Commentary Aristotle Posterior Analytics
Lecture 34
Logical reasons why one does not proceed to infinity in predicates a36. (3) If A is a quality of B, B cannot be a quality of A—a quality of a quality.
a37. Therefore, A and B cannot be predicated reciprocally of one another in strict predication: they can be affirmed without falsehood of one another, but not genuinely predicated of each other.
a39. For one alternative is that they should be substantially predicated of one another, that is, B would become the genus or differentia of A—the predicate now become subject.
b1. But it has been shown that in these substantial predications neither the ascending predicates nor the descending subjects form an infinite series; e.g., neither the series, man is biped, biped is animal, etc., nor the series predicating animal of man, man of Callias, Callias of a further subject as an element of its essential nature, is infinite. For all such substance is definable, and an infinite series cannot be traversed in thought: consequently neither the ascent nor the descent is infinite, since a substance whose predicates were infinite would not be definable.
b8. Hence they will not be predicated each as the genus of the other; for this would equate a genus with one of its own species.
b10. Nor can a quale be reciprocally predicated of a quale, nor any term belonging to an adjectival category of another such term, except by accidental predication; for all such predicates are coincidents and are predicated of substances.
b13. On the other hand, in proof of the impossibility of an infinite ascending series, every predication displays the subject as somehow qualified or quantified or as characterized under one of the other adjectival categories, or else is an element in its substantial nature: these latter are limited in number, and the number of the widest kinds under which predications fall is also limited, for every predication must exhibit its subject as somehow qualified, quantified, essentially related, acting or suffering, or in some place or at some time. I assume first that predication implies a single subject and a single attribute, and second that predicates which are not substantial are not predicated of one another. We assume this because such predicates are all coincidents, and though some are essential coincidents, others of a different type, yet we maintain that all of them alike are predicated of some substratum and that a coincident is never a substratum—since we do not class as a coincident anything which does not owe its designation to its being something other than itself, but always hold that any coincident is predicated of some substratum other than itself, and that another group of coincidents may have a different substratum.
b24. Subject to these assumptions then, neither the ascending nor the descending series of predication in which a single attribute is predicated of a single subject is infinite. For the subjects of which coincidents are predicated are as many as the constitutive elements of each individual substance, and these we have seen are not infinite in number, while in the ascending series are contained those constitutive elements with their coincidents—both of which are finite. We conclude that there is a given subject (D) of which some attribute (C) is primarily predicable; that there must be an attribute (B) primarily predicable of the first attribute, and that the series must end with a term (A) not predicable of any term prior to the last subject of which it was predicated (B), and of which no term prior to it is predicable.
b33. The argument we have given is one of the so-called proofs; an alternative proof follows. Predicates so related to their subjects that there are other predicates prior to them predicable of those subjects are demonstrable; but of demonstrable propositions one cannot have something better than knowledge, nor can one know them without demonstration. Second, if a consequent is only known through an antecedent (viz. premises prior to it) and we neither know this antecedent nor have something better than knowledge of it, then we shall not have scientific knowledge of the consequent. Therefore, if it is possible through demonstration to know anything without qualification and not merely as dependent on the acceptance of certain premises—that is, hypothetically—the series of intermediate predications must terminate. If it does not terminate, and beyond any predicate taken as higher than another there remains another still higher, then every predicate is demonstrable. Consequently, since these demonstrable predicates are infinite in number and therefore cannot be traversed, we shall not know them by demonstration. If, therefore, we have not something better than knowledge of them, we cannot through demonstration have unqualified but only hypothetical science of anything.
As dialectical proofs of our contention these may carry conviction.
If A is a quality of B. Having set forth the distinction of predicates from one another as a necessary preliminary to demonstrating his proposition, the Philosopher now undertakes to show his proposition, namely, that there is no infinite process in predicates.
And his treatment falls into two parts, according to the two ways in which he shows his proposition, the second part beginning at: the argument we have given (83b33).
Concerning the first he does two things. First, he shows that one does not proceed to infinity in predicates after the manner of circularity (see Lect. 8). Second, that one does not proceed to infinity in a direct line upwards or downwards, at: on the other hand, in proof (83b13).
Concerning the first he does three things. First, granting what has gone before, he adds certain things required for showing his proposition. Second, from these and other established facts he concludes the proposition, at: therefore, A and B cannot be (83a37). Third, he proves it, at: for one alternative (83a39).
First, therefore (83a36) he proposes two things: one of these is that since a predicate which signifies an accident signifies some genus of accident, such as quality, it cannot occur that two things be so related to one another that the first is a quality of the second and the second a quality of the first: for the nature of a quality and that of which it is the quality are diverse. The second is that universally it is not possible that a quality have some other quality inhering in it, because no accident is the subject of another accident, absolutely speaking. For to substance alone does the notion of subject properly belong.
