness,
destroys the animal itself. As in the case of every sensible quality excess destroys the organ, so here what is
tangible destroys touch, which is the essential mark of life; for it has been shown that without touch it is
impossible for an animal to be. That is why excess in intensity of tangible qualities destroys not merely the
organ, but the animal itself, because this is the only sense which it must have.

All the other senses are necessary to animals, as we have said, not for their being, but for their well-being.
Such, e.g. is sight, which, since it lives in air or water, or generally in what is pellucid, it must have in order
to see, and taste because of what is pleasant or painful to it, in order that it may perceive these qualities in its
nutriment and so may desire to be set in motion, and hearing that it may have communication made to it, and
a tongue that it may communicate with its fellows.

THE END

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Table of Contents

Topics. 1

Aristotle 1

Book 1 1

Book IL 12

Book III 21

Book IV 28

Book V. 38

Book VI 53

Book VII . 68

Book VIII 73

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Aristotle

translated by W. A. Pickard-Cambridge

• Book I

• Book II

• Book III

• Book IV

• Book V

• Book VI

• Book VII

• Book VIII

• Book IX

• Book X

• Book XI

Book I

OUR treatise proposes to find a line of inquiry whereby we shall be able to reason from opinions that are
generally accepted about every problem propounded to us, and also shall ourselves, when standing up to an
argument, avoid saying anything that will obstruct us. First, then, we must say what reasoning is, and what its
varieties are, in order to grasp dialectical reasoning: for this is the object of our search in the treatise before
us.

Now reasoning is an argument in which, certain things being laid down, something other than these
necessarily comes about through them, (a) It is a 'demonstration', when the premisses from which the
reasoning starts are true and primary, or are such that our knowledge of them has originally come through
premisses which are primary and true: (b) reasoning, on the other hand, is 'dialectical', if it reasons from
opinions that are generally accepted. Things are 'true' and 'primary' which are believed on the strength not of
anything else but of themselves: for in regard to the first principles of science it is improper to ask any further
for the why and wherefore of them; each of the first principles should command belief in and by itself. On the
other hand, those opinions are 'generally accepted' which are accepted by every one or by the majority or by
the philosophers-i.e. by all, or by the majority, or by the most notable and illustrious of them. Again (c),
reasoning is 'contentious' if it starts from opinions that seem to be generally accepted, but are not really such,
or again if it merely seems to reason from opinions that are or seem to be generally accepted. For not every
opinion that seems to be generally accepted actually is generally accepted. For in none of the opinions which
we call generally accepted is the illusion entirely on the surface, as happens in the case of the principles of
contentious arguments; for the nature of the fallacy in these is obvious immediately, and as a rule even to
persons with little power of comprehension. So then, of the contentious reasonings mentioned, the former
really deserves to be called 'reasoning' as well, but the other should be called 'contentious reasoning', but not
'reasoning', since it appears to reason, but does not really do so. Further (d), besides all the reasonings we
have mentioned there are the mis-reasonings that start from the premisses peculiar to the special sciences, as
happens (for example) in the case of geometry and her sister sciences. For this form of reasoning appears to
differ from the reasonings mentioned above; the man who draws a false figure reasons from things that are

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neither true and primary, nor yet generally accepted. For he does not fall within the definition; he does not
assume opinions that are received either by every one or by the majority or by philosophers-that is to say, by
all, or by most, or by the most illustrious of them-but he conducts his reasoning upon assumptions which,
though appropriate to the science in question, are not true; for he effects his mis-reasoning either by
describing the semicircles wrongly or by drawing certain lines in a way in which they could not be drawn.

The foregoing must stand for an outline survey of the species of reasoning. In general, in regard both to all
that we have already discussed and to those which we shall discuss later, we may remark that that amount of
distinction between them may serve, because it is not our purpose to give the exact definition of any of them;
we merely want to describe them in outline; we consider it quite enough from the point of view of the line of
inquiry before us to be able to recognize each of them in some sort of way.

Next in order after the foregoing, we must say for how many and for what purposes the treatise is useful.
They are three-intellectual training, casual encounters, and the philosophical sciences. That it is useful as a
training is obvious on the face of it. The possession of a plan of inquiry will enable us more easily to argue
about the subject proposed. For purposes of casual encounters, it is useful because when we have counted up
the opinions held by most people, we shall meet them on the ground not of other people's convictions but of
their own, while we shift the ground of any argument that they appear to us to state unsoundly. For the study
of the philosophical sciences it is useful, because the ability to raise searching difficulties on both sides of a
subject will make us detect more easily the truth and error about the several points that arise. It has a further
use in relation to the ultimate bases of the principles used in the several sciences. For it is impossible to
discuss them at all from the principles proper to the particular science in hand, seeing that the principles are
the prius of everything else: it is through the opinions generally held on the particular points that these have
to be discussed, and this task belongs properly, or most appropriately, to dialectic: for dialectic is a process of
criticism wherein lies the path to the principles of all inquiries.

We shall be in perfect possession of the way to proceed when we are in a position like that which we occupy
in regard to rhetoric and medicine and faculties of that kind: this means the doing of that which we choose
with the materials that are available. For it is not every method that the rhetorician will employ to persuade,
or the doctor to heal; still, if he omits none of the available means, we shall say that his grasp of the science is
adequate.

First, then, we must see of what parts our inquiry consists. Now if we were to grasp (a) with reference to how
many, and what kind of, things arguments take place, and with what materials they start, and (h) how we are
to become well supplied with these, we should have sufficiently won our goal. Now the materials with which
arguments start are equal in number, and are identical, with the subjects on which reasonings take place. For
arguments start with 'propositions', while the subjects on which reasonings take place are 'problems'. Now
every proposition and every problem indicates either a genus or a peculiarity or an accident-for the
differentia too, applying as it does to a class (or genus), should be ranked together with the genus. Since,
however, of what is peculiar to anything part signifies its essence, while part does not, let us divide the
'peculiar' into both the aforesaid parts, and call that part which indicates the essence a 'definition', while of the
remainder let us adopt the terminology which is generally current about these things, and speak of it as a
'property'. What we have said, then, makes it clear that according to our present division, the elements turn
out to be four, all told, namely either property or definition or genus or accident. Do not let any one suppose
us to mean that each of these enunciated by itself constitutes a proposition or problem, but only that it is from

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these that both problems and propositions are formed. The difference between a problem and a proposition is
a difference in the turn of the phrase. For if it be put in this way, '"An animal that walks on two feet" is the
definition of man, is it not?' or '"Animal" is the genus of man, is it not?' the result is a proposition: but if thus,
'Is "an animal that walks on two feet" a definition of man or no?' [or 'Is "animal" his genus or no?'] the result
is a problem. Similarly too in other cases. Naturally, then, problems and propositions are equal in number: for
out of every proposition you will make a problem if you change the turn of the phrase.

We must now say what are 'definition', 'property', 'genus', and 'accident'. A 'definition' is a phrase signifying a
thing's essence. It is rendered in the form either of a phrase in lieu of a term, or of a phrase in lieu of another
phrase; for it is sometimes possible to define the meaning of a phrase as well. People whose rendering
consists of a term only, try it as they may, clearly do not render the definition of the thing in question,
because a definition is always a phrase of a certain kind. One may, however, use the word 'definitory' also of
such a remark as 'The "becoming" is "beautiful"', and likewise also of the question, Are sensation and
knowledge the same or different?', for argument about definitions is mostly concerned with questions of
sameness and difference. In a word we may call 'definitory' everything that falls under the same branch of
inquiry as definitions; and that all the above-mentioned examples are of this character is clear on the face of
them. For if we are able to argue that two things are the same or are different, we shall be well supplied by
the same turn of argument with lines of attack upon their definitions as well: for when we have shown that
they are not the same we shall have demolished the definition. Observe, please, that the converse of this last
statement does not hold: for to show that they are the same is not enough to establish a definition. To show,
however, that they are not the same is enough of itself to overthrow it.

A 'property' is a predicate which does not indicate the essence of a thing, but yet belongs to that thing alone,
and is predicated convertibly of it. Thus it is a property of man to-be-capable of learning grammar: for if A
be a man, then he is capable of learning grammar, and if he be capable of learning grammar, he is a man. For
no one calls anything a 'property' which may possibly belong to something else, e.g. 'sleep' in the case of
man, even though at a certain time it may happen to belong to him alone. That is to say, if any such thing
were actually to be called a property, it will be called not a 'property' absolutely, but a 'temporary' or a
'relative' property: for 'being on the right hand side' is a temporary property, while 'two-footed' is in point of
fact ascribed as a property in certain relations; e.g. it is a property of man relatively to a horse and a dog. That
nothing which may belong to anything else than A is a convertible predicate of A is clear: for it does not
necessarily follow that if something is asleep it is a man.

A 'genus' is what is predicated in the category of essence of a number of things exhibiting differences in kind.
We should treat as predicates in the category of essence all such things as it would be appropriate to mention
in reply to the question, 'What is the object before you?'; as, for example, in the case of man, if asked that
question, it is appropriate to say 'He is an animal'. The question, 'Is one thing in the same genus as another or
in a different one?' is also a 'generic' question; for a question of that kind as well falls under the same branch
of inquiry as the genus: for having argued that 'animal' is the genus of man, and likewise also of ox, we shall
have argued that they are in the same genus; whereas if we show that it is the genus of the one but not of the
other, we shall have argued that these things are not in the same genus.

An 'accident' is (i) something which, though it is none of the foregoing-i.e. neither a definition nor a property
nor a genus yet belongs to the thing: (something which may possibly either belong or not belong to any one
and the self-same thing, as (e.g.) the 'sitting posture' may belong or not belong to some self-same thing.
Likewise also 'whiteness', for there is nothing to prevent the same thing being at one time white, and at
another not white. Of the definitions of accident the second is the better: for if he adopts the first, any one is
bound, if he is to understand it, to know already what 'definition' and 'genus' and 'property' are, whereas the
second is sufficient of itself to tell us the essential meaning of the term in question. To Accident are to be

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attached also all comparisons of things together, when expressed in language that is drawn in any kind of way
from what happens (accidit) to be true of them; such as, for example, the question, 'Is the honourable or the
expedient preferable?' and 'Is the life of virtue or the life of self-indulgence the pleasanter?', and any other
problem which may happen to be phrased in terms like these. For in all such cases the question is 'to which of
the two does the predicate in question happen (accidit) to belong more closely?' It is clear on the face of it
that there is nothing to prevent an accident from becoming a temporary or relative property. Thus the sitting
posture is an accident, but will be a temporary property, whenever a man is the only person sitting, while if he
be not the only one sitting, it is still a property relatively to those who are not sitting. So then, there is nothing
to prevent an accident from becoming both a relative and a temporary property; but a property absolutely it
will never be.

We must not fail to observe that all remarks made in criticism of a 'property' and 'genus' and 'accident' will be
applicable to 'definitions' as well. For when we have shown that the attribute in question fails to belong only
to the term defined, as we do also in the case of a property, or that the genus rendered in the definition is not
the true genus, or that any of the things mentioned in the phrase used does not belong, as would be remarked
also in the case of an accident, we shall have demolished the definition; so that, to use the phrase previously
employed,' all the points we have enumerated might in a certain sense be called 'definitory'. But we must not
on this account expect to find a single line of inquiry which will apply universally to them all: for this is not
an easy thing to find, and, even were one found, it would be very obscure indeed, and of little service for the
treatise before us. Rather, a special plan of inquiry must be laid down for each of the classes we have
distinguished, and then, starting from the rules that are appropriate in each case, it will probably be easier to
make our way right through the task before us. So then, as was said before,' we must outline a division of our
subject, and other questions we must relegate each to the particular branch to which it most naturally belongs,
speaking of them as 'definitory' and 'generic' questions. The questions I mean have practically been already
assigned to their several branches.

First of all we must define the number of senses borne by the term 'Sameness'. Sameness would be generally
regarded as falling, roughly speaking, into three divisions. We generally apply the term numerically or
specifically or generic ally-numeric ally in cases where there is more than one name but only one thing, e.g.
'doublet' and 'cloak'; specifically, where there is more than one thing, but they present no differences in
respect of their species, as one man and another, or one horse and another: for things like this that fall under
the same species are said to be 'specifically the same'. Similarly, too, those things are called generically the
same which fall under the same genus, such as a horse and a man. It might appear that the sense in which
water from the same spring is called 'the same water' is somehow different and unlike the senses mentioned
above: but really such a case as this ought to be ranked in the same class with the things that in one way or
another are called 'the same' in view of unity of species. For all such things seem to be of one family and to
resemble one another. For the reaon why all water is said to be specifically the same as all other water is
because of a certain likeness it bears to it, and the only difference in the case of water drawn from the same
spring is this, that the likeness is more emphatic: that is why we do not distinguish it from the things that in
one way or another are called 'the same' in view of unity of species. It is generally supposed that the term 'the
same' is most used in a sense agreed on by every one when applied to what is numerically one. But even so, it
is apt to be rendered in more than one sense; its most literal and primary use is found whenever the sameness
is rendered in reference to an alternative name or definition, as when a cloak is said to be the same as a
doublet, or an animal that walks on two feet is said to be the same as a man: a second sense is when it is
rendered in reference to a property, as when what can acquire knowledge is called the same as a man, and
what naturally travels upward the same as fire: while a third use is found when it is rendered in reference to
some term drawn from Accident, as when the creature who is sitting, or who is musical, is called the same as

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Socrates. For all these uses mean to signify numerical unity. That what I have just said is true may be best
seen where one form of appellation is substituted for another. For often when we give the order to call one of
the people who are sitting down, indicating him by name, we change our description, whenever the person to
whom we give the order happens not to understand us; he will, we think, understand better from some
accidental feature; so we bid him call to us 'the man who is sitting' or 'who is conversing over there'-clearly
supposing ourselves to be indicating the same object by its name and by its accident.

Of 'sameness' then, as has been said,' three senses are to be distinguished. Now one way to confirm that the
elements mentioned above are those out of which and through which and to which arguments proceed, is by
induction: for if any one were to survey propositions and problems one by one, it would be seen that each was
formed either from the definition of something or from its property or from its genus or from its accident.
Another way to confirm it is through reasoning. For every predicate of a subject must of necessity be either
convertible with its subject or not: and if it is convertible, it would be its definition or property, for if it
signifies the essence, it is the definition; if not, it is a property: for this was what a property is, viz. what is
predicated convertibly, but does not signify the essence. If, on the other hand, it is not predicated convertibly
of the thing, it either is or is not one of the terms contained in the definition of the subject: and if it be one of
those terms, then it will be the genus or the differentia, inasmuch as the definition consists of genus and
differentiae; whereas, if it be not one of those terms, clearly it would be an accident, for accident was said' to
be what belongs as an attribute to a subject without being either its definition or its genus or a property.

Next, then, we must distinguish between the classes of predicates in which the four orders in question are
found. These are ten in number: Essence, Quantity, Quality, Relation, Place, Time, Position, State, Activity,
Passivity. For the accident and genus and property and definition of anything will always be in one of these
categories: for all the propositions found through these signify either something's essence or its quality or
quantity or some one of the other types of predicate. It is clear, too, on the face of it that the man who
signifies something's essence signifies sometimes a substance, sometimes a quality, sometimes some one of
the other types of predicate. For when man is set before him and he says that what is set there is 'a man' or 'an
animal', he states its essence and signifies a substance; but when a white colour is set before him and he says
that what is set there is 'white' or is 'a colour', he states its essence and signifies a quality. Likewise, also, if a
magnitude of a cubit be set before him and he says that what is set there is a magnitude of a cubit, he will be
describing its essence and signifying a quantity. Likewise, also, in the other cases: for each of these kinds of
predicate, if either it be asserted of itself, or its genus be asserted of it, signifies an essence: if, on the other
hand, one kind of predicate is asserted of another kind, it does not signify an essence, but a quantity or a
quality or one of the other kinds of predicate. Such, then, and so many, are the subjects on which arguments
take place, and the materials with which they start. How we are to acquire them, and by what means we are to
become well supplied with them, falls next to be told.

First, then, a definition must be given of a 'dialectical proposition' and a 'dialectical problem'. For it is not
every proposition nor yet every problem that is to be set down as dialectical: for no one in his senses would
make a proposition of what no one holds, nor yet make a problem of what is obvious to everybody or to most
people: for the latter admits of no doubt, while to the former no one would assent. Now a dialectical
proposition consists in asking something that is held by all men or by most men or by the philosophers, i.e.
either by all, or by most, or by the most notable of these, provided it be not contrary to the general opinion;
for a man would probably assent to the view of the philosophers, if it be not contrary to the opinions of most
men. Dialectical propositions also include views which are like those generally accepted; also propositions

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which contradict the contraries of opinions that are taken to be generally accepted, and also all opinions that
are in accordance with the recognized arts. Thus, supposing it to be a general opinion that the knowledge of
contraries is the same, it might probably pass for a general opinion also that the perception of contraries is the
same: also, supposing it to be a general opinion that there is but one single science of grammar, it might pass
for a general opinion that there is but one science of flute-playing as well, whereas, if it be a general opinion
that there is more than one science of grammar, it might pass for a general opinion that there is more than one
science of flute-playing as well: for all these seem to be alike and akin. Likewise, also, propositions
contradicting the contraries of general opinions will pass as general opinions: for if it be a general opinion
that one ought to do good to one's friends, it will also be a general opinion that one ought not to do them
harm. Here, that one ought to do harm to one's friends is contrary to the general view, and that one ought not
to do them harm is the contradictory of that contrary. Likewise also, if one ought to do good to one's friends,
one ought not to do good to one's enemies: this too is the contradictory of the view contrary to the general
view; the contrary being that one ought to do good to one's enemies. Likewise, also, in other cases. Also, on
comparison, it will look like a general opinion that the contrary predicate belongs to the contrary subject: e.g.
if one ought to do good to one's friends, one ought also to do evil to one's enemies, it might appear also as if
doing good to one's friends were a contrary to doing evil to one's enemies: but whether this is or is not so in
reality as well will be stated in the course of the discussion upon contraries. Clearly also, all opinions that are
in accordance with the arts are dialectical propositions; for people are likely to assent to the views held by
those who have made a study of these things, e.g. on a question of medicine they will agree with the doctor,
and on a question of geometry with the geometrician; and likewise also in other cases.

A dialectical problem is a subject of inquiry that contributes either to choice and avoidance, or to truth and
knowledge, and that either by itself, or as a help to the solution of some other such problem. It must,
moreover, be something on which either people hold no opinion either way, or the masses hold a contrary
opinion to the philosophers, or the philosophers to the masses, or each of them among themselves. For some
problems it is useful to know with a view to choice or avoidance, e.g. whether pleasure is to be chosen or not,
while some it is useful to know merely with a view to knowledge, e.g. whether the universe is eternal or not:
others, again, are not useful in and by themselves for either of these purposes, but yet help us in regard to
some such problems; for there are many things which we do not wish to know in and by themselves, but for
the sake of other things, in order that through them we may come to know something else. Problems also
include questions in regard to which reasonings conflict (the difficulty then being whether so-and so is so or
not, there being convincing arguments for both views); others also in regard to which we have no argument
because they are so vast, and we find it difficult to give our reasons, e.g. the question whether the universe is
eternal or no: for into questions of that kind too it is possible to inquire.

Problems, then, and propositions are to be defined as aforesaid. A 'thesis' is a supposition of some eminent
philosopher that conflicts with the general opinion; e.g. the view that contradiction is impossible, as
Antisthenes said; or the view of Heraclitus that all things are in motion; or that Being is one, as Melissus
says: for to take notice when any ordinary person expresses views contrary to men's usual opinions would be
silly. Or it may be a view about which we have a reasoned theory contrary to men's usual opinions, e.g. the
view maintained by the sophists that what is need not in every case either have come to be or be eternal: for a
musician who is a grammarian 'is' so without ever having 'come to be' so, or being so eternally. For even if a
man does not accept this view, he might do so on the ground that it is reasonable.

Now a 'thesis' also is a problem, though a problem is not always a thesis, inasmuch as some problems are
such that we have no opinion about them either way. That a thesis, however, also forms a problem, is clear:
for it follows of necessity from what has been said that either the mass of men disagree with the philosophers
about the thesis, or that the one or the other class disagree among themselves, seeing that the thesis is a
supposition in conflict with general opinion. Practically all dialectical problems indeed are now called

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'theses'. But it should make no difference whichever description is used; for our object in thus distinguishing
them has not been to create a terminology, but to recognize what differences happen to be found between
them.

Not every problem, nor every thesis, should be examined, but only one which might puzzle one of those who
need argument, not punishment or perception. For people who are puzzled to know whether one ought to
honour the gods and love one's parents or not need punishment, while those who are puzzled to know
whether snow is white or not need perception. The subjects should not border too closely upon the sphere of
demonstration, nor yet be too far removed from it: for the former cases admit of no doubt, while the latter
involve difficulties too great for the art of the trainer.

Having drawn these definitions, we must distinguish how many species there are of dialectical arguments.
There is on the one hand Induction, on the other Reasoning. Now what reasoning is has been said before:
induction is a passage from individuals to universals, e.g. the argument that supposing the skilled pilot is the
most effective, and likewise the skilled charioteer, then in general the skilled man is the best at his particular
task. Induction is the more convincing and clear: it is more readily learnt by the use of the senses, and is
applicable generally to the mass of men, though reasoning is more forcible and effective against
contradictious people.

The classes, then, of things about which, and of things out of which, arguments are constructed, are to be
distinguished in the way we have said before. The means whereby we are to become well supplied with
reasonings are four: (1) the securing of propositions; (2) the power to distinguish in how many senses
particular expression is used; (3) the discovery of the differences of things; (4) the investigation of likeness.
The last three, as well, are in a certain sense propositions: for it is possible to make a proposition
corresponding to each of them, e.g. (1) 'The desirable may mean either the honourable or the pleasant or the
expedient'; and (2) Sensation differs from knowledge in that the latter may be recovered again after it has
been lost, while the former cannot'; and (3) The relation of the healthy to health is like that of the vigorous to
vigour'. The first proposition depends upon the use of one term in several senses, the second upon the
differences of things, the third upon their likenesses.

Propositions should be selected in a number of ways corresponding to the number of distinctions drawn in
regard to the proposition: thus one may first take in hand the opinions held by all or by most men or by the
philosophers, i.e. by all, or most, or the most notable of them; or opinions contrary to those that seem to be
generally held; and, again, all opinions that are in accordance with the arts. We must make propositions also
of the contradictories of opinions contrary to those that seem to be generally held, as was laid down before. It
is useful also to make them by selecting not only those opinions that actually are accepted, but also those that
are like these, e.g. The perception of contraries is the same'-the knowledge of them being so-and 'we see by
admission of something into ourselves, not by an emission'; for so it is, too, in the case of the other senses; for
in hearing we admit something into ourselves; we do not emit; and we taste in the same way. Likewise also in
the other cases. Moreover, all statements that seem to be true in all or in most cases, should be taken as a
principle or accepted position; for they are posited by those who do not also see what exception there may be.
We should select also from the written handbooks of argument, and should draw up sketch-lists of them
upon each several kind of subject, putting them down under separate headings, e.g. 'On Good', or 'On
Life'-and that 'On Good' should deal with every form of good, beginning with the category of essence. In the
margin, too, one should indicate also the opinions of individual thinkers, e.g. 'Empedocles said that the

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elements of bodies were four': for any one might assent to the saying of some generally accepted authority.

Of propositions and problems there are-to comprehend the matter in outline-three divisions: for some are
ethical propositions, some are on natural philosophy, while some are logical. Propositions such as the
following are ethical, e.g. 'Ought one rather to obey one's parents or the laws, if they disagree?'; such as this
are logical, e.g. 'Is the knowledge of opposites the same or not?'; while such as this are on natural philosophy,
e.g. 'Is the universe eternal or not?' Likewise also with problems. The nature of each of the aforesaid kinds of
proposition is not easily rendered in a definition, but we have to try to recognize each of them by means of
the familiarity attained through induction, examining them in the light of the illustrations given above.

For purposes of philosophy we must treat of these things according to their truth, but for dialectic only with
an eye to general opinion. All propositions should be taken in their most universal form; then, the one should
be made into many. E.g. 'The knowledge of opposites is the same'; next, 'The knowledge of contraries is the
same', and that 'of relative terms'. In the same way these two should again be divided, as long as division is
possible, e.g. the knowledge of 'good and evil', of 'white and black', or 'cold and hot'. Likewise also in other
cases.

On the formation, then, of propositions, the above remarks are enough. As regards the number of senses a
term bears, we must not only treat of those terms which bear different senses, but we must also try to render
their definitions; e.g. we must not merely say that justice and courage are called 'good' in one sense, and that
what conduces to vigour and what conduces to health are called so in another, but also that the former are so
called because of a certain intrinsic quality they themselves have, the latter because they are productive of a
certain result and not because of any intrinsic quality in themselves. Similarly also in other cases.

Whether a term bears a number of specific meanings or one only, may be considered by the following means.
First, look and see if its contrary bears a number of meanings, whether the discrepancy between them be one
of kind or one of names. For in some cases a difference is at once displayed even in the names; e.g. the
contrary of 'sharp' in the case of a note is 'flat', while in the case of a solid edge it is 'dull'. Clearly, then, the
contrary of 'sharp' bears several meanings, and if so, also does 'sharp'; for corresponding to each of the former
terms the meaning of its contrary will be different. For 'sharp' will not be the same when contrary to 'dull' and
to 'flat', though 'sharp' is the contrary of each. Again Barhu ('flat', 'heavy') in the case of a note has 'sharp' as
its contrary, but in the case of a solid mass 'light', so that Barhu is used with a number of meanings, inasmuch
as its contrary also is so used. Likewise, also, 'fine' as applied to a picture has 'ugly' as its contrary, but, as
applied to a house, 'ramshackle'; so that 'fine' is an ambiguous term.

In some cases there is no discrepancy of any sort in the names used, but a difference of kind between the
meanings is at once obvious: e.g. in the case of 'clear' and 'obscure': for sound is called 'clear' and 'obscure',
just as 'colour' is too. As regards the names, then, there is no discrepancy, but the difference in kind between
the meanings is at once obvious: for colour is not called 'clear' in a like sense to sound. This is plain also
through sensation: for of things that are the same in kind we have the same sensation, whereas we do not
judge clearness by the same sensation in the case of sound and of colour, but in the latter case we judge by
sight, in the former by hearing. Likewise also with 'sharp' and 'dull' in regard to flavours and solid edges: here
in the latter case we judge by touch, but in the former by taste. For here again there is no discrepancy in the
names used, in the case either of the original terms or of their contraries: for the contrary also of sharp in
either sense is 'dull'.

Moreover, see if one sense of a term has a contrary, while another has absolutely none; e.g. the pleasure of
drinking has a contrary in the pain of thirst, whereas the pleasure of seeing that the diagonal is
incommensurate with the side has none, so that 'pleasure' is used in more than one sense. To 'love' also, used

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of the frame of mind, has to 'hate' as its contrary, while as used of the physical activity (kissing) it has none:
clearly, therefore, to 'love' is an ambiguous term. Further, see in regard to their intermediates, if some
meanings and their contraries have an intermediate, others have none, or if both have one but not the same
one, e.g. 'clear' and 'obscure' in the case of colours have 'grey' as an intermediate, whereas in the case of
sound they have none, or, if they have, it is 'harsh', as some people say that a harsh sound is intermediate.
'Clear', then, is an ambiguous term, and likewise also 'obscure'. See, moreover, if some of them have more
than one intermediate, while others have but one, as is the case with 'clear' and 'obscure', for in the case of
colours there are numbers of intermediates, whereas in regard to sound there is but one, viz. 'harsh'.

Again, in the case of the contradictory opposite, look and see if it bears more than one meaning. For if this
bears more than one meaning, then the opposite of it also will be used in more than one meaning; e.g. 'to fail
to see' a phrase with more than one meaning, viz. (1) to fail to possess the power of sight, (2) to fail to put
that power to active use. But if this has more than one meaning, it follows necessarily that 'to see' also has
more than one meaning: for there will be an opposite to each sense of 'to fail to see'; e.g. the opposite of 'not
to possess the power of sight' is to possess it, while of 'not to put the power of sight to active use', the
opposite is to put it to active use.

Moreover, examine the case of terms that denote the privation or presence of a certain state: for if the one
term bears more than one meaning, then so will the remaining term: e.g. if 'to have sense' be used with more
than one meaning, as applied to the soul and to the body, then 'to be wanting in sense' too will be used with
more than one meaning, as applied to the soul and to the body. That the opposition between the terms now in
question depends upon the privation or presence of a certain state is clear, since animals naturally possess
each kind of 'sense', both as applied to the soul and as applied to the body.

Moreover, examine the inflected forms. For if 'justly' has more than one meaning, then 'just', also, will be
used with more than one meaning; for there will be a meaning of just' to each of the meanings of 'justly'; e.g.
if the word justly' be used of judging according to one's own opinion, and also of judging as one ought, then
'just' also will be used in like manner. In the same way also, if 'healthy' has more than one meaning, then
'healthily' also will be used with more than one meaning: e.g. if 'healthy' describes both what produces health
and what preserves health and what betokens health, then 'healthily' also will be used to mean 'in such a way
as to produce' or 'preserve' or 'betoken' health. Likewise also in other cases, whenever the original term bears
more than one meaning, the inflexion also that is formed from it will be used with more than one meaning,
and vice versa.

Look also at the classes of the predicates signified by the term, and see if they are the same in all cases. For if
they are not the same, then clearly the term is ambiguous: e.g. 'good' in the case of food means 'productive of
pleasure', and in the case of medicine 'productive of health', whereas as applied to the soul it means to be of a
certain quality, e.g. temperate or courageous or just: and likewise also, as applied to 'man'. Sometimes it
signifies what happens at a certain time, as (e.g.) the good that happens at the right time: for what happens at
the right time is called good. Often it signifies what is of certain quantity, e.g. as applied to the proper
amount: for the proper amount too is called good. So then the term 'good' is ambiguous. In the same way also
'clear', as applied to a body, signifies a colour, but in regard to a note it denotes what is 'easy to hear'. 'Sharp',
too, is in a closely similar case: for the same term does not bear the same meaning in all its applications: for a
sharp note is a swift note, as the mathematical theorists of harmony tell us, whereas a sharp (acute) angle is
one that is less than a right angle, while a sharp dagger is one containing a sharp angle (point).

Look also at the genera of the objects denoted by the same term, and see if they are different without being
subaltern, as (e.g.) 'donkey', which denotes both the animal and the engine. For the definition of them that
corresponds to the name is different: for the one will be declared to be an animal of a certain kind, and the
other to be an engine of a certain kind. If, however, the genera be subaltern, there is no necessity for the
definitions to be different. Thus (e.g.) 'animal' is the genus of 'raven', and so is 'bird'. Whenever therefore we

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say that the raven is a bird, we also say that it is a certain kind of animal, so that both the genera are
predicated of it. Likewise also whenever we call the raven a 'flying biped animal', we declare it to be a bird:
in this way, then, as well, both the genera are predicated of raven, and also their definition. But in the case of
genera that are not subaltern this does not happen, for whenever we call a thing an 'engine', we do not call it
an animal, nor vice versa.

Look also and see not only if the genera of the term before you are different without being subaltern, but also
in the case of its contrary: for if its contrary bears several senses, clearly the term before you does so as well.

It is useful also to look at the definition that arises from the use of the term in combination, e.g. of a 'clear (lit.
white) body' of a 'clear note'. For then if what is peculiar in each case be abstracted, the same expression
ought to remain over. This does not happen in the case of ambiguous terms, e.g. in the cases just mentioned.
For the former will be body possessing such and such a colour', while the latter will be 'a note easy to hear'.
Abstract, then, 'a body 'and' a note', and the remainder in each case is not the same. It should, however, have
been had the meaning of 'clear' in each case been synonymous.

Often in the actual definitions as well ambiguity creeps in unawares, and for this reason the definitions also
should be examined. If (e.g.) any one describes what betokens and what produces health as 'related
commensurably to health', we must not desist but go on to examine in what sense he has used the term
'commensurably' in each case, e.g. if in the latter case it means that 'it is of the right amount to produce
health', whereas in the for it means that 'it is such as to betoken what kind of state prevails'.

Moreover, see if the terms cannot be compared as 'more or less' or as 'in like manner', as is the case (e.g.)
with a 'clear' (lit. white) sound and a 'clear' garment, and a 'sharp' flavour and a 'sharp' note. For neither are
these things said to be clear or sharp 'in a like degree', nor yet is the one said to be clearer or sharper than the
other. 'Clear', then, and 'sharp' are ambiguous. For synonyms are always comparable; for they will always be
used either in like manner, or else in a greater degree in one case.

Now since of genera that are different without being subaltern the differentiae also are different in kind, e.g.
those of 'animal' and 'knowledge' (for the differentiae of these are different), look and see if the meanings
comprised under the same term are differentiae of genera that are different without being subaltern, as e.g.
'sharp' is of a 'note' and a 'solid'. For being 'sharp' differentiates note from note, and likewise also one solid
from another. 'Sharp', then, is an ambiguous term: for it forms differentiae of genera that are different without
being subaltern.

Again, see if the actual meanings included under the same term themselves have different differentiae, e.g.
'colour' in bodies and 'colour' in tunes: for the differentiae of 'colour' in bodies are 'sight-piercing' and 'sight
compressing', whereas 'colour' in melodies has not the same differentiae. Colour, then, is an ambiguous term;
for things that are the same have the same differentiae.

Moreover, since the species is never the differentia of anything, look and see if one of the meanings included
under the same term be a species and another a differentia, as (e.g.) clear' (lit. white) as applied to a body is a
species of colour, whereas in the case of a note it is a differentia; for one note is differentiated from another
by being 'clear'.

The presence, then, of a number of meanings in a term may be investigated by these and like means. The
differences which things present to each other should be examined within the same genera, e.g. 'Wherein
does justice differ from courage, and wisdom from temperance?'-for all these belong to the same genus; and
also from one genus to another, provided they be not very much too far apart, e.g. 'Wherein does sensation

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differ from knowledge?: for in the case of genera that are very far apart, the differences are entirely obvious.

Likeness should be studied, first, in the case of things belonging to different genera, the formulae being 'A:B
= C:D' (e.g. as knowledge stands to the object of knowledge, so is sensation related to the object of
sensation), and 'As A is in B, so is C in D' (e.g. as sight is in the eye, so is reason in the soul, and as is a calm
in the sea, so is windlessness in the air). Practice is more especially needed in regard to terms that are far
apart; for in the case of the rest, we shall be more easily able to see in one glance the points of likeness. We
should also look at things which belong to the same genus, to see if any identical attribute belongs to them
all, e.g. to a man and a horse and a dog; for in so far as they have any identical attribute, in so far they are
alike.

It is useful to have examined the number of meanings of a term both for clearness' sake (for a man is more
likely to know what it is he asserts, if it bas been made clear to him how many meanings it may have), and
also with a view to ensuring that our reasonings shall be in accordance with the actual facts and not addressed
merely to the term used. For as long as it is not clear in how many senses a term is used, it is possible that the
answerer and the questioner are not directing their minds upon the same thing: whereas when once it has been
made clear how many meanings there are, and also upon which of them the former directs his mind when he
makes his assertion, the questioner would then look ridiculous if he failed to address his argument to this. It
helps us also both to avoid being misled and to mislead by false reasoning: for if we know the number of
meanings of a term, we shall certainly never be misled by false reasoning, but shall know if the questioner
fails to address his argument to the same point; and when we ourselves put the questions we shall be able to
mislead him, if our answerer happens not to know the number of meanings of our terms. This, however, is not
possible in all cases, but only when of the many senses some are true and others are false. This manner of
argument, however, does not belong properly to dialectic; dialecticians should therefore by all means beware
of this kind of verbal discussion, unless any one is absolutely unable to discuss the subject before him in any
other way.

The discovery of the differences of things helps us both in reasonings about sameness and difference, and
also in recognizing what any particular thing is. That it helps us in reasoning about sameness and difference is
clear: for when we have discovered a difference of any kind whatever between the objects before us, we shall
already have shown that they are not the same: while it helps us in recognizing what a thing is, because we
usually distinguish the expression that is proper to the essence of each particular thing by means of the
differentiae that are proper to it.

The examination of likeness is useful with a view both to inductive arguments and to hypothetical reasonings,
and also with a view to the rendering of definitions. It is useful for inductive arguments, because it is by
means of an induction of individuals in cases that are alike that we claim to bring the universal in evidence:
for it is not easy to do this if we do not know the points of likeness. It is useful for hypothetical reasonings
because it is a general opinion that among similars what is true of one is true also of the rest. If, then, with
regard to any of them we are well supplied with matter for a discussion, we shall secure a preliminary
admission that however it is in these cases, so it is also in the case before us: then when we have shown the
former we shall have shown, on the strength of the hypothesis, the matter before us as well: for we have first
made the hypothesis that however it is in these cases, so it is also in the case before us, and have then proved
the point as regards these cases. It is useful for the rendering of definitions because, if we are able to see in
one glance what is the same in each individual case of it, we shall be at no loss into what genus we ought to
put the object before us when we define it: for of the common predicates that which is most definitely in the
category of essence is likely to be the genus. Likewise, also, in the case of objects widely divergent, the

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examination of likeness is useful for purposes of definition, e.g. the sameness of a calm at sea, and
windlessness in the air (each being a form of rest), and of a point on a line and the unit in number-each being
a starting point. If, then, we render as the genus what is common to all the cases, we shall get the credit of
defining not inappropriately. Definition-mongers too nearly always render them in this way: they declare the
unit to be the startingpoint of number, and the point the startingpoint of a line. It is clear, then, that they place
them in that which is common to both as their genus.

The means, then, whereby reasonings are effected, are these: the commonplace rules, for the observance of
which the aforesaid means are useful, are as follows.

Book II

Of problems some are universal, others particular. Universal problems are such as 'Every pleasure is good'
and 'No pleasure is good'; particular problems are such as 'Some pleasure is good' and 'Some pleasure is not
good'. The methods of establishing and overthrowing a view universally are common to both kinds of
problems; for when we have shown that a predicate belongs in every case, we shall also have shown that it
belongs in some cases. Likewise, also, if we show that it does not belong in any case, we shall also have
shown that it does not belong in every case. First, then, we must speak of the methods of overthrowing a view
universally, because such are common to both universal and particular problems, and because people more
usually introduce theses asserting a predicate than denying it, while those who argue with them overthrow it.
The conversion of an appropriate name which is drawn from the element 'accident' is an extremely precarious
thing; for in the case of accidents and in no other it is possible for something to be true conditionally and not
universally. Names drawn from the elements 'definition' and 'property' and 'genus' are bound to be
convertible; e.g. if 'to be an animal that walks on two feet is an attribute of S', then it will be true by
conversion to say that 'S is an animal that walks on two feet'. Likewise, also, if drawn from the genus; for if
'to be an animal is an attribute of S', then 'S is an animal'. The same is true also in the case of a property; for if
'to be capable of learning grammar is an attribute of S', then 'S will be capable of learning grammar'. For none
of these attributes can possibly belong or not belong in part; they must either belong or not belong absolutely.
In the case of accidents, on the other hand, there is nothing to prevent an attribute (e.g. whiteness or justice)
belonging in part, so that it is not enough to show that whiteness or justice is an attribute of a man in order to
show that he is white or just; for it is open to dispute it and say that he is white or just in part only.
Conversion, then, is not a necessary process in the case of accidents.

We must also define the errors that occur in problems. They are of two kinds, caused either by false statement
or by transgression of the established diction. For those who make false statements, and say that an attribute
belongs to thing which does not belong to it, commit error; and those who call objects by the names of other
objects (e.g. calling a planetree a 'man') transgress the established terminology.

Now one commonplace rule is to look and see if a man has ascribed as an accident what belongs in some
other way. This mistake is most commonly made in regard to the genera of things, e.g. if one were to say that
white happens (accidit) to be a colour-for being a colour does not happen by accident to white, but colour is
its genus. The assertor may of course define it so in so many words, saying (e.g.) that 'Justice happens
(accidit) to be a virtue'; but often even without such definition it is obvious that he has rendered the genus as
an accident; e.g. suppose that one were to say that whiteness is coloured or that walking is in motion. For a
predicate drawn from the genus is never ascribed to the species in an inflected form, but always the genera
are predicated of their species literally; for the species take on both the name and the definition of their
genera. A man therefore who says that white is 'coloured' has not rendered 'coloured' as its genus, seeing that

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he has used an inflected form, nor yet as its property or as its definition: for the definition and property of a
thing belong to it and to nothing else, whereas many things besides white are coloured, e.g. a log, a stone, a
man, and a horse. Clearly then he renders it as an accident.

Another rule is to examine all cases where a predicate has been either asserted or denied universally to belong
to something. Look at them species by species, and not in their infinite multitude: for then the inquiry will
proceed more directly and in fewer steps. You should look and begin with the most primary groups, and then
proceed in order down to those that are not further divisible: e.g. if a man has said that the knowledge of
opposites is the same, you should look and see whether it be so of relative opposites and of contraries and of
terms signifying the privation or presence of certain states, and of contradictory terms. Then, if no clear result
be reached so far in these cases, you should again divide these until you come to those that are not further
divisible, and see (e.g.) whether it be so of just deeds and unjust, or of the double and the half, or of blindness
and sight, or of being and not-being: for if in any case it be shown that the knowledge of them is not the
same we shall have demolished the problem. Likewise, also, if the predicate belongs in no case. This rule is
convertible for both destructive and constructive purposes: for if, when we have suggested a division, the
predicate appears to hold in all or in a large number of cases, we may then claim that the other should
actually assert it universally, or else bring a negative instance to show in what case it is not so: for if he does
neither of these things, a refusal to assert it will make him look absurd.

