Posterior Analytics   

definable nature is possible or, as our recent argument assumed,
impossible.
We might argue it impossible on the following grounds:-(a) syllogism
proves an attribute of a subject through the middle term; on the other
hand (b) its definable nature is both 'peculiar' to a subject and
predicated of it as belonging to its essence. But in that case (1) the
subject, its definition, and the middle term connecting them must be
reciprocally predicable of one another; for if A is to C, obviously
A is 'peculiar' to B and B to C-in fact all three terms are 'peculiar'
to one another: and further (2) if A inheres in the essence of all B
and B is predicated universally of all C as belonging to C's
essence, A also must be predicated of C as belonging to its essence.
If one does not take this relation as thus duplicated-if, that is, A
is predicated as being of the essence of B, but B is not of the
essence of the subjects of which it is predicated-A will not
necessarily be predicated of C as belonging to its essence. So both
premisses will predicate essence, and consequently B also will be
predicated of C as its essence. Since, therefore, both premisses do
predicate essence-i.e. definable form-C's definable form will appear
in the middle term before the conclusion is drawn.
We may generalize by supposing that it is possible to prove the
essential nature of man. Let C be man, A man's essential
nature--two-footed animal, or aught else it may be. Then, if we are to
syllogize, A must be predicated of all B. But this premiss will be
mediated by a fresh definition, which consequently will also be the
essential nature of man. Therefore the argument assumes what it has to
prove, since B too is the essential nature of man. It is, however, the
case in which there are only the two premisses-i.e. in which the
premisses are primary and immediate-which we ought to investigate,
because it best illustrates the point under discussion.
Thus they who prove the essential nature of soul or man or
anything else through reciprocating terms beg the question. It would
be begging the question, for example, to contend that the soul is that
which causes its own life, and that what causes its own life is a
self-moving number; for one would have to postulate that the soul is a
self-moving number in the sense of being identical with it. For if A
is predicable as a mere consequent of B and B of C, A will not on that
account be the definable form of C: A will merely be what it was
true to say of C. Even if A is predicated of all B inasmuch as B is
identical with a species of A, still it will not follow: being an
animal is predicated of being a man-since it is true that in all
instances to be human is to be animal, just as it is also true that
every man is an animal-but not as identical with being man.
We conclude, then, that unless one takes both the premisses as
predicating essence, one cannot infer that A is the definable form and
essence of C: but if one does so take them, in assuming B one will
have assumed, before drawing the conclusion, what the definable form
of C is; so that there has been no inference, for one has begged the
question.

5

Nor, as was said in my formal logic, is the method of division a
process of inference at all, since at no point does the
characterization of the subject follow necessarily from the
premising of certain other facts: division demonstrates as little as
does induction. For in a genuine demonstration the conclusion must not
be put as a question nor depend on a concession, but must follow
necessarily from its premisses, even if the respondent deny it. The
definer asks 'Is man animal or inanimate?' and then assumes-he has not
inferred-that man is animal. 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: