by Aristotle
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 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.
14
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 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 creat
ure,
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
1
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 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 n
ot
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.
Moreover, see whether the one can exist without the other; for, if
so, they could not be the same.
2
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