Another rule is to make definitions both of an accident and of its subject, either of both separately or else of
one of them, and then look and see if anything untrue has been assumed as true in the definitions. Thus (e.g.)
to see if it is possible to wrong a god, ask what is 'to wrong'? For if it be 'to injure deliberately', clearly it is
not possible for a god to be wronged: for it is impossible that God should be injured. Again, to see if the good
man is jealous, ask who is the jealous' man and what is jealousy'. For if 'jealousy' is pain at the apparent
success of some well-behaved person, clearly the good man is not jealous: for then he would be bad. Again,
to see if the indignant man is jealous, ask who each of them is: for then it will be obvious whether the
statement is true or false; e.g. if he is jealous' who grieves at the successes of the good, and he is 'indignant'
who grieves at the successes of the evil, then clearly the indignant man would not be jealous. A man should
substitute definitions also for the terms contained in his definitions, and not stop until he comes to a familiar
term: for often if the definition be rendered whole, the point at issue is not cleared up, whereas if for one of
the terms used in the definition a definition be stated, it becomes obvious.

Moreover, a man should make the problem into a proposition for himself, and then bring a negative instance
against it: for the negative instance will be a ground of attack upon the assertion. This rule is very nearly the
same as the rule to look into cases where a predicate has been attributed or denied universally: but it differs in
the turn of the argument.

Moreover, you should define what kind of things should be called as most men call them, and what should
not. For this is useful both for establishing and for overthrowing a view: e.g. you should say that we ought to
use our terms to mean the same things as most people mean by them, but when we ask what kind of things
are or are not of such and such a kind, we should not here go with the multitude: e.g. it is right to call 'healthy'
whatever tends to produce health, as do most men: but in saying whether the object before us tends to
produce health or not, we should adopt the language no longer of the multitude but of the doctor.

Moreover, if a term be used in several senses, and it has been laid down that it is or that it is not an attribute
of S, you should show your case of one of its several senses, if you cannot show it of both. This rule is to be
observed in cases where the difference of meaning is undetected; for supposing this to be obvious, then the
other man will object that the point which he himself questioned has not been discussed, but only the other
point. This commonplace rule is convertible for purposes both of establishing and of overthrowing a view.

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For if we want to establish a statement, we shall show that in one sense the attribute belongs, if we cannot
show it of both senses: whereas if we are overthrowing a statement, we shall show that in one sense the
attribute does not belong, if we cannot show it of both senses. Of course, in overthrowing a statement there is
no need to start the discussion by securing any admission, either when the statement asserts or when it denies
the attribute universally: for if we show that in any case whatever the attribute does not belong, we shall have
demolished the universal assertion of it, and likewise also if we show that it belongs in a single case, we shall
demolish the universal denial of it. Whereas in establishing a statement we ought to secure a preliminary
admission that if it belongs in any case whatever, it belongs universally, supposing this claim to be a
plausible one. For it is not enough to discuss a single instance in order to show that an attribute belongs
universally; e.g. to argue that if the soul of man be immortal, then every soul is immortal, so that a previous
admission must be secured that if any soul whatever be immortal, then every soul is immortal. This is not to
be done in every case, but only whenever we are not easily able to quote any single argument applying to all
cases in common, as (e.g.) the geometrician can argue that the triangle has its angles equal to two right
angles.

If, again, the variety of meanings of a term be obvious, distinguish how many meanings it has before
proceeding either to demolish or to establish it: e.g. supposing 'the right' to mean 'the expedient' or 'the
honourable', you should try either to establish or to demolish both descriptions of the subject in question; e.g.
by showing that it is honourable and expedient, or that it is neither honourable nor expedient. Supposing,
however, that it is impossible to show both, you should show the one, adding an indication that it is true in
the one sense and not in the other. The same rule applies also when the number of senses into which it is
divided is more than two.

Again, consider those expressions whose meanings are many, but differ not by way of ambiguity of a term,
but in some other way: e.g. The science of many things is one': here 'many things' may mean the end and the
means to that end, as (e.g.) medicine is the science both of producing health and of dieting; or they may be
both of them ends, as the science of contraries is said to be the same (for of contraries the one is no more an
end than the other); or again they may be an essential and an accidental attribute, as (e.g.) the essential fact
that the triangle has its angles equal to two right angles, and the accidental fact that the equilateral figure has
them so: for it is because of the accident of the equilateral triangle happening to be a triangle that we know
that it has its angles equal to two right angles. If, then, it is not possible in any sense of the term that the
science of many things should be the same, it clearly is altogether impossible that it should be so; or, if it is
possible in some sense, then clearly it is possible. Distinguish as many meanings as are required: e.g. if we
want to establish a view, we should bring forward all such meanings as admit that view and should divide
them only into those meanings which also are required for the establishment of our case: whereas if we want
to overthrow a view, we should bring forward all that do not admit that view, and leave the rest aside. We
must deal also in these cases as well with any uncertainty about the number of meanings involved. Further,
that one thing is, or is not, 'of another should be established by means of the same commonplace rules; e.g.
that a particular science is of a particular thing, treated either as an end or as a means to its end, or as
accidentally connected with it; or again that it is not 'of it in any of the aforesaid ways. The same rule holds
true also of desire and all other terms that have more than one object. For the 'desire of X' may mean the
desire of it as an end (e.g. the desire of health) or as a means to an end (e.g. the desire of being doctored), or
as a thing desired accidentally, as, in the case of wine, the sweet-toothed person desires it not because it is
wine but because it is sweet. For essentially he desires the sweet, and only accidentally the wine: for if it be
dry, he no longer desires it. His desire for it is therefore accidental. This rule is useful in dealing with relative
terms: for cases of this kind are generally cases of relative terms.

Moreover, it is well to alter a term into one more familiar, e.g. to substitute 'clear' for 'exact' in describing a
conception, and 'being fussy' for 'being busy': for when the expression is made more familiar, the thesis

Book II 14

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becomes easier to attack. This commonplace rule also is available for both purposes alike, both for
establishing and for overthrowing a view.

In order to show that contrary attributes belong to the same thing, look at its genus; e.g. if we want to show
that rightness and wrongness are possible in regard to perception, and to perceive is to judge, while it is
possible to judge rightly or wrongly, then in regard to perception as well rightness and wrongness must be
possible. In the present instance the proof proceeds from the genus and relates to the species: for 'to judge' is
the genus of 'to -perceive'; for the man who perceives judges in a certain way. But per contra it may proceed
from the species to the genus: for all the attributes that belong to the species belong to the genus as well; e.g.
if there is a bad and a good knowledge there is also a bad and a good disposition: for 'disposition' is the genus
of knowledge. Now the former commonplace argument is fallacious for purposes of establishing a view,
while the second is true. For there is no necessity that all the attributes that belong to the genus should belong
also to the species; for 'animal' is flying and quadruped, but not so 'man'. All the attributes, on the other hand,
that belong to the species must of necessity belong also to the genus; for if 'man' is good, then animal also is
good. On the other hand, for purposes of overthrowing a view, the former argument is true while the latter is
fallacious; for all the attributes which do not belong to the genus do not belong to the species either; whereas
all those that are wanting to the species are not of necessity wanting to the genus.

Since those things of which the genus is predicated must also of necessity have one of its species predicated
of them, and since those things that are possessed of the genus in question, or are described by terms derived
from that genus, must also of necessity be possessed of one of its species or be described by terms derived
from one of its species (e.g. if to anything the term 'scientific knowledge' be applied, then also there will be
applied to it the term 'grammatical' or 'musical' knowledge, or knowledge of one of the other sciences; and if
any one possesses scientific knowledge or is described by a term derived from 'science', then he will also
possess grammatical or musical knowledge or knowledge of one of the other sciences, or will be described by
a term derived from one of them, e.g. as a 'grammarian' or a 'musician')-therefore if any expression be
asserted that is in any way derived from the genus (e.g. that the soul is in motion), look and see whether it be
possible for the soul to be moved with any of the species of motion; whether (e.g.) it can grow or be
destroyed or come to be, and so forth with all the other species of motion. For if it be not moved in any of
these ways, clearly it does not move at all. This commonplace rule is common for both purposes, both for
overthrowing and for establishing a view: for if the soul moves with one of the species of motion, clearly it
does move; while if it does not move with any of the species of motion, clearly it does not move.

If you are not well equipped with an argument against the assertion, look among the definitions, real or
apparent, of the thing before you, and if one is not enough, draw upon several. For it will be easier to attack
people when committed to a definition: for an attack is always more easily made on definitions.

Moreover, look and see in regard to the thing in question, what it is whose reality conditions the reality of the
thing in question, or what it is whose reality necessarily follows if the thing in question be real: if you wish to
establish a view inquire what there is on whose reality the reality of the thing in question will follow (for if
the former be shown to be real, then the thing in question will also have been shown to be real); while if you
want to overthrow a view, ask what it is that is real if the thing in question be real, for if we show that what
follows from the thing in question is unreal, we shall have demolished the thing in question.

Moreover, look at the time involved, to see if there be any discrepancy anywhere: e.g. suppose a man to have
stated that what is being nourished of necessity grows: for animals are always of necessity being nourished,
but they do not always grow. Likewise, also, if he has said that knowing is remembering: for the one is
concerned with past time, whereas the other has to do also with the present and the future. For we are said to
know things present and future (e.g. that there will be an eclipse), whereas it is impossible to remember
anything save what is in the past.

Book II 15

Topics

Moreover, there is the sophistic turn of argument, whereby we draw our opponent into the kind of statement
against which we shall be well supplied with lines of argument. This process is sometimes a real necessity,
sometimes an apparent necessity, sometimes neither an apparent nor a real necessity. It is really necessary
whenever the answerer has denied any view that would be useful in attacking the thesis, and the questioner
thereupon addresses his arguments to the support of this view, and when moreover the view in question
happens to be one of a kind on which he has a good stock of lines of argument. Likewise, also, it is really
necessary whenever he (the questioner) first, by an induction made by means of the view laid down, arrives at
a certain statement and then tries to demolish that statement: for when once this has been demolished, the
view originally laid down is demolished as well. It is an apparent necessity, when the point to which the
discussion comes to be directed appears to be useful, and relevant to the thesis, without being really so;
whether it be that the man who is standing up to the argument has refused to concede something, or whether
he (the questioner) has first reached it by a plausible induction based upon the thesis and then tries to
demolish it. The remaining case is when the point to which the discussion comes to be directed is neither
really nor apparently necessary, and it is the answerer's luck to be confuted on a mere side issue You should
beware of the last of the aforesaid methods; for it appears to be wholly disconnected from, and foreign to, the
art of dialectic. For this reason, moreover, the answerer should not lose his temper, but assent to those
statements that are of no use in attacking the thesis, adding an indication whenever he assents although he
does not agree with the view. For, as a rule, it increases the confusion of questioners if, after all propositions
of this kind have been granted them, they can then draw no conclusion.

Moreover, any one who has made any statement whatever has in a certain sense made several statements,
inasmuch as each statement has a number of necessary consequences: e.g. the man who said 'X is a man' has
also said that it is an animal and that it is animate and a biped and capable of acquiring reason and
knowledge, so that by the demolition of any single one of these consequences, of whatever kind, the original
statement is demolished as well. But you should beware here too of making a change to a more difficult
subject: for sometimes the consequence, and sometimes the original thesis, is the easier to demolish.

In regard to subjects which must have one and one only of two predicates, as (e.g.) a man must have either a
disease or health, supposing we are well supplied as regards the one for arguing its presence or absence, we
shall be well equipped as regards the remaining one as well. This rule is convertible for both purposes: for
when we have shown that the one attribute belongs, we shall have shown that the remaining one does not
belong; while if we show that the one does not belong, we shall have shown that the remaining one does
belong. Clearly then the rule is useful for both purposes.

Moreover, you may devise a line of attack by reinterpreting a term in its literal meaning, with the implication
that it is most fitting so to take it rather than in its established meaning: e.g. the expression 'strong at heart'
will suggest not the courageous man, according to the use now established, but the man the state of whose
heart is strong; just as also the expression 'of a good hope' may be taken to mean the man who hopes for good
things. Likewise also 'well-starred' may be taken to mean the man whose star is good, as Xenocrates says
'well-starred is he who has a noble soul'.' For a man's star is his soul.

Some things occur of necessity, others usually, others however it may chance; if therefore a necessary event
has been asserted to occur usually, or if a usual event (or, failing such an event itself, its contrary) has been
stated to occur of necessity, it always gives an opportunity for attack. For if a necessary event has been
asserted to occur usually, clearly the speaker has denied an attribute to be universal which is universal, and so
has made a mistake: and so he has if he has declared the usual attribute to be necessary: for then he declares it
to belong universally when it does not so belong. Likewise also if he has declared the contrary of what is

Book II 16

Topics

usual to be necessary. For the contrary of a usual attribute is always a comparatively rare attribute: e.g. if men
are usually bad, they are comparatively seldom good, so that his mistake is even worse if he has declared
them to be good of necessity. The same is true also if he has declared a mere matter of chance to happen of
necessity or usually; for a chance event happens neither of necessity nor usually. If the thing happens usually,
then even supposing his statement does not distinguish whether he meant that it happens usually or that it
happens necessarily, it is open to you to discuss it on the assumption that he meant that it happens
necessarily: e.g. if he has stated without any distinction that disinherited persons are bad, you may assume in
discussing it that he means that they are so necessarily.

Moreover, look and see also if he has stated a thing to be an accident of itself, taking it to be a different thing
because it has a different name, as Prodicus used to divide pleasures into joy and delight and good cheer: for
all these are names of the same thing, to wit, Pleasure. If then any one says that joyfulness is an accidental
attribute of cheerfulness, he would be declaring it to be an accidental attribute of itself.

Inasmuch as contraries can be conjoined with each other in six ways, and four of these conjunctions
constitute a contrariety, we must grasp the subject of contraries, in order that it may help us both in
demolishing and in establishing a view. Well then, that the modes of conjunction are six is clear: for either (1)
each of the contrary verbs will be conjoined to each of the contrary objects; and this gives two modes: e.g. to
do good to friends and to do evil to enemies, or per contra to do evil to friends and to do good to enemies. Or
else (2) both verbs may be attached to one object; and this too gives two modes, e.g. to do good to friends and
to do evil to friends, or to do good to enemies and to do evil to enemies. Or (3) a single verb may be attached
to both objects: and this also gives two modes; e.g. to do good to friends and to do good to enemies, or to do
evil to friends and evil to enemies.

The first two then of the aforesaid conjunctions do not constitute any contrariety; for the doing of good to
friends is not contrary to the doing of evil to enemies: for both courses are desirable and belong to the same
disposition. Nor is the doing of evil to friends contrary to the doing of good to enemies: for both of these are
objectionable and belong to the same disposition: and one objectionable thing is not generally thought to be
the contrary of another, unless the one be an expression denoting an excess, and the other an expression
denoting a defect: for an excess is generally thought to belong to the class of objectionable things, and
likewise also a defect. But the other four all constitute a contrariety. For to do good to friends is contrary to
the doing of evil to friends: for it proceeds from the contrary disposition, and the one is desirable, and the
other objectionable. The case is the same also in regard to the other conjunctions: for in each combination the
one course is desirable, and the other objectionable, and the one belongs to a reasonable disposition and the
other to a bad. Clearly, then, from what has been said, the same course has more than one contrary. For the
doing of good to friends has as its contrary both the doing of good to enemies and the doing of evil to friends.
Likewise, if we examine them in the same way, we shall find that the contraries of each of the others also are
two in number. Select therefore whichever of the two contraries is useful in attacking the thesis.

Moreover, if the accident of a thing have a contrary, see whether it belongs to the subject to which the
accident in question has been declared to belong: for if the latter belongs the former could not belong; for it is
impossible that contrary predicates should belong at the same time to the same thing.

Or again, look and see if anything has been said about something, of such a kind that if it be true, contrary
predicates must necessarily belong to the thing: e.g. if he has said that the 'Ideas' exist in us. For then the
result will be that they are both in motion and at rest, and moreover that they are objects both of sensation and
of thought. For according to the views of those who posit the existence of Ideas, those Ideas are at rest and
are objects of thought; while if they exist in us, it is impossible that they should be unmoved: for when we
move, it follows necessarily that all that is in us moves with us as well. Clearly also they are objects of

Book II 17

Topics

sensation, if they exist in us: for it is through the sensation of sight that we recognize the Form present in
each individual.

Again, if there be posited an accident which has a contrary, look and see if that which admits of the accident
will admit of its contrary as well: for the same thing admits of contraries. Thus (e.g.) if he has asserted that
hatred follows anger, hatred would in that case be in the 'spirited faculty': for that is where anger is. You
should therefore look and see if its contrary, to wit, friendship, be also in the 'spirited faculty': for if not-if
friendship is in the faculty of desire-then hatred could not follow anger. Likewise also if he has asserted that
the faculty of desire is ignorant. For if it were capable of ignorance, it would be capable of knowledge as
well: and this is not generally held-I mean that the faculty of desire is capable of knowledge. For purposes,
then, of overthrowing a view, as has been said, this rule should be observed: but for purposes of establishing
one, though the rule will not help you to assert that the accident actually belongs, it will help you to assert
that it may possibly belong. For having shown that the thing in question will not admit of the contrary of the
accident asserted, we shall have shown that the accident neither belongs nor can possibly belong; while on
the other hand, if we show that the contrary belongs, or that the thing is capable of the contrary, we shall not
indeed as yet have shown that the accident asserted does belong as well; our proof will merely have gone to
this point, that it is possible for it to belong.

Seeing that the modes of opposition are four in number, you should look for arguments among the
contradictories of your terms, converting the order of their sequence, both when demolishing and when
establishing a view, and you should secure them by means of induction-such arguments (e.g.) as that man be
an animal, what is not an animal is not a man': and likewise also in other instances of contradictories. For in
those cases the sequence is converse: for 'animal' follows upon 'man but 'not- animal' does not follow upon
'not-man', but conversely 'not-man' upon 'not-animal'. In all cases, therefore, a postulate of this sort should
be made, (e.g.) that 'If the honourable is pleasant, what is not pleasant is not honourable, while if the latter be
untrue, so is the former'. Likewise, also, 'If what is not pleasant be not honourable, then what is honourable is
pleasant'. Clearly, then, the conversion of the sequence formed by contradiction of the terms of the thesis is a
method convertible for both purposes.

Then look also at the case of the contraries of S and P in the thesis, and see if the contrary of the one follows
upon the contrary of the other, either directly or conversely, both when you are demolishing and when you
are establishing a view: secure arguments of this kind as well by means of induction, so far as may be
required. Now the sequence is direct in a case such as that of courage and cowardice: for upon the one of
them virtue follows, and vice upon the other; and upon the one it follows that it is desirable, while upon the
other it follows that it is objectionable. The sequence, therefore, in the latter case also is direct; for the
desirable is the contrary of the objectionable. Likewise also in other cases. The sequence is, on the other
hand, converse in such a case as this: Health follows upon vigour, but disease does not follow upon debility;
rather debility follows upon disease. In this case, then, clearly the sequence is converse. Converse sequence
is, however, rare in the case of contraries; usually the sequence is direct. If, therefore, the contrary of the one
term does not follow upon the contrary of the other either directly or conversely, clearly neither does the one
term follow upon the other in the statement made: whereas if the one followed the other in the case of the
contraries, it must of necessity do so as well in the original statement.

You should look also into cases of the privation or presence of a state in like manner to the case of contraries.
Only, in the case of such privations the converse sequence does not occur: the sequence is always bound to be
direct: e.g. as sensation follows sight, while absence of sensation follows blindness. For the opposition of
sensation to absence of sensation is an opposition of the presence to the privation of a state: for the one of
them is a state, and the other the privation of it.

Book II 18

Topics

The case of relative terms should also be studied in like manner to that of a state and its privation: for the
sequence of these as well is direct; e.g. if 3/1 is a multiple, then 1/3 is a fraction: for 3/1 is relative to 1/3, and
so is a multiple to a fraction. Again, if knowledge be a conceiving, then also the object of knowledge is an
object of conception; and if sight be a sensation, then also the object of sight is an object of sensation. An
objection may be made that there is no necessity for the sequence to take place, in the case of relative terms,
in the way described: for the object of sensation is an object of knowledge, whereas sensation is not
knowledge. The objection is, however, not generally received as really true; for many people deny that there
is knowledge of objects of sensation. Moreover, the principle stated is just as useful for the contrary purpose,
e.g. to show that the object of sensation is not an object of knowledge, on the ground that neither is sensation
knowledge.

Again look at the case of the co-ordinates and inflected forms of the terms in the thesis, both in demolishing
and in establishing it. By co-ordinates' are meant terms such as the following: 'Just deeds' and the 'just man'
are coordinates of 'justice', and 'courageous deeds' and the 'courageous man' are co-ordinates of courage.
Likewise also things that tend to produce and to preserve anything are called co-ordinates of that which they
tend to produce and to preserve, as e.g. 'healthy habits' are co-ordinates of 'health' and a 'vigorous
constitutional' of a 'vigorous constitution' and so forth also in other cases. 'Co-ordinate', then, usually
describes cases such as these, whereas 'inflected forms' are such as the following: 'justly', 'courageously',
'healthily', and such as are formed in this way. It is usually held that words when used in their inflected forms
as well are co-ordinates, as (e.g.) 'justly' in relation to justice, and 'courageously' to courage; and then
'co-ordinate' describes all the members of the same kindred series, e.g. justice', 'just', of a man or an act,
justly'. Clearly, then, when any one member, whatever its kind, of the same kindred series is shown to be
good or praiseworthy, then all the rest as well come to be shown to be so: e.g. if justice' be something
praiseworthy, then so will just', of a man or thing, and justly' connote something praiseworthy. Then justly'
will be rendered also 'praiseworthily', derived will by the same inflexion from 'the praiseworthy' whereby
justly' is derived from justice'.

Look not only in the case of the subject mentioned, but also in the case of its contrary, for the contrary
predicate: e.g. argue that good is not necessarily pleasant; for neither is evil painful: or that, if the latter be the
case, so is the former. Also, if justice be knowledge, then injustice is ignorance: and if justly' means
'knowingly' and 'skilfully', then 'unjustly' means 'ignorantly' and 'unskilfully': whereas if the latter be not true,
neither is the former, as in the instance given just now: for 'unjustly' is more likely to seem equivalent to
'skilfully' than to 'unskilfully'. This commonplace rule has been stated before in dealing with the sequence of
contraries; for all we are claiming now is that the contrary of P shall follow the contrary of S.

Moreover, look at the modes of generation and destruction of a thing, and at the things which tend to produce
or to destroy it, both in demolishing and in establishing a view. For those things whose modes of generation
rank among good things, are themselves also good; and if they themselves be good, so also are their modes of
generation. If, on the other hand, their modes of generation be evil, then they themselves also are evil. In
regard to modes of destruction the converse is true: for if the modes of destruction rank as good things, then
they themselves rank as evil things; whereas if the modes of destruction count as evil, they themselves count
as good. The same argument applies also to things tending to produce and destroy: for things whose
productive causes are good, themselves also rank as good; whereas if causes destructive of them are good,
they themselves rank as evil.

Again, look at things which are like the subject in question, and see if they are in like case; e.g. if one branch
of knowledge has more than one object, so also will one opinion; and if to possess sight be to see, then also to

Book II 19

Topics

possess hearing will be to hear. Likewise also in the case of other things, both those which are and those
which are generally held to be like. The rule in question is useful for both purposes; for if it be as stated in the
case of some one like thing, it is so with the other like things as well, whereas if it be not so in the case of
some one of them, neither is it so in the case of the others. Look and see also whether the cases are alike as
regards a single thing and a number of things: for sometimes there is a discrepancy. Thus, if to 'know' a thing
be to 'think of it, then also to 'know many things' is to 'be thinking of many things'; whereas this is not true;
for it is possible to know many things but not to be thinking of them. If, then, the latter proposition be not
true, neither was the former that dealt with a single thing, viz. that to 'know' a thing is to 'think of it.

Moreover, argue from greater and less degrees. In regard to greater degrees there are four commonplace
rules. One is: See whether a greater degree of the predicate follows a greater degree of the subject: e.g. if
pleasure be good, see whether also a greater pleasure be a greater good: and if to do a wrong be evil, see
whether also to do a greater wrong is a greater evil. Now this rule is of use for both purposes: for if an
increase of the accident follows an increase of the subject, as we have said, clearly the accident belongs;
while if it does not follow, the accident does not belong. You should establish this by induction. Another rule
is: If one predicate be attributed to two subjects; then supposing it does not belong to the subject to which it is
the more likely to belong, neither does it belong where it is less likely to belong; while if it does belong
where it is less likely to belong, then it belongs as well where it is more likely. Again: If two predicates be
attributed to one subject, then if the one which is more generally thought to belong does not belong, neither
does the one that is less generally thought to belong; or, if the one that is less generally thought to belong
does belong, so also does the other. Moreover: If two predicates be attributed to two subjects, then if the one
which is more usually thought to belong to the one subject does not belong, neither does the remaining
predicate belong to the remaining subject; or, if the one which is less usually thought to belong to the one
subject does belong, so too does the remaining predicate to the remaining subject.

Moreover, you can argue from the fact that an attribute belongs, or is generally supposed to belong, in a like
degree, in three ways, viz. those described in the last three rules given in regard to a greater degree.' For
supposing that one predicate belongs, or is supposed to belong, to two subjects in a like degree, then if it does
not belong to the one, neither does it belong to the other; while if it belongs to the one, it belongs to the
remaining one as well. Or, supposing two predicates to belong in a like degree to the same subject, then, if
the one does not belong, neither does the remaining one; while if the one does belong, the remaining one
belongs as well. The case is the same also if two predicates belong in a like degree to two subjects; for if the
one predicate does not belong to the one subject, neither does the remaining predicate belong to the
remaining subject, while if the one predicate does belong to the one subject, the remaining predicate belongs
to the remaining subject as well.

You can argue, then, from greater or less or like degrees of truth in the aforesaid number of ways. Moreover,
you should argue from the addition of one thing to another. If the addition of one thing to another makes that
other good or white, whereas formerly it was not white or good, then the thing added will be white or good-it
will possess the character it imparts to the whole as well. Moreover, if an addition of something to a given
object intensifies the character which it had as given, then the thing added will itself as well be of that
character. Likewise, also, in the case of other attributes. The rule is not applicable in all cases, but only in
those in which the excess described as an 'increased intensity' is found to take place. The above rule is,
however, not convertible for overthrowing a view. For if the thing added does not make the other good, it is
not thereby made clear whether in itself it may not be good: for the addition of good to evil does not
necessarily make the whole good, any more than the addition of white to black makes the whole white.

Again, any predicate of which we can speak of greater or less degrees belongs also absolutely: for greater or
less degrees of good or of white will not be attributed to what is not good or white: for a bad thing will never

Book II 20

Topics

be said to have a greater or less degree of goodness than another, but always of badness. This rule is not
convertible, either, for the purpose of overthrowing a predication: for several predicates of which we cannot
speak of a greater degree belong absolutely: for the term 'man' is not attributed in greater and less degrees, but
a man is a man for all that.

You should examine in the same way predicates attributed in a given respect, and at a given time and place:
for if the predicate be possible in some respect, it is possible also absolutely. Likewise, also, is what is
predicated at a given time or place: for what is absolutely impossible is not possible either in any respect or at
any place or time. An objection may be raised that in a given respect people may be good by nature, e.g. they
may be generous or temperately inclined, while absolutely they are not good by nature, because no one is
prudent by nature. Likewise, also, it is possible for a destructible thing to escape destruction at a given time,
whereas it is not possible for it to escape absolutely. In the same way also it is a good thing at certain places
to follow see and such a diet, e.g. in infected areas, though it is not a good thing absolutely. Moreover, in
certain places it is possible to live singly and alone, but absolutely it is not possible to exist singly and alone.
In the same way also it is in certain places honourable to sacrifice one's father, e.g. among the Triballi,
whereas, absolutely, it is not honourable. Or possibly this may indicate a relativity not to places but to
persons: for it is all the same wherever they may be: for everywhere it will be held honourable among the
Triballi themselves, just because they are Triballi. Again, at certain times it is a good thing to take medicines,
e.g. when one is ill, but it is not so absolutely. Or possibly this again may indicate a relativity not to a certain
time, but to a certain state of health: for it is all the same whenever it occurs, if only one be in that state. A
thing is 'absolutely' so which without any addition you are prepared to say is honourable or the contrary. Thus
(e.g.) you will deny that to sacrifice one's father is honourable: it is honourable only to certain persons: it is
not therefore honourable absolutely. On the other hand, to honour the gods you will declare to be honourable
without adding anything, because that is honourable absolutely. So that whatever without any addition is
generally accounted to be honourable or dishonourable or anything else of that kind, will be said to be so
'absolutely'.

Book III

THE question which is the more desirable, or the better, of two or more things, should be examined upon the
following lines: only first of all it must be clearly laid down that the inquiry we are making concerns not
things that are widely divergent and that exhibit great differences from one another (for nobody raises any
doubt whether happiness or wealth is more desirable), but things that are nearly related and about which we
commonly discuss for which of the two we ought rather to vote, because we do not see any advantage on
either side as compared with the other. Clearly, in such cases if we can show a single advantage, or more than
one, our judgement will record our assent that whichever side happens to have the advantage is the more
desirable.

First, then, that which is more lasting or secure is more desirable than that which is less so: and so is that
which is more likely to be chosen by the prudent or by the good man or by the right law, or by men who are
good in any particular line, when they make their choice as such, or by the experts in regard to any particular
class of things; i.e. either whatever most of them or what all of them would choose; e.g. in medicine or in
carpentry those things are more desirable which most, or all, doctors would choose; or, in general, whatever
most men or all men or all things would choose, e.g. the good: for everything aims at the good. You should
direct the argument you intend to employ to whatever purpose you require. Of what is 'better' or 'more
desirable' the absolute standard is the verdict of the better science, though relatively to a given individual the
standard may be his own particular science.

Book III 21

Topics

In the second place, that which is known as 'an x' is more desirable than that which does not come within the
genus 'x'-e.g. justice than a just man; for the former falls within the genus 'good', whereas the other does not,
and the former is called 'a good', whereas the latter is not: for nothing which does not happen to belong to the
genus in question is called by the generic name; e.g. a 'white man' is not 'a colour'. Likewise also in other
cases.

Also, that which is desired for itself is more desirable than that which is desired for something else; e.g.
health is more desirable than gymnastics: for the former is desired for itself, the latter for something else.
Also, that which is desirable in itself is more desirable than what is desirable per accidens; e.g. justice in our
friends than justice in our enemies: for the former is desirable in itself, the latter per accidens: for we desire
that our enemies should be just per accidens, in order that they may do us no harm. This last principle is the
same as the one that precedes it, with, however, a different turn of expression. For we desire justice in our
friends for itself, even though it will make no difference to us, and even though they be in India; whereas in
our enemies we desire it for something else, in order that they may do us no harm.

Also, that which is in itself the cause of good is more desirable than what is so per accidens, e.g. virtue than
luck (for the former in itself, and the latter per accidens, the cause of good things), and so in other cases of the
same kind. Likewise also in the case of the contrary; for what is in itself the cause of evil is more
objectionable than what is so per accidens, e.g. vice and chance: for the one is bad in itself, whereas chance is
so per accidens.

Also, what is good absolutely is more desirable than what is good for a particular person, e.g. recovery of
health than a surgical operation; for the former is good absolutely, the latter only for a particular person, viz.
the man who needs an operation. So too what is good by nature is more desirable than the good that is not so
by nature, e.g. justice than the just man; for the one is good by nature, whereas in the other case the goodness
is acquired. Also the attribute is more desirable which belongs to the better and more honourable subject, e.g.
to a god rather than to a man, and to the soul rather than to the body. So too the property of the better thing is
better than the property of the worse; e.g. the property of God than the property of man: for whereas in
respect of what is common in both of them they do not differ at all from each other, in respect of their
properties the one surpasses the other. Also that is better which is inherent in things better or prior or more
honourable: thus (e.g.) health is better than strength and beauty: for the former is inherent in the moist and the
dry, and the hot and the cold, in fact in all the primary constituents of an animal, whereas the others are
inherent in what is secondary, strength being a feature of the sinews and bones, while beauty is generally
supposed to consist in a certain symmetry of the limbs. Also the end is generally supposed to be more
desirable than the means, and of two means, that which lies nearer the end. In general, too, a means directed
towards the end of life is more desirable than a means to anything else, e.g. that which contributes to
happiness than that which contributes to prudence. Also the competent is more desirable than the
incompetent. Moreover, of two productive agents that one is more desirable whose end is better; while
between a productive agent and an end we can decide by a proportional sum whenever the excess of the one
end over the other is greater than that of the latter over its own productive means: e.g. supposing the excess of
happiness over health to be greater than that of health over what produces health, then what produces
happiness is better than health. For what produces happiness exceeds what produces health just as much as
happiness exceeds health. But health exceeds what produces health by a smaller amount; ergo, the excess of
what produces happiness over what produces health is greater than that of health over what produces health.
Clearly, therefore, what produces happiness is more desirable than health: for it exceeds the same standard by
a greater amount. Moreover, what is in itself nobler and more precious and praiseworthy is more desirable
than what is less so, e.g. friendship than wealth, and justice than strength. For the former belong in
themselves to the class of things precious and praiseworthy, while the latter do so not in themselves but for
something else: for no one prizes wealth for itself but always for something else, whereas we prize friendship
for itself, even though nothing else is likely to come to us from it.

Book III 22

Topics

Moreover, whenever two things are very much like one another, and we cannot see any superiority in the one
over the other of them, we should look at them from the standpoint of their consequences. For the one which
is followed by the greater good is the more desirable: or, if the consequences be evil, that is more desirable
which is followed by the less evil. For though both may be desirable, yet there may possibly be some
unpleasant consequence involved to turn the scale. Our survey from the point of view of consequences lies in
two directions, for there are prior consequences and later consequences: e.g. if a man learns, it follows that he
was ignorant before and knows afterwards. As a rule, the later consequence is the better to consider. You
should take, therefore, whichever of the consequences suits your purpose.

Moreover, a greater number of good things is more desirable than a smaller, either absolutely or when the one
is included in the other, viz. the smaller number in the greater. An objection may be raised suppose in some
particular case the one is valued for the sake of the other; for then the two together are not more desirable
than the one; e.g. recovery of health and health, than health alone, inasmuch as we desire recovery of health
for the sake of health. Also it is quite possible for what is not good, together with what is, to be more
desirable than a greater number of good things, e.g. the combination of happiness and something else which
is not good may be more desirable than the combination of justice and courage. Also, the same things are
more valuable if accompanied than if unaccompanied by pleasure, and likewise when free from pain than
when attended with pain.

Also, everything is more desirable at the season when it is of greater consequence; e.g. freedom from pain in
old age more than in youth: for it is of greater consequence in old age. On the same principle also, prudence
is more desirable in old age; for no man chooses the young to guide him, because he does not expect them to
be prudent. With courage, the converse is the case, for it is in youth that the active exercise of courage is
more imperatively required. Likewise also with temperance; for the young are more troubled by their
passions than are their elders.

Also, that is more desirable which is more useful at every season or at most seasons, e.g. justice and
temperance rather than courage: for they are always useful, while courage is only useful at times. Also, that
one of two things which if all possess, we do not need the other thing, is more desirable than that which all
may possess and still we want the other one as well. Take the case of justice and courage; if everybody were
just, there would be no use for courage, whereas all might be courageous, and still justice would be of use.

Moreover, judge by the destructions and losses and generations and acquisitions and contraries of things: for
things whose destruction is more objectionable are themselves more desirable. Likewise also with the losses
and contraries of things; for a thing whose loss or whose contrary is more objectionable is itself more
desirable. With the generations or acquisitions of things the opposite is the case: for things whose acquisition
or generation is more desirable are themselves also desirable. Another commonplace rule is that what is
nearer to the good is better and more desirable, i.e. what more nearly resembles the good: thus justice is better
than a just man. Also, that which is more like than another thing to something better than itself, as e.g. some
say that Ajax was a better man than Odysseus because he was more like Achilles. An objection may be raised
to this that it is not true: for it is quite possible that Ajax did not resemble Achilles more nearly than
Odysseus in the points which made Achilles the best of them, and that Odysseus was a good man, though
unlike Achilles. Look also to see whether the resemblance be that of a caricature, like the resemblance of a
monkey to a man, whereas a horse bears none: for the monkey is not the more handsome creature, despite its
nearer resemblance to a man. Again, in the case of two things, if one is more like the better thing while
another is more like the worse, then that is likely to be better which is more like the better. This too, however,
admits of an objection: for quite possibly the one only slightly resembles the better, while the other strongly
resembles the worse, e.g. supposing the resemblance of Ajax to Achilles to be slight, while that of Odysseus
to Nestor is strong. Also it may be that the one which is like the better type shows a degrading likeness,

Book III 23

Topics

whereas the one which is like the worse type improves upon it: witness the likeness of a horse to a donkey,
and that of a monkey to a man.

Another rule is that the more conspicuous good is more desirable than the less conspicuous, and the more
difficult than the easier: for we appreciate better the possession of things that cannot be easily acquired. Also
the more personal possession is more desirable than the more widely shared. Also, that which is more free
from connexion with evil: for what is not attended by any unpleasantness is more desirable than what is so
attended.

Moreover, if A be without qualification better than B, then also the best of the members of A is better than
the best of the members of B; e.g. if Man be better than Horse, then also the best man is better than the best
horse. Also, if the best in A be better than the best in B, then also A is better than B without qualification; e.g.
if the best man be better than the best horse, then also Man is better than Horse without qualification.

Moreover, things which our friends can share are more desirable than those they cannot. Also, things which
we like rather to do to our friend are more desirable than those we like to do to the man in the street, e.g. just
dealing and the doing of good rather than the semblance of them: for we would rather really do good to our
friends than seem to do so, whereas towards the man in the street the converse is the case.

Also, superfluities are better than necessities, and are sometimes more desirable as well: for the good life is
better than mere life, and good life is a superfluity, whereas mere life itself is a necessity. Sometimes, though,
what is better is not also more desirable: for there is no necessity that because it is better it should also be
more desirable: at least to be a philosopher is better than to make money, but it is not more desirable for a
man who lacks the necessities of life. The expression 'superfluity' applies whenever a man possesses the
necessities of life and sets to work to secure as well other noble acquisitions. Roughly speaking, perhaps,
necessities are more desirable, while superfluities are better.

Also, what cannot be got from another is more desirable than what can be got from another as well, as (e.g.)
is the case of justice compared with courage. Also, A is more desirable if A is desirable without B, but not B
without A: power (e.g.) is not desirable without prudence, but prudence is desirable without power. Also, if
of two things we repudiate the one in order to be thought to possess the other, then that one is more desirable
which we wish to be thought to possess; thus (e.g.) we repudiate the love of hard work in order that people
may think us geniuses.

Moreover, that is more desirable in whose absence it is less blameworthy for people to be vexed; and that is
more desirable in whose absence it is more blameworthy for a man not to be vexed.

Moreover, of things that belong to the same species one which possesses the peculiar virtue of the species is
more desirable than one which does not. If both possess it, then the one which possesses it in a greater degree
is more desirable.

Moreover, if one thing makes good whatever it touches, while another does not, the former is more desirable,
just as also what makes things warm is warmer than what does not. If both do so, then that one is more
desirable which does so in a greater degree, or if it render good the better and more important object-if (e.g.),
the one makes good the soul, and the other the body.

Moreover, judge things by their inflexions and uses and actions and works, and judge these by them: for they
go with each other: e.g. if justly' means something more desirable than 'courageously', then also justice
means something more desirable than courage; and if justice be more desirable than courage, then also 'justly'

Book III 24

Topics

means something more desirable than 'courageously'. Similarly also in the other cases.

Moreover, if one thing exceeds while the other falls short of the same standard of good, the one which
exceeds is the more desirable; or if the one exceeds an even higher standard. Nay more, if there be two things
both preferable to something, the one which is more highly preferable to it is more desirable than the less
highly preferable. Moreover, when the excess of a thing is more desirable than the excess of something else,
that thing is itself also more desirable than the other, as (e.g.) friendship than money: for an excess of
friendship is more desirable than an excess of money. So also that of which a man would rather that it were
his by his own doing is more desirable than what he would rather get by another's doing, e.g. friends than
money. Moreover, judge by means of an addition, and see if the addition of A to the same thing as B makes
the whole more desirable than does the addition of B. You must, however, beware of adducing a case in
which the common term uses, or in some other way helps the case of, one of the things added to it, but not the
other, as (e.g.) if you took a saw and a sickle in combination with the art of carpentry: for in the combination
the saw is a more desirable thing, but it is not a more desirable thing without qualification. Again, a thing is
more desirable if, when added to a lesser good, it makes the whole greater good. Likewise, also, you should
judge by means of subtraction: for the thing upon whose subtraction the remainder is a lesser good may be
taken to be a greater good, whichever it be whose subtraction makes the remainder a lesser good.

Also, if one thing be desirable for itself, and the other for the look of it, the former is more desirable, as (e.g.)
health than beauty. A thing is defined as being desired for the look of it if, supposing no one knew of it, you
would not care to have it. Also, it is more desirable both for itself and for the look of it, while the other thing
is desirable on the one ground alone. Also, whichever is the more precious for itself, is also better and more
desirable. A thing may be taken to be more precious in itself which we choose rather for itself, without
anything else being likely to come of it.

Moreover, you should distinguish in how many senses 'desirable' is used, and with a view to what ends, e.g.
expediency or honour or pleasure. For what is useful for all or most of them may be taken to be more
desirable than what is not useful in like manner. If the same characters belong to both things you should look
and see which possesses them more markedly, i.e. which of the two is the more pleasant or more honourable
or more expedient. Again, that is more desirable which serves the better purpose, e.g. that which serves to
promote virtue more than that which serves to promote pleasure. Likewise also in the case of objectionable
things; for that is more objectionable which stands more in the way of what is desirable, e.g. disease more
than ugliness: for disease is a greater hindrance both to pleasure and to being good.

Moreover, argue by showing that the thing in question is in like measure objectionable and desirable: for a
thing of such a character that a man might well desire and object to it alike is less desirable than the other
which is desirable only.

Comparisons of things together should therefore be conducted in the manner prescribed. The same
commonplace rules are useful also for showing that anything is simply desirable or objectionable: for we
have only to subtract the excess of one thing over another. For if what is more precious be more desirable,
then also what is precious is desirable; and if what is more useful be more desirable, then also what is useful
is desirable. Likewise, also, in the case of other things which admit of comparisons of that kind. For in some
cases in the very course of comparing the things together we at once assert also that each of them, or the one
of them, is desirable, e.g. whenever we call the one good 'by nature' and the other 'not by nature': for dearly
what is good by nature is desirable.

