1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.