Commentary Aristotle Posterior Analytics
Lecture 3
Whether the quod quid signified by the definition can be demonstrated by taking convertible terms a12. The next step is to raise the question whether syllogism—that is, demonstration—of the definable nature is possible or, as our recent argument assumed, impossible.
a14. 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;
a18. 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:
a19. 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.
a22. 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 premises will predicate essence, and consequently B also will be predicated of C as its essence.
a25. Since, therefore, both premises do predicate essence—that is, definable form—C’s definable form will appear in the middle term before the conclusion is drawn.
a28. 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 premise 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.
a32. It is, however, the case in which there are only the two premises—that is, in which the premises are primary and immediate—which we ought to investigate, because it best illustrates the point under discussion.
a35. 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.
b1. 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 premises 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.
The next step is to raise the question. After inquiring disputatively whether the definition signifying 'quod quid' can be demonstrated, the Philosopher continues to inquire disputatively and asks whether the 'quod quid' itself, which is signified by a definition, can be proved demonstratively.
First, he states what he intends.
Second, he pursues his proposal, at: we might argue it impossible (92a14; [433]).
First, therefore (92a12), he raises the question whether there can be a syllogism or demonstration of that which is the 'quod quid', namely, in such a way as to conclude that this is the quod quid of this; or can this not be done, as the immediately preceding reason supposed?
Now it was necessary to undertake this disputation on the heels of the previous one, because in a definition one must be sure not only that what it signifies is the quod quid, but also that it be formulated in such a way as to be suitable for manifesting the quod quid, that is, in such a way as to be composed of prior and better known items and possess the other characteristics which mark a definition. It is significant that he says, "whether there be syllogism or demonstration", for some of the reasons which follow conclude that there is not demonstration of the 'quod quid', and others that there is no syllogism at all of it.
Then, at: we might argue it impossible (92a14) he proceeds disputatively to show that there is not syllogism, or demonstration of the quod quid.
First, he excludes certain special ways by which it might seem possible to demonstrate the 'quod quid'.
Second, he presents common reasons for this, at: to put it another way (93b3).
Concerning the first he does three things.
First, he shows that 'quod quid' cannot be demonstrated by using convertible terms.
Second, that it cannot be demonstrated by division, at: nor, as was said in my formal logic (92b12).
Third, that it cannot be demonstrated by accepting that which is required for 'quod quid', at: can we nevertheless (93a6).
First, he prefaces certain notions required for showing the proposal.
Second, he induces a reason, at: for if A is to C (92a18).
Third, he discloses the inconvenience which follows, at: it is, however, the case (92a32).
With respect to the first (92a12) he presupposes two things:
the first of these pertains to the syllogism, namely, that every syllogism proves something about something by means of some middle, as is clear from the above.
The other pertains to what is to be proved by the syllogism, namely, the 'quod quid', for which two conditions are required.
The first of these is that the 'quod quid' be proper, for each thing has its own proper essence or quiddity.
But because not everything which is proper to something pertains to its essence, a second condition is required, namely, that it be predicated in quid.
Furthermore, a third condition must follow on these two, namely, that the 'quod quid' be convertible with that of which it is.
Then, at: for if A is to C (92a18) he lays down a reason in support of his proposal.
Regarding this he does three things.
First, he states what sort of syllogism would be required for concluding a 'quod quid', if this were possible.
Second, he concludes to the inconvenience that follows from this, at: since, therefore, both premises (92a25).
Third, he uses terms to exemplify this, at: we may generalize (92a28).
Concerning the first he does three things.
First, he shows what is required for a syllogism concluding the 'quod quid' so far as it is something proper.
Second, what is required so far as it is predicated in quid, at: and further if A (92a19).
Third, he shows that without these characteristics such a syllogism would not be possible, at: if one does not take (92a22).
He says therefore first (92a18) that if A which is to be proved of C as its 'quod quid' is proper to C (which is required of the 'quod quid', as has been said), it will be necessary that the first, namely, A, be proper to the middle which is B; for if A exceeded [that is, were more universal than] B, which is predicated universally of C, it would follow that A exceeds C even more. In like manner, it is clear that B will have to be proper to C: for if B were to exceed C, it would follow that A, which is predicated universally of B, exceeds C; consequently, it would not be proper to it, as was supposed. What remains, therefore, is that if there is to be a syllogism concluding 'quod quid', the terms will have to be so related that all are mutually convertible.
Then, at: and further if A (92a19) he shows what the syllogism in question must have, if the condition is to be fulfilled that what it concludes be predicated in quod quid.
And he says that such a syllogism must be so formulated that the major extreme, which is A, be predicated in quod quid of the middle, which is B; in like manner, B will have to be predicated in quod quid of the minor extreme, which is C. In this way it can be concluded that A is predicated of C in quod quid.
Then, at: if one does not take (92a22) he shows that the aforesaid way of syllogizing is required.
