Commentary Aristotle Posterior Analytics
Lecture 33
That one does not proceed to infinity in essential predicates is shown logically b34. That in fact the regress terminates in both these cases may be made clear by the following dialectical considerations. In the case of predicates constituting the essential nature of a thing, it clearly terminates, seeing that if definition is possible, or in other words, if essential form is knowable, and an infinite series cannot be traversed, predicates constituting a thing’s essential nature must be finite in number.
a1. But as regards predicates generally we have the following prefatory remarks to make. (1) We can affirm without falsehood ‘the white (thing) is walking’, and ‘that big (thing) is a log’; or again, ‘the log is big’, and ‘the man walks’. But the affirmation differs in the two cases. When I affirm ‘the white is a log’, I mean that something which happens to be white is a log—not that white is the substratum in which log inheres, for it was not qua white or qua a species of white that the white (thing) came to be a log, and the white (thing) is consequently not a log except incidentally. On the other hand, when I affirm ‘the log is white’, I do not mean that something else, which happens also to be a log, is white (as I should if I said ‘the musician is white,’ which would mean ‘the man who happens also to be a musician is white’); on the contrary, log is here the substratum—the substratum which actually came to be white, and did so qua wood or qua some wood and qua nothing else. If we must lay down a rule, let us entitle the latter kind of statement predication, and the former not predication at all, or not strict but accidental predication. ‘White’ and ‘log’ will thus serve as types respectively of predicate and subject. We shall assume, then, that the predicate is invariably predicated strictly and not accidentally of the subject, for on such predication demonstrations depend for their force.
a21. It follows from this that when a single attribute is predicated of a single subject, the predicate must affirm of the subject either some element constituting its essential nature, or that it is in some way qualified, quantified, essentially related, active, passive, placed, or dated.
a24. (2) Predicates which signify substance signify that the subject is identical with the predicate or with a species of the predicate. Predicates not signifying substance which are predicated of a subject not identical with themselves or with a species of themselves are accidental or coincidental; a27. For example, white is a coincident of man, seeing that man is not identical with white or a species of white, but rather with animal, since man is identical with a species of animal. These predicates which do not signify substance must be predicates of some other subject, and nothing can be white which is not also other than white.
a33. The Forms we can dispense with, for they are mere sound without sense; and even if there are such things, they are not relevant to our discussion, since demonstrations are concerned with predicates such as we have defined.
That in fact the regress terminates. After showing that if there is a stop in the extremes there must be a stop in the middles, and if there is a stop in affirmatives there must be a stop in negatives, the Philosopher now shows that there is a stop in affirmatives both upwards and downwards.
And his treatment is divided into two parts. In the first part he shows his thesis “logically,” that is, through characteristics common to every syllogism, which are based on predicates considered commonly. In the second he shows the same thing analytically, that is, through characteristics proper to demonstration, which are based on per se predicates which are proper to demonstration, at: but an analytic process will show (84a8) [L. 35].
The first is divided into two parts. In the first he shows that one does not proceed to infinity in predicates which are predicated in eo quod quid (that is, pertaining to the essence of the subject). In the second he shows universally that one does not proceed to infinity in affirmative predicates, at: but as regards predicates (83a1).
He says therefore first (82b34) that since we have established that an infinite process does not occur in negatives if there is a stop in affirmatives, our present task will be to show how one speculates through logical reasons that there is a stop in those, that is, in affirmatives. (These reasons are called “logical,” because they proceed from certain common notions that pertain to the considerations of logic). Now, this truth is clear in regard to things predicated as constituting the essence of a thing, namely, the predicates from which the quod quid est, that is, the definition, is formed. For if such predicates were agreed to be infinite, the result would be that nothing can be defined, and that if something is defined, its definition cannot be known: and all because the infinite cannot be traversed. For a thing cannot be defined, or its definition known, except by reaching the ultimate through descent and the first through ascent. Therefore, if something can be defined, or if a thing’s definition can be known, then in either case this consequence will follow, namely, there is no infinite process in the aforementioned predicates, but there is a stop in them.
Then, at: but as regards predicates generally (83a1) he shows universally that there is not a process to infinity in affirmative predicates.
In regard to this he does two things. First, he prefaces certain things needed for establishing the thesis. Second, he establishes it, at: if A is a quality of B (83a36) [L. 34].
In regard to the first he does two things. First, he distinguishes per accidens from per se predicates. Second, he distinguishes among the per se predicates, at: it follows from this (83a21).
He says therefore first (83a1) that since it has been established in regard to certain predicates that there is no infinite process in them, namely, in those which are predicated as pertaining to the essence, our task is to show that this is universally so in all affirmative predicates.
