The Complete Aristotle (eng.)

of which all triangles
constitute the whole. But in the case before us the fact and the
essential nature are not so related to one another, since the one
is not a part of the other.
    So it emerges that not all the definable is demonstrable nor all
the demonstrable definable; and we may draw the general conclusion
that there is no identical object of which it is possible to
possess both a definition and a demonstration. It follows obviously
that definition and demonstration are neither identical nor
contained either within the other: if they were, their objects
would be related either as identical or as whole and part.
4
    So much, then, for the first stage of our problem. The next step
is to raise the question whether syllogism-i.e. demonstration-of
the 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.