Book III 25

Topics

The commonplace rules relating to comparative degrees and amounts ought to be taken in the most general
possible form: for when so taken they are likely to be useful in a larger number of instances. It is possible to
render some of the actual rules given above more universal by a slight alteration of the expression, e.g. that
what by nature exhibits such and such a quality exhibits that quality in a greater degree than what exhibits it
not by nature. Also, if one thing does, and another does not, impart such and such a quality to that which
possesses it, or to which it belongs, then whichever does impart it is of that quality in greater degree than the
one which does not impart it; and if both impart it, then that one exhibits it in a greater degree which imparts
it in a greater degree.

Moreover, if in any character one thing exceeds and another falls short of the same standard; also, if the one
exceeds something which exceeds a given standard, while the other does not reach that standard, then clearly
the first-named thing exhibits that character in a greater degree. Moreover, you should judge by means of
addition, and see if A when added to the same thing as B imparts to the whole such and such a character in a
more marked degree than B, or if, when added to a thing which exhibits that character in a less degree, it
imparts that character to the whole in a greater degree. Likewise, also, you may judge by means of
subtraction: for a thing upon whose subtraction the remainder exhibits such and such a character in a less
degree, itself exhibits that character in a greater degree. Also, things exhibit such and such a character in a
greater degree if more free from admixture with their contraries; e.g. that is whiter which is more free from
admixture with black. Moreover, apart from the rules given above, that has such and such a character in
greater degree which admits in a greater degree of the definition proper to the given character; e.g. if the
definition of 'white' be 'a colour which pierces the vision', then that is whiter which is in a greater degree a
colour that pierces the vision.

If the question be put in a particular and not in a universal form, in the first place the universal constructive or
destructive commonplace rules that have been given may all be brought into use. For in demolishing or
establishing a thing universally we also show it in particular: for if it be true of all, it is true also of some, and
if untrue of all, it is untrue of some. Especially handy and of general application are the commonplace rules
that are drawn from the opposites and co-ordinates and inflexions of a thing: for public opinion grants alike
the claim that if all pleasure be good, then also all pain is evil, and the claim that if some pleasure be good,
then also some pain is evil. Moreover, if some form of sensation be not a capacity, then also some form of
failure of sensation is not a failure of capacity. Also, if the object of conception is in some cases an object of
knowledge, then also some form of conceiving is knowledge. Again, if what is unjust be in some cases good,
then also what is just is in some cases evil; and if what happens justly is in some cases evil, then also what
happens unjustly is in some cases good. Also, if what is pleasant is in some cases objectionable, then pleasure
is in some cases an objectionable thing. On the same principle, also, if what is pleasant is in some cases
beneficial, then pleasure is in some cases a beneficial thing. The case is the same also as regards the things
that destroy, and the processes of generation and destruction. For if anything that destroys pleasure or
knowledge be in some cases good, then we may take it that pleasure or knowledge is in some cases an evil
thing. Likewise, also, if the destruction of knowledge be in some cases a good thing or its production an evil
thing, then knowledge will be in some cases an evil thing; e.g. if for a man to forget his disgraceful conduct
be a good thing, and to remember it be an evil thing, then the knowledge of his disgraceful conduct may be
taken to be an evil thing. The same holds also in other cases: in all such cases the premiss and the conclusion
are equally likely to be accepted.

Moreover you should judge by means of greater or smaller or like degrees: for if some member of another
genus exhibit such and such a character in a more marked degree than your object, while no member of that
genus exhibits that character at all, then you may take it that neither does the object in question exhibit it; e.g.
if some form of knowledge be good in a greater degree than pleasure, while no form of knowledge is good,
then you may take it that pleasure is not good either. Also, you should judge by a smaller or like degree in the

Book III 26

Topics

same way: for so you will find it possible both to demolish and to establish a view, except that whereas both
are possible by means of like degrees, by means of a smaller degree it is possible only to establish, not to
overthrow. For if a certain form of capacity be good in a like degree to knowledge, and a certain form of
capacity be good, then so also is knowledge; while if no form of capacity be good, then neither is knowledge.
If, too, a certain form of capacity be good in a less degree than knowledge, and a certain form of capacity be
good, then so also is knowledge; but if no form of capacity be good, there is no necessity that no form of
knowledge either should be good. Clearly, then, it is only possible to establish a view by means of a less
degree.

Not only by means of another genus can you overthrow a view, but also by means of the same, if you take the
most marked instance of the character in question; e.g. if it be maintained that some form of knowledge is
good, then, suppose it to be shown that prudence is not good, neither will any other kind be good, seeing that
not even the kind upon which there is most general agreement is so. Moreover, you should go to work by
means of an hypothesis; you should claim that the attribute, if it belongs or does not belong in one case, does
so in a like degree in all, e.g. that if the soul of man be immortal, so are other souls as well, while if this one
be not so, neither are the others. If, then, it be maintained that in some instance the attribute belongs, you
must show that in some instance it does not belong: for then it will follow, by reason of the hypothesis, that it
does not belong to any instance at all. If, on the other hand, it be maintained that it does not belong in some
instance, you must show that it does belong in some instance, for in this way it will follow that it belongs to
all instances. It is clear that the maker of the hypothesis universalizes the question, whereas it was stated in a
particular form: for he claims that the maker of a particular admission should make a universal admission,
inasmuch as he claims that if the attribute belongs in one instance, it belongs also in all instances alike.

If the problem be indefinite, it is possible to overthrow a statement in only one way; e.g. if a man has asserted
that pleasure is good or is not good, without any further definition. For if he meant that a particular pleasure
is good, you must show universally that no pleasure is good, if the proposition in question is to be
demolished. And likewise, also, if he meant that some particular pleasure is not good you must show
universally that all pleasure is good: it is impossible to demolish it in any other way. For if we show that
some particular pleasure is not good or is good, the proposition in question is not yet demolished. It is clear,
then, that it is possible to demolish an indefinite statement in one way only, whereas it can be established in
two ways: for whether we show universally that all pleasure is good, or whether we show that a particular
pleasure is good, the proposition in question will have been proved. Likewise, also, supposing we are
required to argue that some particular pleasure is not good, if we show that no pleasure is good or that a
particular pleasure is not good, we shall have produced an argument in both ways, both universally and in
particular, to show that some particular pleasure is not good. If, on the other hand, the statement made be
definite, it will be possible to demolish it in two ways; e.g. if it be maintained that it is an attribute of some
particular pleasure to be good, while of some it is not: for whether it be shown that all pleasure, or that no
pleasure, is good, the proposition in question will have been demolished. If, however, he has stated that only
one single pleasure is good, it is possible to demolish it in three ways: for by showing that all pleasure, or that
no pleasure, or that more than one pleasure, is good, we shall have demolished the statement in question. If
the statement be made still more definite, e.g. that prudence alone of the virtues is knowledge, there are four
ways of demolishing it: for if it be shown that all virtue is knowledge, or that no virtue is so, or that some
other virtue (e.g. justice) is so, or that prudence itself is not knowledge, the proposition in question will have
been demolished.

It is useful also to take a look at individual instances, in cases where some attribute has been said to belong or
not to belong, as in the case of universal questions. Moreover, you should take a glance among genera,
dividing them by their species until you come to those that are not further divisible, as has been said before:'
for whether the attribute is found to belong in all cases or in none, you should, after adducing several
instances, claim that he should either admit your point universally, or else bring an objection showing in what
case it does not hold. Moreover, in cases where it is possible to make the accident definite either specifically

Book III 27

Topics

or numerically, you should look and see whether perhaps none of them belongs, showing e.g. that time is not
moved, nor yet a movement, by enumerating how many species there are of movement: for if none of these
belong to time, clearly it does not move, nor yet is a movement. Likewise, also, you can show that the soul is
not a number, by dividing all numbers into either odd or even: for then, if the soul be neither odd nor even,
clearly it is not a number.

In regard then to Accident, you should set to work by means like these, and in this manner.

Book IV

NEXT we must go on to examine questions relating to Genus and Property. These are elements in the
questions that relate to definitions, but dialecticians seldom address their inquiries to these by themselves. If,
then, a genus be suggested for something that is, first take a look at all objects which belong to the same
genus as the thing mentioned, and see whether the genus suggested is not predicated of one of them, as
happens in the case of an accident: e.g. if 'good' be laid down to be the genus of 'pleasure', see whether some
particular pleasure be not good: for, if so, clearly good' is not the genus of pleasure: for the genus is
predicated of all the members of the same species. Secondly, see whether it be predicated not in the category
of essence, but as an accident, as 'white' is predicated of 'snow', or 'self-moved' of the soul. For 'snow' is not a
kind of 'white', and therefore 'white' is not the genus of snow, nor is the soul a kind of 'moving object': its
motion is an accident of it, as it often is of an animal to walk or to be walking. Moreover, 'moving' does not
seem to indicate the essence, but rather a state of doing or of having something done to it. Likewise, also,
'white': for it indicates not the essence of snow, but a certain quality of it. So that neither of them is predicated
in the category of 'essence'.

Especially you should take a look at the definition of Accident, and see whether it fits the genus mentioned,
as (e.g.) is also the case in the instances just given. For it is possible for a thing to be and not to be
self-moved, and likewise, also, for it to be and not to be white. So that neither of these attributes is the genus
but an accident, since we were saying that an accident is an attribute which can belong to a thing and also not
belong.

Moreover, see whether the genus and the species be not found in the same division, but the one be a
substance while the other is a quality, or the one be a relative while the other is a quality, as (e.g.) 'slow' and
'swan' are each a substance, while 'white' is not a substance but a quality, so that 'white' is not the genus either
of 'snow' or of 'swan'. Again, knowledge' is a relative, while 'good' and 'noble' are each a quality, so that
good, or noble, is not the genus of knowledge. For the genera of relatives ought themselves also to be
relatives, as is the case with 'double': for multiple', which is the genus of 'double', is itself also a relative. To
speak generally, the genus ought to fall under the same division as the species: for if the species be a
substance, so too should be the genus, and if the species be a quality, so too the genus should be a quality;
e.g. if white be a quality, so too should colour be. Likewise, also, in other cases.

Again, see whether it be necessary or possible for the genus to partake of the object which has been placed in
the genus. To partake' is defined as 'to admit the definition of that which is partaken. Clearly, therefore, the
species partake of the genera, but not the genera of the species: for the species admits the definition of the
genus, whereas the genus does not admit that of the species. You must look, therefore, and see whether the
genus rendered partakes or can possibly partake of the species, e.g. if any one were to render anything as
genus of 'being' or of 'unity': for then the result will be that the genus partakes of the species: for of
everything that is, 'being' and 'unity' are predicated, and therefore their definition as well.

Book IV 28

Topics

Moreover, see if there be anything of which the species rendered is true, while the genus is not so, e.g.
supposing 'being' or 'object of knowledge' were stated to be the genus of 'object of opinion'. For 'object of
opinion' will be a predicate of what does not exist; for many things which do not exist are objects of opinion;
whereas that 'being' or 'object of knowledge' is not predicated of what does not exist is clear. So that neither
'being' nor 'object of knowledge' is the genus of 'object of opinion': for of the objects of which the species is
predicated, the genus ought to be predicated as well.

Again, see whether the object placed in the genus be quite unable to partake of any of its species: for it is
impossible that it should partake of the genus if it do not partake of any of its species, except it be one of the
species reached by the first division: these do partake of the genus alone. If, therefore, 'Motion' be stated as
the genus of pleasure, you should look and see if pleasure be neither locomotion nor alteration, nor any of the
rest of the given modes of motion: for clearly you may then take it that it does not partake of any of the
species, and therefore not of the genus either, since what partakes of the genus must necessarily partake of
one of the species as well: so that pleasure could not be a species of Motion, nor yet be one of the individual
phenomena comprised under the term 'motion'. For individuals as well partake in the genus and the species,
as (e.g.) an individual man partakes of both 'man' and 'animal'.

Moreover, see if the term placed in the genus has a wider denotation than the genus, as (e.g.) 'object of
opinion' has, as compared with 'being': for both what is and what is not are objects of opinion, so that 'object
of opinion' could not be a species of being: for the genus is always of wider denotation than the species.
Again, see if the species and its genus have an equal denotation; suppose, for instance, that of the attributes
which go with everything, one were to be stated as a species and the other as its genus, as for example Being
and Unity: for everything has being and unity, so that neither is the genus of the other, since their denotation
is equal. Likewise, also, if the 'first' of a series and the 'beginning' were to be placed one under the other: for
the beginning is first and the first is the beginning, so that either both expressions are identical or at any rate
neither is the genus of the other. The elementary principle in regard to all such cases is that the genus has a
wider denotation than the species and its differentia: for the differentia as well has a narrower denotation than
the genus.

See also whether the genus mentioned fails, or might be generally thought to fail, to apply to some object
which is not specifically different from the thing in question; or, if your argument be constructive, whether it
does so apply. For all things that are not specifically different have the same genus. If, therefore, it be shown
to apply to one, then clearly it applies to all, and if it fails to apply to one, clearly it fails to apply to any; e.g.
if any one who assumes 'indivisible lines' were to say that the 'indivisible' is their genus. For the aforesaid
term is not the genus of divisible lines, and these do not differ as regards their species from indivisible: for
straight lines are never different from each other as regards their species.

Look and see, also, if there be any other genus of the given species which neither embraces the genus
rendered nor yet falls under it, e.g. suppose any one were to lay down that 'knowledge' is the genus of justice.
For virtue is its genus as well, and neither of these genera embraces the remaining one, so that knowledge
could not be the genus of justice: for it is generally accepted that whenever one species falls under two
genera, the one is embraced by the other. Yet a principle of this kind gives rise to a difficulty in some cases.
For some people hold that prudence is both virtue and knowledge, and that neither of its genera is embraced
by the other: although certainly not everybody admits that prudence is knowledge. If, however, any one were
to admit the truth of this assertion, yet it would still be generally agreed to be necessary that the genera of the
same object must at any rate be subordinate either the one to the other or both to the same, as actually is the
case with virtue and knowledge. For both fall under the same genus; for each of them is a state and a
disposition. You should look, therefore, and see whether neither of these things is true of the genus rendered;
for if the genera be subordinate neither the one to the other nor both to the same, then what is rendered could

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not be the true genus.

Look, also, at the genus of the genus rendered, and so continually at the next higher genus, and see whether
all are predicated of the species, and predicated in the category of essence: for all the higher genera should be
predicated of the species in the category of essence. If, then, there be anywhere a discrepancy, clearly what is
rendered is not the true genus. [Again, see whether either the genus itself, or one of its higher genera, partakes
of the species: for the higher genus does not partake of any of the lower.] If, then, you are overthrowing a
view, follow the rule as given: if establishing one, then-suppose that what has been named as genus be
admitted to belong to the species, only it be disputed whether it belongs as genus-it is enough to show that
one of its higher genera is predicated of the species in the category of essence. For if one of them be
predicated in the category of essence, all of them, both higher and lower than this one, if predicated at all of
the species, will be predicated of it in the category of essence: so that what has been rendered as genus is also
predicated in the category of essence. The premiss that when one genus is predicated in the category of
essence, all the rest, if predicated at all, will be predicated in the category of essence, should be secured by
induction. Supposing, however, that it be disputed whether what has been rendered as genus belongs at all, it
is not enough to show that one of the higher genera is predicated of the species in the category of essence:
e.g. if any one has rendered 'locomotion' as the genus of walking, it is not enough to show that walking is
'motion' in order to show that it is 'locomotion', seeing that there are other forms of motion as well; but one
must show in addition that walking does not partake of any of the species of motion produced by the same
division except locomotion. For of necessity what partakes of the genus partakes also of one of the species
produced by the first division of the genus. If, therefore, walking does not partake either of increase or
decrease or of the other kinds of motion, clearly it would partake of locomotion, so that locomotion would be
the genus of walking.

Again, look among the things of which the given species is predicated as genus, and see if what is rendered as
its genus be also predicated in the category of essence of the very things of which the species is so predicated,
and likewise if all the genera higher than this genus are so predicated as well. For if there be anywhere a
discrepancy, clearly what has been rendered is not the true genus: for had it been the genus, then both the
genera higher than it, and it itself, would all have been predicated in the category of essence of those objects
of which the species too is predicated in the category of essence. If, then, you are overthrowing a view, it is
useful to see whether the genus fails to be predicated in the category of essence of those things of which the
species too is predicated. If establishing a view, it is useful to see whether it is predicated in the category of
essence: for if so, the result will be that the genus and the species will be predicated of the same object in the
category of essence, so that the same object falls under two genera: the genera must therefore of necessity be
subordinate one to the other, and therefore if it be shown that the one we wish to establish as genus is not
subordinate to the species, clearly the species would be subordinate to it, so that you may take it as shown
that it is the genus.

Look, also, at the definitions of the genera, and see whether they apply both to the given species and to the
objects which partake of the species. For of necessity the definitions of its genera must be predicated of the
species and of the objects which partake of the species: if, then, there be anywhere a discrepancy, clearly
what has been rendered is not the genus.

Again, see if he has rendered the differentia as the genus, e.g. 'immortal' as the genus of 'God'. For 'immortal'
is a differentia of 'living being', seeing that of living beings some are mortal and others immortal. Clearly,
then, a bad mistake has been made; for the differentia of a thing is never its genus. And that this is true is
clear: for a thing's differentia never signifies its essence, but rather some quality, as do 'walking' and 'biped'.

Also, see whether he has placed the differentia inside the genus, e.g. by taking 'odd' as a number'. For 'odd' is
a differentia of number, not a species. Nor is the differentia generally thought to partake of the genus: for
what partakes of the genus is always either a species or an individual, whereas the differentia is neither a

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species nor an individual. Clearly, therefore, the differentia does not partake of the genus, so that 'odd' too is
no species but a differentia, seeing that it does not partake of the genus.

Moreover, see whether he has placed the genus inside the species, e.g. by taking 'contact' to be a 'juncture', or
'mixture' a 'fusion', or, as in Plato's definition,' 'locomotion' to be the same as 'carriage'. For there is no
necessity that contact should be juncture: rather, conversely, juncture must be contact: for what is in contact
is not always joined, though what is joined is always in contact. Likewise, also, in the remaining instances:
for mixture is not always a 'fusion' (for to mix dry things does not fuse them), nor is locomotion always
'carriage'. For walking is not generally thought to be carriage: for 'carriage' is mostly used of things that
change one place for another involuntarily, as happens in the case of inanimate things. Clearly, also, the
species, in the instances given, has a wider denotation than the genus, whereas it ought to be vice versa.
Again, see whether he has placed the differentia inside the species, by taking (e.g.) 'immortal' to be 'a god'.
For the result will be that the species has an equal or wider denotation: and this cannot be, for always the
differentia has an equal or a wider denotation than the species. Moreover, see whether he has placed the
genus inside the differentia, by making 'colour' (e.g.) to be a thing that 'pierces', or 'number' a thing that is
'odd'. Also, see if he has mentioned the genus as differentia: for it is possible for a man to bring forward a
statement of this kind as well, e.g. that 'mixture' is the differentia of 'fusion', or that change of place' is the
differentia of 'carriage'. All such cases should be examined by means of the same principles: for they depend
upon common rules: for the genus should have a wider denotation that its differentia, and also should not
partake of its differentia; whereas, if it be rendered in this manner, neither of the aforesaid requirements can
be satisfied: for the genus will both have a narrower denotation than its differentia, and will partake of it.

Again, if no differentia belonging to the genus be predicated of the given species, neither will the genus be
predicated of it; e.g. of 'soul' neither 'odd' nor 'even' is predicated: neither therefore is 'number'. Moreover, see
whether the species is naturally prior and abolishes the genus along with itself: for the contrary is the general
view. Moreover, if it be possible for the genus stated, or for its differentia, to be absent from the alleged
species, e.g. for 'movement' to be absent from the 'soul', or 'truth and falsehood' from 'opinion', then neither of
the terms stated could be its genus or its differentia: for the general view is that the genus and the differentia
accompany the species, as long as it exists.

Look and see, also, if what is placed in the genus partakes or could possibly partake of any contrary of the
genus: for in that case the same thing will at the same time partake of contrary things, seeing that the genus is
never absent from it, while it partakes, or can possibly partake, of the contrary genus as well. Moreover, see
whether the species shares in any character which it is utterly impossible for any member of the genus to
have. Thus (e.g.) if the soul has a share in life, while it is impossible for any number to live, then the soul
could not be a species of number.

You should look and see, also, if the species be a homonym of the genus, and employ as your elementary
principles those already stated for dealing with homonymity: for the genus and the species are synonymous.

Seeing that of every genus there is more than one species, look and see if it be impossible that there should be
another species than the given one belonging to the genus stated: for if there should be none, then clearly
what has been stated could not be a genus at all.

Look and see, also, if he has rendered as genus a metaphorical expression, describing (e.g. 'temperance' as a
'harmony': a 'harmony': for a genus is always predicated of its species in its literal sense, whereas 'harmony' is
predicated of temperance not in a literal sense but metaphorically: for a harmony always consists in notes.

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Moreover, if there be any contrary of the species, examine it. The examination may take different forms; first
of all see if the contrary as well be found in the same genus as the species, supposing the genus to have no
contrary; for contraries ought to be found in the same genus, if there be no contrary to the genus. Supposing,
on the other hand, that there is a contrary to the genus, see if the contrary of the species be found in the
contrary genus: for of necessity the contrary species must be in the contrary genus, if there be any contrary to
the genus. Each of these points is made plain by means of induction. Again, see whether the contrary of the
species be not found in any genus at all, but be itself a genus, e.g. 'good': for if this be not found in any genus,
neither will its contrary be found in any genus, but will itself be a genus, as happens in the case of 'good' and
'evil': for neither of these is found in a genus, but each of them is a genus. Moreover, see if both genus and
species be contrary to something, and one pair of contraries have an intermediary, but not the other. For if the
genera have an intermediary, so should their species as well, and if the species have, so should their genera as
well, as is the case with (1) virtue and vice and (2) justice and injustice: for each pair has an intermediary. An
objection to this is that there is no intermediary between health and disease, although there is one between
evil and good. Or see whether, though there be indeed an intermediary between both pairs, i.e. both between
the species and between the genera, yet it be not similarly related, but in one case be a mere negation of the
extremes, whereas in the other case it is a subject. For the general view is that the relation should be similar in
both cases, as it is in the cases of virtue and vice and of justice and injustice: for the intermediaries between
both are mere negations. Moreover, whenever the genus has no contrary, look and see not merely whether the
contrary of the species be found in the same genus, but the intermediate as well: for the genus containing the
extremes contains the intermediates as well, as (e.g.) in the case of white and black: for 'colour' is the genus
both of these and of all the intermediate colours as well. An objection may be raised that 'defect' and 'excess'
are found in the same genus (for both are in the genus 'evil'), whereas moderate amount', the intermediate
between them, is found not in 'evil' but in 'good'. Look and see also whether, while the genus has a contrary,
the species has none; for if the genus be contrary to anything, so too is the species, as virtue to vice and
justice to injustice.

Likewise, also, if one were to look at other instances, one would come to see clearly a fact like this. An
objection may be raised in the case of health and disease: for health in general is the contrary of disease,
whereas a particular disease, being a species of disease, e.g. fever and ophthalmia and any other particular
disease, has no contrary.

If, therefore, you are demolishing a view, there are all these ways in which you should make your
examination: for if the aforesaid characters do not belong to it, clearly what has been rendered is not the
genus. If, on the other hand, you are establishing a view, there are three ways: in the first place, see whether
the contrary of the species be found in the genus stated, suppose the genus have no contrary: for if the
contrary be found in it, clearly the species in question is found in it as well. Moreover, see if the intermediate
species is found in the genus stated: for whatever genus contains the intermediate contains the extremes as
well. Again, if the genus have a contrary, look and see whether also the contrary species is found in the
contrary genus: for if so, clearly also the species in question is found in the genus in question.

Again, consider in the case of the inflexions and the co-ordinates of species and genus, and see whether they
follow likewise, both in demolishing and in establishing a view. For whatever attribute belongs or does not
belong to one belongs or does not belong at the same time to all; e.g. if justice be a particular form of
knowledge, then also justly' is 'knowingly' and the just man is a man of knowledge: whereas if any of these
things be not so, then neither is any of the rest of them.

Again, consider the case of things that bear a like relation to one another. Thus (e.g.) the relation of the
pleasant to pleasure is like that of the useful to the good: for in each case the one produces the other. If
therefore pleasure be a kind of 'good', then also the pleasant will be a kind of 'useful': for clearly it may be

Book IV 32

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taken to be productive of good, seeing that pleasure is good. In the same way also consider the case of
processes of generation and destruction; if (e.g.) to build be to be active, then to have built is to have been
active, and if to learn be to recollect, then also to have learnt is to have recollected, and if to be decomposed
be to be destroyed, then to have been decomposed is to have been destroyed, and decomposition is a kind of
destruction. Consider also in the same way the case of things that generate or destroy, and of the capacities
and uses of things; and in general, both in demolishing and in establishing an argument, you should examine
things in the light of any resemblance of whatever description, as we were saying in the case of generation
and destruction. For if what tends to destroy tends to decompose, then also to be destroyed is to be
decomposed: and if what tends to generate tends to produce, then to be generated is to be produced, and
generation is production. Likewise, also, in the case of the capacities and uses of things: for if a capacity be a
disposition, then also to be capable of something is to be disposed to it, and if the use of anything be an
activity, then to use it is to be active, and to have used it is to have been active.

If the opposite of the species be a privation, there are two ways of demolishing an argument, first of all by
looking to see if the opposite be found in the genus rendered: for either the privation is to be found absolutely
nowhere in the same genus, or at least not in the same ultimate genus: e.g. if the ultimate genus containing
sight be sensation, then blindness will not be a sensation. Secondly, if there be a sensation. Secondly, if there
be a privation opposed to both genus and species, but the opposite of the species be not found in the opposite
of the genus, then neither could the species rendered be in the genus rendered. If, then, you are demolishing a
view, you should follow the rule as stated; but if establishing one there is but one way: for if the opposite
species be found in the opposite genus, then also the species in question would be found in the genus in
question: e.g. if 'blindness' be a form of 'insensibility', then 'sight' is a form of 'sensation'.

Again, look at the negations of the genus and species and convert the order of terms, according to the method
described in the case of Accident: e.g. if the pleasant be a kind of good, what is not good is not pleasant. For
were this no something not good as well would then be pleasant. That, however, cannot be, for it is
impossible, if 'good' be the genus of pleasant, that anything not good should be pleasant: for of things of
which the genus is not predicated, none of the species is predicated either. Also, in establishing a view, you
should adopt the same method of examination: for if what is not good be not pleasant, then what is pleasant is
good, so that 'good' is the genus of 'pleasant'.

If the species be a relative term, see whether the genus be a relative term as well: for if the species be a
relative term, so too is the genus, as is the case with 'double' and 'multiple': for each is a relative term. If, on
the other hand, the genus be a relative term, there is no necessity that the species should be so as well: for
'knowledge'is a relative term, but not so 'grammar'. Or possibly not even the first statement would be
generally considered true: for virtue is a kind of 'noble' and a kind of 'good' thing, and yet, while 'virtue' is a
relative term, 'good' and 'noble' are not relatives but qualities. Again, see whether the species fails to be used
in the same relation when called by its own name, and when called by the name of its genus: e.g. if the term
'double' be used to mean the double of a 'half, then also the term 'multiple' ought to be used to mean multiple
of a 'half. Otherwise 'multiple' could not be the genus of 'double'.

Moreover, see whether the term fail to be used in the same relation both when called by the name of its
genus, and also when called by those of all the genera of its genus. For if the double be a multiple of a half,
then 'in excess of 'will also be used in relation to a 'half: and, in general, the double will be called by the
names of all the higher genera in relation to a 'half. An objection may be raised that there is no necessity for a
term to be used in the same relation when called by its own name and when called by that of its genus: for
'knowledge' is called knowledge 'of an object', whereas it is called a 'state' and 'disposition' not of an 'object'
but of the 'soul'.

Again, see whether the genus and the species be used in the same way in respect of the inflexions they take,
e.g. datives and genitives and all the rest. For as the species is used, so should the genus be as well, as in the

Book IV 33

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case of 'double' and its higher genera: for we say both 'double of and 'multiple of a thing. Likewise, also, in
the case of 'knowledge': for both knowledge' itself and its genera, e.g. 'disposition' and 'state', are said to be
'of something. An objection may be raised that in some cases it is not so: for we say 'superior to' and
'contrary to' so and so, whereas 'other', which is the genus of these terms, demands not 'to' but 'than': for the
expression is 'other than' so and so.

Again, see whether terms used in like case relationships fail to yield a like construction when converted, as
do 'double' and 'multiple'. For each of these terms takes a genitive both in itself and in its converted form: for
we say both a half of and 'a fraction of something. The case is the same also as regards both 'knowledge' and
'conception': for these take a genitive, and by conversion an 'object of knowledge' and an 'object of
conception' are both alike used with a dative. If, then, in any cases the constructions after conversion be not
alike, clearly the one term is not the genus of the other.

Again, see whether the species and the genus fail to be used in relation to an equal number of things: for the
general view is that the uses of both are alike and equal in number, as is the case with 'present' and 'grant'. For
a present' is of something or to some one, and also a 'grant' is of something and to some one: and 'grant' is the
genus of 'present', for a 'present' is a 'grant that need not be returned'. In some cases, however, the number of
relations in which the terms are used happens not to be equal, for while 'double' is double of something, we
speak of 'in excess' or 'greater' in something, as well as of or than something: for what is in excess or greater
is always in excess in something, as well as in excess of something. Hence the terms in question are not the
genera of 'double', inasmuch as they are not used in relation to an equal number of things with the species. Or
possibly it is not universally true that species and genus are used in relation to an equal number of things.

See, also, if the opposite of the species have the opposite of the genus as its genus, e.g. whether, if 'multiple'
be the genus of 'double', 'fraction' be also the genus of 'half. For the opposite of the genus should always be
the genus of the opposite species. If, then, any one were to assert that knowledge is a kind of sensation, then
also the object of knowledge will have to be a kind of object of sensation, whereas it is not: for an object of
knowledge is not always an object of sensation: for objects of knowledge include some of the objects of
intuition as well. Hence 'object of sensation' is not the genus of 'object of knowledge': and if this be so,
neither is 'sensation' the genus of 'knowledge'.

Seeing that of relative terms some are of necessity found in, or used of, the things in relation to which they
happen at any time to be used (e.g. 'disposition' and 'state' and 'balance'; for in nothing else can the aforesaid
terms possibly be found except in the things in relation to which they are used), while others need not be
found in the things in relation to which they are used at any time, though they still may be (e.g. if the term
'object of knowledge' be applied to the soul: for it is quite possible that the knowledge of itself should be
possessed by the soul itself, but it is not necessary, for it is possible for this same knowledge to be found in
some one else), while for others, again, it is absolutely impossible that they should be found in the things in
relation to which they happen at any time to be used (as e.g. that the contrary should be found in the contrary
or knowledge in the object of knowledge, unless the object of knowledge happen to be a soul or a man)-you
should look, therefore, and see whether he places a term of one kind inside a genus that is not of that kind,
e.g. suppose he has said that 'memory' is the 'abiding of knowledge'. For 'abiding' is always found in that
which abides, and is used of that, so that the abiding of knowledge also will be found in knowledge. Memory,
then, is found in knowledge, seeing that it is the abiding of knowledge. But this is impossible, for memory is
always found in the soul. The aforesaid commonplace rule is common to the subject of Accident as well: for
it is all the same to say that 'abiding' is the genus of memory, or to allege that it is an accident of it. For if in
any way whatever memory be the abiding of knowledge, the same argument in regard to it will apply.

Book IV 34

Topics

Again, see if he has placed what is a 'state' inside the genus 'activity', or an activity inside the genus 'state',
e.g. by defining 'sensation' as 'movement communicated through the body': for sensation is a 'state', whereas
movement is an 'activity'. Likewise, also, if he has said that memory is a 'state that is retentive of a
conception', for memory is never a state, but rather an activity.

They also make a bad mistake who rank a 'state' within the 'capacity' that attends it, e.g. by defining 'good
temper' as the 'control of anger', and 'courage' and 'justice' as 'control of fears' and of 'gains': for the terms
'courageous' and 'good-tempered' are applied to a man who is immune from passion, whereas
'self-controlled' describes the man who is exposed to passion and not led by it. Quite possibly, indeed, each
of the former is attended by a capacity such that, if he were exposed to passion, he would control it and not be
led by it: but, for all that, this is not what is meant by being 'courageous' in the one case, and 'good tempered'
in the other; what is meant is an absolute immunity from any passions of that kind at all.

Sometimes, also, people state any kind of attendant feature as the genus, e.g. 'pain' as the genus of 'anger' and
'conception' as that of conviction'. For both of the things in question follow in a certain sense upon the given
species, but neither of them is genus to it. For when the angry man feels pain, the pain bas appeared in him
earlier than the anger: for his anger is not the cause of his pain, but his pain of his anger, so that anger
emphatically is not pain. By the same reasoning, neither is conviction conception: for it is possible to have
the same conception even without being convinced of it, whereas this is impossible if conviction be a species
of conception: for it is impossible for a thing still to remain the same if it be entirely transferred out of its
species, just as neither could the same animal at one time be, and at another not be, a man. If, on the other
hand, any one says that a man who has a conception must of necessity be also convinced of it, then
'conception' and 'conviction' will be used with an equal denotation, so that not even so could the former be the
genus of the latter: for the denotation of the genus should be wider.

See, also, whether both naturally come to be anywhere in the same thing: for what contains the species
contains the genus as well: e.g. what contains 'white' contains 'colour' as well, and what contains 'knowledge
of grammar' contains 'knowledge' as well. If, therefore, any one says that 'shame' is 'fear', or that 'anger' is
'pain', the result will be that genus and species are not found in the same thing: for shame is found in the
'reasoning' faculty, whereas fear is in the 'spirited' faculty, and 'pain' is found in the faculty of 'desires', (for in
this pleasure also is found), whereas 'anger' is found in the 'spirited' faculty. Hence the terms rendered are not
the genera, seeing that they do not naturally come to be in the same faculty as the species. Likewise, also, if
'friendship' be found in the faculty of desires, you may take it that it is not a form of 'wishing': for wishing is
always found in the 'reasoning' faculty. This commonplace rule is useful also in dealing with Accident: for
the accident and that of which it is an accident are both found in the same thing, so that if they do not appear
in the same thing, clearly it is not an accident.

Again, see if the species partakes of the genus attributed only in some particular respect: for it is the general
view that the genus is not thus imparted only in some particular respect: for a man is not an animal in a
particular respect, nor is grammar knowledge in a particular respect only. Likewise also in other instances.
Look, therefore, and see if in the case of any of its species the genus be imparted only in a certain respect;
e.g. if 'animal' has been described as an 'object of perception' or of 'sight'. For an animal is an object of
perception or of sight in a particular respect only; for it is in respect of its body that it is perceived and seen,
not in respect of its soul, so that-'object of sight' and 'object of perception' could not be the genus of 'animal'.

Sometimes also people place the whole inside the part without detection, defining (e.g.) 'animal' as an
'animate body'; whereas the part is not predicated in any sense of the whole, so that 'body' could not be the
genus of animal, seeing that it is a part.

See also if he has put anything that is blameworthy or objectionable into the class 'capacity' or 'capable', e.g.
by defining a 'sophist' or a 'slanderer', or a 'thief as 'one who is capable of secretly thieving other people's

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property'. For none of the aforesaid characters is so called because he is 'capable' in one of these respects: for
even God and the good man are capable of doing bad things, but that is not their character: for it is always in
respect of their choice that bad men are so called. Moreover, a capacity is always a desirable thing: for even
the capacities for doing bad things are desirable, and therefore it is we say that even God and the good man
possess them; for they are capable (we say) of doing evil. So then 'capacity' can never be the genus of
anything blameworthy. Else, the result will be that what is blameworthy is sometimes desirable: for there will
be a certain form of capacity that is blameworthy.

Also, see if he has put anything that is precious or desirable for its own sake into the class 'capacity' or
'capable' or 'productive' of anything. For capacity, and what is capable or productive of anything, is always
desirable for the sake of something else.

Or see if he has put anything that exists in two genera or more into one of them only. For some things it is
impossible to place in a single genus, e.g. the 'cheat' and the 'slanderer': for neither he who has the will
without the capacity, nor he who has the capacity without the will, is a slanderer or cheat, but he who has
both of them. Hence he must be put not into one genus, but into both the aforesaid genera.

Moreover, people sometimes in converse order render genus as differentia, and differentia as genus, defining
(e.g.) astonishment as 'excess of wonderment' and conviction as 'vehemence of conception'. For neither
'excess' nor 'vehemence' is the genus, but the differentia: for astonishment is usually taken to be an 'excessive
wonderment', and conviction to be a 'vehement conception', so that 'wonderment' and 'conception' are the
genus, while 'excess' and 'vehemence' are the differentia. Moreover, if any one renders 'excess' and
'vehemence' as genera, then inanimate things will be convinced and astonished. For 'vehemence' and 'excess'
of a thing are found in a thing which is thus vehement and in excess. If, therefore, astonishment be excess of
wonderment the astonishment will be found in the wonderment, so that 'wonderment' will be astonished!
Likewise, also, conviction will be found in the conception, if it be 'vehemence of conception', so that the
conception will be convinced. Moreover, a man who renders an answer in this style will in consequence find
himself calling vehemence vehement and excess excessive: for there is such a thing as a vehement
conviction: if then conviction be 'vehemence', there would be a 'vehement vehemence'. Likewise, also, there
is such a thing as excessive astonishment: if then astonishment be an excess, there would be an 'excessive
excess'. Whereas neither of these things is generally believed, any more than that knowledge is a knower or
motion a moving thing.

Sometimes, too, people make the bad mistake of putting an affection into that which is affected, as its genus,
e.g. those who say that immortality is everlasting life: for immortality seems to be a certain affection or
accidental feature of life. That this saying is true would appear clear if any one were to admit that a man can
pass from being mortal and become immortal: for no one will assert that he takes another life, but that a
certain accidental feature or affection enters into this one as it is. So then 'life' is not the genus of immortality.

Again, see if to an affection he has ascribed as genus the object of which it is an affection, by defining (e.g.)
wind as 'air in motion'. Rather, wind is 'a movement of air': for the same air persists both when it is in motion
and when it is still. Hence wind is not 'air' at all: for then there would also have been wind when the air was
not in motion, seeing that the same air which formed the wind persists. Likewise, also, in other cases of the
kind. Even, then, if we ought in this instance to admit the point that wind is 'air in motion', yet we should
accept a definition of the kind, not about all those things of which the genus is not true, but only in cases
where the genus rendered is a true predicate. For in some cases, e.g. 'mud' or 'snow', it is not generally held to
be true. For people tell you that snow is 'frozen water' and mud is earth mixed with moisture', whereas snow
is not water, nor mud earth, so that neither of the terms rendered could be the genus: for the genus should be
true of all its species. Likewise neither is wine 'fermented water', as Empedocles speaks of 'water fermented
in wood';' for it simply is not water at all.

Book IV 36

Topics

Moreover, see whether the term rendered fail to be the genus of anything at all; for then clearly it also fails to
be the genus of the species mentioned. Examine the point by seeing whether the objects that partake of the
genus fail to be specifically different from one another, e.g. white objects: for these do not differ specifically
from one another, whereas of a genus the species are always different, so that 'white' could not be the genus
of anything.

Again, see whether he has named as genus or differentia some feature that goes with everything: for the
number of attributes that follow everything is comparatively large: thus (e.g.) 'Being' and 'Unity' are among
the number of attributes that follow everything. If, therefore, he has rendered 'Being' as a genus, clearly it
would be the genus of everything, seeing that it is predicated of everything; for the genus is never predicated
of anything except of its species. Hence Unity, inter alia, will be a species of Being. The result, therefore, is
that of all things of which the genus is predicated, the species is predicated as well, seeing that Being and
Unity are predicates of absolutely everything, whereas the predication of the species ought to be of narrower
range. If, on the other hand, he has named as differentia some attribute that follows everything, clearly the
denotation of the differentia will be equal to, or wider than, that of the genus. For if the genus, too, be some
attribute that follows everything, the denotation of the differentia will be equal to its denotation, while if the
genus do not follow everything, it will be still wider.

Moreover, see if the description 'inherent in S' be used of the genus rendered in relation to its species, as it is
used of 'white' in the case of snow, thus showing clearly that it could not be the genus: for 'true of S' is the
only description used of the genus in relation to its species. Look and see also if the genus fails to be
synonymous with its species. For the genus is always predicated of its species synonymously.

Moreover, beware, whenever both species and genus have a contrary, and he places the better of the
contraries inside the worse genus: for the result will be that the remaining species will be found in the
remaining genus, seeing that contraries are found in contrary genera, so that the better species will be found
in the worse genus and the worse in the better: whereas the usual view is that of the better species the genus
too is better. Also see if he has placed the species inside the worse and not inside the better genus, when it is
at the same time related in like manner to both, as (e.g.) if he has defined the 'soul' as a 'form of motion' or 'a
form of moving thing'. For the same soul is usually thought to be a principle alike of rest and of motion, so
that, if rest is the better of the two, this is the genus into which the soul should have been put.

Moreover, judge by means of greater and less degrees: if overthrowing a view, see whether the genus admits
of a greater degree, whereas neither the species itself does so, nor any term that is called after it: e.g. if virtue
admits of a greater degree, so too does justice and the just man: for one man is called 'more just than another'.
If, therefore, the genus rendered admits of a greater degree, whereas neither the species does so itself nor yet
any term called after it, then what has been rendered could not be the genus.