Then, at: therefore, A and B cannot be (83a37) he proposes, as though concluding from these antecedents, what he intends to prove.
He says, if our preliminary rules are true, it is impossible that there be equal reciprocal predication, that is, according to any of the above-mentioned ways. But this does not exclude the possibility of one thing’s being truly predicated of another and conversely. For we say truly that man is white and that something white is a man. However, this is not done equally, that is, according to an equal manner of predicating. And it is the same in essential predicates.
Then, at: for one alternative is that (83a39) he shows the proposition.
First, in essential predicates. Second, in accidental ones, at: nor can a quale be reciprocally (83b10).
In regard to the first he does three things. First, he lays down a division of essential predicates. Second, he recalls something established above, at: but it has been shown (83b1). Third, he proves the proposition, at: hence they will not be predicated (83b8).
He says therefore first (83a39) that in order to show that they are not reciprocally predicated equally, it will be necessary to consider this in essential predicates. For that which is predicated equally will be predicated either as a substance or some other way: and if as a substance, then either as a genus or as a difference. For these are the two parts of a definition which signify the essence.
Then, at: but it has been shown (83b1) he recalls what he had proved above at the beginning of the previous lecture, namely, that predicates of this kind are not infinite; because if they were to proceed to infinity, reciprocity or circularity would find no place therein.
He says, therefore, that as has been shown above, an infinite process does not take place in such predicates either by ascending or by descending: for example, if two-footed be predicated of man, and animal of two-footed, something else of animal, there is no process to infinity either upwards or downwards. Thus, if animal were said essentially of man, and “man” of Callias, and this of someone else (supposing that there were a genus containing under it species, one of which would be Callias), it would not be possible to go on in this way to infinity. And he recalls the reason he used earlier to prove this: for every such substance which has something more universal that can be predicated of it and which can be predicated of some inferior is capable of being defined; but the most general genera of which other more universal things are not predicated, and singulars which are not predicated of any inferiors, are not capable of definition. Only the substance between these can be defined. But that substance of which an infinite number of things is predicated turns out to be indefinable, because one who would define it must go through and understand all the items which are substantially predicated of the defined, since all of them occur in the definition either as a genus or as a difference. But the infinite cannot be gone through. Therefore, it is required that neither a universal substance, which is not a supreme genus, nor a lowest subject, can have an infinitude of predicates which are predicated of it substantially. Consequently, there is no infinite process either upwards or downwards.
Then, at: hence they will not be predicated (83b8) he shows that there is no process to infinity after the manner of circularity in substantial predicates.
And he says that if certain substantial predicates are predicated as genera of something, they are not predicated of one another equally, that is, convertibly, that is, so that one would be the genus of another and vice versa. To prove this he continues, for the one will be what something truly is. As if to say: if something is predicated of something as a genus, that of which it is predicated is something which truly is that, that is, something particular which receives that predication substantially. Therefore, if this be predicated of that as a genus, it will follow that something which belongs to something particularly would conversely receive the predication of it, which is tantamount to saying that a same thing is both a whole and a part in relation to the same thing—which is impossible. And the same reasoning applies to differences. Hence in Topics I it is stated that problems concerning a difference are reduced to problems concerning the genus.
Then, at: nor can a quale be reciprocally (83b10) he shows that there cannot be an infinite circular process in predications in which an accident is predicated of a subject.
And he says that there cannot be conversion of a quality with its subject; furthermore, none of the others which are predicated accidentally can have that sort of predication, unless the predication be made per accidens in the sense described above, namely, that accidents are not predicated of their subjects except per accidens. For quality and all these others are accidental to the subject; hence they are predicated of their substances as an accident of a subject.
Then, at: on the other hand, in proof (83b13) he shows universally that in no genus of predication is there an infinite process upwards or downwards.
And he says that not only is there no infinite process in predications according to circulation, but also that in proceeding upwards or downwards the predicates will not be infinite.
To prove this: First, he recalls certain things which were established above. Second, from these he concludes his proposition, at: subject to these assumptions (83b24).
In regard to the first he reaffirms (83b13) that certain things can be predicated of a subject, whether they signify quality or quantity or any other genus of accident, or even items which constitute the substance of a thing, that is, essential predicates. Second, he reiterates, that the latter, that is, the substantial predicates, are finite. Third, he reaffirms that the genera of predicaments are finite, namely, quality, quantity and so on. For if someone were to say that quantity is predicated of substance, and quality of quantity, and so on to infinity, he excludes this on the ground that the genera of predicaments are finite. Fourth, he reaffirms that, as stated above, one thing is predicated of one thing in simple predication.