And he asserts that if one does not so take the terms by thus duplicating, that is, observing the two conditions laid down above, that is, taking the 'quod quid' on the side of both, it does not follow of necessity that A would be predicated of C in quod quid. Indeed, if the aforesaid conditions are observed on the part of one only, it is not sufficient for the purpose intended. For even if A were predicated of B in quod quid, it would not on that account follow that it must be predicated in quod quid of everything of which B might happen to be predicated in some random way. Consequently, it follows that the 'quod quid' must be taken on the side of both in such a way, namely, that not only must A be the 'quod quid' of B, but also that B must be the 'quod quid' of C, as being predicated convertibly and in quod quid.
Then, at: since, therefore, both premises (92a25) he leads to the inconvenience.
If, as has been indicated, not only is there found on the side of both something which is predicated in quod quid—as a genus predicated of a species—but it is further found on the side of both that this something is the 'quod quid erat esse'—which a definition signifies—it follows that the 'quod quid erat esse' was already in the middle term, that is, that the middle term is the 'quod quid erat esse' of the minor extreme. Consequently, we would have been supposing the very thing we had set out to prove, namely, the quiddity of C.
Then, at: we may generalize by supposing (92a28) he clarifies what he has just said, using terms.
Thus, if we wish to show what man is, let C, that is, the minor extreme, be 'man', and A, the major extreme, be the 'quod quid' of man, say 'two-footed animal', or something similar to this. Therefore, if this is what we intend to prove by the syllogism, it is necessary to find the definition of some middle, namely, B, such that A will be predicated of every B. Furthermore, to this middle will pertain some other middle definition which, namely, was the definition of the minor extreme. Hence it will follow that this middle will also be the 'quod quid' of man. Consequently, one who syllogizes in this way would be supposing what he was required to prove, namely, that B is the 'quod quid erat esse' of man.
Then, at: it is, however, the case (92a32) he shows how this inconvenience follows from the premises.
To this end he does three things.
First, he indicates the method by which this may be fittingly done.
And he says that what has been said should be considered in two propositions which are first and which have terms that belong to each other immediately. For it would be possible to prove our point either with several propositions (which would lead to several syllogisms), or with only two propositions, but taking them as mediate. But because in the final analysis we must always arrive at two immediate propositions, then for the sake of brevity and dispatch let us assume such propositions from the very start. Thus we shall be able to manifest our point quite easily.
Second, at: thus they who prove (92a35), he states what he intends.
He says, concluding from the foregoing, that those who would demonstrate through convertible terms the 'quod quid' of some thing (say, what is a soul, or what is man, or anything else of this sort), necessarily commit the fault of begging the question. And he cites as an example Plato’s definition of soul. For since the soul is alive and is the body’s cause of being alive, it follows that it differs from the body in the fact that the body lives in virtue of some cause other than itself, but the soul lives in virtue of itself. But Plato posited that number is the substance of all things: for he failed to distinguish between one, which is converted with being and refers to the substance of that of which it is predicated, and one which is the principle of number. As a consequence, it followed that the soul as to its substance is a number, just as any other thing containing many things in itself. Likewise Plato posited that to live is one of the ways of being moved. For the living are distinguished from the non-living on two scores, namely, sense and movement, as it is stated in On the Soul I. Furthermore, he asserted that sensing or knowing is one way of being moved. Thus, therefore, he said that the soul is a self-moving number in addition to saying that the soul is its own cause of being alive. Consequently, if anyone desired to prove what a soul is, namely, that it is something which is its own cause of being alive, and assumed as middle that the soul is a number which moves itself, it would be necessary to beg this, namely, that the soul is a self-moving number, such that this is identical with the soul as being its 'quod quid'. Otherwise, it would not follow, if something is the 'quod quid' of self-moving number, that it is the 'quod quid' of the soul itself.
Third, at: for if A is predicable (92b1), he proves his proposal, namely, that such a proof involves begging the question.
And he says that it does not follow from the fact that A follows on B and B on C, that the major extreme, A, is the 'quod quid' of the minor extreme, C; what follows is simply that A is in C. And if it is further granted that A is the 'quod quid' of something and is predicated universally of B, it does not yet follow that A is the 'quod quid' of C: for it is plain that this, that is, the 'quod quid' of animal is universally predicated of this which is man’s 'quod quid'. For just as it is true that animal is universally predicated of man, so it is true that the definition of animal is universally predicated of the definition of man; but that does not mean that they are entirely one and the same. And so it is clear that unless one takes the terms in such a way that the first is entirely one and the same with the middle, and the middle with the last, it will not be possible to syllogize that A, which is the first, is the 'quod quid' of C—which is the last—and its essence. But if the terms are taken in that way, it follows that prior to its being concluded, the 'quod quid' of C, namely, B, was assumed in the premises. From this it follows that there is not a demonstration but a begging or assuming of the question.