Again, if what is more generally, or as generally, thought to be the genus be not so, clearly neither is the
genus rendered. The commonplace rule in question is useful especially in cases where the species appears to
have several predicates in the category of essence, and where no distinction has been drawn between them,
and we cannot say which of them is genus; e.g. both 'pain' and the 'conception of a slight' are usually thought
to be predicates of 'anger in the category of essence: for the angry man is both in pain and also conceives that
he is slighted. The same mode of inquiry may be applied also to the case of the species, by comparing it with
some other species: for if the one which is more generally, or as generally, thought to be found in the genus
rendered be not found therein, then clearly neither could the species rendered be found therein.

In demolishing a view, therefore, you should follow the rule as stated. In establishing one, on the other hand,
the commonplace rule that you should see if both the genus rendered and the species admit of a greater

Book IV 37

Topics

degree will not serve: for even though both admit it, it is still possible for one not to be the genus of the other.
For both 'beautiful' and 'white' admit of a greater degree, and neither is the genus of the other. On the other
hand, the comparison of the genera and of the species one with another is of use: e.g. supposing A and B to
have a like claim to be genus, then if one be a genus, so also is the other. Likewise, also, if what has less
claim be a genus, so also is what has more claim: e.g. if 'capacity' have more claim than 'virtue' to be the
genus of self-control, and virtue be the genus, so also is capacity. The same observations will apply also in
the case of the species. For instance, supposing A and B to have a like claim to be a species of the genus in
question, then if the one be a species, so also is the other: and if that which is less generally thought to be so
be a species, so also is that which is more generally thought to be so.

Moreover, to establish a view, you should look and see if the genus is predicated in the category of essence of
those things of which it has been rendered as the genus, supposing the species rendered to be not one single
species but several different ones: for then clearly it will be the genus. If, on the other, the species rendered be
single, look and see whether the genus be predicated in the category of essence of other species as well: for
then, again, the result will be that it is predicated of several different species.

Since some people think that the differentia, too, is a predicate of the various species in the category of
essence, you should distinguish the genus from the differentia by employing the aforesaid elementary
principles-(a) that the genus has a wider denotation than the differentia; (b) that in rendering the essence of a
thing it is more fitting to state the genus than the differentia: for any one who says that 'man' is an 'animal'
shows what man is better than he who describes him as 'walking'; also (c) that the differentia always signifies
a quality of the genus, whereas the genus does not do this of the differentia: for he who says 'walking'
describes an animal of a certain quality, whereas he who says 'animal' describes an animal of a certain
quality, whereas he who says 'animal' does not describe a walking thing of a certain quality.

The differentia, then, should be distinguished from the genus in this manner. Now seeing it is generally held
that if what is musical, in being musical, possesses knowledge in some respect, then also 'music' is a
particular kind of 'knowledge'; and also that if what walks is moved in walking, then 'walking' is a particular
kind of 'movement'; you should therefore examine in the aforesaid manner any genus in which you want to
establish the existence of something; e.g. if you wish to prove that 'knowledge' is a form of 'conviction', see
whether the knower in knowing is convinced: for then clearly knowledge would be a particular kind of
conviction. You should proceed in the same way also in regard to the other cases of this kind.

Moreover, seeing that it is difficult to distinguish whatever always follows along with a thing, and is not
convertible with it, from its genus, if A follows B universally, whereas B does not follow A universally-as
e.g. 'rest' always follows a 'calm' and 'divisibility' follows 'number', but not conversely (for the divisible is not
always a number, nor rest a calm)-you may yourself assume in your treatment of them that the one which
always follows is the genus, whenever the other is not convertible with it: if, on the other hand, some one else
puts forward the proposition, do not accept it universally. An objection to it is that 'not-being' always follows
what is 'coming to be' (for what is coming to be is not) and is not convertible with it (for what is not is not
always coming to be), and that still 'not-being' is not the genus of 'coming to be': for 'not-being' has not any
species at all. Questions, then, in regard to Genus should be investigated in the ways described.

BookV

THE question whether the attribute stated is or is not a property, should be examined by the following
methods:

Book V 38

Topics

Any 'property' rendered is always either essential and permanent or relative and temporary: e.g. it is an
'essential property' of man to be 'by nature a civilized animal': a 'relative property' is one like that of the soul
in relation to the body, viz. that the one is fitted to command, and the other to obey: a 'permanent property' is
one like the property which belongs to God, of being an 'immortal living being': a 'temporary property' is one
like the property which belongs to any particular man of walking in the gymnasium.

[The rendering of a property 'relatively' gives rise either to two problems or to four. For if he at the same time
render this property of one thing and deny it of another, only two problems arise, as in the case of a statement
that it is a property of a man, in relation to a horse, to be a biped. For one might try both to show that a man is
not a biped, and also that a horse is a biped: in both ways the property would be upset. If on the other hand he
render one apiece of two attributes to each of two things, and deny it in each case of the other, there will then
be four problems; as in the case of a statement that it is a property of a man in relation to a horse for the
former to be a biped and the latter a quadruped. For then it is possible to try to show both that a man is not
naturally a biped, and that he is a quadruped, and also that the horse both is a biped, and is not a quadruped. If
you show any of these at all, the intended attribute is demolished.]

An 'essential' property is one which is rendered of a thing in comparison with everything else and
distinguishes the said thing from everything else, as does 'a mortal living being capable of receiving
knowledge' in the case of man. A 'relative' property is one which separates its subject off not from everything
else but only from a particular definite thing, as does the property which virtue possesses, in comparison with
knowledge, viz. that the former is naturally produced in more than one faculty, whereas the latter is produced
in that of reason alone, and in those who have a reasoning faculty. A 'permanent' property is one which is true
at every time, and never fails, like being' compounded of soul and body', in the case of a living creature. A
'temporary' property is one which is true at some particular time, and does not of necessity always follow; as,
of some particular man, that he walks in the market-place.

To render a property 'relatively' to something else means to state the difference between them as it is found
either universally and always, or generally and in most cases: thus a difference that is found universally and
always, is one such as man possesses in comparison with a horse, viz. being a biped: for a man is always and
in every case a biped, whereas a horse is never a biped at any time. On the other hand, a difference that is
found generally and in most cases, is one such as the faculty of reason possesses in comparison with that of
desire and spirit, in that the former commands, while the latter obeys: for the reasoning faculty does not
always command, but sometimes also is under command, nor is that of desire and spirit always under
command, but also on occasion assumes the command, whenever the soul of a man is vicious.

Of 'properties' the most 'arguable' are the essential and permanent and the relative. For a relative property
gives rise, as we said before, to several questions: for of necessity the questions arising are either two or four,
or that arguments in regard to these are several. An essential and a permanent property you can discuss in
relation to many things, or can observe in relation to many periods of time: if essential', discuss it in
comparison with many things: for the property ought to belong to its subject in comparison with every single
thing that is, so that if the subject be not distinguished by it in comparison with everything else, the property
could not have been rendered correctly. So a permanent property you should observe in relation to many
periods of time; for if it does not or did not, or is not going to, belong, it will not be a property. On the other
hand, about a temporary property we do not inquire further than in regard to the time called 'the present'; and
so arguments in regard to it are not many; whereas an arguable' question is one in regard to which it is
possible for arguments both numerous and good to arise.

The so-called 'relative' property, then, should be examined by means of the commonplace arguments relating
to Accident, to see whether it belongs to the one thing and not to the other: on the other hand, permanent and
essential properties should be considered by the following methods.

Book V 39

Topics

First, see whether the property has or has not been rendered correctly. Of a rendering being incorrect or
correct, one test is to see whether the terms in which the property is stated are not or are more intelligible-for
destructive purposes, whether they are not so, and for constructive purposes, whether they are so. Of the
terms not being more intelligible, one test is to see whether the property which he renders is altogether more
unintelligible than the subject whose property he has stated: for, if so, the property will not have been stated
correctly. For the object of getting a property constituted is to be intelligible: the terms therefore in which it is
rendered should be more intelligible: for in that case it will be possible to conceive it more adequately, e.g.
any one who has stated that it is a property of 'fire' to 'bear a very close resemblance to the soul', uses the term
'soul', which is less intelligible than 'fire'-for we know better what fire is than what soul is-, and therefore a
'very close resemblance to the soul' could not be correctly stated to be a property of fire. Another test is to see
whether the attribution of A (property) to B (subject) fails to be more intelligible. For not only should the
property be more intelligible than its subject, but also it should be something whose attribution to the
particular subject is a more intelligible attribution. For he who does not know whether it is an attribute of the
particular subject at all, will not know either whether it belongs to it alone, so that whichever of these results
happens, its character as a property becomes obscure. Thus (e.g.) a man who has stated that it is a property of
fire to be 'the primary element wherein the soul is naturally found', has introduced a subject which is less
intelligible than 'fire', viz. whether the soul is found in it, and whether it is found there primarily; and
therefore to be 'the primary element in which the soul is naturally found' could not be correctly stated to be a
property of 'fire'. On the other hand, for constructive purposes, see whether the terms in which the property is
stated are more intelligible, and if they are more intelligible in each of the aforesaid ways. For then the
property will have been correctly stated in this respect: for of constructive arguments, showing the
correctness of a rendering, some will show the correctness merely in this respect, while others will show it
without qualification. Thus (e.g.) a man who has said that the 'possession of sensation' is a property of
'animal' has both used more intelligible terms and has rendered the property more intelligible in each of the
aforesaid senses; so that to 'possess sensation' would in this respect have been correctly rendered as a
property of 'animal'.

Next, for destructive purposes, see whether any of the terms rendered in the property is used in more than one
sense, or whether the whole expression too signifies more than one thing. For then the property will not have
been correctly stated. Thus (e.g.) seeing that to 'being natural sentient' signifies more than one thing, viz. (1)
to possess sensation, (2) to use one's sensation, being naturally sentient' could not be a correct statement of a
property of 'animal'. The reason why the term you use, or the whole expression signifying the property,
should not bear more than one meaning is this, that an expression bearing more than one meaning makes the
object described obscure, because the man who is about to attempt an argument is in doubt which of the
various senses the expression bears: and this will not do, for the object of rendering the property is that he
may understand. Moreover, in addition to this, it is inevitable that those who render a property after this
fashion should be somehow refuted whenever any one addresses his syllogism to that one of the term's
several meanings which does not agree. For constructive purposes, on the other hand, see whether both all the
terms and also the expression as a whole avoid bearing more than one sense: for then the property will have
been correctly stated in this respect. Thus (e.g.) seeing that 'body' does not bear several meanings, nor
quickest to move upwards in space', nor yet the whole expression made by putting them together, it would be
correct in this respect to say that it is a property of fire to be the 'body quickest to move upwards in space'.

Next, for destructive purposes, see if the term of which he renders the property is used in more than one
sense, and no distinction has been drawn as to which of them it is whose property he is stating: for then the
property will not have been correctly rendered. The reasons why this is so are quite clear from what has been
said above: for the same results are bound to follow. Thus (e.g.) seeing that 'the knowledge of this' signifies
many things for it means (1) the possession of knowledge by it, (2) the use of its knowledge by it, (3) the
existence of knowledge about it, (4) the use of knowledge about it-no property of the 'knowledge of this'

Book V 40

Topics

could be rendered correctly unless he draw a distinction as to which of these it is whose property he is
rendering. For constructive purposes, a man should see if the term of which he is rendering the property
avoids bearing many senses and is one and simple: for then the property will have been correctly stated in this
respect. Thus (e.g.) seeing that 'man' is used in a single sense, 'naturally civilized animal' would be correctly
stated as a property of man.

Next, for destructive purposes, see whether the same term has been repeated in the property. For people often
do this undetected in rendering 'properties' also, just as they do in their 'definitions' as well: but a property to
which this has happened will not have been correctly stated: for the repetition of it confuses the hearer; thus
inevitably the meaning becomes obscure, and further, such people are thought to babble. Repetition of the
same term is likely to happen in two ways; one is, when a man repeatedly uses the same word, as would
happen if any one were to render, as a property of fire, 'the body which is the most rarefied of bodies' (for he
has repeated the word 'body'); the second is, if a man replaces words by their definitions, as would happen if
any one were to render, as a property of earth, 'the substance which is by its nature most easily of all bodies
borne downwards in space', and were then to substitute 'substances of such and such a kind' for the word
'bodies': for 'body' and 'a substance of such and such a kind' mean one and the same thing. For he will have
repeated the word 'substance', and accordingly neither of the properties would be correctly stated. For
constructive purposes, on the other hand, see whether he avoids ever repeating the same term; for then the
property will in this respect have been correctly rendered. Thus (e.g.) seeing that he who has stated 'animal
capable of acquiring knowledge' as a property of man has avoided repeating the same term several times, the
property would in this respect have been correctly rendered of man.

Next, for destructive purposes, see whether he has rendered in the property any such term as is a universal
attribute. For one which does not distinguish its subject from other things is useless, and it is the business of
the language Of 'properties', as also of the language of definitions, to distinguish. In the case contemplated,
therefore, the property will not have been correctly rendered. Thus (e.g.) a man who has stated that it is a
property of knowledge to be a 'conception incontrovertible by argument, because of its unity', has used in the
property a term of that kind, viz. 'unity', which is a universal attribute; and therefore the property of
knowledge could not have been correctly stated. For constructive purposes, on the other hand, see whether he
has avoided all terms that are common to everything and used a term that distinguishes the subject from
something: for then the property will in this respect have been correctly stated. Thus (e.g.) inasmuch as he
who has said that it is a property of a 'living creature' to 'have a soul' has used no term that is common to
everything, it would in this respect have been correctly stated to be a property of a 'living creature' to 'have a
soul'.

Next, for destructive purposes see whether he renders more than one property of the same thing, without a
definite proviso that he is stating more than one: for then the property will not have been correctly stated. For
just as in the case of definitions too there should be no further addition beside the expression which shows the
essence, so too in the case of properties nothing further should be rendered beside the expression that
constitutes the property mentioned: for such an addition is made to no purpose. Thus (e.g.) a man who has
said that it is a property of fire to be 'the most rarefied and lightest body' has rendered more than one property
(for each term is a true predicate of fire alone); and so it could not be a correctly stated property of fire to be
'the most rarefied and lightest body'. On the other hand, for constructive purposes, see whether he has avoided
rendering more than one property of the same thing, and has rendered one only: for then the property will in
this respect have been correctly stated. Thus (e.g.) a man who has said that it is a property of a liquid to be a
'body adaptable to every shape' has rendered as its property a single character and not several, and so the
property of 'liquid' would in this respect have been correctly stated.

BookV 41

Topics

Next, for destructive purposes, see whether he has employed either the actual subject whose property he is
rendering, or any of its species: for then the property will not have been correctly stated. For the object of
rendering the property is that people may understand: now the subject itself is just as unintelligible as it was
to start with, while any one of its species is posterior to it, and so is no more intelligible. Accordingly it is
impossible to understand anything further by the use of these terms. Thus (e.g.) any one who has said that it
is property of 'animal' to be 'the substance to which "man" belongs as a species' has employed one of its
species, and therefore the property could not have been correctly stated. For constructive purposes, on the
other hand, see whether he avoids introducing either the subject itself or any of its species: for then the
property will in this respect have been correctly stated. Thus (e.g.) a man who has stated that it is a property
of a living creature to be 'compounded of soul and body' has avoided introducing among the rest either the
subject itself or any of its species, and therefore in this respect the property of a 'living creature' would have
been correctly rendered.

You should inquire in the same way also in the case of other terms that do or do not make the subject more
intelligible: thus, for destructive purposes, see whether he has employed anything either opposite to the
subject or, in general, anything simultaneous by nature with it or posterior to it: for then the property will not
have been correctly stated. For an opposite is simultaneous by nature with its opposite, and what is
simultaneous by nature or is posterior to it does not make its subject more intelligible. Thus (e.g.) any one
who has said that it is a property of good to be 'the most direct opposite of evil', has employed the opposite of
good, and so the property of good could not have been correctly rendered. For constructive purposes, on the
other hand, see whether he has avoided employing anything either opposite to, or, in general, simultaneous by
nature with the subject, or posterior to it: for then the property will in this respect have been correctly
rendered. Thus (e.g.) a man who has stated that it is a property of knowledge to be 'the most convincing
conception' has avoided employing anything either opposite to, or simultaneous by nature with, or posterior
to, the subject; and so the property of knowledge would in this respect have been correctly stated.

Next, for destructive purposes, see whether he has rendered as property something that does not always
follow the subject but sometimes ceases to be its property: for then the property will not have been correctly
described. For there is no necessity either that the name of the subject must also be true of anything to which
we find such an attribute belonging; nor yet that the name of the subject will be untrue of anything to which
such an attribute is found not to belong. Moreover, in addition to this, even after he has rendered the property
it will not be clear whether it belongs, seeing that it is the kind of attribute that may fall: and so the property
will not be clear. Thus (e.g.) a man who has stated that it is a property of animal 'sometimes to move and
sometimes to stand still' rendered the kind of property which sometimes is not a property, and so the property
could not have been correctly stated. For constructive purposes, on the other hand, see whether he has
rendered something that of necessity must always be a property: for then the property will have been in this
respect correctly stated. Thus (e.g.) a man who has stated that it is a property of virtue to be 'what makes its
possessor good' has rendered as property something that always follows, and so the property of virtue would
in this respect have been correctly rendered.

Next, for destructive purposes, see whether in rendering the property of the present time he has omitted to
make a definite proviso that it is the property of the present time which he is rendering: for else the property
will not have been correctly stated. For in the first place, any unusual procedure always needs a definite
proviso: and it is the usual procedure for everybody to render as property some attribute that always follows.
In the second place, a man who omits to provide definitely whether it was the property of the present time
which he intended to state, is obscure: and one should not give any occasion for adverse criticism. Thus (e.g.)
a man who has stated it as the property of a particular man 'to be sitting with a particular man', states the
property of the present time, and so he cannot have rendered the property correctly, seeing that he has
described it without any definite proviso. For constructive purposes, on the other hand, see whether, in
rendering the property of the present time, he has, in stating it, made a definite proviso that it is the property
of the present time that he is stating: for then the property will in this respect have been correctly stated. Thus

Book V 42

Topics

(e.g.) a man who has said that it is the property of a particular man 'to be walking now', has made this
distinction in his statement, and so the property would have been correctly stated.

Next, for destructive purposes, see whether he has rendered a property of the kind whose appropriateness is
not obvious except by sensation: for then the property will not have been correctly stated. For every sensible
attribute, once it is taken beyond the sphere of sensation, becomes uncertain. For it is not clear whether it still
belongs, because it is evidenced only by sensation. This principle will be true in the case of any attributes that
do not always and necessarily follow. Thus (e.g.) any one who has stated that it is a property of the sun to be
'the brightest star that moves over the earth', has used in describing the property an expression of that kind,
viz. 'to move over the earth', which is evidenced by sensation; and so the sun's property could not have been
correctly rendered: for it will be uncertain, whenever the sun sets, whether it continues to move over the
earth, because sensation then fails us. For constructive purposes, on the other hand, see whether he has
rendered the property of a kind that is not obvious to sensation, or, if it be sensible, must clearly belong of
necessity: for then the property will in this respect have been correctly stated. Thus (e.g.) a man who has
stated that it is a property of a surface to be 'the primary thing that is coloured', has introduced amongst the
rest a sensible quality, 'to be coloured', but still a quality such as manifestly always belongs, and so the
property of 'surface' would in this respect have been correctly rendered.

Next, for destructive purposes, see whether he has rendered the definition as a property: for then the property
will not have been correctly stated: for the property of a thing ought not to show its essence. Thus (e.g.) a
man who has said that it is the property of man to be 'a walking, biped animal' has rendered a property of man
so as to signify his essence, and so the property of man could not have been correctly rendered. For
constructive purposes, on the other hand, see whether the property which he has rendered forms a predicate
convertible with its subject, without, however, signifying its essence: for then the property will in this respect
have been correctly rendered. Thus (e.g.) he who has stated that it is a property of man to be a 'naturally
civilized animal' has rendered the property so as to be convertible with its subject, without, however, showing
its essence, and so the property of man' would in this respect have been correctly rendered.

Next, for destructive purposes, see whether he has rendered the property without having placed the subject
within its essence. For of properties, as also of definitions, the first term to be rendered should be the genus,
and then the rest of it should be appended immediately afterwards, and should distinguish its subject from
other things. Hence a property which is not stated in this way could not have been correctly rendered. Thus
(e.g.) a man who has said that it is a property of a living creature to 'have a soul' has not placed 'living
creature' within its essence, and so the property of a living creature could not have been correctly stated. For
constructive purposes, on the other hand, see whether a man first places within its essence the subject whose
property he is rendering, and then appends the rest: for then the property will in this respect have been
correctly rendered. Thus (e.g.) he who has stated that is a property of man to be an 'animal capable of
receiving knowledge', has rendered the property after placing the subject within its essence, and so the
property of 'man' would in this respect have been correctly rendered.

The inquiry, then, whether the property has been correctly rendered or no, should be made by these means.
The question, on the other hand, whether what is stated is or is not a property at all, you should examine from
the following points of view. For the commonplace arguments which establish absolutely that the property is
accurately stated will be the same as those that constitute it a property at all: accordingly they will be
described in the course of them.

Firstly, then, for destructive purposes, take a look at each subject of which he has rendered the property, and
see (e.g.) if it fails to belong to any of them at all, or to be true of them in that particular respect, or to be a
property of each of them in respect of that character of which he has rendered the property: for then what is

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stated to be a property will not be a property. Thus, for example, inasmuch as it is not true of the
geometrician that he 'cannot be deceived by an argument' (for a geometrician is deceived when his figure is
misdrawn), it could not be a property of the man of science that he is not deceived by an argument. For
constructive purposes, on the other hand, see whether the property rendered be true of every instance, and
true in that particular respect: for then what is stated not to be a property will be a property. Thus, for
example, in as much as the description 'an animal capable of receiving knowledge' is true of every man, and
true of him qua man, it would be a property of man to be 'an animal capable of receiving knowledge',
commonplace rule means-for destructive purposes, see if the description fails to be true of that of which the
name is true; and if the name fails to be true of that of which the description is true: for constructive purposes,
on the other hand, see if the description too is predicated of that of which the name is predicated, and if the
name too is predicated of that of which the description is predicated.]

Next, for destructive purposes, see if the description fails to apply to that to which the name applies, and if
the name fails to apply to that to which the description applies: for then what is stated to be a property will
not be a property. Thus (e.g.) inasmuch as the description 'a living being that partakes of knowledge' is true of
God, while 'man' is not predicated of God, to be a living being that partakes of knowledge' could not be a
property of man. For constructive purposes, on the other hand, see if the name as well be predicated of that of
which the description is predicated, and if the description as well be predicated of that of which the name is
predicated. For then what is stated not to be a property will be a property. Thus (e.g.) the predicate 'living
creature' is true of that of which 'having a soul' is true, and 'having a soul' is true of that of which the predicate
'living creature' is true; and so 'having a soul would be a property of 'living creature'.

Next, for destructive purposes, see if he has rendered a subject as a property of that which is described as 'in
the subject': for then what has been stated to be a property will not be a property. Thus (e.g.) inasmuch as he
who has rendered 'fire' as the property of 'the body with the most rarefied particles', has rendered the subject
as the property of its predicate, 'fire' could not be a property of 'the body with the most rarefied particles'. The
reason why the subject will not be a property of that which is found in the subject is this, that then the same
thing will be the property of a number of things that are specifically different. For the same thing has quite a
number of specifically different predicates that belong to it alone, and the subject will be a property of all of
these, if any one states the property in this way. For constructive purposes, on the other hand, see if he has
rendered what is found in the subject as a property of the subject: for then what has been stated not to be a
property will be a property, if it be predicated only of the things of which it has been stated to be the property.
Thus (e.g.) he who has said that it is a property of 'earth' to be 'specifically the heaviest body' has rendered of
the subject as its property something that is said of the thing in question alone, and is said of it in the manner
in which a property is predicated, and so the property of earth would have been rightly stated.

Next, for destructive purposes, see if he has rendered the property as partaken of: for then what is stated to be
a property will not be a property. For an attribute of which the subject partakes is a constituent part of its
essence: and an attribute of that kind would be a differentia applying to some one species. E.g. inasmuch as
he who has said that 'walking on two feet' is property of man has rendered the property as partaken of,
'walking on two feet' could not be a property of 'man'. For constructive purposes, on the other hand, see if he
has avoided rendering the property as partaken of, or as showing the essence, though the subject is predicated
convertibly with it: for then what is stated not to be a property will be a property. Thus (e.g.) he who has
stated that to be 'naturally sentient' is a property of 'animal' has rendered the property neither as partaken of
nor as showing the essence, though the subject is predicated convertibly with it; and so to be 'naturally
sentient' would be a property of 'animal'.

Next, for destructive purposes, see if the property cannot possibly belong simultaneously, but must belong
either as posterior or as prior to the attribute described in the name: for then what is stated to be a property
will not be a property either never, or not always. Thus (e.g.) inasmuch as it is possible for the attribute
'walking through the market-place' to belong to an object as prior and as posterior to the attribute 'man',

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'walking through the market-place' could not be a property of 'man' either never, or not always. For
constructive purposes, on the other hand, see if it always and of necessity belongs simultaneously, without
being either a definition or a differentia: for then what is stated not to be a property will be a property. Thus
(e.g.) the attribute 'an animal capable of receiving knowledge' always and of necessity belongs
simultaneously with the attribute 'man', and is neither differentia nor definition of its subject, and so 'an
animal capable of receiving knowledge' would be a property of 'man'.

Next, for destructive purposes, see if the same thing fails to be a property of things that are the same as the
subject, so far as they are the same: for then what is stated to be a property will not be a property. Thus, for
example, inasmuch as it is no property of a 'proper object of pursuit' to 'appear good to certain persons', it
could not be a property of the 'desirable' either to 'appear good to certain persons': for 'proper object of
pursuit' and 'desirable' mean the same. For constructive purposes, on the other hand, see if the same thing be a
property of something that is the same as the subject, in so far as it is the same. For then is stated not to be a
property will be a property. Thus (e.g.) inasmuch as it is called a property of a man, in so far as he is a man,
'to have a tripartite soul', it would also be a property of a mortal, in so far as he is a mortal, to have a tripartite
soul. This commonplace rule is useful also in dealing with Accident: for the same attributes ought either to
belong or not belong to the same things, in so far as they are the same.

Next, for destructive purposes, see if the property of things that are the same in kind as the subject fails to be
always the same in kind as the alleged property: for then neither will what is stated to be the property of the
subject in question. Thus (e.g.) inasmuch as a man and a horse are the same in kind, and it is not always a
property of a horse to stand by its own initiative, it could not be a property of a man to move by his own
initiative; for to stand and to move by his own initiative are the same in kind, because they belong to each of
them in so far as each is an 'animal'. For constructive purposes, on the other hand, see if of things that are the
same in kind as the subject the property that is the same as the alleged property is always true: for then what
is stated not to be a property will be a property. Thus (e.g.) since it is a property of man to be a 'walking
biped,' it would also be a property of a bird to be a 'flying biped': for each of these is the same in kind, in so
far as the one pair have the sameness of species that fall under the same genus, being under the genus
'animal', while the other pair have that of differentiae of the genus, viz. of 'animal'. This commonplace rule is
deceptive whenever one of the properties mentioned belongs to some one species only while the other
belongs to many, as does 'walking quadruped'.

Inasmuch as 'same' and 'different' are terms used in several senses, it is a job to render to a sophistical
questioner a property that belongs to one thing and that only. For an attribute that belongs to something
qualified by an accident will also belong to the accident taken along with the subject which it qualifies; e.g.
an attribute that belongs to 'man' will belong also to 'white man', if there be a white man, and one that belongs
to 'white man' will belong also to 'man'. One might, then, bring captious criticism against the majority of
properties, by representing the subject as being one thing in itself, and another thing when combined with its
accident, saying, for example, that 'man' is one thing, and white man' another, and moreover by representing
as different a certain state and what is called after that state. For an attribute that belongs to the state will
belong also to what is called after that state, and one that belongs to what is called after a state will belong
also to the state: e.g. inasmuch as the condition of the scientist is called after his science, it could not be a
property of 'science' that it is 'incontrovertible by argument'; for then the scientist also will be incontrovertible
by argument. For constructive purposes, however, you should say that the subject of an accident is not
absolutely different from the accident taken along with its subject; though it is called 'another' thing because
the mode of being of the two is different: for it is not the same thing for a man to be a man and for a white
man to be a white man. Moreover, you should take a look along at the inflections, and say that the description
of the man of science is wrong: one should say not 'it' but 'he is incontrovertible by argument'; while the
description of Science is wrong too: one should say not 'it' but 'she is incontrovertible by argument'. For
against an objector who sticks at nothing the defence should stick at nothing.

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Next, for destructive purposes, see if, while intending to render an attribute that naturally belongs, he states it
in his language in such a way as to indicate one that invariably belongs: for then it would be generally agreed
that what has been stated to be a property is upset. Thus (e.g.) the man who has said that 'biped' is a property
of man intends to render the attribute that naturally belongs, but his expression actually indicates one that
invariably belongs: accordingly, 'biped' could not be a property of man: for not every man is possessed of two
feet. For constructive purposes, on the other hand, see if he intends to render the property that naturally
belongs, and indicates it in that way in his language: for then the property will not be upset in this respect.
Thus (e.g.) he who renders as a property of 'man' the phrase 'an animal capable of receiving knowledge' both
intends, and by his language indicates, the property that belongs by nature, and so 'an animal capable of
receiving knowledge' would not be upset or shown in that respect not to be a property of man.

Moreover, as regards all the things that are called as they are primarily after something else, or primarily in
themselves, it is a job to render the property of such things. For if you render a property as belonging to the
subject that is so called after something else, then it will be true of its primary subject as well; whereas if you
state it of its primary subject, then it will be predicated also of the thing that is so called after this other. Thus
(e.g.) if any one renders , coloured' as the property of 'surface', 'coloured' will be true of body as well;
whereas if he render it of 'body', it will be predicated also of 'surface'. Hence the name as well will not be true
of that of which the description is true.

In the case of some properties it mostly happens that some error is incurred because of a failure to define how
as well as to what things the property is stated to belong. For every one tries to render as the property of a
thing something that belongs to it either naturally, as 'biped' belongs to 'man', or actually, as 'having four
fingers' belongs to a particular man, or specifically, as 'consisting of most rarefied particles' belongs to 'fire',
or absolutely, as 'life' to 'living being', or one that belongs to a thing only as called after something else, as
'wisdom' to the 'soul', or on the other hand primarily, as 'wisdom' to the 'rational faculty', or because the thing
is in a certain state, as 'incontrovertible by argument' belongs to a 'scientist' (for simply and solely by reason
of his being in a certain state will he be 'incontrovertible by argument'), or because it is the state possessed by
something, as 'incontrovertible by argument' belongs to 'science', or because it is partaken of, as 'sensation'
belongs to 'animal' (for other things as well have sensation, e.g. man, but they have it because they already
partake of 'animal'), or because it partakes of something else, as 'life' belongs to a particular kind of 'living
being'. Accordingly he makes a mistake if he has failed to add the word 'naturally', because what belongs
naturally may fail to belong to the thing to which it naturally belongs, as (e.g.) it belongs to a man to have
two feet: so too he errs if he does not make a definite proviso that he is rendering what actually belongs,
because one day that attribute will not be what it now is, e.g. the man's possession of four fingers. So he errs
if he has not shown that he states a thing to be such and such primarily, or that he calls it so after something
else, because then its name too will not be true of that of which the description is true, as is the case with
'coloured', whether rendered as a property of 'surface' or of 'body'. So he errs if he has not said beforehand
that he has rendered a property to a thing either because that thing possesses a state, or because it is a state
possessed by something; because then it will not be a property. For, supposing he renders the property to
something as being a state possessed, it will belong to what possesses that state; while supposing he renders it
to what possesses the state, it will belong to the state possessed, as did 'incontrovertible by argument' when
stated as a property of 'science' or of the 'scientist'. So he errs if he has not indicated beforehand that the
property belongs because the thing partakes of, or is partaken of by, something; because then the property
will belong to certain other things as well. For if he renders it because its subject is partaken of, it will belong
to the things which partake of it; whereas if he renders it because its subject partakes of something else, it will
belong to the things partaken of, as (e.g.) if he were to state 'life' to be a property of a 'particular kind of living
being', or just of 'living being. So he errs if he has not expressly distinguished the property that belongs
specifically, because then it will belong only to one of the things that fall under the term of which he states
the property: for the superlative belongs only to one of them, e.g. 'lightest' as applied to 'fire'. Sometimes, too,

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a man may even add the word 'specifically', and still make a mistake. For the things in question should all be
of one species, whenever the word 'specifically' is added: and in some cases this does not occur, as it does
not, in fact, in the case of fire. For fire is not all of one species; for live coals and flame and light are each of
them 'fire', but are of different species. The reason why, whenever 'specifically' is added, there should not be
any species other than the one mentioned, is this, that if there be, then the property in question will belong to
some of them in a greater and to others in a less degree, as happens with 'consisting of most rarefied particles'
in the case of fire: for 'light' consists of more rarefied particles than live coals and flame. And this should not
happen unless the name too be predicated in a greater degree of that of which the description is truer;
otherwise the rule that where the description is truer the name too should be truer is not fulfilled. Moreover,
in addition to this, the same attribute will be the property both of the term which has it absolutely and of that
element therein which has it in the highest degree, as is the condition of the property 'consisting of most
rarefied particles' in the case of 'fire': for this same attribute will be the property of 'light' as well: for it is
'light' that 'consists of the most rarefied particles'. If, then, any one else renders a property in this way one
should attack it; for oneself, one should not give occasion for this objection, but should define in what
manner one states the property at the actual time of making the statement.

Next, for destructive purposes, see if he has stated a thing as a property of itself: for then what has been stated
to be a property will not be a property. For a thing itself always shows its own essence, and what shows the
essence is not a property but a definition. Thus (e.g.) he who has said that 'becoming' is a property of
'beautiful' has rendered the term as a property of itself (for 'beautiful' and 'becoming' are the same); and so
'becoming' could not be a property of 'beautiful'. For constructive purposes, on the other hand, see if he has
avoided rendering a thing as a property of itself, but has yet stated a convertible predicate: for then what is
stated not to be a property will be a property. Thus he who has stated 'animate substance' as a property of
'living-creature' has not stated 'living-creature' as a property of itself, but has rendered a convertible
predicate, so that 'animate substance' would be a property of 'living-creature'.

Next, in the case of things consisting of like parts, you should look and see, for destructive purposes, if the
property of the whole be not true of the part, or if that of the part be not predicated of the whole: for then
what has been stated to be the property will not be a property. In some cases it happens that this is so: for
sometimes in rendering a property in the case of things that consist of like parts a man may have his eye on
the whole, while sometimes he may address himself to what is predicated of the part: and then in neither case
will it have been rightly rendered. Take an instance referring to the whole: the man who has said that it is a
property of the 'sea' to be 'the largest volume of salt water', has stated the property of something that consists
of like parts, but has rendered an attribute of such a kind as is not true of the part (for a particular sea is not
'the largest volume of salt water'); and so the largest volume of salt water' could not be a property of the 'sea'.
Now take one referring to the part: the man who has stated that it is a property of 'air' to be 'breathable' has
stated the property of something that consists of like parts, but he has stated an attribute such as, though true
of some air, is still not predicable of the whole (for the whole of the air is not breathable); and so 'breathable'
could not be a property of 'air'. For constructive purposes, on the other hand, see whether, while it is true of
each of the things with similar parts, it is on the other hand a property of them taken as a collective whole: for
then what has been stated not to be a property will be a property. Thus (e.g.) while it is true of earth
everywhere that it naturally falls downwards, it is a property of the various particular pieces of earth taken as
'the Earth', so that it would be a property of 'earth' 'naturally to fall downwards'.

Next, look from the point of view of the respective opposites, and first (a) from that of the contraries, and see,
for destructive purposes, if the contrary of the term rendered fails to be a property of the contrary subject. For
then neither will the contrary of the first be a property of the contrary of the second. Thus (e.g.) inasmuch as
injustice is contrary to justice, and the lowest evil to the highest good, but 'to be the highest good' is not a
property of justice', therefore 'to be the lowest evil' could not be a property of 'injustice'. For constructive

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purposes, on the other hand, see if the contrary is the property of the contrary: for then also the contrary of the
first will be the property of the contrary of the second. Thus (e.g.) inasmuch as evil is contrary to good, and
objectionable to desirable, and 'desirable' is a property of 'good', 'objectionable' would be a property of 'evil'.

Secondly (h) look from the point of view of relative opposites and see, for destructive purposes, if the
correlative of the term rendered fails to be a property of the correlative of the subject: for then neither will the
correlative of the first be a property of the correlative of the second. Thus (e.g.) inasmuch as 'double' is
relative to 'half, and 'in excess' to 'exceeded', while 'in excess' is not a property of 'double', exceeded' could
not be a property of 'half. For constructive purposes, on the other hand, see if the correlative of the alleged
property is a property of the subject's correlative: for then also the correlative of the first will be a property of
the correlative of the second: e.g. inasmuch as 'double' is relative to 'half, and the proportion 1:2 is relative to
the proportion 2:1, while it is a property of 'double' to be 'in the proportion of 2 to T, it would be a property of
'half to be 'in the proportion of 1 to 2'.

Thirdly (c) for destructive purposes, see if an attribute described in terms of a state (X) fails to be a property
of the given state (Y): for then neither will the attribute described in terms of the privation (of X) be a
property of the privation (of Y). Also if, on the other hand, an attribute described in terms of the privation (of
X) be not a property of the given privation (of Y), neither will the attribute described in terms of the state (X)
be a property of the state (Y). Thus, for example, inasmuch as it is not predicated as a property of 'deafness' to
be a 'lack of sensation', neither could it be a property of 'hearing' to be a 'sensation'. For constructive
purposes, on the other hand, see if an attribute described in terms of a state (X) is a property of the given state
(Y): for then also the attribute that is described in terms of the privation (of X) will be a property of the
privation (of Y). Also, if an attribute described in terms of a privation (of X) be a property of the privation (of
Y), then also the attribute that is described in terms of the state (X) will be a property of the state (Y). Thus
(e.g.) inasmuch as 'to see' is a property of 'sight', inasmuch as we have sight, 'failure to see' would be a
property of 'blindness', inasmuch as we have not got the sight we should naturally have.

Next, look from the point of view of positive and negative terms; and first (a) from the point of view of the
predicates taken by themselves. This common-place rule is useful only for a destructive purpose. Thus (e.g.)
see if the positive term or the attribute described in terms of it is a property of the subject: for then the
negative term or the attribute described in terms of it will not be a property of the subject. Also if, on the
other hand, the negative term or the attribute described in terms of it is a property of the subject, then the
positive term or the attribute described in terms of it will not be a property of the subject: e.g. inasmuch as
'animate' is a property of 'living creature', 'inanimate' could not be a property of 'living creature'.

Secondly (b) look from the point of view of the predicates, positive or negative, and their respective subjects;
and see, for destructive purposes, if the positive term falls to be a property of the positive subject: for then
neither will the negative term be a property of the negative subject. Also, if the negative term fails to be a
property of the negative subject, neither will the positive term be a property of the positive subject. Thus
(e.g.) inasmuch as 'animal' is not a property of 'man', neither could 'not-animal' be a property of 'not-man'.
Also if 'not-animal' seems not to be a property of 'not-man', neither will 'animal' be a property of 'man'. For
constructive purposes, on the other hand, see if the positive term is a property of the positive subject: for then
the negative term will be a property of the negative subject as well. Also if the negative term be a property of
the negative subject, the positive will be a property of the positive as well. Thus (e.g.) inasmuch as it is a
property of 'not-living being' 'not to live', it would be a property of 'living being' 'to live': also if it seems to
be a property of 'living being' 'to live', it will also seem to be a property of 'not-living being' 'not to live'.

Thirdly (c) look from the point of view of the subjects taken by themselves, and see, for destructive purposes,
if the property rendered is a property of the positive subject: for then the same term will not be a property of
the negative subject as well. Also, if the term rendered be a property of the negative subject, it will not be a
property of the positive. Thus (e.g.) inasmuch as 'animate' is a property of 'living creature', 'animate' could not

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be a property of 'not-living creature'. For constructive purposes, on the other hand, if the term rendered fails
to be a property of the affirmative subject it would be a property of the negative. This commonplace rule is,
however, deceptive: for a positive term is not a property of a negative, or a negative of a positive. For a
positive term does not belong at all to a negative, while a negative term, though it belongs to a positive, does
not belong as a property.

Next, look from the point of view of the coordinate members of a division, and see, for destructive purposes,
if none of the co-ordinate members (parallel with the property rendered) be a property of any of the
remaining set of co-ordinate members (parallel with the subject): for then neither will the term stated be a
property of that of which it is stated to be a property. Thus (e.g.) inasmuch as 'sensible living being' is not a
property of any of the other living beings, 'intelligible living being' could not be a property of God. For
constructive purposes, on the other hand, see if some one or other of the remaining co-ordinate members
(parallel with the property rendered) be a property of each of these co-ordinate members (parallel with the
subject): for then the remaining one too will be a property of that of which it has been stated not to be a
property. Thus (e.g.) inasmuch as it is a property of 'wisdom' to be essentially 'the natural virtue of the
rational faculty', then, taking each of the other virtues as well in this way, it would be a property of
'temperance' to be essentially 'the natural virtue of the faculty of desire'.

Next, look from the point of view of the inflexions, and see, for destructive purposes, if the inflexion of the
property rendered fails to be a property of the inflexion of the subject: for then neither will the other inflexion
be a property of the other inflexion. Thus (e.g.) inasmuch as 'beautifully' is not a property of justly', neither
could 'beautiful' be a property of just'. For constructive purposes, on the other hand, see if the inflexion of the
property rendered is a property of the inflexion of the subject: for then also the other inflexion will be a
property of the other inflexion. Thus (e.g.) inasmuch as 'walking biped' is a property of man, it would also be
any one's property 'as a man' to be described 'as a walking biped'. Not only in the case of the actual term
mentioned should one look at the inflexions, but also in the case of its opposites, just as has been laid down in
the case of the former commonplace rules as well' Thus, for destructive purposes, see if the inflexion of the
opposite of the property rendered fails to be the property of the inflexion of the opposite of the subject: for
then neither will the inflexion of the other opposite be a property of the inflexion of the other opposite. Thus
(e.g.) inasmuch as 'well' is not a property of justly', neither could 'badly' be a property of 'unjustly'. For
constructive purposes, on the other hand, see if the inflexion of the opposite of the property originally
suggested is a property of the inflexion of the opposite of the original subject: for then also the inflexion of
the other opposite will be a property of the inflexion of the other opposite. Thus (e.g.) inasmuch as 'best' is a
property of 'the good', 'worst' also will be a property of 'the evil'.

