Posterior Analytics   

this too is an assumption, and equally an assumption whether the
division comprises many differentiae or few. (Indeed as this method of
division is used by those who proceed by it, even truths that can be
inferred actually fail to appear as such.) For why should not the
whole of this formula be true of man, and yet not exhibit his
essential nature or definable form? Again, what guarantee is there
against an unessential addition, or against the omission of the
final or of an intermediate determinant of the substantial being?
The champion of division might here urge that though these lapses do
occur, yet we can solve that difficulty if all the attributes we
assume are constituents of the definable form, and if, postulating the
genus, we produce by division the requisite uninterrupted sequence
of terms, and omit nothing; and that indeed we cannot fail to fulfil
these conditions if what is to be divided falls whole into the
division at each stage, and none of it is omitted; and that this-the
dividendum-must without further question be (ultimately) incapable
of fresh specific division. Nevertheless, we reply, division does
not involve inference; if it gives knowledge, it gives it in another
way. Nor is there any absurdity in this: induction, perhaps, is not
demonstration any more than is division, et it does make evident
some truth. Yet to state a definition reached by division is not to
state a conclusion: as, when conclusions are drawn without their
appropriate middles, the alleged necessity by which the inference
follows from the premisses is open to a question as to the reason
for it, so definitions reached by division invite the same question.
Thus to the question 'What is the essential nature of man?' the
divider replies 'Animal, mortal, footed, biped, wingless'; and when at
each step he is asked 'Why?', he will say, and, as he thinks, proves
by division, that all animal is mortal or immortal: but such a formula
taken in its entirety is not definition; so that even if division does
demonstrate its formula, definition at any rate does not turn out to
be a conclusion of inference.

6

Can we nevertheless actually demonstrate what a thing essentially
and substantially is, but hypothetically, i.e. by premising (1) that
its definable form is constituted by the 'peculiar' attributes of
its essential nature; (2) that such and such are the only attributes
of its essential nature, and that the complete synthesis of them is
peculiar to the thing; and thus-since in this synthesis consists the
being of the thing-obtaining our conclusion? Or is the truth that,
since proof must be through the middle term, the definable form is
once more assumed in this minor premiss too?
Further, just as in syllogizing we do not premise what syllogistic
inference is (since the premisses from which we conclude must be
related as whole and part), so the definable form must not fall within
the syllogism but remain outside the premisses posited. It is only
against a doubt as to its having been a syllogistic inference at all
that we have to defend our argument as conforming to the definition of
syllogism. It is only when some one doubts whether the conclusion
proved is the definable form that we have to defend it as conforming
to the definition of definable form which we assumed. Hence
syllogistic inference must be possible even without the express
statement of what syllogism is or what definable form is.
The following type of hypothetical proof also begs the question.
If evil is definable as the divisible, and the definition of a thing's
contrary-if it has one the contrary of the thing's definition; then,
if good is the contrary of evil and the indivisible of the
divisible, we conclude that to be good is essentially to be
indivisible. The question is begged because definable form is
assumed as a premiss, and as a premiss which is to prove definable
form. 'But not the same definable form', you may object. That I admit,
for in demonstrations also we premise that 'this' is predicable of