And he mentions this because someone might say that one thing may well be first predicated of one thing, as “animal” of man, and this predication will be multiplied until something else can be found predicable of man, and when this is found, two things will be predicated of one, so that it will be said that man is a white animal. Thus, many more predicates might be found according to various combinations of predicates. And so by continually adding to this number, the predicates will be increased more and more, so that there will be a process to infinity in predicates, just as there is in the succession of numbers. But he excludes this by predicating one of one.
Fifth, he repeats that we should not say that certain items are predicated absolutely of things which are not something, that is, of accidents, none of which is a subsistent being. For, as shown above, neither the subject nor an accident is properly predicated of an accident. For all things of this sort that are not substantial are accidents, and nothing is predicated, simply speaking, of such things. Yet whether they be substantial predicates or accidental, they are predicated per se of their subjects; but if they are subjects or accidents being predicated of an accident, they are predicated in another way, that is, per accidens. For it belongs to the very notion of all accidents that they be said of a subject; and since an accident is not a subject, nothing can, properly speaking, be predicated of it, because none of such, that is, no accidents, are stated to be such that they are said to be that which is said, that is, stated to be such that they themselves, rather than something else distinct from them, receives the predication of that which is predicated of them, as happens in the case of substances. For man is not called “animal” or “white” because something else is “animal” or “white,” but because the very thing which is a man is animal or white; but a white thing is called “man” or “musician” because something else, namely, the subject of white is the man or musician. But the accident itself is in something distinct from it; and others which are predicated of an accident are predicated of something other than that accident, namely, of the subject of the accident: it is on this ground that they are predicated of the accident, as has been stated. (Now he mentioned this because if an accident is predicated of a subject and vice versa, and all accidents of a subject can be mutually predicated of one another, it will follow that predication could proceed to infinity, because an infinitude of things can happen to one thing).
Then, at: subject to these assumptions (83b24) from these premises he shows his proposition, namely, that in a predication in which one thing is predicated of one thing there is no upward or downward process to infinity, because, as the fifth supposition states, all accidents are predicated of items which pertain to the substance of the thing. Furthermore, according to the second supposition, substantial predicates are not infinite; consequently, on the part of the subjects there is no infinite process downwards in these predications. Again, neither of these is infinite in the upward movement, that is, neither the substantial nor the accidental predicates, both because the genera of accidents are finite, and because there is no infinite process upwards or downwards in any of these genera any more than there is in substantial predicates, because in each predicament the genus is predicated of a species in regard to something essential. Hence we can conclude universally that there must be some first subject of which something is predicated, thus establishing a stop in downward predication; then something else will be predicated of this, but it will come to a stop in the ascending process, so that something will be found which is not found predicated of another, either as the subsequent is predicated of its prior per accidens, or as the prior is predicated per se of its subsequent. This, therefore, is one way of demonstrating the proposition logically, and it is based on the diverse modes of predicating.
Then, at: the argument we have given (83b33) he sets forth the second way of proving.
And he says that when a proposition in which something is predicated of a subject is such that certain things can be predicated per prius of that subject, that proposition will be demonstrable: (for example, this proposition, “Man is a substance,” is demonstrated by the proposition, “Animal is a substance,” because “substance” is predicated of animal before it is predicated of man.) But if a proposition is demonstrable, there is no better way of knowing it than to know it by demonstration, just as we know indemonstrable principles better than by way of demonstration because we know them as self-evident. Besides, we cannot scientifically know such demonstrable propositions except through demonstration, because a demonstration is a syllogism productive of scientific knowledge, as we showed above. Furthermore, if a proposition is known through another one, and if we do not scientifically know the one through which it is known, or know it in the way which is better than knowing scientifically, then we do not scientifically know that proposition which is made known through it.
With these three suppositions in mind he proceeds thus: If one does know something purely through demonstration and not from something or from supposition, it is necessary that there be a stop in the predicates which are taken as middles.
He says: "purely and not from something", to exclude demonstrations leading to the impossible, in which one proceeds, against certain positions by arguing from propositions that have been agreed upon. Furthermore, he says: "or from supposition", to exclude such demonstrations as are formed in subalternate sciences, which suppose the conclusion of higher sciences, as explained above. Therefore, one knows purely through demonstration when each one of the premised propositions, if it is demonstrable, is known through demonstration; and if it is not demonstrable, is known in virtue of itself.
Under these suppositions it is necessary that there be a stop in predications, because if there is no stop but something prior can always be taken, it follows that there is demonstration of everything, as was said above. Therefore, if a conclusion is demonstrated, each of the premises must be demonstrable. But if we can have knowledge of it in no better way than by knowing it through demonstration, and if it will be necessary to demonstrate it through other propositions, and those through others again, and so on to infinity, then, since it is not possible to go through those infinites, we shall not be able to make it known through demonstration or through the method better than demonstration, since all things are demonstrable. The consequence will be that one knows nothing purely through demonstration, but only from supposition.
Finally, by way of summary he concludes the main proposition.