Next, look from the point of view of things that are in a like relation, and see, for destructive purposes, if
what is in a relation like that of the property rendered fails to be a property of what is in a relation like that of
the subject: for then neither will what is in a relation like that of the first be a property of what is in a relation
like that of the second. Thus (e.g.) inasmuch as the relation of the builder towards the production of a house is
like that of the doctor towards the production of health, and it is not a property of a doctor to produce health,
it could not be a property of a builder to produce a house. For constructive purposes, on the other hand, see if
what is in a relation like that of the property rendered is a property of what is in a relation like that of the
subject: for then also what is in a relation like that of the first will be a property of what is in a relation like
that of the second. Thus (e.g.) inasmuch as the relation of a doctor towards the possession of ability to
produce health is like that of a trainer towards the possession of ability to produce vigour, and it is a property
of a trainer to possess the ability to produce vigour, it would be a property of a doctor to possess the ability to
produce health.

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Next look from the point of view of things that are identically related, and see, for destructive purposes, if the
predicate that is identically related towards two subjects fails to be a property of the subject which is
identically related to it as the subject in question; for then neither will the predicate that is identically related
to both subjects be a property of the subject which is identically related to it as the first. If, on the other hand,
the predicate which is identically related to two subjects is the property of the subject which is identically
related to it as the subject in question, then it will not be a property of that of which it has been stated to be a
property, (e.g.) inasmuch as prudence is identically related to both the noble and the base, since it is
knowledge of each of them, and it is not a property of prudence to be knowledge of the noble, it could not be
a property of prudence to be knowledge of the base. If, on the other hand, it is a property of prudence to be
the knowledge of the noble, it could not be a property of it to be the knowledge of the base.] For it is
impossible for the same thing to be a property of more than one subject. For constructive purposes, on the
other hand, this commonplace rule is of no use: for what is 'identically related' is a single predicate in process
of comparison with more than one subject.

Next, for destructive purposes, see if the predicate qualified by the verb 'to be' fails to be a property of the
subject qualified by the verb 'to be': for then neither will the destruction of the one be a property of the other
qualified by the verb 'to be destroyed', nor will the 'becoming'the one be a property of the other qualified by
the verb 'to become'. Thus (e.g.) inasmuch as it is not a property of 'man' to be an animal, neither could it be a
property of becoming a man to become an animal; nor could the destruction of an animal be a property of the
destruction of a man. In the same way one should derive arguments also from 'becoming' to 'being' and 'being
destroyed', and from 'being destroyed' to 'being' and to 'becoming' exactly as they have just been given from
'being' to 'becoming' and 'being destroyed'. For constructive purposes, on the other hand, see if the subject set
down as qualified by the verb 'to be' has the predicate set down as so qualified, as its property: for then also
the subject qualified by the very 'to become' will have the predicate qualified by 'to become' as its property,
and the subject qualified by the verb to be destroyed' will have as its property the predicate rendered with this
qualification. Thus, for example, inasmuch as it is a property of man to be a mortal, it would be a property of
becoming a man to become a mortal, and the destruction of a mortal would be a property of the destruction of
a man. In the same way one should derive arguments also from 'becoming' and 'being destroyed' both to
'being' and to the conclusions that follow from them, exactly as was directed also for the purpose of
destruction.

Next take a look at the 'idea' of the subject stated, and see, for destructive purposes, if the suggested property
fails to belong to the 'idea' in question, or fails to belong to it in virtue of that character which causes it to bear
the description of which the property was rendered: for then what has been stated to be a property will not be
a property. Thus (e.g.) inasmuch as 'being motionless' does not belong to 'man-himself qua 'man', but qua
'idea', it could not be a property of 'man' to be motionless. For constructive purposes, on the other hand, see if
the property in question belongs to the idea, and belongs to it in that respect in virtue of which there is
predicated of it that character of which the predicate in question has been stated not to be a property: for then
what has been stated not to be a property will be a property. Thus (e.g.) inasmuch as it belongs to
'living-creature-itself to be compounded of soul and body, and further this belongs to it qua
'living-creature', it would be a property of 'living-creature' to be compounded of soul and body.

Next look from the point of view of greater and less degrees, and first (a) for destructive purposes, see if what
is more-P fails to be a property of what is more-S: for then neither will what is less-P be a property of what
is less-S, nor least-P of least-S, nor most-P of most-S, nor P simply of S simply. Thus (e.g.) inasmuch as
being more highly coloured is not a property of what is more a body, neither could being less highly coloured
be a property of what is less a body, nor being coloured be a property of body at all. For constructive
purposes, on the other hand, see if what is more-P is a property of what is more-S: for then also what is
less-P will be a property of what is less S, and least-P of least-S, and most-P of most-S, and P simply of S

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simply. Thus (e.g.) inasmuch as a higher degree of sensation is a property of a higher degree of life, a lower
degree of sensation also would be a property of a lower degree of life, and the highest of the highest and the
lowest of the lowest degree, and sensation simply of life simply.

Also you should look at the argument from a simple predication to the same qualified types of predication,
and see, for destructive purposes, if P simply fails to be a property of S simply; for then neither will more-P
be a property of more-S, nor less-P of less-S, nor most-P of most-S, nor least-P of least-S. Thus (e.g.)
inasmuch as 'virtuous' is not a property of 'man', neither could 'more virtuous' be a property of what is 'more
human'. For constructive purposes, on the other hand, see if P simply is a property of S simply: for then more
P also will be a property of more-S, and less-P of less-S, and least-P of least-S, and most-P of most-S.
Thus (e.g.) a tendency to move upwards by nature is a property of fire, and so also a greater tendency to
move upwards by nature would be a property of what is more fiery. In the same way too one should look at
all these matters from the point of view of the others as well.

Secondly (b) for destructive purposes, see if the more likely property fails to be a property of the more likely
subject: for then neither will the less likely property be a property of the less likely subject. Thus (e.g.)
inasmuch as 'perceiving' is more likely to be a property of 'animal' than 'knowing' of 'man', and 'perceiving' is
not a property of 'animal', 'knowing' could not be a property of 'man'. For constructive purposes, on the other
hand, see if the less likely property is a property of the less likely subject; for then too the more likely
property will be a property of the more likely subject. Thus (e.g.) inasmuch as 'to be naturally civilized' is less
likely to be a property of man than 'to live' of an animal, and it is a property of man to be naturally civilized,
it would be a property of animal to live.

Thirdly (c) for destructive purposes, see if the predicate fails to be a property of that of which it is more likely
to be a property: for then neither will it be a property of that of which it is less likely to be a property: while if
it is a property of the former, it will not be a property of the latter. Thus (e.g.) inasmuch as 'to be coloured' is
more likely to be a property of a 'surface' than of a 'body', and it is not a property of a surface, 'to be coloured'
could not be a property of 'body'; while if it is a property of a 'surface', it could not be a property of a 'body'.
For constructive purposes, on the other hand, this commonplace rule is not of any use: for it is impossible for
the same thing to be a property of more than one thing.

Fourthly (d) for destructive purposes, see if what is more likely to be a property of a given subject fails to be
its property: for then neither will what is less likely to be a property of it be its property. Thus (e.g.) inasmuch
as 'sensible' is more likely than 'divisible' to be a property of 'animal', and 'sensible' is not a property of
animal, 'divisible' could not be a property of animal. For constructive purposes, on the other hand, see if what
is less likely to be a property of it is a property; for then what is more likely to be a property of it will be a
property as well. Thus, for example, inasmuch as 'sensation' is less likely to be a property of 'animal' than
life', and 'sensation' is a property of animal, 'life' would be a property of animal.

Next, look from the point of view of the attributes that belong in a like manner, and first (a) for destructive
purposes, see if what is as much a property fails to be a property of that of which it is as much a property: for
then neither will that which is as much a property as it be a property of that of which it is as much a property.
Thus (e.g.) inasmuch as 'desiring' is as much a property of the faculty of desire as reasoning' is a property of
the faculty of reason, and desiring is not a property of the faculty of desire, reasoning could not be a property
of the faculty of reason. For constructive purposes, on the other hand, see if what is as much a property is a
property of that of which it is as much a property: for then also what is as much a property as it will be a
property of that of which it is as much a property. Thus (e.g.) inasmuch as it is as much a property of 'the
faculty of reason' to be 'the primary seat of wisdom' as it is of 'the faculty of desire' to be 'the primary seat of
temperance', and it is a property of the faculty of reason to be the primary seat of wisdom, it would be a
property of the faculty of desire to be the primary seat of temperance.

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Secondly (b) for destructive purposes, see if what is as much a property of anything fails to be a property of
it: for then neither will what is as much a property be a property of it. Thus (e.g.) inasmuch as 'seeing' is as
much a property of man as 'hearing', and 'seeing' is not a property of man, 'hearing' could not be a property of
man. For constructive purposes, on the other hand, see if what is as much a property of it is its property: for
then what is as much a property of it as the former will be its property as well. Thus (e.g.) it is as much a
property of the soul to be the primary possessor of a part that desires as of a part that reasons, and it is a
property of the soul to be the primary possessor of a part that desires, and so it be a property of the soul to be
the primary possessor of a part that reasons.

Thirdly (c) for destructive purposes, see if it fails to be a property of that of which it is as much a property:
for then neither will it be a property of that of which it is as much a property as of the former, while if it be a
property of the former, it will not be a property of the other. Thus (e.g.) inasmuch as 'to burn' is as much a
property of 'flame' as of 'live coals', and 'to burn' is not a property of flame, 'to burn' could not be a property
of live coals: while if it is a property of flame, it could not be a property of live coals. For constructive
purposes, on the other hand, this commonplace rule is of no use.

The rule based on things that are in a like relation' differs from the rule based on attributes that belong in a
like manner,' because the former point is secured by analogy, not from reflection on the belonging of any
attribute, while the latter is judged by a comparison based on the fact that an attribute belongs.

Next, for destructive purposes, see if in rendering the property potentially, he has also through that
potentiality rendered the property relatively to something that does not exist, when the potentiality in question
cannot belong to what does not exist: for then what is stated to be a property will not be a property. Thus
(e.g.) he who has said that 'breathable' is a property of 'air' has, on the one hand, rendered the property
potentially (for that is 'breathable' which is such as can be breathed), and on the other hand has also rendered
the property relatively to what does not exist:-for while air may exist, even though there exist no animal so
constituted as to breathe the air, it is not possible to breathe it if no animal exist: so that it will not, either, be a
property of air to be such as can be breathed at a time when there exists no animal such as to breathe it and so
it follows that 'breathable' could not be a property of air.

For constructive purposes, see if in rendering the property potentially he renders the property either relatively
to something that exists, or to something that does not exist, when the potentiality in question can belong to
what does not exist: for then what has been stated not to be a property will be a property. Thus e.g.) he who
renders it as a property of 'being' to be 'capable of being acted upon or of acting', in rendering the property
potentially, has rendered the property relatively to something that exists: for when 'being' exists, it will also
be capable of being acted upon or of acting in a certain way: so that to be 'capable of being acted upon or of
acting' would be a property of 'being'.

Next, for destructive purposes, see if he has stated the property in the superlative: for then what has been
stated to be a property will not be a property. For people who render the property in that way find that of the
object of which the description is true, the name is not true as well: for though the object perish the
description will continue in being none the less; for it belongs most nearly to something that is in being. An
example would be supposing any one were to render 'the lightest body' as a property of 'fire': for, though fire
perish, there eh re will still be some form of body that is the lightest, so that 'the lightest body' could not be a
property of fire. For constructive purposes, on the other hand, see if he has avoided rendering the property in
the superlative: for then the property will in this respect have been property of man has not rendered the
property correctly stated. Thus (e.g.) inasmuch as he in the superlative, the property would in who states 'a
naturally civilized animal' as a this respect have been correctly stated.

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Book VI

THE discussion of Definitions falls into five parts. For you have to show either (1) that it is not true at all to
apply the expression as well to that to which the term is applied (for the definition of Man ought to be true of
every man); or (2) that though the object has a genus, he has failed to put the object defined into the genus, or
to put it into the appropriate genus (for the framer of a definition should first place the object in its genus, and
then append its differences: for of all the elements of the definition the genus is usually supposed to be the
principal mark of the essence of what is defined): or (3) that the expression is not peculiar to the object (for,
as we said above as well, a definition ought to be peculiar): or else (4) see if, though he has observed all the
aforesaid cautions, he has yet failed to define the object, that is, to express its essence. (5) It remains, apart
from the foregoing, to see if he has defined it, but defined it incorrectly.

Whether, then, the expression be not also true of that of which the term is true you should proceed to examine
according to the commonplace rules that relate to Accident. For there too the question is always 'Is so and so
true or untrue?': for whenever we argue that an accident belongs, we declare it to be true, while whenever we
argue that it does not belong, we declare it to be untrue. If, again, he has failed to place the object in the
appropriate genus, or if the expression be not peculiar to the object, we must go on to examine the case
according to the commonplace rules that relate to genus and property.

It remains, then, to prescribe how to investigate whether the object has been either not defined at all, or else
defined incorrectly. First, then, we must proceed to examine if it has been defined incorrectly: for with
anything it is easier to do it than to do it correctly. Clearly, then, more mistakes are made in the latter task on
account of its greater difficulty. Accordingly the attack becomes easier in the latter case than in the former.

Incorrectness falls into two branches: (1) first, the use of obscure language (for the language of a definition
ought to be the very clearest possible, seeing that the whole purpose of rendering it is to make something
known); (secondly, if the expression used be longer than is necessary: for all additional matter in a definition
is superfluous. Again, each of the aforesaid branches is divided into a number of others.

One commonplace rule, then, in regard to obscurity is, See if the meaning intended by the definition involves
an ambiguity with any other, e.g. 'Becoming is a passage into being', or 'Health is the balance of hot and cold
elements'. Here 'passage' and 'balance' are ambiguous terms: it is accordingly not clear which of the several
possible senses of the term he intends to convey. Likewise also, if the term defined be used in different senses
and he has spoken without distinguishing between them: for then it is not clear to which of them the
definition rendered applies, and one can then bring a captious objection on the ground that the definition does
not apply to all the things whose definition he has rendered: and this kind of thing is particularly easy in the
case where the definer does not see the ambiguity of his terms. Or, again, the questioner may himself
distinguish the various senses of the term rendered in the definition, and then institute his argument against
each: for if the expression used be not adequate to the subject in any of its senses, it is clear that he cannot
have defined it in any sense aright.

Another rule is, See if he has used a metaphorical expression, as, for instance, if he has defined knowledge as
'unsupplantable', or the earth as a 'nurse', or temperance as a 'harmony'. For a metaphorical expression is
always obscure. It is possible, also, to argue sophistically against the user of a metaphorical expression as
though he had used it in its literal sense: for the definition stated will not apply to the term defined, e.g. in the
case of temperance: for harmony is always found between notes. Moreover, if harmony be the genus of
temperance, then the same object will occur in two genera of which neither contains the other: for harmony

Book VI 53

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does not contain virtue, nor virtue harmony. Again, see if he uses terms that are unfamiliar, as when Plato
describes the eye as 'brow-shaded', or a certain spider as poison-fanged', or the marrow as 'boneformed'. For
an unusual phrase is always obscure.

Sometimes a phrase is used neither ambiguously, nor yet metaphorically, nor yet literally, as when the law is
said to be the 'measure' or 'image' of the things that are by nature just. Such phrases are worse than metaphor;
for the latter does make its meaning to some extent clear because of the likeness involved; for those who use
metaphors do so always in view of some likeness: whereas this kind of phrase makes nothing clear; for there
is no likeness to justify the description 'measure' or 'image', as applied to the law, nor is the law ordinarily so
called in a literal sense. So then, if a man says that the law is literally a 'measure' or an 'image', he speaks
falsely: for an image is something produced by imitation, and this is not found in the case of the law. If, on
the other hand, he does not mean the term literally, it is clear that he has used an unclear expression, and one
that is worse than any sort of metaphorical expression.

Moreover, see if from the expression used the definition of the contrary be not clear; for definitions that have
been correctly rendered also indicate their contraries as well. Or, again, see if, when it is merely stated by
itself, it is not evident what it defines: just as in the works of the old painters, unless there were an inscription,
the figures used to be unrecognizable.

If, then, the definition be not clear, you should proceed to examine on lines such as these. If, on the other
hand, he has phrased the definition redundantly, first of all look and see whether he has used any attribute that
belongs universally, either to real objects in general, or to all that fall under the same genus as the object
defined: for the mention of this is sure to be redundant. For the genus ought to divide the object from things
in general, and the differentia from any of the things contained in the same genus. Now any term that belongs
to everything separates off the given object from absolutely nothing, while any that belongs to all the things
that fall under the same genus does not separate it off from the things contained in the same genus. Any
addition, then, of that kind will be pointless.

Or see if, though the additional matter may be peculiar to the given term, yet even when it is struck out the
rest of the expression too is peculiar and makes clear the essence of the term. Thus, in the definition of man,
the addition 'capable of receiving knowledge' is superfluous; for strike it out, and still the expression is
peculiar and makes clear his essence. Speaking generally, everything is superfluous upon whose removal the
remainder still makes the term that is being defined clear. Such, for instance, would also be the definition of
the soul, assuming it to be stated as a 'self-moving number'; for the soul is just 'the self-moving', as Plato
defined it. Or perhaps the expression used, though appropriate, yet does not declare the essence, if the word
'number' be eliminated. Which of the two is the real state of the case it is difficult to determine clearly: the
right way to treat the matter in all cases is to be guided by convenience. Thus (e.g.) it is said that the
definition of phlegm is the 'undigested moisture that comes first off food'. Here the addition of the word
'undigested' is superfluous, seeing that 'the first' is one and not many, so that even when undigested' is left out
the definition will still be peculiar to the subject: for it is impossible that both phlegm and also something else
should both be the first to arise from the food. Or perhaps the phlegm is not absolutely the first thing to come
off the food, but only the first of the undigested matters, so that the addition 'undigested' is required; for
stated the other way the definition would not be true unless the phlegm comes first of all.

Moreover, see if anything contained in the definition fails to apply to everything that falls under the same
species: for this sort of definition is worse than those which include an attribute belonging to all things
universally. For in that case, if the remainder of the expression be peculiar, the whole too will be peculiar: for
absolutely always, if to something peculiar anything whatever that is true be added, the whole too becomes
peculiar. Whereas if any part of the expression do not apply to everything that falls under the same species, it

Book VI 54

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is impossible that the expression as a whole should be peculiar: for it will not be predicated convertibly with
the object; e.g. 'a walking biped animal six feet high': for an expression of that kind is not predicated
convertibly with the term, because the attribute 'six feet high' does not belong to everything that falls under
the same species.

Again, see if he has said the same thing more than once, saying (e.g.) 'desire' is a 'conation for the pleasant'.
For 'desire' is always 'for the pleasant', so that what is the same as desire will also be 'for the pleasant'.
Accordingly our definition of desire becomes 'conation-for-the-pleasant': for the word 'desire' is the exact
equivalent of the words 'conation for-the-pleasant', so that both alike will be 'for the pleasant'. Or perhaps
there is no absurdity in this; for consider this instance:-Man is a biped': therefore, what is the same as man is
a biped: but 'a walking biped animal' is the same as man, and therefore walking biped animal is a biped'. But
this involves no real absurdity. For 'biped' is not a predicate of 'walking animal': if it were, then we should
certainly have 'biped' predicated twice of the same thing; but as a matter of fact the subject said to be a biped
is'a walking biped animal', so that the word 'biped' is only used as a predicate once. Likewise also in the case
of 'desire' as well: for it is not 'conation' that is said to be 'for the pleasant', but rather the whole idea, so that
there too the predication is only made once. Absurdity results, not when the same word is uttered twice, but
when the same thing is more than once predicated of a subject; e.g. if he says, like Xenocrates, that wisdom
defines and contemplates reality:' for definition is a certain type of contemplation, so that by adding the
words 'and contemplates' over again he says the same thing twice over. Likewise, too, those fail who say that
'cooling' is 'the privation of natural heat'. For all privation is a privation of some natural attribute, so that the
addition of the word 'natural' is superfluous: it would have been enough to say 'privation of heat', for the word
'privation' shows of itself that the heat meant is natural heat.

Again, see if a universal have been mentioned and then a particular case of it be added as well, e.g. 'Equity is
a remission of what is expedient and just'; for what is just is a branch of what is expedient and is therefore
included in the latter term: its mention is therefore redundant, an addition of the particular after the universal
has been already stated. So also, if he defines 'medicine' as 'knowledge of what makes for health in animals
and men', or 'the law' as 'the image of what is by nature noble and just'; for what is just is a branch of what is
noble, so that he says the same thing more than once.

Whether, then, a man defines a thing correctly or incorrectly you should proceed to examine on these and
similar lines. But whether he has mentioned and defined its essence or no, should be examined as follows:
First of all, see if he has failed to make the definition through terms that are prior and more intelligible. For
the reason why the definition is rendered is to make known the term stated, and we make things known by
taking not any random terms, but such as are prior and more intelligible, as is done in demonstrations (for so
it is with all teaching and learning); accordingly, it is clear that a man who does not define through terms of
this kind has not defined at all. Otherwise, there will be more than one definition of the same thing: for
clearly he who defines through terms that are prior and more intelligible has also framed a definition, and a
better one, so that both would then be definitions of the same object. This sort of view, however, does not
generally find acceptance: for of each real object the essence is single: if, then, there are to be a number of
definitions of the same thing, the essence of the object will be the same as it is represented to be in each of
the definitions, and these representations are not the same, inasmuch as the definitions are different. Clearly,
then, any one who has not defined a thing through terms that are prior and more intelligible has not defined it
at all.

The statement that a definition has not been made through more intelligible terms may be understood in two
senses, either supposing that its terms are absolutely less intelligible, or supposing that they are less
intelligible to us: for either sense is possible. Thus absolutely the prior is more intelligible than the posterior,
a point, for instance, than a line, a line than a plane, and a plane than a solid; just as also a unit is more

Book VI 55

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intelligible than a number; for it is the prius and starting-point of all number. Likewise, also, a letter is more
intelligible than a syllable. Whereas to us it sometimes happens that the converse is the case: for the solid
falls under perception most of all-more than a plane-and a plane more than a line, and a line more than a
point; for most people learn things like the former earlier than the latter; for any ordinary intelligence can
grasp them, whereas the others require an exact and exceptional understanding.

Absolutely, then, it is better to try to make what is posterior known through what is prior, inasmuch as such a
way of procedure is more scientific. Of course, in dealing with persons who cannot recognize things through
terms of that kind, it may perhaps be necessary to frame the expression through terms that are intelligible to
them. Among definitions of this kind are those of a point, a line, and a plane, all of which explain the prior by
the posterior; for they say that a point is the limit of a line, a line of a plane, a plane of a solid. One must,
however, not fail to observe that those who define in this way cannot show the essential nature of the term
they define, unless it so happens that the same thing is more intelligible both to us and also absolutely, since a
correct definition must define a thing through its genus and its differentiae, and these belong to the order of
things which are absolutely more intelligible than, and prior to, the species. For annul the genus and
differentia, and the species too is annulled, so that these are prior to the species. They are also more
intelligible; for if the species be known, the genus and differentia must of necessity be known as well (for any
one who knows what a man is knows also what 'animal' and 'walking' are), whereas if the genus or the
differentia be known it does not follow of necessity that the species is known as well: thus the species is less
intelligible. Moreover, those who say that such definitions, viz. those which proceed from what is intelligible
to this, that, or the other man, are really and truly definitions, will have to say that there are several
definitions of one and the same thing. For, as it happens, different things are more intelligible to different
people, not the same things to all; and so a different definition would have to be rendered to each several
person, if the definition is to be constructed from what is more intelligible to particular individuals.
Moreover, to the same people different things are more intelligible at different times; first of all the objects of
sense; then, as they become more sharpwitted, the converse; so that those who hold that a definition ought to
be rendered through what is more intelligible to particular individuals would not have to render the same
definition at all times even to the same person. It is clear, then, that the right way to define is not through
terms of that kind, but through what is absolutely more intelligible: for only in this way could the definition
come always to be one and the same. Perhaps, also, what is absolutely intelligible is what is intelligible, not
to all, but to those who are in a sound state of understanding, just as what is absolutely healthy is what is
healthy to those in a sound state of body. All such points as this ought to be made very precise, and made use
of in the course of discussion as occasion requires. The demolition of a definition will most surely win a
general approval if the definer happens to have framed his expression neither from what is absolutely more
intelligible nor yet from what is so to us.

One form, then, of the failure to work through more intelligible terms is the exhibition of the prior through
the posterior, as we remarked before.' Another form occurs if we find that the definition has been rendered of
what is at rest and definite through what is indefinite and in motion: for what is still and definite is prior to
what is indefinite and in motion.

Of the failure to use terms that are prior there are three forms:

(1) The first is when an opposite has been defined through its opposite, e.g.i. good through evil: for opposites
are always simultaneous by nature. Some people think, also, that both are objects of the same science, so that
the one is not even more intelligible than the other. One must, however, observe that it is perhaps not possible
to define some things in any other way, e.g. the double without the half, and all the terms that are essentially
relative: for in all such cases the essential being is the same as a certain relation to something, so that it is
impossible to understand the one term without the other, and accordingly in the definition of the one the other
too must be embraced. One ought to learn up all such points as these, and use them as occasion may seem to
require.

Book VI 56

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(2) Another is-if he has used the term defined itself. This passes unobserved when the actual name of the
object is not used, e.g. supposing any one had defined the sun as a star that appears by day'. For in bringing in
'day' he brings in the sun. To detect errors of this sort, exchange the word for its definition, e.g. the definition
of 'day' as the 'passage of the sun over the earth'. Clearly, whoever has said 'the passage of the sun over the
earth' has said 'the sun', so that in bringing in the 'day' he has brought in the sun.

(3) Again, see if he has defined one coordinate member of a division by another, e.g. 'an odd number' as 'that
which is greater by one than an even number'. For the co-ordinate members of a division that are derived
from the same genus are simultaneous by nature and 'odd' and 'even' are such terms: for both are differentiae
of number.

Likewise also, see if he has defined a superior through a subordinate term, e.g. An "even number" is "a
number divisible into halves'", or '"the good" is a "state of virtue" '. For 'half is derived from 'two', and 'two'
is an even number: virtue also is a kind of good, so that the latter terms are subordinate to the former.
Moreover, in using the subordinate term one is bound to use the other as well: for whoever employs the term
'virtue' employs the term 'good', seeing that virtue is a certain kind of good: likewise, also, whoever employs
the term 'half employs the term 'even', for to be 'divided in half means to be divided into two, and two is
even.

Generally speaking, then, one commonplace rule relates to the failure to frame the expression by means of
terms that are prior and more intelligible: and of this the subdivisions are those specified above. A second is,
see whether, though the object is in a genus, it has not been placed in a genus. This sort of error is always
found where the essence of the object does not stand first in the expression, e.g. the definition of 'body' as
'that which has three dimensions', or the definition of 'man', supposing any one to give it, as 'that which
knows how to count': for it is not stated what it is that has three dimensions, or what it is that knows how to
count: whereas the genus is meant to indicate just this, and is submitted first of the terms in the definition.

Moreover, see if, while the term to be defined is used in relation to many things, he has failed to render it in
relation to all of them; as (e.g.) if he define 'grammar' as the 'knowledge how to write from dictation': for he
ought also to say that it is a knowledge how to read as well. For in rendering it as 'knowledge of writing' has
no more defined it than by rendering it as 'knowledge of reading': neither in fact has succeeded, but only he
who mentions both these things, since it is impossible that there should be more than one definition of the
same thing. It is only, however, in some cases that what has been said corresponds to the actual state of
things: in some it does not, e.g. all those terms which are not used essentially in relation to both things: as
medicine is said to deal with the production of disease and health; for it is said essentially to do the latter, but
the former only by accident: for it is absolutely alien to medicine to produce disease. Here, then, the man who
renders medicine as relative to both of these things has not defined it any better than he who mentions the one
only. In fact he has done it perhaps worse, for any one else besides the doctor is capable of producing disease.

Moreover, in a case where the term to be defined is used in relation to several things, see if he has rendered it
as relative to the worse rather than to the better; for every form of knowledge and potentiality is generally
thought to be relative to the best.

Again, if the thing in question be not placed in its own proper genus, one must examine it according to the
elementary rules in regard to genera, as has been said before.'

Moreover, see if he uses language which transgresses the genera of the things he defines, defining, e.g. justice
as a 'state that produces equality' or 'distributes what is equal': for by defining it so he passes outside the
sphere of virtue, and so by leaving out the genus of justice he fails to express its essence: for the essence of a

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thing must in each case bring in its genus. It is the same thing if the object be not put into its nearest genus;
for the man who puts it into the nearest one has stated all the higher genera, seeing that all the higher genera
are predicated of the lower. Either, then, it ought to be put into its nearest genus, or else to the higher genus
all the differentiae ought to be appended whereby the nearest genus is defined. For then he would not have
left out anything: but would merely have mentioned the subordinate genus by an expression instead of by
name. On the other hand, he who mentions merely the higher genus by itself, does not state the subordinate
genus as well: in saying 'plant' a man does not specify 'a tree'.

Again, in regard to the differentiae, we must examine in like manner whether the differentiae, too, that he has
stated be those of the genus. For if a man has not defined the object by the differentiae peculiar to it, or has
mentioned something such as is utterly incapable of being a differentia of anything, e.g. 'animal' or
'substance', clearly he has not defined it at all: for the aforesaid terms do not differentiate anything at all.
Further, we must see whether the differentia stated possesses anything that is co-ordinate with it in a
division; for, if not, clearly the one stated could not be a differentia of the genus. For a genus is always
divided by differentiae that are co-ordinate members of a division, as, for instance, by the terms 'walking',
'flying', 'aquatic', and 'biped'. Or see if, though the contrasted differentia exists, it yet is not true of the genus,
for then, clearly, neither of them could be a differentia of the genus; for differentiae that are co-ordinates in a
division with the differentia of a thing are all true of the genus to which the thing belongs. Likewise, also, see
if, though it be true, yet the addition of it to the genus fails to make a species. For then, clearly, this could not
be a specific differentia of the genus: for a specific differentia, if added to the genus, always makes a species.
If, however, this be no true differentia, no more is the one adduced, seeing that it is a co-ordinate member of
a division with this.

Moreover, see if he divides the genus by a negation, as those do who define line as 'length without breadth':
for this means simply that it has not any breadth. The genus will then be found to partake of its own species:
for, since of everything either an affirmation or its negation is true, length must always either lack breadth or
possess it, so that 'length' as well, i.e. the genus of 'line', will be either with or without breadth. But 'length
without breadth' is the definition of a species, as also is 'length with breadth': for 'without breadth' and 'with
breadth' are differentiae, and the genus and differentia constitute the definition of the species. Hence the
genus would admit of the definition of its species. Likewise, also, it will admit of the definition of the
differentia, seeing that one or the other of the aforesaid differentiae is of necessity predicated of the genus.
The usefulness of this principle is found in meeting those who assert the existence of 'Ideas': for if absolute
length exist, how will it be predicable of the genus that it has breadth or that it lacks it? For one assertion or
the other will have to be true of 'length' universally, if it is to be true of the genus at all: and this is contrary to
the fact: for there exist both lengths which have, and lengths which have not, breadth. Hence the only people
against whom the rule can be employed are those who assert that a genus is always numerically one; and this
is what is done by those who assert the real existence of the 'Ideas'; for they allege that absolute length and
absolute animal are the genus.

It may be that in some cases the definer is obliged to employ a negation as well, e.g. in defining privations.
For 'blind' means a thing which cannot see when its nature is to see. There is no difference between dividing
the genus by a negation, and dividing it by such an affirmation as is bound to have a negation as its
co-ordinate in a division, e.g. supposing he had defined something as 'length possessed of breadth'; for
co-ordinate in the division with that which is possessed of breadth is that which possesses no breadth and
that only, so that again the genus is divided by a negation.

Again, see if he rendered the species as a differentia, as do those who define 'contumely' as 'insolence
accompanied by jeering'; for jeering is a kind of insolence, i.e. it is a species and not a differentia.

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Moreover, see if he has stated the genus as the differentia, e.g. 'Virtue is a good or noble state: for 'good' is
the genus of 'virtue'. Or possibly 'good' here is not the genus but the differentia, on the principle that the same
thing cannot be in two genera of which neither contains the other: for 'good' does not include 'state', nor vice
versa: for not every state is good nor every good a 'state'. Both, then, could not be genera, and consequently,
if 'state' is the genus of virtue, clearly 'good' cannot be its genus: it must rather be the differentia'. Moreover,
'a state' indicates the essence of virtue, whereas 'good' indicates not the essence but a quality: and to indicate a
quality is generally held to be the function of the differentia. See, further, whether the differentia rendered
indicates an individual rather than a quality: for the general view is that the differentia always expresses a
quality.

Look and see, further, whether the differentia belongs only by accident to the object defined. For the
differentia is never an accidental attribute, any more than the genus is: for the differentia of a thing cannot
both belong and not belong to it.

Moreover, if either the differentia or the species, or any of the things which are under the species, is
predicable of the genus, then he could not have defined the term. For none of the aforesaid can possibly be
predicated of the genus, seeing that the genus is the term with the widest range of all. Again, see if the genus
be predicated of the differentia; for the general view is that the genus is predicated, not of the differentia, but
of the objects of which the differentia is predicated. Animal (e.g.) is predicated of 'man' or 'ox' or other
walking animals, not of the actual differentia itself which we predicate of the species. For if 'animal' is to be
predicated of each of its differentiae, then 'animal' would be predicated of the species several times over; for
the differentiae are predicates of the species. Moreover, the differentiae will be all either species or
individuals, if they are animals; for every animal is either a species or an individual.

Likewise you must inquire also if the species or any of the objects that come under it is predicated of the
differentia: for this is impossible, seeing that the differentia is a term with a wider range than the various
species. Moreover, if any of the species be predicated of it, the result will be that the differentia is a species:
if, for instance, 'man' be predicated, the differentia is clearly the human race. Again, see if the differentia fails
to be prior to the species: for the differentia ought to be posterior to the genus, but prior to the species.

Look and see also if the differentia mentioned belongs to a different genus, neither contained in nor
containing the genus in question. For the general view is that the same differentia cannot be used of two
non-subaltern genera. Else the result will be that the same species as well will be in two non-subaltern
genera: for each of the differentiae imports its own genus, e.g. 'walking' and 'biped' import with them the
genus 'animal'. If, then, each of the genera as well is true of that of which the differentia is true, it clearly
follows that the species must be in two non-subaltern genera. Or perhaps it is not impossible for the same
differentia to be used of two non-subaltern genera, and we ought to add the words 'except they both be
subordinate members of the same genus'. Thus 'walking animal' and 'flying animal' are non-subaltern genera,
and 'biped' is the differentia of both. The words 'except they both be subordinate members of the same genus'
ought therefore to be added; for both these are subordinate to 'animal'. From this possibility, that the same
differentia may be used of two non-subaltern genera, it is clear also that there is no necessity for the
differentia to carry with it the whole of the genus to which it belongs, but only the one or the other of its
limbs together with the genera that are higher than this, as 'biped' carries with it either 'flying' or 'walking
animal'.

See, too, if he has rendered 'existence in' something as the differentia of a thing's essence: for the general
view is that locality cannot differentiate between one essence and another. Hence, too, people condemn those
who divide animals by means of the terms 'walking' and 'aquatic', on the ground that 'walking' and 'aquatic'
indicate mere locality. Or possibly in this case the censure is undeserved; for 'aquatic' does not mean 'in'
anything; nor does it denote a locality, but a certain quality: for even if the thing be on the dry land, still it is
aquatic: and likewise a land-animal, even though it be in the water, will still be a and not an aquatic-animal.

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But all the same, if ever the differentia does denote existence in something, clearly he will have made a bad
mistake.

Again, see if he has rendered an affection as the differentia: for every affection, if intensified, subverts the
essence of the thing, while the differentia is not of that kind: for the differentia is generally considered rather
to preserve that which it differentiates; and it is absolutely impossible for a thing to exist without its own
special differentia: for if there be no 'walking', there will be no 'man'. In fact, we may lay down absolutely
that a thing cannot have as its differentia anything in respect of which it is subject to alteration: for all things
of that kind, if intensified, destroy its essence. If, then, a man has rendered any differentia of this kind, he has
made a mistake: for we undergo absolutely no alteration in respect of our differentiae.

Again, see if he has failed to render the differentia of a relative term relatively to something else; for the
differentiae of relative terms are themselves relative, as in the case also of knowledge. This is classed as
speculative, practical and productive; and each of these denotes a relation: for it speculates upon something,
and produces something and does something.

Look and see also if the definer renders each relative term relatively to its natural purpose: for while in some
cases the particular relative term can be used in relation to its natural purpose only and to nothing else, some
can be used in relation to something else as well. Thus sight can only be used for seeing, but a strigil can also
be used to dip up water. Still, if any one were to define a strigil as an instrument for dipping water, he has
made a mistake: for that is not its natural function. The definition of a thing's natural function is 'that for
which it would be used by the prudent man, acting as such, and by the science that deals specially with that
thing'.

Or see if, whenever a term happens to be used in a number of relations, he has failed to introduce it in its
primary relation: e.g. by defining 'wisdom' as the virtue of 'man' or of the 'soul,' rather than of the 'reasoning
faculty': for 'wisdom' is the virtue primarily of the reasoning faculty: for it is in virtue of this that both the
man and his soul are said to be wise.

Moreover, if the thing of which the term defined has been stated to be an affection or disposition, or whatever
it may be, be unable to admit it, the definer has made a mistake. For every disposition and every affection is
formed naturally in that of which it is an affection or disposition, as knowledge, too, is formed in the soul,
being a disposition of soul. Sometimes, however, people make bad mistakes in matters of this sort, e.g. all
those who say that 'sleep' is a 'failure of sensation', or that 'perplexity' is a state of 'equality between contrary
reasonings', or that 'pain' is a 'violent disruption of parts that are naturally conjoined'. For sleep is not an
attribute of sensation, whereas it ought to be, if it is a failure of sensation. Likewise, perplexity is not an
attribute of opposite reasonings, nor pain of parts naturally conjoined: for then inanimate things will be in
pain, since pain will be present in them. Similar in character, too, is the definition of 'health', say, as a
'balance of hot and cold elements': for then health will be necessarily exhibited by the hot and cold elements:
for balance of anything is an attribute inherent in those things of which it is the balance, so that health would
be an attribute of them. Moreover, people who define in this way put effect for cause, or cause for effect. For
the disruption of parts naturally conjoined is not pain, but only a cause of pain: nor again is a failure of
sensation sleep, but the one is the cause of the other: for either we go to sleep because sensation fails, or
sensation fails because we go to sleep. Likewise also an equality between contrary reasonings would be
generally considered to be a cause of perplexity: for it is when we reflect on both sides of a question and find
everything alike to be in keeping with either course that we are perplexed which of the two we are to do.

Moreover, with regard to all periods of time look and see whether there be any discrepancy between the
differentia and the thing defined: e.g. supposing the 'immortal' to be defined as a 'living thing immune at
present from destruction'. For a living thing that is immune 'at present' from destruction will be immortal 'at
present'. Possibly, indeed, in this case this result does not follow, owing to the ambiguity of the words

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'immune at present from destruction': for it may mean either that the thing has not been destroyed at present,
or that it cannot be destroyed at present, or that at present it is such that it never can be destroyed. Whenever,
then, we say that a living thing is at present immune from destruction, we mean that it is at present a living
thing of such a kind as never to be destroyed: and this is equivalent to saying that it is immortal, so that it is
not meant that it is immortal only at present. Still, if ever it does happen that what has been rendered
according to the definition belongs in the present only or past, whereas what is meant by the word does not so
belong, then the two could not be the same. So, then, this commonplace rule ought to be followed, as we have
said.

You should look and see also whether the term being defined is applied in consideration of something other
than the definition rendered. Suppose (e.g.) a definition of 'justice' as the 'ability to distribute what is equal'.
This would not be right, for 'just' describes rather the man who chooses, than the man who is able to distribute
what is equal: so that justice could not be an ability to distribute what is equal: for then also the most just man
would be the man with the most ability to distribute what is equal.

Moreover, see if the thing admits of degrees, whereas what is rendered according to the definition does not,
or, vice versa, what is rendered according to the definition admits of degrees while the thing does not. For
either both must admit them or else neither, if indeed what is rendered according to the definition is the same
as the thing. Moreover, see if, while both of them admit of degrees, they yet do not both become greater
together: e.g. suppose sexual love to be the desire for intercourse: for he who is more intensely in love has not
a more intense desire for intercourse, so that both do not become intensified at once: they certainly should,
however, had they been the same thing.

Moreover, suppose two things to be before you, see if the term to be defined applies more particularly to the
one to which the content of the definition is less applicable. Take, for instance, the definition of 'fire' as the
'body that consists of the most rarefied particles'. For 'fire' denotes flame rather than light, but flame is less
the body that consists of the most rarefied particles than is light: whereas both ought to be more applicable to
the same thing, if they had been the same. Again, see if the one expression applies alike to both the objects
before you, while the other does not apply to both alike, but more particularly to one of them.

Moreover, see if he renders the definition relative to two things taken separately: thus, the beautiful' is 'what
is pleasant to the eyes or to the ears": or 'the real' is 'what is capable of being acted upon or of acting'. For
then the same thing will be both beautiful and not beautiful, and likewise will be both real and not real. For
'pleasant to the ears' will be the same as 'beautiful', so that 'not pleasant to the ears' will be the same as 'not
beautiful': for of identical things the opposites, too, are identical, and the opposite of 'beautiful' is 'not
beautiful', while of 'pleasant to the ears' the opposite is not pleasant to the cars': clearly, then, 'not pleasant to
the ears' is the same thing as 'not beautiful'. If, therefore, something be pleasant to the eyes but not to the ears,
it will be both beautiful and not beautiful. In like manner we shall show also that the same thing is both real
and unreal.

