The Complete Aristotle (eng.)

Next, when
presented with an exhaustive division of animal into terrestrial
and aquatic, he assumes that man is terrestrial. Moreover, that man
is the complete formula, terrestrial-animal, does not follow
necessarily from the premisses: 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 ‘that’; but in this premiss the term we
assert of the minor is neither the major itself nor a term
identical in definition, or convertible, with the major.
    Again, both proof by division and the