Moreover, of both genera and differentiae and all the other terms rendered in definitions you should frame
definitions in lieu of the terms, and then see if there be any discrepancy between them.

If the term defined be relative, either in itself or in respect of its genus, see whether the definition fails to
mention that to which the term, either in itself or in respect of its genus, is relative, e.g. if he has defined
'knowledge' as an 'incontrovertible conception' or 'wishing' as 'painless conation'. For of everything relative
the essence is relative to something else, seeing that the being of every relative term is identical with being in

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a certain relation to something. He ought, therefore, to have said that knowledge is 'conception of a knowable'
and that wishing is 'conation for a good'. Likewise, also, if he has defined 'grammar' as 'knowledge of letters':
whereas in the definition there ought to be rendered either the thing to which the term itself is relative, or that,
whatever it is, to which its genus is relative. Or see if a relative term has been described not in relation to its
end, the end in anything being whatever is best in it or gives its purpose to the rest. Certainly it is what is best
or final that should be stated, e.g. that desire is not for the pleasant but for pleasure: for this is our purpose in
choosing what is pleasant as well.

Look and see also if that in relation to which he has rendered the term be a process or an activity: for nothing
of that kind is an end, for the completion of the activity or process is the end rather than the process or
activity itself. Or perhaps this rule is not true in all cases, for almost everybody prefers the present experience
of pleasure to its cessation, so that they would count the activity as the end rather than its completion.

Again see in some cases if he has failed to distinguish the quantity or quality or place or other differentiae of
an object; e.g. the quality and quantity of the honour the striving for which makes a man ambitious: for all
men strive for honour, so that it is not enough to define the ambitious man as him who strives for honour, but
the aforesaid differentiae must be added. Likewise, also, in defining the covetous man the quantity of money
he aims at, or in the case of the incontinent man the quality of the pleasures, should be stated. For it is not the
man who gives way to any sort of pleasure whatever who is called incontinent, but only he who gives way to
a certain kind of pleasure. Or again, people sometimes define night as a 'shadow on the earth', or an
earthquake as a movement of the earth', or a cloud as 'condensation of the air', or a wind as a 'movement of
the air'; whereas they ought to specify as well quantity, quality, place, and cause. Likewise, also, in other
cases of the kind: for by omitting any differentiae whatever he fails to state the essence of the term. One
should always attack deficiency. For a movement of the earth does not constitute an earthquake, nor a
movement of the air a wind, irrespective of its manner and the amount involved.

Moreover, in the case of conations, and in any other cases where it applies, see if the word 'apparent' is left
out, e.g. 'wishing is a conation after the good', or 'desire is a conation after the pleasant' -instead of saying 'the
apparently good', or 'pleasant'. For often those who exhibit the conation do not perceive what is good or
pleasant, so that their aim need not be really good or pleasant, but only apparently so. They ought, therefore,
to have rendered the definition also accordingly. On the other hand, any one who maintains the existence of
Ideas ought to be brought face to face with his Ideas, even though he does render the word in question: for
there can be no Idea of anything merely apparent: the general view is that an Idea is always spoken of in
relation to an Idea: thus absolute desire is for the absolutely pleasant, and absolute wishing is for the
absolutely good; they therefore cannot be for an apparent good or an apparently pleasant: for the existence of
an absolutely-apparently-good or pleasant would be an absurdity.

Moreover, if the definition be of the state of anything, look at what is in the state, while if it be of what is in
the state, look at the state: and likewise also in other cases of the kind. Thus if the pleasant be identical with
the beneficial, then, too, the man who is pleased is benefited. Speaking generally, in definitions of this sort it
happens that what the definer defines is in a sense more than one thing: for in defining knowledge, a man in a
sense defines ignorance as well, and likewise also what has knowledge and what lacks it, and what it is to
know and to be ignorant. For if the first be made clear, the others become in a certain sense clear as well. We
have, then, to be on our guard in all such cases against discrepancy, using the elementary principles drawn
from consideration of contraries and of coordinates.

Moreover, in the case of relative terms, see if the species is rendered as relative to a species of that to which
the genus is rendered as relative, e.g. supposing belief to be relative to some object of belief, see whether a
particular belief is made relative to some particular object of belief: and, if a multiple be relative to a fraction,

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see whether a particular multiple be made relative to a particular fraction. For if it be not so rendered, clearly
a mistake has been made.

See, also, if the opposite of the term has the opposite definition, whether (e.g.) the definition of 'half is the
opposite of that of 'double': for if 'double' is 'that which exceeds another by an equal amount to that other',
'half is 'that which is exceeded by an amount equal to itself. In the same way, too, with contraries. For to the
contrary term will apply the definition that is contrary in some one of the ways in which contraries are
conjoined. Thus (e.g.) if 'useful'='productive of good', 'injurious'=productive of evil' or 'destructive of good',
for one or the other of thee is bound to be contrary to the term originally used. Suppose, then, neither of these
things to be the contrary of the term originally used, then clearly neither of the definitions rendered later
could be the definition of the contrary of the term originally defined: and therefore the definition originally
rendered of the original term has not been rightly rendered either. Seeing, moreover, that of contraries, the
one is sometimes a word forced to denote the privation of the other, as (e.g.) inequality is generally held to be
the privation of equality (for 'unequal' merely describes things that are not equal'), it is therefore clear that
that contrary whose form denotes the privation must of necessity be defined through the other; whereas the
other cannot then be defined through the one whose form denotes the privation; for else we should find that
each is being interpreted by the other. We must in the case of contrary terms keep an eye on this mistake, e.g.
supposing any one were to define equality as the contrary of inequality: for then he is defining it through the
term which denotes privation of it. Moreover, a man who so defines is bound to use in his definition the very
term he is defining; and this becomes clear, if for the word we substitute its definition. For to say 'inequality'
is the same as to say 'privation of equality'. Therefore equality so defined will be 'the contrary of the privation
of equality', so that he would have used the very word to be defined. Suppose, however, that neither of the
contraries be so formed as to denote privation, but yet the definition of it be rendered in a manner like the
above, e.g. suppose 'good' to be defined as 'the contrary of evil', then, since it is clear that 'evil' too will be 'the
contrary of good' (for the definition of things that are contrary in this must be rendered in a like manner), the
result again is that he uses the very term being defined: for 'good' is inherent in the definition of 'evil'. If, then,
'good' be the contrary of evil, and evil be nothing other than the 'contrary of good', then 'good' will be the
'contrary of the contrary of good'. Clearly, then, he has used the very word to be defined.

Moreover, see if in rendering a term formed to denote privation, he has failed to render the term of which it is
the privation, e.g. the state, or contrary, or whatever it may be whose privation it is: also if he has omitted to
add either any term at all in which the privation is naturally formed, or else that in which it is naturally
formed primarily, e.g. whether in defining 'ignorance' a privation he has failed to say that it is the privation of
'knowledge'; or has failed to add in what it is naturally formed, or, though he has added this, has failed to
render the thing in which it is primarily formed, placing it (e.g.) in 'man' or in 'the soul', and not in the
'reasoning faculty': for if in any of these respects he fails, he has made a mistake. Likewise, also, if he has
failed to say that 'blindness' is the 'privation of sight in an eye': for a proper rendering of its essence must state
both of what it is the privation and what it is that is deprived.

Examine further whether he has defined by the expression 'a privation' a term that is not used to denote a
privation: thus a mistake of this sort also would be generally thought to be incurred in the case of 'error' by
any one who is not using it as a merely negative term. For what is generally thought to be in error is not that
which has no knowledge, but rather that which has been deceived, and for this reason we do not talk of
inanimate things or of children as 'erring'. 'Error', then, is not used to denote a mere privation of knowledge.

Moreover, see whether the like inflexions in the definition apply to the like inflexions of the term; e.g. if
'beneficial' means 'productive of health', does 'beneficially' mean productively of health' and a 'benefactor' a
'producer of health'?

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Look too and see whether the definition given will apply to the Idea as well. For in some cases it will not do
so; e.g. in the Platonic definition where he adds the word 'mortal' in his definitions of living creatures: for the
Idea (e.g. the absolute Man) is not mortal, so that the definition will not fit the Idea. So always wherever the
words 'capable of acting on' or 'capable of being acted upon' are added, the definition and the Idea are
absolutely bound to be discrepant: for those who assert the existence of Ideas hold that they are incapable of
being acted upon, or of motion. In dealing with these people even arguments of this kind are useful.

Further, see if he has rendered a single common definition of terms that are used ambiguously. For terms
whose definition corresponding their common name is one and the same, are synonymous; if, then, the
definition applies in a like manner to the whole range of the ambiguous term, it is not true of any one of the
objects described by the term. This is, moreover, what happens to Dionysius' definition of 'life' when stated as
'a movement of a creature sustained by nutriment, congeni tally present with it': for this is found in plants as
much as in animals, whereas 'life' is generally understood to mean not one kind of thing only, but to be one
thing in animals and another in plants. It is possible to hold the view that life is a synonymous term and is
always used to describe one thing only, and therefore to render the definition in this way on purpose: or it
may quite well happen that a man may see the ambiguous character of the word, and wish to render the
definition of the one sense only, and yet fail to see that he has rendered a definition common to both senses
instead of one peculiar to the sense he intends. In either case, whichever course he pursues, he is equally at
fault. Since ambiguous terms sometimes pass unobserved, it is best in questioning to treat such terms as
though they were synonymous (for the definition of the one sense will not apply to the other, so that the
answerer will be generally thought not to have defined it correctly, for to a synonymous term the definition
should apply in its full range), whereas in answering you should yourself distinguish between the senses.
Further, as some answerers call 'ambiguous' what is really synonymous, whenever the definition rendered
fails to apply universally, and, vice versa, call synonymous what is really ambiguous supposing their
definition applies to both senses of the term, one should secure a preliminary admission on such points, or
else prove beforehand that so-and-so is ambiguous or synonymous, as the case may be: for people are more
ready to agree when they do not foresee what the consequence will be. If, however, no admission has been
made, and the man asserts that what is really synonymous is ambiguous because the definition he has
rendered will not apply to the second sense as well, see if the definition of this second meaning applies also to
the other meanings: for if so, this meaning must clearly be synonymous with those others. Otherwise, there
will be more than one definition of those other meanings, for there are applicable to them two distinct
definitions in explanation of the term, viz. the one previously rendered and also the later one. Again, if any
one were to define a term used in several senses, and, finding that his definition does not apply to them all,
were to contend not that the term is ambiguous, but that even the term does not properly apply to all those
senses, just because his definition will not do so either, then one may retort to such a man that though in some
things one must not use the language of the people, yet in a question of terminology one is bound to employ
the received and traditional usage and not to upset matters of that sort.

Suppose now that a definition has been rendered of some complex term, take away the definition of one of
the elements in the complex, and see if also the rest of the definition defines the rest of it: if not, it is clear
that neither does the whole definition define the whole complex. Suppose, e.g. that some one has defined a
'finite straight line' as 'the limit of a finite plane, such that its centre is in a line with its extremes'; if now the
definition of a finite line' be the 'limit of a finite plane', the rest (viz. 'such that its centre is in a line with its
extremes') ought to be a definition of straight'. But an infinite straight line has neither centre nor extremes and
yet is straight so that this remainder does not define the remainder of the term.

Moreover, if the term defined be a compound notion, see if the definition rendered be equimembral with the
term defined. A definition is said to be equimembral with the term defined when the number of the elements
compounded in the latter is the same as the number of nouns and verbs in the definition. For the exchange in

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such cases is bound to be merely one of term for term, in the case of some if not of all, seeing that there are
no more terms used now than formerly; whereas in a definition terms ought to be rendered by phrases, if
possible in every case, or if not, in the majority. For at that rate, simple objects too could be defined by
merely calling them by a different name, e.g. 'cloak' instead of 'doublet'.

The mistake is even worse, if actually a less well known term be substituted, e.g. 'pellucid mortal' for 'white
man': for it is no definition, and moreover is less intelligible when put in that form.

Look and see also whether, in the exchange of words, the sense fails still to be the same. Take, for instance,
the explanation of 'speculative knowledge' as 'speculative conception': for conception is not the same as
knowledge-as it certainly ought to be if the whole is to be the same too: for though the word 'speculative' is
common to both expressions, yet the remainder is different.

Moreover, see if in replacing one of the terms by something else he has exchanged the genus and not the
differentia, as in the example just given: for 'speculative' is a less familiar term than knowledge; for the one is
the genus and the other the differentia, and the genus is always the most familiar term of all; so that it is not
this, but the differentia, that ought to have been changed, seeing that it is the less familiar. It might be held
that this criticism is ridiculous: because there is no reason why the most familiar term should not describe the
differentia, and not the genus; in which case, clearly, the term to be altered would also be that denoting the
genus and not the differentia. If, however, a man is substituting for a term not merely another term but a
phrase, clearly it is of the differentia rather than of the genus that a definition should be rendered, seeing that
the object of rendering the definition is to make the subject familiar; for the differentia is less familiar than
the genus.

If he has rendered the definition of the differentia, see whether the definition rendered is common to it and
something else as well: e.g. whenever he says that an odd number is a 'number with a middle', further
definition is required of how it has a middle: for the word 'number' is common to both expressions, and it is
the word 'odd' for which the phrase has been substituted. Now both a line and a body have a middle, yet they
are not 'odd'; so that this could not be a definition of 'odd'. If, on the other hand, the phrase 'with a middle' be
used in several senses, the sense here intended requires to be defined. So that this will either discredit the
definition or prove that it is no definition at all.

Again, see if the term of which he renders the definition is a reality, whereas what is contained in the
definition is not, e.g. Suppose 'white' to be defined as 'colour mingled with fire': for what is bodiless cannot
be mingled with body, so that 'colour' 'mingled with fire' could not exist, whereas 'white' does exist.

Moreover, those who in the case of relative terms do not distinguish to what the object is related, but have
described it only so as to include it among too large a number of things, are wrong either wholly or in part;
e.g. suppose some one to have defined 'medicine' as a science of Reality'. For if medicine be not a science of
anything that is real, the definition is clearly altogether false; while if it be a science of some real thing, but
not of another, it is partly false; for it ought to hold of all reality, if it is said to be of Reality essentially and
not accidentally: as is the case with other relative terms: for every object of knowledge is a term relative to
knowledge: likewise, also, with other relative terms, inasmuch as all such are convertible. Moreover, if the
right way to render account of a thing be to render it as it is not in itself but accidentally, then each and every
relative term would be used in relation not to one thing but to a number of things. For there is no reason why
the same thing should not be both real and white and good, so that it would be a correct rendering to render
the object in relation to any one whatsoever of these, if to render what it is accidentally be a correct way to
render it. It is, moreover, impossible that a definition of this sort should be peculiar to the term rendered: for
not only but the majority of the other sciences too, have for their object some real thing, so that each will be a

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science of reality. Clearly, then, such a definition does not define any science at all; for a definition ought to
be peculiar to its own term, not general.

Sometimes, again, people define not the thing but only the thing in a good or perfect condition. Such is the
definition of a rhetorician as 'one who can always see what will persuade in the given circumstances, and
omit nothing'; or of a thief, as 'one who pilfers in secret': for clearly, if they each do this, then the one will be
a good rhetorician, and the other a good thief: whereas it is not the actual pilfering in secret, but the wish to
do it, that constitutes the thief.

Again, see if he has rendered what is desirable for its own sake as desirable for what it produces or does, or as
in any way desirable because of something else, e.g. by saying that justice is 'what preserves the laws' or that
wisdom is 'what produces happiness'; for what produces or preserves something else is one of the things
desirable for something else. It might be said that it is possible for what is desirable in itself to be desirable
for something else as well: but still to define what is desirable in itself in such a way is none the less wrong:
for the essence contains par excellence what is best in anything, and it is better for a thing to be desirable in
itself than to be desirable for something else, so that this is rather what the definition too ought to have
indicated.

See also whether in defining anything a man has defined it as an 'A and B', or as a 'product of A and B' or as
an A+B'. If he defines it as and B', the definition will be true of both and yet of neither of them; suppose, e.g.
justice to be defined as 'temperance and courage.' For if of two persons each has one of the two only, both
and yet neither will be just: for both together have justice, and yet each singly fails to have it. Even if the
situation here described does not so far appear very absurd because of the occurrence of this kind of thing in
other cases also (for it is quite possible for two men to have a mina between them, though neither of them has
it by himself), yet least that they should have contrary attributes surely seems quite absurd; and yet this will
follow if the one be temperate and yet a coward, and the other, though brave, be a profligate; for then both
will exhibit both justice and injustice: for if justice be temperance and bravery, then injustice will be
cowardice and profligacy. In general, too, all the ways of showing that the whole is not the same as the sum
of its parts are useful in meeting the type just described; for a man who defines in this way seems to assert
that the parts are the same as the whole. The arguments are particularly appropriate in cases where the
process of putting the parts together is obvious, as in a house and other things of that sort: for there, clearly,
you may have the parts and yet not have the whole, so that parts and whole cannot be the same.

If, however, he has said that the term being defined is not A and B' but the 'product of A and B', look and see
in the first place if A and B cannot in the nature of things have a single product: for some things are so related
to one another that nothing can come of them, e.g. a line and a number. Moreover, see if the term that has
been defined is in the nature of things found primarily in some single subject, whereas the things which he
has said produce it are not found primarily in any single subject, but each in a separate one. If so, clearly that
term could not be the product of these things: for the whole is bound to be in the same things wherein its parts
are, so that the whole will then be found primarily not in one subject only, but in a number of them. If, on the
other hand, both parts and whole are found primarily in some single subject, see if that medium is not the
same, but one thing in the case of the whole and another in that of the parts. Again, see whether the parts
perish together with the whole: for it ought to happen, vice versa, that the whole perishes when the parts
perish; when the whole perishes, there is no necessity that the parts should perish too. Or again, see if the
whole be good or evil, and the parts neither, or, vice versa, if the parts be good or evil and the whole neither.
For it is impossible either for a neutral thing to produce something good or bad, or for things good or bad to
produce a neutral thing. Or again, see if the one thing is more distinctly good than the other is evil, and yet
the product be no more good than evil, e.g. suppose shamelessness be defined as 'the product of courage and
false opinion': here the goodness of courage exceeds the evil of false opinion; accordingly the product of

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these ought to have corresponded to this excess, and to be either good without qualification, or at least more
good than evil. Or it may be that this does not necessarily follow, unless each be in itself good or bad; for
many things that are productive are not good in themselves, but only in combination; or, per contra, they are
good taken singly, and bad or neutral in combination. What has just been said is most clearly illustrated in the
case of things that make for health or sickness; for some drugs are such that each taken alone is good, but if
they are both administered in a mixture, bad.

Again, see whether the whole, as produced from a better and worse, fails to be worse than the better and
better than the worse element. This again, however, need not necessarily be the case, unless the elements
compounded be in themselves good; if they are not, the whole may very well not be good, as in the cases just
instanced.

Moreover, see if the whole be synonymous with one of the elements: for it ought not to be, any more than in
the case of syllables: for the syllable is not synonymous with any of the letters of which it is made up.

Moreover, see if he has failed to state the manner of their composition: for the mere mention of its elements is
not enough to make the thing intelligible. For the essence of any compound thing is not merely that it is a
product of so-and-so, but that it is a product of them compounded in such and such a way, just as in the case
of a house: for here the materials do not make a house irrespective of the way they are put together.

If a man has defined an object as 'A+B', the first thing to be said is that A+B' means the same either as A and
B', or as the 'product of A and B.' for 'honey+water' means either the honey and the water, or the 'drink made
of honey and water'. If, then, he admits that A+B' is + B' is the same as either of these two things, the same
criticisms will apply as have already been given for meeting each of them. Moreover, distinguish between the
different senses in which one thing may be said to be '+' another, and see if there is none of them in which A
could be said to exist '+ B.' Thus e.g. supposing the expression to mean that they exist either in some identical
thing capable of containing them (as e.g. justice and courage are found in the soul), or else in the same place
or in the same time, and if this be in no way true of the A and B in question, clearly the definition rendered
could not hold of anything, as there is no possible way in which A can exist B'. If, however, among the
various senses above distinguished, it be true that A and B are each found in the same time as the other, look
and see if possibly the two are not used in the same relation. Thus e.g. suppose courage to have been defined
as 'daring with right reasoning': here it is possible that the person exhibits daring in robbery, and right
reasoning in regard to the means of health: but he may have 'the former quality+the latter' at the same time,
and not as yet be courageous! Moreover, even though both be used in the same relation as well, e.g. in
relation to medical treatment (for a man may exhibit both daring and right reasoning in respect of medical
treatment), still, none the less, not even this combination of 'the one+the other 'makes him 'courageous'. For
the two must not relate to any casual object that is the same, any more than each to a different object; rather,
they must relate to the function of courage, e.g. meeting the perils of war, or whatever is more properly
speaking its function than this.

Some definitions rendered in this form fail to come under the aforesaid division at all, e.g. a definition of
anger as 'pain with a consciousness of being slighted'. For what this means to say is that it is because of a
consciousness of this sort that the pain occurs; but to occur 'because of a thing is not the same as to occur '+ a
thing' in any of its aforesaid senses.

Again, if he have described the whole compounded as the 'composition' of these things (e.g. 'a living creature'
as a 'composition of soul and body'), first of all see whether he has omitted to state the kind of composition,
as (e.g.) in a definition of 'flesh' or 'bone' as the 'composition of fire, earth, and air'. For it is not enough to say
it is a composition, but you should also go on to define the kind of composition: for these things do not form

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flesh irrespective of the manner of their composition, but when compounded in one way they form flesh,
when in another, bone. It appears, moreover, that neither of the aforesaid substances is the same as a
'composition' at all: for a composition always has a decomposition as its contrary, whereas neither of the
aforesaid has any contrary. Moreover, if it is equally probable that every compound is a composition or else
that none is, and every kind of living creature, though a compound, is never a composition, then no other
compound could be a composition either.

Again, if in the nature of a thing two contraries are equally liable to occur, and the thing has been defined
through the one, clearly it has not been defined; else there will be more than one definition of the same thing;
for how is it any more a definition to define it through this one than through the other, seeing that both alike
are naturally liable to occur in it? Such is the definition of the soul, if defined as a substance capable of
receiving knowledge: for it has a like capacity for receiving ignorance.

Also, even when one cannot attack the definition as a whole for lack of acquaintance with the whole, one
should attack some part of it, if one knows that part and sees it to be incorrectly rendered: for if the part be
demolished, so too is the whole definition. Where, again, a definition is obscure, one should first of all correct
and reshape it in order to make some part of it clear and get a handle for attack, and then proceed to examine
it. For the answerer is bound either to accept the sense as taken by the questioner, or else himself to explain
clearly whatever it is that his definition means. Moreover, just as in the assemblies the ordinary practice is to
move an emendation of the existing law and, if the emendation is better, they repeal the existing law, so one
ought to do in the case of definitions as well: one ought oneself to propose a second definition: for if it is seen
to be better, and more indicative of the object defined, clearly the definition already laid down will have been
demolished, on the principle that there cannot be more than one definition of the same thing.

In combating definitions it is always one of the chief elementary principles to take by oneself a happy shot at
a definition of the object before one, or to adopt some correctly expressed definition. For one is bound, with
the model (as it were) before one's eyes, to discern both any shortcoming in any features that the definition
ought to have, and also any superfluous addition, so that one is better supplied with lines of attack.

As to definitions, then, let so much suffice.

Book VII

WHETHER two things are 'the same' or 'different', in the most literal of the meanings ascribed to 'sameness'
(and we said' that 'the same' applies in the most literal sense to what is numerically one), may be examined in
the light of their inflexions and coordinates and opposites. For if justice be the same as courage, then too the
just man is the same as the brave man, and justly' is the same as 'bravely'. Likewise, too, in the case of their
opposites: for if two things be the same, their opposites also will be the same, in any of the recognized forms
of opposition. For it is the same thing to take the opposite of the one or that of the other, seeing that they are
the same. Again it may be examined in the light of those things which tend to produce or to destroy the things
in question of their formation and destruction, and in general of any thing that is related in like manner to
each. For where things are absolutely the same, their formations and destructions also are the same, and so
are the things that tend to produce or to destroy them. Look and see also, in a case where one of two things is
said to be something or other in a superlative degree, if the other of these alleged identical things can also be
described by a superlative in the same respect. Thus Xenocrates argues that the happy life and the good life
are the same, seeing that of all forms of life the good life is the most desirable and so also is the happy life:
for 'the most desirable' and the greatest' apply but to one thing.' Likewise also in other cases of the kind. Each,
however, of the two things termed 'greatest' or most desirable' must be numerically one: otherwise no proof
will have been given that they are the same; for it does not follow because Peloponnesians and Spartans are

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the bravest of the Greeks, that Peloponnesians are the same as Spartans, seeing that 'Peloponnesian' is not any
one person nor yet 'Spartan'; it only follows that the one must be included under the other as 'Spartans' are
under 'Peloponnesians': for otherwise, if the one class be not included under the other, each will be better than
the other. For then the Peloponnesians are bound to be better than the Spartans, seeing that the one class is
not included under the other; for they are better than anybody else. Likewise also the Spartans must perforce
be better than the Peloponnesians; for they too are better than anybody else; each then is better than the other!
Clearly therefore what is styled 'best' and 'greatest' must be a single thing, if it is to be proved to be 'the same'
as another. This also is why Xenocrates fails to prove his case: for the happy life is not numerically single,
nor yet the good life, so that it does not follow that, because they are both the most desirable, they are
therefore the same, but only that the one falls under the other.

Again, look and see if, supposing the one to be the same as something, the other also is the same as it: for if
they be not both the same as the same thing, clearly neither are they the same as one another.

Moreover, examine them in the light of their accidents or of the things of which they are accidents: for any
accident belonging to the one must belong also to the other, and if the one belong to anything as an accident,
so must the other also. If in any of these respects there is a discrepancy, clearly they are not the same.

See further whether, instead of both being found in one class of predicates, the one signifies a quality and the
other a quantity or relation. Again, see if the genus of each be not the same, the one being 'good' and the other
evil', or the one being 'virtue' and the other 'knowledge': or see if, though the genus is the same, the
differentiae predicted of either be not the same, the one (e.g.) being distinguished as a 'speculative' science,
the other as a 'practical' science. Likewise also in other cases.

Moreover, from the point of view of 'degrees', see if the one admits an increase of degree but not the other, or
if though both admit it, they do not admit it at the same time; just as it is not the case that a man desires
intercourse more intensely, the more intensely he is in love, so that love and the desire for intercourse are not
the same.

Moreover, examine them by means of an addition, and see whether the addition of each to the same thing
fails to make the same whole; or if the subtraction of the same thing from each leaves a different remainder.
Suppose (e.g.) that he has declared 'double a half to be the same as 'a multiple of a half: then, subtracting the
words 'a half from each, the remainders ought to have signified the same thing: but they do not; for 'double'
and 'a multiple of do not signify the same thing.

Inquire also not only if some impossible consequence results directly from the statement made, that A and B
are the same, but also whether it is possible for a supposition to bring it about; as happens to those who assert
that 'empty' is the same as 'full of air': for clearly if the air be exhausted, the vessel will not be less but more
empty, though it will no longer be full of air. So that by a supposition, which may be true or may be false (it
makes no difference which), the one character is annulled and not the other, showing that they are not the
same.

Speaking generally, one ought to be on the look-out for any discrepancy anywhere in any sort of predicate of
each term, and in the things of which they are predicated. For all that is predicated of the one should be
predicated also of the other, and of whatever the one is a predicate, the other should be a predicate of it as
well.

Moreover, as 'sameness' is a term used in many senses, see whether things that are the same in one way are
the same also in a different way. For there is either no necessity or even no possibility that things that are the
same specifically or generically should be numerically the same, and it is with the question whether they are
or are not the same in that sense that we are concerned.

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Moreover, see whether the one can exist without the other; for, if so, they could not be the same.

Such is the number of the commonplace rules that relate to 'sameness'. It is clear from what has been said that
all the destructive commonplaces relating to sameness are useful also in questions of definition, as was said
before:' for if what is signified by the term and by the expression be not the same, clearly the expression
rendered could not be a definition. None of the constructive commonplaces, on the other hand, helps in the
matter of definition; for it is not enough to show the sameness of content between the expression and the
term, in order to establish that the former is a definition, but a definition must have also all the other
characters already announced.

This then is the way, and these the arguments, whereby the attempt to demolish a definition should always be
made. If, on the other hand, we desire to establish one, the first thing to observe is that few if any who engage
in discussion arrive at a definition by reasoning: they always assume something of the kind as their starting
points-both in geometry and in arithmetic and the other studies of that kind. In the second place, to say
accurately what a definition is, and how it should be given, belongs to another inquiry. At present it concerns
us only so far as is required for our present purpose, and accordingly we need only make the bare statement
that to reason to a thing's definition and essence is quite possible. For if a definition is an expression
signifying the essence of the thing and the predicates contained therein ought also to be the only ones which
are predicated of the thing in the category of essence; and genera and differentiae are so predicated in that
category: it is obvious that if one were to get an admission that so and so are the only attributes predicated in
that category, the expression containing so and so would of necessity be a definition; for it is impossible that
anything else should be a definition, seeing that there is not anything else predicated of the thing in the
category of essence.

That a definition may thus be reached by a process of reasoning is obvious. The means whereby it should be
established have been more precisely defined elsewhere, but for the purposes of the inquiry now before us the
same commonplace rules serve. For we have to examine into the contraries and other opposites of the thing,
surveying the expressions used both as wholes and in detail: for if the opposite definition defines that
opposite term, the definition given must of necessity be that of the term before us. Seeing, however, that
contraries may be conjoined in more than one way, we have to select from those contraries the one whose
contrary definition seems most obvious. The expressions, then, have to be examined each as a whole in the
way we have said, and also in detail as follows. First of all, see that the genus rendered is correctly rendered;
for if the contrary thing be found in the contrary genus to that stated in the definition, and the thing before
you is not in that same genus, then it would clearly be in the contrary genus: for contraries must of necessity
be either in the same genus or in contrary genera. The differentiae, too, that are predicated of contraries we
expect to be contrary, e.g. those of white and black, for the one tends to pierce the vision, while the other
tends to compress it. So that if contrary differentiae to those in the definition are predicated of the contrary
term, then those rendered in the definition would be predicated of the term before us. Seeing, then, that both
the genus and the differentiae have been rightly rendered, clearly the expression given must be the right
definition. It might be replied that there is no necessity why contrary differentiae should be predicated of
contraries, unless the contraries be found within the same genus: of things whose genera are themselves
contraries it may very well be that the same differentia is used of both, e.g. of justice and injustice; for the
one is a virtue and the other a vice of the soul: 'of the soul', therefore, is the differentia in both cases, seeing
that the body as well has its virtue and vice. But this much at least is true, that the differentiae of contraries
are either contrary or else the same. If, then, the contrary differentia to that given be predicated of the
contrary term and not of the one in hand, clearly the differentia stated must be predicated of the latter.
Speaking generally, seeing that the definition consists of genus and differentiae, if the definition of the

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contrary term be apparent, the definition of the term before you will be apparent also: for since its contrary is
found either in the same genus or in the contrary genus, and likewise also the differentiae predicated of
opposites are either contrary to, or the same as, each other, clearly of the term before you there will be
predicated either the same genus as of its contrary, while, of its differentiae, either all are contrary to those of
its contrary, or at least some of them are so while the rest remain the same; or, vice versa, the differentiae will
be the same and the genera contrary; or both genera and differentiae will be contrary. And that is all; for that
both should be the same is not possible; else contraries will have the same definition.

Moreover, look at it from the point of view of its inflexions and coordinates. For genera and definitions are
bound to correspond in either case. Thus if forgetfulness be the loss of knowledge, to forget is to lose
knowledge, and to have forgotten is to have lost knowledge. If, then, any one whatever of these is agreed to,
the others must of necessity be agreed to as well. Likewise, also, if destruction is the decomposition of the
thing's essence, then to be destroyed is to have its essence decomposed, and 'destructively' means 'in such a
way as to decompose its essence'; if again 'destructive' means 'apt to decompose something's essence', then
also 'destruction' means 'the decomposition of its essence'. Likewise also with the rest: an admission of any
one of them whatever, and all the rest are admitted too.

Moreover, look at it from the point of view of things that stand in relations that are like each other. For if
'healthy' means 'productive of health', 'vigorous' too will mean 'productive of vigour', and 'useful' will mean
'productive of good.' For each of these things is related in like manner to its own peculiar end, so that if one
of them is defined as 'productive of that end, this will also be the definition of each of the rest as well.

Moreover, look at it from the point of and like degrees, in all the ways in which it is possible to establish a
result by comparing two and two together. Thus if A defines a better than B defines and B is a definition of so
too is A of a. Further, if A's claim to define a is like B's to define B, and B defines B, then A too defines a.
This examination from the point of view of greater degrees is of no use when a single definition is compared
with two things, or two definitions with one thing; for there cannot possibly be one definition of two things or
two of the same thing.

The most handy of all the commonplace arguments are those just mentioned and those from co-ordinates and
inflexions, and these therefore are those which it is most important to master and to have ready to hand: for
they are the most useful on the greatest number of occasions. Of the rest, too, the most important are those of
most general application: for these are the most effective, e.g. that you should examine the individual cases,
and then look to see in the case of their various species whether the definition applies. For the species is
synonymous with its individuals. This sort of inquiry is of service against those who assume the existence of
Ideas, as has been said before.' Moreover see if a man has used a term metaphorically, or predicated it of
itself as though it were something different. So too if any other of the commonplace rules is of general
application and effective, it should be employed.

That it is more difficult to establish than to overthrow a definition, is obvious from considerations presently
to be urged. For to see for oneself, and to secure from those whom one is questioning, an admission of
premisses of this sort is no simple matter, e.g. that of the elements of the definition rendered the one is genus
and the other differentia, and that only the genus and differentiae are predicated in the category of essence.
Yet without these premisses it is impossible to reason to a definition; for if any other things as well are
predicated of the thing in the category of essence, there is no telling whether the formula stated or some other
one is its definition, for a definition is an expression indicating the essence of a thing. The point is clear also
from the following: It is easier to draw one conclusion than many. Now in demolishing a definition it is

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sufficient to argue against one point only (for if we have overthrown any single point whatsoever, we shall
have demolished the definition); whereas in establishing a definition, one is bound to bring people to the view
that everything contained in the definition is attributable. Moreover, in establishing a case, the reasoning
brought forward must be universal: for the definition put forward must be predicated of everything of which
the term is predicated, and must moreover be convertible, if the definition rendered is to be peculiar to the
subject. In overthrowing a view, on the other hand, there is no longer any necessity to show one's point
universally: for it is enough to show that the formula is untrue of any one of the things embraced under the
term.

Further, even supposing it should be necessary to overthrow something by a universal proposition, not even
so is there any need to prove the converse of the proposition in the process of overthrowing the definition.
For merely to show that the definition fails to be predicated of every one of the things of which the term is
predicated, is enough to overthrow it universally: and there is no need to prove the converse of this in order to
show that the term is predicated of things of which the expression is not predicated. Moreover, even if it
applies to everything embraced under the term, but not to it alone, the definition is thereby demolished.

The case stands likewise in regard to the property and genus of a term also. For in both cases it is easier to
overthrow than to establish. As regards the property this is clear from what has been said: for as a rule the
property is rendered in a complex phrase, so that to overthrow it, it is only necessary to demolish one of the
terms used, whereas to establish it is necessary to reason to them all. Then, too, nearly all the other rules that
apply to the definition will apply also to the property of a thing. For in establishing a property one has to
show that it is true of everything included under the term in question, whereas to overthrow one it is enough
to show in a single case only that it fails to belong: further, even if it belongs to everything falling under the
term, but not to that only, it is overthrown in this case as well, as was explained in the case of the definition.
In regard to the genus, it is clear that you are bound to establish it in one way only, viz. by showing that it
belongs in every case, while of overthrowing it there are two ways: for if it has been shown that it belongs
either never or not in a certain case, the original statement has been demolished. Moreover, in establishing a
genus it is not enough to show that it belongs, but also that it belongs as genus has to be shown; whereas in
overthrowing it, it is enough to show its failure to belong either in some particular case or in every case. It
appears, in fact, as though, just as in other things to destroy is easier than to create, so in these matters too to
overthrow is easier than to establish.

In the case of an accidental attribute the universal proposition is easier to overthrow than to establish; for to
establish it, one has to show that it belongs in every case, whereas to overthrow it, it is enough to show that it
does not belong in one single case. The particular proposition is, on the contrary, easier to establish than to
overthrow: for to establish it, it is enough to show that it belongs in a particular instance, whereas to
overthrow it, it has to be shown that it never belongs at all.

It is clear also that the easiest thing of all is to overthrow a definition. For on account of the number of
statements involved we are presented in the definition with the greatest number of points for attack, and the
more plentiful the material, the quicker an argument comes: for there is more likelihood of a mistake
occurring in a large than in a small number of things. Moreover, the other rules too may be used as means for
attacking a definition: for if either the formula be not peculiar, or the genus rendered be the wrong one, or
something included in the formula fail to belong, the definition is thereby demolished. On the other hand,
against the others we cannot bring all of the arguments drawn from definitions, nor yet of the rest: for only
those relating to accidental attributes apply generally to all the aforesaid kinds of attribute. For while each of
the aforesaid kinds of attribute must belong to the thing in question, yet the genus may very well not belong
as a property without as yet being thereby demolished. Likewise also the property need not belong as a genus,
nor the accident as a genus or property, so long as they do belong. So that it is impossible to use one set as a
basis of attack upon the other except in the case of definition. Clearly, then, it is the easiest of all things to
demolish a definition, while to establish one is the hardest. For there one both has to establish all those other

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points by reasoning (i.e. that the attributes stated belong, and that the genus rendered is the true genus, and
that the formula is peculiar to the term), and moreover, besides this, that the formula indicates the essence of
the thing; and this has to be done correctly.

Of the rest, the property is most nearly of this kind: for it is easier to demolish, because as a rule it contains
several terms; while it is the hardest to establish, both because of the number of things that people must be
brought to accept, and, besides this, because it belongs to its subject alone and is predicated convertibly with
its subject.

The easiest thing of all to establish is an accidental predicate: for in other cases one has to show not only that
the predicate belongs, but also that it belongs in such and such a particular way: whereas in the case of the
accident it is enough to show merely that it belongs. On the other hand, an accidental predicate is the hardest
thing to overthrow, because it affords the least material: for in stating accident a man does not add how the
predicate belongs; and accordingly, while in other cases it is possible to demolish what is said in two ways,
by showing either that the predicate does not belong, or that it does not belong in the particular way stated, in
the case of an accidental predicate the only way to demolish it is to show that it does not belong at all.

The commonplace arguments through which we shall be well supplied with lines of argument with regard to
our several problems have now been enumerated at about sufficient length.

Book VIM

NEXT there fall to be discussed the problems of arrangement and method in pitting questions. Any one who
intends to frame questions must, first of all, select the ground from which he should make his attack;
secondly, he must frame them and arrange them one by one to himself; thirdly and lastly, he must proceed
actually to put them to the other party. Now so far as the selection of his ground is concerned the problem is
one alike for the philosopher and the dialectician; but how to go on to arrange his points and frame his
questions concerns the dialectician only: for in every problem of that kind a reference to another party is
involved. Not so with the philosopher, and the man who is investigating by himself: the premisses of his
reasoning, although true and familiar, may be refused by the answerer because they lie too near the original
statement and so he foresees what will follow if he grants them: but for this the philosopher does not care.
Nay, he may possibly be even anxious to secure axioms as familiar and as near to the question in hand as
possible: for these are the bases on which scientific reasonings are built up.

The sources from which one's commonplace arguments should be drawn have already been described:' we
have now to discuss the arrangement and formation of questions and first to distinguish the premisses, other
than the necessary premisses, which have to be adopted. By necessary premisses are meant those through
which the actual reasoning is constructed. Those which are secured other than these are of four kinds; they
serve either inductively to secure the universal premiss being granted, or to lend weight to the argument, or to
conceal the conclusion, or to render the argument more clear. Beside these there is no other premiss which
need be secured: these are the ones whereby you should try to multiply and formulate your questions. Those
which are used to conceal the conclusion serve a controversial purpose only; but inasmuch as an undertaking
of this sort is always conducted against another person, we are obliged to employ them as well.

The necessary premisses through which the reasoning is effected, ought not to be propounded directly in so
many words. Rather one should soar as far aloof from them as possible. Thus if one desires to secure an
admission that the knowledge of contraries is one, one should ask him to admit it not of contraries, but of
opposites: for, if he grants this, one will then argue that the knowledge of contraries is also the same, seeing
that contraries are opposites; if he does not, one should secure the admission by induction, by formulating a

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proposition to that effect in the case of some particular pair of contraries. For one must secure the necessary
premisses either by reasoning or by induction, or else partly by one and partly by the other, although any
propositions which are too obvious to be denied may be formulated in so many words. This is because the
coming conclusion is less easily discerned at the greater distance and in the process of induction, while at the
same time, even if one cannot reach the required premisses in this way, it is still open to one to formulate
them in so many words. The premisses, other than these, that were mentioned above, must be secured with a
view to the latter. The way to employ them respectively is as follows: Induction should proceed from
individual cases to the universal and from the known to the unknown; and the objects of perception are better
known, to most people if not invariably. Concealment of one's plan is obtained by securing through
prosyllogisms the premisses through which the proof of the original proposition is going to be
constructed-and as many of them as possible. This is likely to be effected by making syllogisms to prove not
only the necessary premisses but also some of those which are required to establish them. Moreover, do not
state the conclusions of these premisses but draw them later one after another; for this is likely to keep the
answerer at the greatest possible distance from the original proposition. Speaking generally, a man who
desires to get information by a concealed method should so put his questions that when he has put his whole
argument and has stated the conclusion, people still ask 'Well, but why is that?' This result will be secured
best of all by the method above described: for if one states only the final conclusion, it is unclear how it
comes about; for the answerer does not foresee on what grounds it is based, because the previous syllogisms
have not been made articulate to him: while the final syllogism, showing the conclusion, is likely to be kept
least articulate if we lay down not the secured propositions on which it is based, but only the grounds on
which we reason to them.

It is a useful rule, too, not to secure the admissions claimed as the bases of the syllogisms in their proper
order, but alternately those that conduce to one conclusion and those that conduce to another; for, if those
which go together are set side by side, the conclusion that will result from them is more obvious in advance.

One should also, wherever possible, secure the universal premiss by a definition relating not to the precise
terms themselves but to their co-ordinates; for people deceive themselves, whenever the definition is taken in
regard to a co-ordinate, into thinking that they are not making the admission universally. An instance would
be, supposing one had to secure the admission that the angry man desires vengeance on account of an
apparent slight, and were to secure this, that 'anger' is a desire for vengeance on account of an apparent slight:
for, clearly, if this were secured, we should have universally what we intend. If, on the other hand, people
formulate propositions relating to the actual terms themselves, they often find that the answerer refuses to
grant them because on the actual term itself he is readier with his objection, e.g. that the 'angry man' does not
desire vengeance, because we become angry with our parents, but we do not desire vengeance on them. Very
likely the objection is not valid; for upon some people it is vengeance enough to cause them pain and make
them sorry; but still it gives a certain plausibility and air of reasonableness to the denial of the proposition. In
the case, however, of the definition of 'anger' it is not so easy to find an objection.

Moreover, formulate your proposition as though you did so not for its own sake, but in order to get at
something else: for people are shy of granting what an opponent's case really requires. Speaking generally, a
questioner should leave it as far as possible doubtful whether he wishes to secure an admission of his
proposition or of its opposite: for if it be uncertain what their opponent's argument requires, people are more
ready to say what they themselves think.

Moreover, try to secure admissions by means of likeness: for such admissions are plausible, and the universal
involved is less patent; e.g. make the other person admit that as knowledge and ignorance of contraries is the
same, so too perception of contraries is the same; or vice versa, that since the perception is the same, so is the
knowledge also. This argument resembles induction, but is not the same thing; for in induction it is the
universal whose admission is secured from the particulars, whereas in arguments from likeness, what is
secured is not the universal under which all the like cases fall.

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It is a good rule also, occasionally to bring an objection against oneself: for answerers are put off their guard
against those who appear to be arguing impartially. It is useful too, to add that 'So and so is generally held or
commonly said'; for people are shy of upsetting the received opinion unless they have some positive
objection to urge: and at the same time they are cautious about upsetting such things because they themselves
too find them useful. Moreover, do not be insistent, even though you really require the point: for insistence
always arouses the more opposition. Further, formulate your premiss as though it were a mere illustration: for
people admit the more readily a proposition made to serve some other purpose, and not required on its own
account. Moreover, do not formulate the very proposition you need to secure, but rather something from
which that necessarily follows: for people are more willing to admit the latter, because it is not so clear from
this what the result will be, and if the one has been secured, the other has been secured also. Again, one
should put last the point which one most wishes to have conceded; for people are specially inclined to deny
the first questions put to them, because most people in asking questions put first the points which they are
most eager to secure. On the other hand, in dealing with some people propositions of this sort should be put
forward first: for ill-tempered men admit most readily what comes first, unless the conclusion that will result
actually stares them in the face, while at the close of an argument they show their ill-temper. Likewise also
with those who consider themselves smart at answering: for when they have admitted most of what you want
they finally talk clap-trap to the effect that the conclusion does not follow from their admissions: yet they say
'Yes' readily, confident in their own character, and imagining that they cannot suffer any reverse. Moreover, it
is well to expand the argument and insert things that it does not require at all, as do those who draw false
geometrical figures: for in the multitude of details the whereabouts of the fallacy is obscured. For this reason
also a questioner sometimes evades observation as he adds in a corner what, if he formulated it by itself,
would not be granted.

For concealment, then, the rules which should be followed are the above. Ornament is attained by induction
and distinction of things closely akin. What sort of process induction is obvious: as for distinction, an
instance of the kind of thing meant is the distinction of one form of knowledge as better than another by
being either more accurate, or concerned with better objects; or the distinction of sciences into speculative,
practical, and productive. For everything of this kind lends additional ornament to the argument, though there
is no necessity to say them, so far as the conclusion goes.

For clearness, examples and comparisons should be adduced, and let the illustrations be relevant and drawn
from things that we know, as in Homer and not as in Choerilus; for then the proposition is likely to become
clearer.

In dialectics, syllogism should be employed in reasoning against dialecticians rather than against the crowd:
induction, on the other hand, is most useful against the crowd. This point has been treated previously as well.'
In induction, it is possible in some cases to ask the question in its universal form, but in others this is not
easy, because there is no established general term that covers all the resemblances: in this case, when people
need to secure the universal, they use the phrase 'in all cases of this sort'. But it is one of the very hardest
things to distinguish which of the things adduced are 'of this sort', and which are not: and in this connexion
people often throw dust in each others' eyes in their discussion, the one party asserting the likeness of things
that are not alike, and the other disputing the likeness of things that are. One ought, therefore, to try oneself to
coin a word to cover all things of the given sort, so as to leave no opportunity either to the answerer to
dispute, and say that the thing advanced does not answer to a like description, or to the questioner to suggest
falsely that it does answer to a like description, for many things appear to answer to like descriptions that do
not really do so.

If one has made an induction on the strength of several cases and yet the answerer refuses to grant the
universal proposition, then it is fair to demand his objection. But until one has oneself stated in what cases it

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is so, it is not fair to demand that he shall say in what cases it is not so: for one should make the induction
first, and then demand the objection. One ought, moreover, to claim that the objections should not be brought
in reference to the actual subject of the proposition, unless that subject happen to be the one and only thing of
the kind, as for instance two is the one prime number among the even numbers: for, unless he can say that
this subject is unique of its kind, the objector ought to make his objection in regard to some other. People
sometimes object to a universal proposition, and bring their objection not in regard to the thing itself, but in
regard to some homonym of it: thus they argue that a man can very well have a colour or a foot or a hand
other than his own, for a painter may have a colour that is not his own, and a cook may have a foot that is not
his own. To meet them, therefore, you should draw the distinction before putting your question in such cases:
for so long as the ambiguity remains undetected, so long will the objection to the proposition be deemed
valid. If, however, he checks the series of questions by an objection in regard not to some homonym, but to
the actual thing asserted, the questioner should withdraw the point objected to, and form the remainder into a
universal proposition, until he secures what he requires; e.g. in the case of forgetfulness and having forgotten:
for people refuse to admit that the man who has lost his knowledge of a thing has forgotten it, because if the
thing alters, he has lost knowledge of it, but he has not forgotten it. Accordingly the thing to do is to
withdraw the part objected to, and assert the remainder, e.g. that if a person have lost knowledge of a thing
while it still remains, he then has forgotten it. One should similarly treat those who object to the statement
that 'the greater the good, the greater the evil that is its opposite': for they allege that health, which is a less
good thing than vigour, has a greater evil as its opposite: for disease is a greater evil than debility. In this case
too, therefore, we have to withdraw the point objected to; for when it has been withdrawn, the man is more
likely to admit the proposition, e.g. that 'the greater good has the greater evil as its opposite, unless the one
good involves the other as well', as vigour involves health. This should be done not only when he formulates
an objection, but also if, without so doing, he refuses to admit the point because he foresees something of the
kind: for if the point objected to be withdrawn, he will be forced to admit the proposition because he cannot
foresee in the rest of it any case where it does not hold true: if he refuse to admit it, then when asked for an
objection he certainly will be unable to render one. Propositions that are partly false and partly true are of this
type: for in the case of these it is possible by withdrawing a part to leave the rest true. If, however, you
formulate the proposition on the strength of many cases and he has no objection to bring, you may claim that
he shall admit it: for a premiss is valid in dialectics which thus holds in several instances and to which no
objection is forthcoming.

Whenever it is possible to reason to the same conclusion either through or without a reduction per
impossibile, if one is demonstrating and not arguing dialectically it makes no difference which method of
reasoning be adopted, but in argument with another reasoning per impossibile should be avoided. For where
one has reasoned without the reduction per impossibile, no dispute can arise; if, on the other hand, one does
reason to an impossible conclusion, unless its falsehood is too plainly manifest, people deny that it is
impossible, so that the questioners do not get what they want.

One should put forward all propositions that hold true of several cases, and to which either no objection
whatever appears or at least not any on the surface: for when people cannot see any case in which it is not so,
they admit it for true.

The conclusion should not be put in the form of a question; if it be, and the man shakes his head, it looks as if
the reasoning had failed. For often, even if it be not put as a question but advanced as a consequence, people
deny it, and then those who do not see that it follows upon the previous admissions do not realize that those
who deny it have been refuted: when, then, the one man merely asks it as a question without even saying that
it so follows, and the other denies it, it looks altogether as if the reasoning had failed.

Not every universal question can form a dialectical proposition as ordinarily understood, e.g. 'What is man?'
or 'How many meanings has "the good"?' For a dialectical premiss must be of a form to which it is possible to
reply 'Yes' or 'No', whereas to the aforesaid it is not possible. For this reason questions of this kind are not

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dialectical unless the questioner himself draws distinctions or divisions before expressing them, e.g. 'Good
means this, or this, does it not?' For questions of this sort are easily answered by a Yes or a No. Hence one
should endeavour to formulate propositions of this kind in this form. It is at the same time also perhaps fair to
ask the other man how many meanings of 'the good' there are, whenever you have yourself distinguished and
formulated them, and he will not admit them at all.

Any one who keeps on asking one thing for a long time is a bad inquirer. For if he does so though the person
questioned keeps on answering the questions, clearly he asks a large number of questions, or else asks the
same question a large number of times: in the one case he merely babbles, in the other he fails to reason: for
reasoning always consists of a small number of premisses. If, on the other hand, he does it because the person
questioned does not answer the questions, he is at fault in not taking him to task or breaking off the
discussion.

There are certain hypotheses upon which it is at once difficult to bring, and easy to stand up to, an argument.
Such (e.g.) are those things which stand first and those which stand last in the order of nature. For the former
require definition, while the latter have to be arrived at through many steps if one wishes to secure a
continuous proof from first principles, or else all discussion about them wears the air of mere sophistry: for to
prove anything is impossible unless one begins with the appropriate principles, and connects inference with
inference till the last are reached. Now to define first principles is just what answerers do not care to do, nor
do they pay any attention if the questioner makes a definition: and yet until it is clear what it is that is
proposed, it is not easy to discuss it. This sort of thing happens particularly in the case of the first principles:
for while the other propositions are shown through these, these cannot be shown through anything else: we
are obliged to understand every item of that sort by a definition. The inferences, too, that lie too close to the
first principle are hard to treat in argument: for it is not possible to bring many arguments in regard to them,
because of the small number of those steps, between the conclusion and the principle, whereby the
succeeding propositions have to be shown. The hardest, however, of all definitions to treat in argument are
those that employ terms about which, in the first place, it is uncertain whether they are used in one sense or
several, and, further, whether they are used literally or metaphorically by the definer. For because of their
obscurity, it is impossible to argue upon such terms; and because of the impossibility of saying whether this
obscurity is due to their being used metaphorically, it is impossible to refute them.

In general, it is safe to suppose that, whenever any problem proves intractable, it either needs definition or
else bears either several senses, or a metaphorical sense, or it is not far removed from the first principles; or
else the reason is that we have yet to discover in the first place just this-in which of the aforesaid directions
the source of our difficulty lies: when we have made this clear, then obviously our business must be either to
define or to distinguish, or to supply the intermediate premisses: for it is through these that the final
conclusions are shown.

It often happens that a difficulty is found in discussing or arguing a given position because the definition has
not been correctly rendered: e.g. 'Has one thing one contrary or many?': here when the term 'contraries' has
been properly defined, it is easy to bring people to see whether it is possible for the same thing to have
several contraries or not: in the same way also with other terms requiring definition. It appears also in
mathematics that the difficulty in using a figure is sometimes due to a defect in definition; e.g. in proving that
the line which cuts the plane parallel to one side divides similarly both the line which it cuts and the area;
whereas if the definition be given, the fact asserted becomes immediately clear: for the areas have the same
fraction subtracted from them as have the sides: and this is the definition of 'the same ratio'. The most primary
of the elementary principles are without exception very easy to show, if the definitions involved, e.g. the
nature of a line or of a circle, be laid down; only the arguments that can be brought in regard to each of them
are not many, because there are not many intermediate steps. If, on the other hand, the definition of the

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starting-points be not laid down, to show them is difficult and may even prove quite impossible. The case of
the significance of verbal expressions is like that of these mathematical conceptions.

One may be sure then, whenever a position is hard to discuss, that one or other of the aforesaid things has
happened to it. Whenever, on the other hand, it is a harder task to argue to the point claimed, i.e. the premiss,
than to the resulting position, a doubt may arise whether such claims should be admitted or not: for if a man
is going to refuse to admit it and claim that you shall argue to it as well, he will be giving the signal for a
harder undertaking than was originally proposed: if, on the other hand, he grants it, he will be giving the
original thesis credence on the strength of what is less credible than itself. If, then, it is essential not to
enhance the difficulty of the problem, he had better grant it; if, on the other hand, it be essential to reason
through premisses that are better assured, he had better refuse. In other words, in serious inquiry he ought not
to grant it, unless he be more sure about it than about the conclusion; whereas in a dialectical exercise he may
do so if he is merely satisfied of its truth. Clearly, then, the circumstances under which such admissions
should be claimed are different for a mere questioner and for a serious teacher.

As to the formulation, then, and arrangement of one's questions, about enough has been said.

With regard to the giving of answers, we must first define what is the business of a good answerer, as of a
good questioner. The business of the questioner is so to develop the argument as to make the answerer utter
the most extrvagant paradoxes that necessarily follow because of his position: while that of the answerer is to
make it appear that it is not he who is responsible for the absurdity or paradox, but only his position: for one
may, perhaps, distinguish between the mistake of taking up a wrong position to start with, and that of not
maintaining it properly, when once taken up.

Inasmuch as no rules are laid down for those who argue for the sake of training and of examination:-and the
aim of those engaged in teaching or learning is quite different from that of those engaged in a competition; as
is the latter from that of those who discuss things together in the spirit of inquiry: for a learner should always
state what he thinks: for no one is even trying to teach him what is false; whereas in a competition the
business of the questioner is to appear by all means to produce an effect upon the other, while that of the
answerer is to appear unaffected by him; on the other hand, in an assembly of disputants discussing in the
spirit not of a competition but of an examination and inquiry, there are as yet no articulate rules about what
the answerer should aim at, and what kind of things he should and should not grant for the correct or incorrect
defence of his position:-inasmuch, then, as we have no tradition bequeathed to us by others, let us try to say
something upon the matter for ourselves.

The thesis laid down by the answerer before facing the questioner's argument is bound of necessity to be one
that is either generally accepted or generally rejected or else is neither: and moreover is so accepted or
rejected either absolutely or else with a restriction, e.g. by some given person, by the speaker or by some one
else. The manner, however, of its acceptance or rejection, whatever it be, makes no difference: for the right
way to answer, i.e. to admit or to refuse to admit what has been asked, will be the same in either case. If,
then, the statement laid down by the answerer be generally rejected, the conclusion aimed at by the questioner
is bound to be one generally accepted, whereas if the former be generally accepted, the latter is generally
rejected: for the conclusion which the questioner tries to draw is always the opposite of the statement laid
down. If, on the other hand, what is laid down is generally neither rejected nor accepted, the conclusion will
be of the same type as well. Now since a man who reasons correctly demonstrates his proposed conclusion
from premisses that are more generally accepted, and more familiar, it is clear that (1) where the view laid
down by him is one that generally is absolutely rejected, the answerer ought not to grant either what is thus

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absolutely not accepted at all, or what is accepted indeed, but accepted less generally than the questioner's
conclusion. For if the statement laid down by the answerer be generally rejected, the conclusion aimed at by
the questioner will be one that is generally accepted, so that the premisses secured by the questioner should
all be views generally accepted, and more generally accepted than his proposed conclusion, if the less
familiar is to be inferred through the more familiar. Consequently, if any of the questions put to him be not of
this character, the answerer should not grant them. (2) If, on the other hand, the statement laid down by the
answerer be generally accepted without qualification, clearly the conclusion sought by the questioner will be
one generally rejected without qualification. Accordingly, the answerer should admit all views that are
generally accepted and, of those that are not generally accepted, all that are less generally rejected than the
conclusion sought by the questioner. For then he will probably be thought to have argued sufficiently well.
(3) Likewise, too, if the statement laid down by the answerer be neither rejected generally nor generally
accepted; for then, too, anything that appears to be true should be granted, and, of the views not generally
accepted, any that are more generally accepted than the questioner's conclusion; for in that case the result will
be that the arguments will be more generally accepted. If, then, the view laid down by the answerer be one
that is generally accepted or rejected without qualification, then the views that are accepted absolutely must
be taken as the standard of comparison: whereas if the view laid down be one that is not generally accepted or
rejected, but only by the answerer, then the standard whereby the latter must judge what is generally accepted
or not, and must grant or refuse to grant the point asked, is himself. If, again, the answerer be defending some
one else's opinion, then clearly it will be the latter's judgement to which he must have regard in granting or
denying the various points. This is why those, too, who introduce other's opinions, e.g. that 'good and evil are
the same thing, as Heraclitus says,' refuse to admit the impossibility of contraries belonging at the same time
to the same thing; not because they do not themselves believe this, but because on Heraclitus' principles one
has to say so. The same thing is done also by those who take on the defence of one another's positions; their
aim being to speak as would the man who stated the position.

It is clear, then, what the aims of the answerer should be, whether the position he lays down be a view
generally accepted without qualification or accepted by some definite person. Now every question asked is
bound to involve some view that is either generally held or generally rejected or neither, and is also bound to
be either relevant to the argument or irrelevant: if then it be a view generally accepted and irrelevant, the
answerer should grant it and remark that it is the accepted view: if it be a view not generally accepted and
irrelevant, he should grant it but add a comment that it is not generally accepted, in order to avoid the
appearance of being a simpleton. If it be relevant and also be generally accepted, he should admit that it is the
view generally accepted but say that it lies too close to the original proposition, and that if it be granted the
problem proposed collapses. If what is claimed by the questioner be relevant but too generally rejected, the
answerer, while admitting that if it be granted the conclusion sought follows, should yet protest that the
proposition is too absurd to be admitted. Suppose, again, it be a view that is neither rejected generally nor
generally accepted, then, if it be irrelevant to the argument, it may be granted without restriction; if, however,
it be relevant, the answerer should add the comment that, if it be granted, the original problem collapses. For
then the answerer will not be held to be personally accountable for what happens to him, if he grants the
several points with his eyes open, and also the questioner will be able to draw his inference, seeing that all the
premisses that are more generally accepted than the conclusion are granted him. Those who try to draw an
inference from premisses more generally rejected than the conclusion clearly do not reason correctly: hence,
when men ask these things, they ought not to be granted.

The questioner should be met in a like manner also in the case of terms used obscurely, i.e. in several senses.
For the answerer, if he does not understand, is always permitted to say 'I do not understand': he is not
compelled to reply 'Yes' or 'No' to a question which may mean different things. Clearly, then, in the first

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place, if what is said be not clear, he ought not to hesitate to say that he does not understand it; for often
people encounter some difficulty from assenting to questions that are not clearly put. If he understands the
question and yet it covers many senses, then supposing what it says to be universally true or false, he should
give it an unqualified assent or denial: if, on the other hand, it be partly true and partly false, he should add a
comment that it bears different senses, and also that in one it is true, in the other false: for if he leave this
distinction till later, it becomes uncertain whether originally as well he perceived the ambiguity or not. If he
does not foresee the ambiguity, but assents to the question having in view the one sense of the words, then, if
the questioner takes it in the other sense, he should say, 'That was not what I had in view when I admitted it; I
meant the other sense': for if a term or expression covers more than one thing, it is easy to disagree. If,
however, the question is both clear and simple, he should answer either 'Yes' or 'No'.

A premiss in reasoning always either is one of the constituent elements in the reasoning, or else goes to
establish one of these: (and you can always tell when it is secured in order to establish something else by the
fact of a number of similar questions being put: for as a rule people secure their universal by means either of
induction or of likeness):-accordingly the particular propositions should all be admitted, if they are true and
generally held. On the other hand, against the universal one should try to bring some negative instance; for to
bring the argument to a standstill without a negative instance, either real or apparent, shows ill-temper. If,
then, a man refuses to grant the universal when supported by many instances, although he has no negative
instance to show, he obviously shows ill-temper. If, moreover, he cannot even attempt a counter-proof that it
is not true, far more likely is he to be thought ill-tempered-although even counter-proof is not enough: for
we often hear arguments that are contrary to common opinions, whose solution is yet difficult, e.g. the
argument of Zeno that it is impossible to move or to traverse the stadium;-but still, this is no reason for
omitting to assert the opposites of these views. If, then, a man refuses to admit the proposition without having
either a negative instance or some counter-argument to bring against it, clearly he is ill-tempered: for
ill-temper in argument consists in answering in ways other than the above, so as to wreck the reasoning.

Before maintaining either a thesis or a definition the answerer should try his hand at attacking it by himself;
for clearly his business is to oppose those positions from which questioners demolish what he has laid down.

He should beware of maintaining a hypothesis that is generally rejected: and this it may be in two ways: for it
may be one which results in absurd statements, e.g. suppose any one were to say that everything is in motion
or that nothing is; and also there are all those which only a bad character would choose, and which are
implicitly opposed to men's wishes, e.g. that pleasure is the good, and that to do injustice is better than to
suffer it. For people then hate him, supposing him to maintain them not for the sake of argument but because
he really thinks them.

Of all arguments that reason to a false conclusion the right solution is to demolish the point on which the
fallacy that occurs depends: for the demolition of any random point is no solution, even though the point
demolished be false. For the argument may contain many falsehoods, e.g. suppose some one to secure the
premisses, 'He who sits, writes' and 'Socrates is sitting': for from these it follows that 'Socrates is writing'.
Now we may demolish the proposition 'Socrates is sitting', and still be no nearer a solution of the argument; it
may be true that the point claimed is false; but it is not on that that fallacy of the argument depends: for
supposing that any one should happen to be sitting and not writing, it would be impossible in such a case to
apply the same solution. Accordingly, it is not this that needs to be demolished, but rather that 'He who sits,
writes': for he who sits does not always write. He, then, who has demolished the point on which the fallacy

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depends, has given the solution of the argument completely. Any one who knows that it is on such and such a
point that the argument depends, knows the solution of it, just as in the case of a figure falsely drawn. For it is
not enough to object, even if the point demolished be a falsehood, but the reason of the fallacy should also be
proved: for then it would be clear whether the man makes his objection with his eyes open or not.

There are four possible ways of preventing a man from working his argument to a conclusion. It can be done
either by demolishing the point on which the falsehood that comes about depends, or by stating an objection
directed against the questioner: for often when a solution has not as a matter of fact been brought, yet the
questioner is rendered thereby unable to pursue the argument any farther. Thirdly, one may object to the
questions asked: for it may happen that what the questioner wants does not follow from the questions he has
asked because he has asked them badly, whereas if something additional be granted the conclusion comes
about. If, then, the questioner be unable to pursue his argument farther, the objection would properly be
directed against the questioner; if he can do so, then it would be against his questions. The fourth and worst
kind of objection is that which is directed to the time allowed for discussion: for some people bring
objections of a kind which would take longer to answer than the length of the discussion in hand.

There are then, as we said, four ways of making objections: but of them the first alone is a solution: the others
are just hindrances and stumbling-blocks to prevent the conclusions.

Adverse criticism of an argument on its own merits, and of it when presented in the form of questions, are
two different things. For often the failure to carry through the argument correctly in discussion is due to the
person questioned, because he will not grant the steps of which a correct argument might have been made
against his position: for it is not in the power of the one side only to effect properly a result that depends on
both alike. Accordingly it sometimes becomes necessary to attack the speaker and not his position, when the
answerer lies in wait for the points that are contrary to the questioner and becomes abusive as well: when
people lose their tempers in this way, their argument becomes a contest, not a discussion. Moreover, since
arguments of this kind are held not for the sake of instruction but for purposes of practice and examination,
clearly one has to reason not only to true conclusions, but also to false ones, and not always through true
premisses, but sometimes through false as well. For often, when a true proposition is put forward, the
dialectician is compelled to demolish it: and then false propositions have to be formulated. Sometimes also
when a false proposition is put forward, it has to be demolished by means of false propositions: for it is
possible for a given man to believe what is not the fact more firmly than the truth. Accordingly, if the
argument be made to depend on something that he holds, it will be easier to persuade or help him. He,
however, who would rightly convert any one to a different opinion should do so in a dialectical and not in a
contentious manner, just as a geometrician should reason geometrically, whether his conclusion be false or
true: what kind of syllogisms are dialectical has already been said. The principle that a man who hinders the
common business is a bad partner, clearly applies to an argument as well; for in arguments as well there is a
common aim in view, except with mere contestants, for these cannot both reach the same goal; for more than
one cannot possibly win. It makes no difference whether he effects this as answerer or as questioner: for both
he who asks contentious questions is a bad dialectician, and also he who in answering fails to grant the
obvious answer or to understand the point of the questioner's inquiry. What has been said, then, makes it clear
that adverse criticism is not to be passed in a like strain upon the argument on its own merits, and upon the
questioner: for it may very well be that the argument is bad, but that the questioner has argued with the
answerer in the best possible way: for when men lose their tempers, it may perhaps be impossible to make
one's inferences straight-forwardly as one would wish: we have to do as we can.

Inasmuch as it is indeterminate when people are claiming the admission of contrary things, and when they are
claiming what originally they set out to prove-for often when they are talking by themselves they say
contrary things, and admit afterwards what they have previously denied; for which reason they often assent,

Book VIII 81

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when questioned, to contrary things and to what originally had to be proved-the argument is sure to become
vitiated. The responsibility, however, for this rests with the answerer, because while refusing to grant other
points, he does grant points of that kind. It is, then, clear that adverse criticism is not to be passed in a like
manner upon questioners and upon their arguments.

In itself an argument is liable to five kinds of adverse criticism:

(1) The first is when neither the proposed conclusion nor indeed any conclusion at all is drawn from the
questions asked, and when most, if not all, of the premisses on which the conclusion rests are false or
generally rejected, when, moreover, neither any withdrawals nor additions nor both together can bring the
conclusions about.

(2) The second is, supposing the reasoning, though constructed from the premisses, and in the manner,
described above, were to be irrelevant to the original position.

(3) The third is, supposing certain additions would bring an inference about but yet these additions were to be
weaker than those that were put as questions and less generally held than the conclusion.

(4) Again, supposing certain withdrawals could effect the same: for sometimes people secure more premisses
than are necessary, so that it is not through them that the inference comes about.

(5) Moreover, suppose the premisses be less generally held and less credible than the conclusion, or if,
though true, they require more trouble to prove than the proposed view.

One must not claim that the reasoning to a proposed view shall in every case equally be a view generally
accepted and convincing: for it is a direct result of the nature of things that some subjects of inquiry shall be
easier and some harder, so that if a man brings people to accept his point from opinions that are as generally
received as the case admits, he has argued his case correctly. Clearly, then, not even the argument itself is
open to the same adverse criticism when taken in relation to the proposed conclusion and when taken by
itself. For there is nothing to prevent the argument being open to reproach in itself, and yet commendable in
relation to the proposed conclusion, or again, vice versa, being commendable in itself, and yet open to
reproach in relation to the proposed conclusion, whenever there are many propositions both generally held
and also true whereby it could easily be proved. It is possible also that an argument, even though brought to a
conclusion, may sometimes be worse than one which is not so concluded, whenever the premisses of the
former are silly, while its conclusion is not so; whereas the latter, though requiring certain additions, requires
only such as are generally held and true, and moreover does not rest as an argument on these additions. With
those which bring about a true conclusion by means of false premisses, it is not fair to find fault: for a false
conclusion must of necessity always be reached from a false premiss, but a true conclusion may sometimes
be drawn even from false premisses; as is clear from the Analytics.

Whenever by the argument stated something is demonstrated, but that something is other than what is wanted
and has no bearing whatever on the conclusion, then no inference as to the latter can be drawn from it: and if
there appears to be, it will be a sophism, not a proof. A philosopheme is a demonstrative inference: an
epichireme is a dialectical inference: a sophism is a contentious inference: an aporeme is an inference that
reasons dialectically to a contradiction.

If something were to be shown from premisses, both of which are views generally accepted, but not accepted
with like conviction, it may very well be that the conclusion shown is something held more strongly than
either. If, on the other hand, general opinion be for the one and neither for nor against the other, or if it be for
the one and against the other, then, if the pro and con be alike in the case of the premisses, they will be alike
for the conclusion also: if, on the other hand, the one preponderates, the conclusion too will follow suit.

Book VIII 82

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It is also a fault in reasoning when a man shows something through a long chain of steps, when he might
employ fewer steps and those already included in his argument: suppose him to be showing (e.g.) that one
opinion is more properly so called than another, and suppose him to make his postulates as follows:
'x-in-itself is more fully x than anything else': 'there genuinely exists an object of opinion in itself: therefore
'the object-of-opinion-in-itself is more fully an object of opinion than the particular objects of opinion'.
Now 'a relative term is more fully itself when its correlate is more fully itself: and 'there exists a genuine
opinion-in-itself, which will be "opinion" in a more accurate sense than the particular opinions': and it has
been postulated both that 'a genuine opinion-in-itself exists', and that 'x-in-itself is more fully x than
anything else': therefore 'this will be opinion in a more accurate sense'. Wherein lies the viciousness of the
reasoning? Simply in that it conceals the ground on which the argument depends.

An argument is clear in one, and that the most ordinary, sense, if it be so brought to a conclusion as to make
no further questions necessary: in another sense, and this is the type most usually advanced, when the
propositions secured are such as compel the conclusion, and the argument is concluded through premisses
that are themselves conclusions: moreover, it is so also if some step is omitted that generally is firmly
accepted.

An argument is called fallacious in four senses: (1) when it appears to be brought to a conclusion, and is not
really so-what is called 'contentious' reasoning: (2) when it comes to a conclusion but not to the conclusion
proposed-which happens principally in the case of reductiones ad impossibile: (3) when it comes to the
proposed conclusion but not according to the mode of inquiry appropriate to the case, as happens when a
non-medical argument is taken to be a medical one, or one which is not geometrical for a geometrical
argument, or one which is not dialectical for dialectical, whether the result reached be true or false: (4) if the
conclusion be reached through false premisses: of this type the conclusion is sometimes false, sometimes
true: for while a false conclusion is always the result of false premisses, a true conclusion may be drawn even
from premisses that are not true, as was said above as well.

Fallacy in argument is due to a mistake of the arguer rather than of the argument: yet it is not always the fault
of the arguer either, but only when he is not aware of it: for we often accept on its merits in preference to
many true ones an argument which demolishes some true proposition if it does so from premisses as far as
possible generally accepted. For an argument of that kind does demonstrate other things that are true: for one
of the premisses laid down ought never to be there at all, and this will then be demonstrated. If, however, a
true conclusion were to be reached through premisses that are false and utterly childish, the argument is
worse than many arguments that lead to a false conclusion, though an argument which leads to a false
conclusion may also be of this type. Clearly then the first thing to ask in regard to the argument in itself is,
'Has it a conclusion?'; the second, 'Is the conclusion true or false?'; the third, 'Of what kind of premisses does
it consist?': for if the latter, though false, be generally accepted, the argument is dialectical, whereas if,
though true, they be generally rejected, it is bad: if they be both false and also entirely contrary to general
opinion, clearly it is bad, either altogether or else in relation to the particular matter in hand.

Of the ways in which a questioner may beg the original question and also beg contraries the true account has
been given in the Analytics:' but an account on the level of general opinion must be given now.

People appear to beg their original question in five ways: the first and most obvious being if any one begs the
actual point requiring to be shown: this is easily detected when put in so many words; but it is more apt to
escape detection in the case of different terms, or a term and an expression, that mean the same thing. A
second way occurs whenever any one begs universally something which he has to demonstrate in a particular

Book VIII 83

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case: suppose (e.g.) he were trying to prove that the knowledge of contraries is one and were to claim that the
knowledge of opposites in general is one: for then he is generally thought to be begging, along with a number
of other things, that which he ought to have shown by itself. A third way is if any one were to beg in
particular cases what he undertakes to show universally: e.g. if he undertook to show that the knowledge of
contraries is always one, and begged it of certain pairs of contraries: for he also is generally considered to be
begging independently and by itself what, together with a number of other things, he ought to have shown.
Again, a man begs the question if he begs his conclusion piecemeal: supposing e.g. that he had to show that
medicine is a science of what leads to health and to disease, and were to claim first the one, then the other; or,
fifthly, if he were to beg the one or the other of a pair of statements that necessarily involve one other; e.g. if
he had to show that the diagonal is incommensurable with the side, and were to beg that the side is
incommensurable with the diagonal.

The ways in which people assume contraries are equal in number to those in which they beg their original
question. For it would happen, firstly, if any one were to beg an opposite affirmation and negation; secondly,
if he were to beg the contrary terms of an antithesis, e.g. that the same thing is good and evil; thirdly, suppose
any one were to claim something universally and then proceed to beg its contradictory in some particular
case, e.g. if having secured that the knowledge of contraries is one, he were to claim that the knowledge of
what makes for health or for disease is different; or, fourthly, suppose him, after postulating the latter view, to
try to secure universally the contradictory statement. Again, fifthly, suppose a man begs the contrary of the
conclusion which necessarily comes about through the premisses laid down; and this would happen suppose,
even without begging the opposites in so many words, he were to beg two premisses such that this
contradictory statement that is opposite to the first conclusion will follow from them. The securing of
contraries differs from begging the original question in this way: in the latter case the mistake lies in regard to
the conclusion; for it is by a glance at the conclusion that we tell that the original question has been begged:
whereas contrary views lie in the premisses, viz. in a certain relation which they bear to one another.

The best way to secure training and practice in arguments of this kind is in the first place to get into the habit
of converting the arguments. For in this way we shall be better equipped for dealing with the proposition
stated, and after a few attempts we shall know several arguments by heart. For by 'conversion' of an argument
is meant the taking the reverse of the conclusion together with the remaining propositions asked and so
demolishing one of those that were conceded: for it follows necessarily that if the conclusion be untrue, some
one of the premisses is demolished, seeing that, given all the premisses, the conclusion was bound to follow.
Always, in dealing with any proposition, be on the look-out for a line of argument both pro and con: and on
discovering it at once set about looking for the solution of it: for in this way you will soon find that you have
trained yourself at the same time in both asking questions and answering them. If we cannot find any one else
to argue with, we should argue with ourselves. Select, moreover, arguments relating to the same thesis and
range them side by side: for this produces a plentiful supply of arguments for carrying a point by sheer force,
and in refutation also it is of great service, whenever one is well stocked with arguments pro and con: for then
you find yourself on your guard against contrary statements to the one you wish to secure. Moreover, as
contributing to knowledge and to philosophic wisdom the power of discerning and holding in one view the
results of either of two hypotheses is no mean instrument; for it then only remains to make a right choice of
one of them. For a task of this kind a certain natural ability is required: in fact real natural ability just is the
power right to choose the true and shun the false. Men of natural ability can do this; for by a right liking or
disliking for whatever is proposed to them they rightly select what is best.

It is best to know by heart arguments upon those questions which are of most frequent occurrence, and
particularly in regard to those propositions which are ultimate: for in discussing these answerers frequently
give up in despair. Moreover, get a good stock of definitions: and have those of familiar and primary ideas at
your fingers' ends: for it is through these that reasonings are effected. You should try, moreover, to master the

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heads under which other arguments mostly tend to fall. For just as in geometry it is useful to be practised in
the elements, and in arithmetic to have the multiplication table up to ten at one's fingers' ends-and indeed it
makes a great difference in one's knowledge of the multiples of other numbers too-likewise also in
arguments it is a great advantage to be well up in regard to first principles, and to have a thorough knowledge
of premisses at the tip of one's tongue. For just as in a person with a trained memory, a memory of things
themselves is immediately caused by the mere mention of their loci, so these habits too will make a man
readier in reasoning, because he has his premisses classified before his mind's eye, each under its number. It
is better to commit to memory a premiss of general application than an argument: for it is difficult to be even
moderately ready with a first principle, or hypothesis.

Moreover, you should get into the habit of turning one argument into several, and conceal your procedure as
darkly as you can: this kind of effect is best produced by keeping as far as possible away from topics akin to
the subject of the argument. This can be done with arguments that are entirely universal, e.g. the statement
that 'there cannot be one knowledge of more than one thing': for that is the case with both relative terms and
contraries and co-ordinates.

Records of discussions should be made in a universal form, even though one has argued only some particular
case: for this will enable one to turn a single rule into several. A like rule applies in Rhetoric as well to
enthymemes. For yourself, however, you should as far as possible avoid universalizing your reasonings. You
should, moreover, always examine arguments to see whether they rest on principles of general application:
for all particular arguments really reason universally, as well, i.e. a particular demonstration always contains
a universal demonstration, because it is impossible to reason at all without using universals.

You should display your training in inductive reasoning against a young man, in deductive against an expert.
You should try, moreover, to secure from those skilled in deduction their premisses, from inductive reasoners
their parallel cases; for this is the thing in which they are respectively trained. In general, too, from your
exercises in argumentation you should try to carry away either a syllogism on some subject or a refutation or
a proposition or an objection, or whether some one put his question properly or improperly (whether it was
yourself or some one else) and the point which made it the one or the other. For this is what gives one ability,
and the whole object of training is to acquire ability, especially in regard to propositions and objections. For it
is the skilled propounder and objector who is, speaking generally, a dialectician. To formulate a proposition is
to form a number of things into one-for the conclusion to which the argument leads must be taken generally,
as a single thing-whereas to formulate an objection is to make one thing into many; for the objector either
distinguishes or demolishes, partly granting, partly denying the statements proposed.

Do not argue with every one, nor practise upon the man in the street: for there are some people with whom
any argument is bound to degenerate. For against any one who is ready to try all means in order to seem not
to be beaten, it is indeed fair to try all means of bringing about one's conclusion: but it is not good form.
Wherefore the best rule is, not lightly to engage with casual acquaintances, or bad argument is sure to result.
For you see how in practising together people cannot refrain from contentious argument.

It is best also to have ready-made arguments relating to those questions in which a very small stock will
furnish us with arguments serviceable on a very large number of occasions. These are those that are universal,
and those in regard to which it is rather difficult to produce points for ourselves from matters of everyday
experience.

THE END

Book VIII 85

ON YOUTH AND OLD AGE, ON LIFE AND DEATH, ON BREATH

by Aristotle

ON YOUTH AND OLD AGE, ON LIFE AND DEATH, ON BREATHING

Table of Contents

ON YOUTH AND OLD AGE. ON LIFE AND DEATH. ON BREATHING. 1

by Aristotle 1

_1 1

2 2

1 3

A 3

_5 4

6 4

1 5

_9 6

10 6

11 7

\1 7

13 8

14 9

15 9

16 10

17 11

18 11

19 12

20 12

11 13

22 13

23 14

24 14

15 15

16 15

27 15

ON YOUTH AND OLD AGE, ON LIFE AND DEATH,

ON BREATHING

by Aristotle

translated by G. R. T. Ross

11
13
14
15
16
II
18
19
22
21
22
23

21
25
26
27

WE must now treat of youth and old age and life and death. We must probably also at the same time state the
causes of respiration as well, since in some cases living and the reverse depend on this.

ON YOUTH AND OLD AGE, ON LIFE AND DEATH, ON BREATHING

We have elsewhere given a precise account of the soul, and while it is clear that its essential reality cannot be
corporeal, yet manifestly it must exist in some bodily part which must be one of those possessing control over
the members. Let us for the present set aside the other divisions or faculties of the soul (whichever of the two
be the correct name). But as to being what is called an animal and a living thing, we find that in all beings
endowed with both characteristics (viz. being an animal and being alive) there must be a single identical part
in virtue of which they live and are called animals; for an animal qua animal cannot avoid being alive. But a
thing need not, though alive, be animal, for plants live without having sensation, and it is by sensation that we
distinguish animal from what is not animal.

This organ, then, must be numerically one and the same and yet possess multiple and disparate aspects, for
being animal and living are not identical. Since then the organs of special sensation have one common organ
in which the senses when functioning must meet, and this must be situated midway between what is called
before and behind (we call 'before' the direction from which sensation comes, 'behind' the opposite), further,
since in all living things the body is divided into upper and lower (they all have upper and lower parts, so that
this is true of plants as well), clearly the nutritive principle must be situated midway between these regions.
That part where food enters we call upper, considering it by itself and not relatively to the surrounding
universe, while downward is that part by which the primary excrement is discharged.

Plants are the reverse of animals in this respect. To man in particular among the animals, on account of his
erect stature, belongs the characteristic of having his upper parts pointing upwards in the sense in which that
applies to the universe, while in the others these are in an intermediate position. But in plants, owing to their
being stationary and drawing their sustenance from the ground, the upper part must always be down; for there
is a correspondence between the roots in a plant and what is called the mouth in animals, by means of which
they take in their food, whether the source of supply be the earth or each other's bodies.

All perfectly formed animals are to be divided into three parts, one that by which food is taken in, one that by
which excrement is discharged, and the third the region intermediate between them. In the largest animals
this latter is called the chest and in the others something corresponding; in some also it is more distinctly
marked off than in others. All those also that are capable of progression have additional members subservient
to this purpose, by means of which they bear the whole trunk, to wit legs and feet and whatever parts are
possessed of the same powers. Now it is evident both by observation and by inference that the source of the
nutritive soul is in the midst of the three parts. For many animals, when either part-the head or the receptacle
of the food-is cut off, retain life in that member to which the middle remains attached. This can be seen to
occur in many insects, e.g. wasps and bees, and many animals also besides insects can, though divided,
continue to live by means of the part connected with nutrition.

While this member is indeed in actuality single, yet potentially it is multiple, for these animals have a
constitution similar to that of Plants; plants when cut into sections continue to live, and a number of trees can
be derived from one single source. A separate account will be given of the reason why some plants cannot
live when divided, while others can be propagated by the taking of slips. In this respect, however, plants and
insects are alike.

It is true that the nutritive soul, in beings possessing it, while actually single must be potentially plural. And it
is too with the principle of sensation, for evidently the divided segments of these animals have sensation.
They are unable, however, to preserve their constitution, as plants can, not possessing the organs on which
the continuance of life depends, for some lack the means for seizing, others for receiving their food; or again
they may be destitute of other organs as well.

ON YOUTH AND OLD AGE, ON LIFE AND DEATH, ON BREATHING

Divisible animals are like a number of animals grown together, but animals of superior construction behave
differently because their constitution is a unity of the highest possible kind. Hence some of the organs on
division display slight sensitiveness because they retain some psychical susceptibility; the animals continue
to move after the vitals have been abstracted: tortoises, for example, do so even after the heart has been
removed.

The same phenomenon is evident both in plants and in animals, and in plants we note it both in their
propagation by seed and in grafts and cuttings. Genesis from seeds always starts from the middle. All seeds
are bivalvular, and the place of junction is situated at the point of attachment (to the plant), an intermediate
part belonging to both halves. It is from this part that both root and stem of growing things emerge; the
starting-point is in a central position between them. In the case of grafts and cuttings this is particularly true
of the buds; for the bud is in a way the starting-point of the branch, but at the same time it is in a central
position. Hence it is either this that is cut off, or into this that the new shoot is inserted, when we wish either a
new branch or a new root to spring from it; which proves that the point of origin in growth is intermediate
between stem and root.

Likewise in sanguineous animals the heart is the first organ developed; this is evident from what has been
observed in those cases where observation of their growth is possible. Hence in bloodless animals also what
corresponds to the heart must develop first. We have already asserted in our treatise on The Parts of Animals
that it is from the heart that the veins issue, and that in sanguineous animals the blood is the final nutriment
from which the members are formed. Hence it is clear that there is one function in nutrition which the mouth
has the faculty of performing, and a different one appertaining to the stomach. But it is the heart that has
supreme control, exercising an additional and completing function. Hence in sanguineous animals the source
both of the sensitive and of the nutritive soul must be in the heart, for the functions relative to nutrition
exercised by the other parts are ancillary to the activity of the heart. It is the part of the dominating organ to
achieve the final result, as of the physician's efforts to be directed towards health, and not to be occupied with
subordinate offices.

Certainly, however, all saguineous animals have the supreme organ of the sensefaculties in the heart, for it is
here that we must look for the common sensorium belonging to all the sense-organs. These in two cases,
taste and touch, can be clearly seen to extend to the heart, and hence the others also must lead to it, for in it
the other organs may possibly initiate changes, whereas with the upper region of the body taste and touch
have no connexion. Apart from these considerations, if the life is always located in this part, evidently the
principle of sensation must be situated there too, for it is qua animal that an animal is said to be a living thing,
and it is called animal because endowed with sensation. Elsewhere in other works we have stated the reasons
why some of the sense-organs are, as is evident, connected with the heart, while others are situated in the
head. (It is this fact that causes some people to think that it is in virtue of the brain that the function of
perception belongs to animals.)

Thus if, on the one hand, we look to the observed facts, what we have said makes it clear that the source of
the sensitive soul, together with that connected with growth and nutrition, is situated in this organ and in the
central one of the three divisions of the body. But it follows by deduction also; for we see that in every case,
when several results are open to her, Nature always brings to pass the best. Now if both principles are located
in the midst of the substance, the two parts of the body, viz. that which elaborates and that which receives the
nutriment in its final form will best perform their appropriate function; for the soul will then be close to each,
and the central situation which it will, as such, occupy is the position of a dominating power.

ON YOUTH AND OLD AGE, ON LIFE AND DEATH, ON BREATHING

Further, that which employs an instrument and the instrument it employs must be distinct (and must be
spatially diverse too, if possible, as in capacity), just as the flute and that which plays it-the hand-are diverse.
Thus if animal is defined by the possession of sensitive soul, this soul must in the sanguineous animals be in
the heart, and, in the bloodless ones, in the corresponding part of their body. But in animals all the members
and the whole body possess some connate warmth of constitution, and hence when alive they are observed to
be warm, but when dead and deprived of life they are the opposite. Indeed, the source of this warmth must be
in the heart in sanguineous animals, and in the case of bloodless animals in the corresponding organ, for,
though all parts of the body by means of their natural heat elaborate and concoct the nutriment, the governing
organ takes the chief share in this process. Hence, though the other members become cold, life remains; but
when the warmth here is quenched, death always ensues, because the source of heat in all the other members
depends on this, and the soul is, as it were, set aglow with fire in this part, which in sanguineous animals is
the heart and in the bloodless order the analogous member. Hence, of necessity, life must be coincident with
the maintenance of heat, and what we call death is its destruction.

However, it is to be noticed that there are two ways in which fire ceases to exist; it may go out either by
exhaustion or by extinction. That which is self-caused we call exhaustion, that due to its opposites extinction.
[The former is that due to old age, the latter to violence.] But either of these ways in which fire ceases to be
may be brought about by the same cause, for, when there is a deficiency of nutriment and the warmth can
obtain no maintenance, the fire fails; and the reason is that the opposite, checking digestion, prevents the fire
from being fed. But in other cases the result is exhaustion,-when the heat accumulates excessively owing to
lack of respiration and of refrigeration. For in this case what happens is that the heat, accumulating in great
quantity, quickly uses up its nutriment and consumes it all before more is sent up by evaporation. Hence not
only is a smaller fire readily put out by a large one, but of itself the candle flame is consumed when inserted
in a large blaze just as is the case with any other combustible. The reason is that the nutriment in the flame is
seized by the larger one before fresh fuel can be added, for fire is ever coming into being and rushing just like
a river, but so speedily as to elude observation.

Clearly therefore, if the bodily heat must be conserved (as is necessary if life is to continue), there must be
some way of cooling the heat resident in the source of warmth. Take as an illustration what occurs when
coals are confined in a brazier. If they are kept covered up continuously by the so-called 'choker', they are
quickly extinguished, but, if the lid is in rapid alternation lifted up and put on again they remain glowing for a
long time. Banking up a fire also keeps it in, for the ashes, being porous, do not prevent the passage of air,
and again they enable it to resist extinction by the surrounding air by means of the supply of heat which it
possesses. However, we have stated in The Problems the reasons why these operations, namely banking up
and covering up a fire, have the opposite effects (in the one case the fire goes out, in the other it continues
alive for a considerable time).

Everything living has soul, and it, as we have said, cannot exist without the presence of heat in the
constitution. In plants the natural heat is sufficiently well kept alive by the aid which their nutriment and the
surrounding air supply. For the food has a cooling effect [as it enters, just as it has in man] when first it is
taken in, whereas abstinence from food produces heat and thirst. The air, if it be motionless, becomes hot, but
by the entry of food a motion is set up which lasts until digestion is completed and so cools it. If the
surrounding air is excessively cold owing to the time of year, there being severe frost, plants shrivel, or if, in
the extreme heats of summer the moisture drawn from the ground cannot produce its cooling effect, the heat
comes to an end by exhaustion. Trees suffering at such seasons are said to be blighted or star-stricken. Hence
the practice of laying beneath the roots stones of certain species or water in pots, for the purpose of cooling

ON YOUTH AND OLD AGE, ON LIFE AND DEATH, ON BREATHING

the roots of the plants.

Some animals pass their life in the water, others in the air, and therefore these media furnish the source and
means of refrigeration, water in the one case, air in the other. We must proceed-and it will require further
application on our part-to give an account of the way and manner in which this refrigeration occurs.

A few of the previous physical philosophers have spoken of respiration. The reason, however, why it exists in
animals they have either not declared or, when they have, their statements are not correct and show a
comparative lack of acquaintance with the facts. Moreover they assert that all animals respire-which is
untrue. Hence these points must first claim our attention, in order that we may not be thought to make
unsubstantiated charges against authors no longer alive.

First then, it is evident that all animals with lungs breathe, but in some cases breathing animals have a
bloodless and spongy lung, and then there is less need for respiration. These animals can remain under water
for a time, which relatively to their bodily strength, is considerable. All oviparous animals, e.g. the
frog-tribe, have a spongy lung. Also hemydes and tortoises can remain for a long time immersed in water;
for their lung, containing little blood, has not much heat. Hence, when once it is inflated, it itself, by means of
its motion, produces a cooling effect and enables the animal to remain immersed for a long time. Suffocation,
however, always ensues if the animal is forced to hold its breath for too long a time, for none of this class
take in water in the way fishes do. On the other hand, animals which have the lung charged with blood have
greater need of respiration on account of the amount of their heat, while none at all of the others which do not
possess lungs breathe.

Democritus of Abdera and certain others who have treated of respiration, while saying nothing definite about
the lungless animals, nevertheless seem to speak as if all breathed. But Anaxagoras and Diogenes both
maintain that all breathe, and state the manner in which fishes and oysters respire. Anaxagoras says that when
fishes discharge water through their gills, air is formed in the mouth, for there can be no vacuum, and that it
is by drawing in this that they respire. Diogenes' statement is that, when they discharge water through their
gills, they suck the air out of the water surrounding the mouth by means of the vacuum formed in the mouth,
for he believes there is air in the water.

But these theories are untenable. Firstly, they state only what is the common element in both operations and
so leave out the half of the matter. For what goes by the name of respiration consists, on the one hand, of
inhalation, and, on the other, of the exhalation of breath; but, about the latter they say nothing, nor do they
describe how such animals emit their breath. Indeed, explanation is for them impossible for, when the
creatures respire, they must discharge their breath by the same passage as that by which they draw it in, and
this must happen in alternation. Hence, as a result, they must take the water into their mouth at the same time
as they breathe out. But the air and the water must meet and obstruct each other. Further, when they discharge
the water they must emit their breath by the mouth or the gills, and the result will be that they will breathe in
and breathe out at the same time, for it is at that moment that respiration is said to occur. But it is impossible
that they should do both at the same time. Hence, if respiring creatures must both exhale and inhale the air,
and if none of these animals can breathe out, evidently none can respire at all.

ON YOUTH AND OLD AGE, ON LIFE AND DEATH, ON BREATHING

Further, the assertion that they draw in air out of the mouth or out of the water by means of the mouth is an
impossibility, for, not having a lung, they have no windpipe; rather the stomach is closely juxtaposed to the
mouth, so that they must do the sucking with the stomach. But in that case the other animals would do so
also, which is not the truth; and the water-animals also would be seen to do it when out of the water, whereas
quite evidently they do not. Further, in all animals that respire and draw breath there is to be observed a
certain motion in the part of the body which draws in the air, but in the fishes this does not occur. Fishes do
not appear to move any of the parts in the region of the stomach, except the gills alone, and these move both
when they are in the water and when they are thrown on to dry land and gasp. Moreover, always when
respiring animals are killed by being suffocated in water, bubbles are formed of the air which is forcibly
discharged, as happens, e.g. when one forces a tortoise or a frog or any other animal of a similar class to stay
beneath water. But with fishes this result never occurs, in whatsoever way we try to obtain it, since they do
not contain air drawn from an external source. Again, the manner of respiration said to exist in them might
occur in the case of men also when they are under water. For if fishes draw in air out of the surrounding water
by means of their mouth why should not men too and other animals do so also; they should also, in the same
way as fishes, draw in air out of the mouth. If in the former case it were possible, so also should it be in the
latter. But, since in the one it is not so, neither does it occur in the other. Furthermore, why do fishes, if they
respire, die in the air and gasp (as can be seen) as in suffocation? It is not want of food that produces this
effect upon them, and the reason given by Diogenes is foolish, for he says that in air they take in too much air
and hence die, but in the water they take in a moderate amount. But that should be a possible occurrence with
land animals also; as facts are, however, no land animal seems to be suffocated by excessive respiration.
Again, if all animals breathe, insects must do so also, many of them seem to live though divided not merely
into two, but into several parts, e.g. the class called Scolopendra. But how can they, when thus divided,
breathe, and what is the organ they employ? The main reason why these writers have not given a good
account of these facts is that they have no acquaintance with the internal organs, and that they did not accept
the doctrine that there is a final cause for whatever Nature does. If they had asked for what purpose
respiration exists in animals, and had considered this with reference to the organs, e.g. the gills and the lungs,
they would have discovered the reason more speedily.

Democritus, however, does teach that in the breathing animals there is a certain result produced by
respiration; he asserts that it prevents the soul from being extruded from the body. Nevertheless, he by no
means asserts that it is for this purpose that Nature so contrives it, for he, like the other physical philosophers,
altogether fails to attain to any such explanation. His statement is that the soul and the hot element are
identical, being the primary forms among the spherical particles. Hence, when these are being crushed
together by the surrounding atmosphere thrusting them out, respiration, according to his account, comes in to
succour them. For in the air there are many of those particles which he calls mind and soul. Hence, when we
breathe and the air enters, these enter along with it, and by their action cancel the pressure, thus preventing
the expulsion of the soul which resides in the animal.

This explains why life and death are bound up with the taking in and letting out of the breath; for death
occurs when the compression by the surrounding air gains the upper hand, and, the animal being unable to
respire, the air from outside can no longer enter and counteract the compression. Death is the departure of
those forms owing to the expulsive pressure exerted by the surrounding air. Death, however, occurs not by
haphazard but, when natural, owing to old age, and, when unnatural, to violence.

But the reason for this and why all must die Democritus has by no means made clear. And yet, since
evidently death occurs at one time of life and not at another, he should have said whether the cause is external

ON YOUTH AND OLD AGE, ON LIFE AND DEATH, ON BREATHING

or internal. Neither does he assign the cause of the beginning of respiration, nor say whether it is internal or
external. Indeed, it is not the case that the external mind superintends the reinforcement; rather the origin of
breathing and of the respiratory motion must be within: it is not due to pressure from around. It is absurd also
that what surrounds should compress and at the same time by entering dilate. This then is practically his
theory, and how he puts it.

But if we must consider that our previous account is true, and that respiration does not occur in every animal,
we must deem that this explains death not universally, but only in respiring animals. Yet neither is it a good
account of these even, as may clearly be seen from the facts and phenomena of which we all have experience.
For in hot weather we grow warmer, and, having more need of respiration, we always breathe faster. But,
when the air around is cold and contracts and solidifies the body, retardation of the breathing results. Yet this
was just the time when the external air should enter and annul the expulsive movement, whereas it is the
opposite that occurs. For when the breath is not let out and the heat accumulates too much then we need to
respire, and to respire we must draw in the breath. When hot, people breathe rapidly, because they must do so
in order to cool themselves, just when the theory of Democritus would make them add fire to fire.

The theory found in the Timaeus, of the passing round of the breath by pushing, by no means determines
how, in the case of the animals other than land-animals, their heat is preserved, and whether it is due to the
same or a different cause. For if respiration occurs only in land-animals we should be told what is the reason
of that. Likewise, if it is found in others also, but in a different form, this form of respiration, if they all can
breathe, must also be described.

Further, the method of explaining involves a fiction. It is said that when the hot air issues from the mouth it
pushes the surrounding air, which being carried on enters the very place whence the internal warmth issued,
through the interstices of the porous flesh; and this reciprocal replacement is due to the fact that a vacuum
cannot exist. But when it has become hot the air passes out again by the same route, and pushes back inwards
through the mouth the air that had been discharged in a warm condition. It is said that it is this action which
goes on continuously when the breath is taken in and let out.

But according to this way of thinking it will follow that we breathe out before we breathe in. But the opposite
is the case, as evidence shows, for though these two functions go on in alternation, yet the last act when life
comes to a close is the letting out of the breath, and hence its admission must have been the beginning of the
process.

Once more, those who give this kind of explanation by no means state the final cause of the presence in
animals of this function (to wit the admission and emission of the breath), but treat it as though it were a
contingent accompaniment of life. Yet it evidently has control over life and death, for it results synchronously
that when respiring animals are unable to breathe they perish. Again, it is absurd that the passage of the hot
air out through the mouth and back again should be quite perceptible, while we were not able to detect the
thoracic influx and the return outwards once more of the heated breath. It is also nonsense that respiration
should consist in the entrance of heat, for the evidence is to the contrary effect; what is breathed out is hot,
and what is breathed in is cold. When it is hot we pant in breathing, for, because what enters does not
adequately perform its cooling function, we have as a consequence to draw the breath frequently.

It is certain, however, that we must not entertain the notion that it is for purposes of nutrition that respiration
is designed, and believe that the internal fire is fed by the breath; respiration, as it were, adding fuel to the

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fire, while the feeding of the flame results in the outward passage of the breath. To combat this doctrine I
shall repeat what I said in opposition to the previous theories. This, or something analogous to it, should
occur in the other animals also (on this theory), for all possess vital heat. Further, how are we to describe this
fictitious process of the generation of heat from the breath? Observation shows rather that it is a product of
the food. A consequence also of this theory is that the nutriment would enter and the refuse be discharged by
the same channel, but this does not appear to occur in the other instances.

Empedocles also gives an account of respiration without, however, making clear what its purpose is, or
whether or not it is universal in animals. Also when dealing with respiration by means of the nostrils he
imagines he is dealing with what is the primary kind of respiration. Even the breath which passes through the
nostrils passes through the windpipe out of the chest as well, and without the latter the nostrils cannot act.
Again, when animals are bereft of respiration through the nostrils, no detrimental result ensues, but, when
prevented from breathing through the windpipe, they die. Nature employs respiration through the nostrils as a
secondary function in certain animals in order to enable them to smell. But the reason why it exists in some
only is that though almost all animals are endowed with the sense of smell, the sense-organ is not the same in
all.

A more precise account has been given about this elsewhere. Empedocles, however, explains the passage
inwards and outwards of the breath, by the theory that there are certain blood-vessels, which, while
containing blood, are not filled by it, but have passages leading to the outer air, the calibre of which is fine in
contrast to the size of the solid particles, but large relatively to those in the air. Hence, since it is the nature of
the blood to move upwards and downwards, when it moves down the air rushes in and inspiration occurs;
when the blood rises, the air is forced out and the outward motion of the breath results. He compares this
process to what occurs in a clepsydra.

Thus all things outwards breathe and in;- their flesh has tubes

Bloodless, that stretch towards the body's outmost edge,

Which, at their mouths, full many frequent channels pierce,

Cleaving the extreme nostrils through; thus, while the gore

Lies hid, for air is cut a thoroughfare most plain.

And thence, whenever shrinks away the tender blood,

Enters the blustering wind with swelling billow wild.

But when the blood leaps up, backward it breathes. As when

With water-clock of polished bronze a maiden sporting,

Sets on her comely hand the narrow of the tube

And dips it in the frail-formed water's silvery sheen;

Not then the flood the vessel enters, but the air,

Until she frees the crowded stream. But then indeed

Upon the escape runs in the water meet.

So also when within the vessel's deeps the water

Remains, the opening by the hand of flesh being closed,

The outer air that entrance craves restrains the flood

At the gates of the sounding narrow,

upon the surface pressing,
Until the maid withdraws her hand. But then in contrariwise
Once more the air comes in and water meet flows out.
Thus to the to the subtle blood, surging throughout the limbs,
Whene'er it shrinks away into the far recesses
Admits a stream of air rushing with swelling wave,
But, when it backward leaps, in like bulk air flows out.

This then is what he says of respiration. But, as we said, all animals that evidently respire do so by means of
the windpipe, when they breathe either through the mouth or through the nostrils. Hence, if it is of this kind

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of respiration that he is talking, we must ask how it tallies with the explanation given. But the facts seem to
be quite opposed. The chest is raised in the manner of a forge-bellows when the breath is drawn in-it is quite
reasonable that it should be heat which raises up and that the blood should occupy the hot region-but it
collapses and sinks down, like the bellows once more, when the breath is let out. The difference is that in a
bellows it is not by the same channel that the air is taken in and let out, but in breathing it is.

But, if Empedocles is accounting only for respiration through the nostrils, he is much in error, for that does
not involve the nostrils alone, but passes by the channel beside the uvula where the extremity of the roof of
the mouth is, some of the air going this way through the apertures of the nostrils and some through the mouth,
both when it enters and when it passes out. Such then is the nature and magnitude of the difficulties besetting
the theories of other writers concerning respiration.

We have already stated that life and the presence of soul involve a certain heat. Not even the digesting
process to which is due the nutrition of animals occurs apart from soul and warmth, for it is to fire that in all
cases elaboration is due. It is for this reason, precisely, that the primary nutritive soul also must be located in
that part of the body and in that division of this region which is the immediate vehicle of this principle. The
region in question is intermediate between that where food enters and that where excrement is discharged. In
bloodless animals it has no name, but in the sanguineous class this organ is called the heart. The blood
constitutes the nutriment from which the organs of the animal are directly formed. Likewise the bloodvessels
must have the same originating source, since the one exists for the other's behoof-as a vessel or receptacle for
it. In sanguineous animals the heart is the starting-point of the veins; they do not traverse it, but are found to
stretch out from it, as dissections enable us to see.

Now the other psychical faculties cannot exist apart from the power of nutrition (the reason has already been
stated in the treatise On the Soul), and this depends on the natural fire, by the union with which Nature has set
it aglow. But fire, as we have already stated, is destroyed in two ways, either by extinction or by exhaustion.
It suffers extinction from its opposites. Hence it can be extinguished by the surrounding cold both when in
mass and (though more speedily) when scattered. Now this way of perishing is due to violence equally in
living and in lifeless objects, for the division of an animal by instruments and consequent congelation by
excess of cold cause death. But exhaustion is due to excess of heat; if there is too much heat close at hand and
the thing burning does not have a fresh supply of fuel added to it, it goes out by exhaustion, not by the action
of cold. Hence, if it is going to continue it must be cooled, for cold is a preventive against this form of
extinction.

Some animals occupy the water, others live on land, and, that being so, in the case of those which are very
small and bloodless the refrigeration due to the surrounding water or air is sufficient to prevent destruction
from this cause. Having little heat, they require little cold to combat it. Hence too such animals are almost all
short-lived, for, being small, they have less scope for deflection towards either extreme. But some insects are
longer-lived though bloodless, like all the others), and these have a deep indentation beneath the waist, in
order to secure cooling through the membrane, which there is thinner. They are warmer animals and hence
require more refrigeration, and such are bees (some of which live as long as seven years) and all that make a
humming noise, like wasps, cockchafers, and crickets. They make a sound as if of panting by means of air,
for, in the middle section itself, the air which exists internally and is involved in their construction, causing a
rising and falling movement, produces friction against the membrane. The way in which they move this
region is like the motion due to the lungs in animals that breathe the outer air, or to the gills in fishes. What
occurs is comparable to the suffocation of a respiring animal by holding its mouth, for then the lung causes a

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heaving motion of this kind. In the case of these animals this internal motion is not sufficient for
refrigeration, but in insects it is. It is by friction against the membrane that they produce the humming sound,
as we said, in the way that children do by blowing through the holes of a reed covered by a fine membrane. It
is thus that the singing crickets too produce their song; they possess greater warmth and are indented at the
waist, but the songless variety have no fissure there.

Animals also which are sanguineous and possess a lung, though that contains little blood and is spongy, can
in some cases, owing to the latter fact, live a long time without breathing; for the lung, containing little blood
or fluid, can rise a long way: its own motion can for a long time produce sufficient refrigeration. But at last it
ceases to suffice, and the animal dies of suffocation if it does not respire-as we have already said. For of
exhaustion that kind which is destruction due to lack of refrigeration is called suffocation, and whatsoever is
thus destroyed is said to be suffocated.

We have already stated that among animals insects do not respire, and the fact is open to observation in the
case of even small creatures like flies and bees, for they can swim about in a fluid for a long time if it is not
too hot or too cold. Yet animals with little strength tend to breathe more frequently. These, however, die of
what is called suffocation when the stomach becomes filled and the heat in the central segment is destroyed.
This explains also why they revive after being among ashes for a time.

Again among water-animals those that are bloodless remain alive longer in air than those that have blood and
admit the sea-water, as, for example, fishes. Since it is a small quantity of heat they possess, the air is for a
long time adequate for the purposes of refrigeration in such animals as the Crustacea and the polyps. It does
not however suffice, owing to their want of heat, to keep them finally in life, for most fishes also live though
among earth, yet in a motionless state, and are to be found by digging. For all animals that have no lung at all
or have a bloodless one require less refrigeration.

Concerning the bloodless animals we have declared that in some cases it is the surrounding air, in others
fluid, that aids the maintenance of life. But in the case of animals possessing blood and heart, all which have
a lung admit the air and produce the cooling effect by breathing in and out. All animals have a lung that are
viviparous and are so internally, not externally merely (the Selachia are viviparous, but not internally), and of
the oviparous class those that have wings, e.g. birds, and those with scales, e.g. tortoises, lizards, and snakes.
The former class have a lung charged with blood, but in the most part of the latter it is spongy. Hence they
employ respiration more sparingly as already said. The function is found also in all that frequent and pass
their life in the water, e.g. the class of water-snakes and frogs and crocodiles and hemydes, both sea- and
land-tortoises, and seals.

All these and similar animals both bring forth on land and sleep on shore or, when they do so in the water,
keep the head above the surface in order to respire. But all with gills produce refrigeration by taking in water;
the Selachia and all other footless animals have gills. Fish are footless, and the limbs they have get their name
(pterugion) from their similarity to wings (pterux). But of those with feet one only, so far as observed, has
gills. It is called the tadpole.

No animal yet has been seen to possess both lungs and gills, and the reason for this is that the lung is
designed for the purpose of refrigeration by means of the air (it seems to have derived its name (pneumon)
from its function as a receptacle of the breath (pneuma)), while gills are relevant to refrigeration by water.
Now for one purpose one organ is adapted and one single means of refrigeration is sufficient in every case.
Hence, since we see that Nature does nothing in vain, and if there were two organs one would be purposeless,
this is the reason why some animals have gills, others lungs, but none possess both.

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17

Every animal in order to exist requires nutriment, in order to prevent itself from dying, refrigeration; and so
Nature employs the same organ for both purposes. For, as in some cases the tongue serves both for discerning
tastes and for speech, so in animals with lungs the mouth is employed both in working up the food and in the
passage of the breath outwards and inwards. In lungless and non-respiring animals it is employed in working
up the food, while in those of them that require refrigeration it is the gills that are created for this purpose.

We shall state further on how it is that these organs have the faculty of producing refrigeration. But to prevent
their food from impeding these operations there is a similar contrivance in the respiring animals and in those
that admit water. At the moment of respiration they do not take in food, for otherwise suffocation results
owing to the food, whether liquid or dry, slipping in through the windpipe and lying on the lung. The
windpipe is situated before the oesophagus, through which food passes into what is called the stomach, but in
quadrupeds which are sanguineous there is, as it were, a lid over the windpipe-the epiglottis. In birds and
oviparous quadrupeds this covering is absent, but its office is discharged by a contraction of the windpipe.
The latter class contract the windpipe when swallowing their food; the former close down the epiglottis.
When the food has passed, the epiglottis is in the one case raised, and in the other the windpipe is expanded,
and the air enters to effect refrigeration. In animals with gills the water is first discharged through them and
then the food passes in through the mouth; they have no windpipe and hence can take no harm from liquid
lodging in this organ, only from its entering the stomach. For these reasons the expulsion of water and the
seizing of their food is rapid, and their teeth are sharp and in almost all cases arranged in a saw-like fashion,
for they are debarred from chewing their food.

Among water-animals the cetaceans may give rise to some perplexity, though they too can be rationally
explained.

Examples of such animals are dolphins and whales, and all others that have a blowhole. They have no feet,
yet possess a lung though admitting the sea-water. The reason for possessing a lung is that which we have
now stated [refrigeration] ; the admission of water is not for the purpose of refrigeration. That is effected by
respiration, for they have a lung. Hence they sleep with their head out of the water, and dolphins, at any rate,
snore. Further, if they are entangled in nets they soon die of suffocation owing to lack of respiration, and
hence they can be seen to come to the surface owing to the necessity of breathing. But, since they have to
feed in the water, they must admit it, and it is in order to discharge this that they all have a blow-hole; after
admitting the water they expel it through the blow-hole as the fishes do through the gills. The position of the
blow-hole is an indication of this, for it leads to none of the organs which are charged with blood; but it lies
before the brain and thence discharges water.

It is for the very same reason that molluscs and crustaceans admit water-I mean such animals as Carabi and
Carcini. For none of these is refrigeration a necessity, for in every case they have little heat and are bloodless,
and hence are sufficiently cooled by the surrounding water. But in feeding they admit water, and hence must
expel it in order to prevent its being swallowed simultaneously with the food. Thus crustaceans, like the
Carcini and Carabi, discharge water through the folds beside their shaggy parts, while cuttlefish and the
polyps employ for this purpose the hollow above the head. There is, however, a more precise account of these
in the History of Animals.

Thus it has been explained that the cause of the admission of the water is refrigeration, and the fact that
animals constituted for a life in water must feed in it.

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An account must next be given of refrigeration and the manner in which it occurs in respiring animals and
those possessed of gills. We have already said that all animals with lungs respire. The reason why some
creatures have this organ, and why those having it need respiration, is that the higher animals have a greater
proportion of heat, for at the same time they must have been assigned a higher soul and they have a higher
nature than plants. Hence too those with most blood and most warmth in the lung are of greater size, and
animal in which the blood in the lung is purest and most plentiful is the most erect, namely man; and the
reason why he alone has his upper part directed to the upper part of the universe is that he possesses such a
lung. Hence this organ as much as any other must be assigned to the essence of the animal both in man and in
other cases.

This then is the purpose of refrigeration. As for the constraining and efficient cause, we must believe that it
created animals like this, just as it created many others also not of this constitution. For some have a greater
proportion of earth in their composition, like plants, and others, e.g. aquatic animals, contain a larger amount
of water; while winged and terrestrial animals have an excess of air and fire respectively. It is always in the
region proper to the element preponderating in the scheme of their constitution that things exist.

Empedocles is then in error when he says that those animals which have the most warmth and fire live in the
water to counterbalance the excess of heat in their constitution, in order that, since they are deficient in cold
and fluid, they may be kept in life by the contrary character of the region they occupy; for water has less heat
than air. But it is wholly absurd that the water-animals should in every case originate on dry land, and
afterwards change their place of abode to the water; for they are almost all footless. He, however, when
describing their original structure says that, though originating on dry land, they have abandoned it and
migrated to the water. But again it is evident that they are not warmer than land-animals, for in some cases
they have no blood at all, in others little.

The question, however, as to what sorts of animals should be called warm and what cold, has in each special
case received consideration. Though in one respect there is reason in the explanation which Empedocles aims
at establishing, yet his account is not correct. Excess in a bodily state is cured by a situation or season of
opposite character, but the constitution is best maintained by an environment akin to it. There is a difference
between the material of which any animal is constituted and the states and dispositions of that material. For
example, if nature were to constitute a thing of wax or of ice, she would not preserve it by putting it in a hot
place, for the opposing quality would quickly destroy it, seeing that heat dissolves that which cold congeals.
Again, a thing composed of salt or nitre would not be taken and placed in water, for fluid dissolves that of
which the consistency is due to the hot and the dry.

Hence if the fluid and the dry supply the material for all bodies, it is reasonable that things the composition of
which is due to the fluid and the cold should have liquid for their medium [and, if they are cold, they will
exist in the cold], while that which is due to the dry will be found in the dry. Thus trees grow not in water but
on dry land. But the same theory would relegate them to the water, on account of their excess of dryness, just
as it does the things that are excessively fiery. They would migrate thither not on account of its cold but
owing to its fluidity.

Thus the natural character of the material of objects is of the same nature as the region in which they exist;
the liquid is found in liquid, the dry on land, the warm in air. With regard, however, to states of body, a cold
situation has, on the other hand, a beneficial effect on excess of heat, and a warm environment on excess of
cold, for the region reduces to a mean the excess in the bodily condition. The regions appropriate to each

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material and the revolutions of the seasons which all experience supply the means which must be sought in
order to correct such excesses; but, while states of the body can be opposed in character to the environment,
the material of which it is composed can never be so. This, then, is a sufficient explanation of why it is not
owing to the heat in their constitution that some animals are aquatic, others terrestrial, as Empedocles
maintains, and of why some possess lungs and others do not.

The explanation of the admission of air and respiration in those animals in which a lung is found, and
especially in those in which it is full of blood, is to be found in the fact that it is of a spongy nature and full of
tubes, and that it is the most fully charged with blood of all the visceral organs. All animals with a
full-blooded lung require rapid refrigeration because there is little scope for deviation from the normal
amount of their vital fire; the air also must penetrate all through it on account of the large quantity of blood
and heat it contains. But both these operations can be easily performed by air, for, being of a subtle nature, it
penetrates everywhere and that rapidly, and so performs its cooling function; but water has the opposite
characteristics.

The reason why animals with a full-blooded lung respire most is hence manifest; the more heat there is, the
greater is the need for refrigeration, and at the same time breath can easily pass to the source of heat in the
heart.

In order to understand the way in which the heart is connected with the lung by means of passages, we must
consult both dissections and the account in the History of Animals. The universal cause of the need which the
animal has for refrigeration, is the union of the soul with fire that takes place in the heart. Respiration is the
means of effecting refrigeration, of which those animals make use that possess a lung as well as a heart. But
when they, as for example the fishes, which on account of their aquatic nature have no lung, possess the latter
organ without the former, the cooling is effected through the gills by means of water. For ocular evidence as
to how the heart is situated relatively to the gills we must employ dissections, and for precise details we must
refer to Natural History. As a summarizing statement, however, and for present purposes, the following is the
account of the matter.

It might appear that the heart has not the same position in terrestrial animals and fishes, but the position really
is identical, for the apex of the heart is in the direction in which they incline their heads. But it is towards the
mouth in fishes that the apex of the heart points, seeing that they do not incline their heads in the same
direction as land-animals do. Now from the extremity of the heart a tube of a sinewy, arterial character runs
to the centre where the gills all join. This then is the largest of those ducts, but on either side of the heart
others also issue and run to the extremity of each gill, and by means of the ceaseless flow of water through
the gills, effect the cooling which passes to the heart.

In similar fashion as the fish move their gills, respiring animals with rapid action raise and let fall the chest
according as the breath is admitted or expelled. If air is limited in amount and unchanged they are suffocated,
for either medium, owing to contact with the blood, rapidly becomes hot. The heat of the blood counteracts
the refrigeration and, when respiring animals can no longer move the lung aquatic animals their gills, whether
owing to disease or old age, their death ensues.

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To be born and to die are common to all animals, but there are specifically diverse ways in which these
phenomena occur; of destruction there are different types, though yet something is common to them all.
There is violent death and again natural death, and the former occurs when the cause of death is external, the
latter when it is internal, and involved from the beginning in the constitution of the organ, and not an
affection derived from a foreign source. In the case of plants the name given to this is withering, in animals
senility. Death and decay pertain to all things that are not imperfectly developed; to the imperfect also they
may be ascribed in nearly the same but not an identical sense. Under the imperfect I class eggs and seeds of
plants as they are before the root appears.

It is always to some lack of heat that death is due, and in perfect creatures the cause is its failure in the organ
containing the source of the creature's essential nature. This member is situate, as has been said, at the
junction of the upper and lower parts; in plants it is intermediate between the root and the stem, in
sanguineous animals it is the heart, and in those that are bloodless the corresponding part of their body. But
some of these animals have potentially many sources of life, though in actuality they possess only one. This
is why some insects live when divided, and why, even among sanguineous animals, all whose vitality is not
intense live for a long time after the heart has been removed. Tortoises, for example, do so and make
movements with their feet, so long as the shell is left, a fact to be explained by the natural inferiority of their
constitution, as it is in insects also.

The source of life is lost to its possessors when the heat with which it is bound up is no longer tempered by
cooling, for, as I have often remarked, it is consumed by itself. Hence when, owing to lapse of time, the lung
in the one class and the gills in the other get dried up, these organs become hard and earthy and incapable of
movement, and cannot be expanded or contracted. Finally things come to a climax, and the fire goes out from
exhaustion.

Hence a small disturbance will speedily cause death in old age. Little heat remains, for the most of it has been
breathed away in the long period of life preceding, and hence any increase of strain on the organ quickly
causes extinction. It is just as though the heart contained a tiny feeble flame which the slightest movement
puts out. Hence in old age death is painless, for no violent disturbance is required to cause death, and there is
an entire absence of feeling when the soul's connexion is severed. All diseases which harden the lung by
forming tumours or waste residues, or by excess of morbid heat, as happens in fevers, accelerate the
breathing owing to the inability of the lung to move far either upwards or downwards. Finally, when motion
is no longer possible, the breath is given out and death ensues.

Generation is the initial participation, mediated by warm substance, in the nutritive soul, and life is the
maintenance of this participation. Youth is the period of the growth of the primary organ of refrigeration, old
age of its decay, while the intervening time is the prime of life.

A violent death or dissolution consists in the extinction or exhaustion of the vital heat (for either of these may
cause dissolution), while natural death is the exhaustion of the heat owing to lapse of time, and occurring at
the end of life. In plants this is to wither, in animals to die. Death, in old age, is the exhaustion due to inability
on the part of the organ, owing to old age, to produce refrigeration. This then is our account of generation and
life and death, and the reason for their occurrence in animals.

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ON YOUTH AND OLD AGE, ON LIFE AND DEATH, ON BREATHING

It is hence also clear why respiring animals are suffocated in water and fishes in air. For it is by water in the
latter class, by air in the former that refrigeration is effected, and either of these means of performing the
function is removed by a change of environment.

There is also to be explained in either case the cause of the cause of the motion of the gills and of the lungs,
the rise and fall of which effects the admission and expulsion of the breath or of water. The following,
moreover, is the manner of the constitution of the organ.

In connexion with the heart there are three phenomena, which, though apparently of the same nature, are
really not so, namely palpitation, pulsation, and respiration.

Palpitation is the rushing together of the hot substance in the heart owing to the chilling influence of residual
or waste products. It occurs, for example, in the ailment known as 'spasms' and in other diseases. It occurs
also in fear, for when one is afraid the upper parts become cold, and the hot substance, fleeing away, by its
concentration in the heart produces palpitation. It is crushed into so small a space that sometimes life is
extinguished, and the animals die of the fright and morbid disturbance.

The beating of the heart, which, as can be seen, goes on continuously, is similar to the throbbing of an
abscess. That, however, is accompanied by pain, because the change produced in the blood is unnatural, and
it goes on until the matter formed by concoction is discharged. There is a similarity between this phenomenon
and that of boiling; for boiling is due to the volatilization of fluid by heat and the expansion consequent on
increase of bulk. But in an abscess, if there is no evaporation through the walls, the process terminates in
suppuration due to the thickening of the liquid, while in boiling it ends in the escape of the fluid out of the
containing vessel.

In the heart the beating is produced by the heat expanding the fluid, of which the food furnishes a constant
supply. It occurs when the fluid rises to the outer wall of the heart, and it goes on continuously; for there is a
constant flow of the fluid that goes to constitute the blood, it being in the heart that the blood receives its
primary elaboration. That this is so we can perceive in the initial stages of generation, for the heart can be
seen to contain blood before the veins become distinct. This explains why pulsation in youth exceeds that in
older people, for in the young the formation of vapour is more abundant.

All the veins pulse, and do so simultaneously with each other, owing to their connexion with the heart. The
heart always beats, and hence they also beat continuously and simultaneously with each other and with it.

Palpitation, then, is the recoil of the heart against the compression due to cold; and pulsation is the
volatilization of the heated fluid.

Respiration takes place when the hot substance which is the seat of the nutritive principle increases. For it,
like the rest of the body, requires nutrition, and more so than the members, for it is through it that they are
nourished. But when it increases it necessarily causes the organ to rise. This organ we must to be constructed
like the bellows in a smithy, for both heart and lungs conform pretty well to this shape. Such a structure must
be double, for the nutritive principle must be situated in the centre of the natural force.

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ON YOUTH AND OLD AGE, ON LIFE AND DEATH, ON BREATHING

Thus on increase of bulk expansion results, which necessarily causes the surrounding parts to rise. Now this
can be seen to occur when people respire; they raise their chest because the motive principle of the organ
described resident within the chest causes an identical expansion of this organ. When it dilates the outer air
must rush in as into a bellows, and, being cold, by its chilling influence reduces by extinction the excess of
the fire. But, as the increase of bulk causes the organ to dilate, so diminution causes contraction, and when it
collapses the air which entered must pass out again. When it enters the air is cold, but on issuing it is warm
owing to its contact with the heat resident in this organ, and this is specially the case in those animals that
possess a full-blooded lung. The numerous canal-like ducts in the lung, into which it passes, have each a
blood-vessel lying alongside, so that the whole lung is thought to be full of blood. The inward passage of the
air is called respiration, the outward expiration, and this double movement goes on continuously just so long
as the animal lives and keeps this organ in continuous motion; it is for this reason that life is bound up with
the passage of the breath outwards and inwards.

It is in the same way that the motion of the gills in fishes takes place. When the hot substance in the blood
throughout the members rises, the gills rise too, and let the water pass through, but when it is chilled and
retreats through its channels to the heart, they contract and eject the water. Continually as the heat in the heart
rises, continually on being chilled it returns thither again. Hence, as in respiring animals life and death are
bound up with respiration, so in the other animals class they depend on the admission of water.

Our discussion of life and death and kindred topics is now practically complete. But health and disease also
claim the attention of the scientist, and not merely of the physician, in so far as an account of their causes is
concerned. The extent to which these two differ and investigate diverse provinces must not escape us, since
facts show that their inquiries are, to a certain extent, at least conterminous. For physicians of culture and
refinement make some mention of natural science, and claim to derive their principles from it, while the most
accomplished investigators into nature generally push their studies so far as to conclude with an account of
medical principles.

-THE END-

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The Complete Works of Aristotle - Part 7