And he begins his consideration with per accidens predicates in which there are three modes of true predication. One mode is when an accident is predicated of an accident, as when we say, “Something white is walking.” The second mode is when the subject is predicated of an accident, as when we say, “Something white is wood.” The third mode is when an accident is predicated of a subject, as when we say, “Wood is white,” or “Man walks.” Now, these modes of predicating are mutually other and diverse, because when its subject is predicated of an accident, say “Something white is wood,” what is signified is that the universal predicate, “wood,” is being predicated of a subject which happens to be wood, that is, this particular wood in which there is whiteness. For when I say, “Something white is wood,” the meaning is the same as “This wood which happens to be white is wood”; in other words, the sense is not that “white” is the subject of wood. And he proves this on the ground that it is either according to its totality or according to a part that a subject comes to be that which is predicated of it as of a subject, as a man comes to be white. But neither the white nor its white part, which is really white, that is, which pertains to the very essence of whiteness, becomes wood: for an accident is not the subject of change whereby wood comes to be from non-wood. But whatever begins to be such and such, comes to be it; therefore, if it does not come to be this, it is not it—unless it is granted that it always was this. But it was not always true to say that the white [object] is wood, because at some time the whiteness and the wood were not together. Therefore, since it is not true to say that the white [object] becomes wood, it is obvious that the white [object], properly and per se speaking, is not wood. Yet if it be granted that something white is wood, it is understood per accidens, namely, because that particular subject, which happens to be white, is wood. This, therefore, is the sense of any predication in which a subject is predicated of an accident. But when I say, “Wood is white,” predicating an accident of the subject, I do not signify, as I did in the previous mode of predication, that there is something else substantially white, such that to be wood happens to it:
which, of course, is signified both in the previous mode, where a subject is predicated of an accident, and in the other mode, where an accident is predicated of an accident, as when I say, “The musician is white”: for this signifies nothing but the fact that this particular man, say Socrates, who happens to be a musician, is white. But when I say, “The wood is white,” I signify that the wood itself has become the subject of white, and not that something other than the wood or other than a section of the wood (which is some wood) has become white.
Therefore, there is a difference among these three modes of predicating, because when an accident is predicated of a subject, it is not predicated in virtue of some other subject; but when the subject is predicated of an accident or an accident of an accident, the predication is made in virtue of that which is subjected to the terms acting as the subject, of which another accident is predicated accidentally in the second case, and the species of the subject is predicated essentially in the first case.
Now since in each of the above modes we use the name, 'predication', and since it lies within our power to employ names as well as to restrict them, let us agree so to use our names in the following proof that only those things are said to be predicated which are said in this way, namely, not in virtue of some other subject. Consequently, whatever is said in another way, namely, by reason of another subject, as when a subject is predicated of an accident or an accident of an accident, shall not be said to be predicated—or if it is said to be predicated, it shall be said to be predicated not absolutely but per accidens. Furthermore, that which is after the manner of “white,” let us always take on the part of the predicate, and that which is after the manner of “wood,” let it be taken on the part of the subject. Therefore, in the following proof let us suppose this always to be predicated which is predicated not per accidens, but absolutely, of that of which it is predicated. And the reason why we should use the word “predication” in this way is that we are speaking of demonstrative matters, and demonstrations use only such predications.
Then, at: it follows from this (83a21) he shows the differences among per se predicates.
In regard to this he does two things. First, he distinguishes these predicates into diverse genera. Second, he shows the differences among them, at: predicates which signify substance (83a24).
He says therefore first (83a21) that because we are saying that those things alone are being predicated which are predicated not in virtue of some other subject, and this is diversified according to the ten predicaments, it follows that whatever is thus predicated is predicated either in quod quid est, that is, after the manner of an essential predicate, or after the manner of quality or quantity or one of the other predicaments discussed in the Categories. And he adds, when one is predicated of one, because if a predicate is not one but several, it cannot be said to be predicated precisely as quid or quale, but perhaps jointly as quale quid, as when I say “Man is a white animal.”
Now it was necessary to add this because if several things are predicated of one in such a way that they function as one predicate, predications will be multipliable to infinity according to the infinite modes of combining predicates one to another. Hence when there is question of a stop in things that are predicated, it is necessary to take one thing predicated of one thing.
Then, at: predicates which signify substance (83a24) he indicates the difference among the aforesaid predicates.
In regard to this he does three things. First, he proposes the difference. Second, he clarifies it with examples, at: for example, white is a coincident (83a27). Third, he excludes an objection, at: the Forms we can dispense with (83a33).
He says therefore first (83a24) that those which signify substance must signify, in respect to that of which they are predicated, what it truly is or something that it truly is.
This can be understood in two ways: in one way, as showing a distinction on the part of the predicate which might signify either the entire essence of the subject, as a definition does (and he signifies this when he says, "what it truly is"), or part of the essence, as a genus or a difference does (and he signifies this when he says, "or something that it truly is".) In another way, and better, as showing a distinction on the part of the subject, which is sometimes convertible with an essential predicate, as the definitum with the definition (and he signifies this, when he says, "what it truly is"), and sometimes is a subjective part of the predicate, as man is of animal (and he signifies this when he says, "or something that it truly is", for man is a certain animal).
But those which do not signify substance but are said of some subject (which subject is not truly, that is, essentially, that predicate nor something of it), all such predicates are accidental.
Then, at: for example, white is a coincident (83a27) he clarifies the aforesaid difference with examples, saying that when we say, “Man is white,” the predicate is accidental, because man is not that which white truly is, that is, to be white is not the essence of man or anything of what white truly is, as was explained above. But, when it is stated, “Man is an animal,” perhaps man is that which animal truly is. For animal signifies the essence of man, because that which is man is essentially animal. And although predicates that do not signify substance are accidents, they are not predicated per accidens. For they are not predicated of some subject in virtue of some other subject; for when I say, “Man is white,” 'white' is not predicated of man by reason of some other subject’s being white in virtue of which man is called white as was explained above in regard to things predicated per accidens.
Then, at: the Forms we can dispense (83a33) he excludes an objection.
For someone could say that predicates which signify the substance are not truly and essentially that which they are predicated of, nor are they something of it; and that accidents which exist in individuals as in subjects, do not correspond to any common essential predicates, because such universal predicates signify certain separated essences always subsisting by themselves, as the Platonists say.
But he answers that if Forms, that is, Ideas, are assumed to exist, they should be happy, because according to the Platonists they have a nobler existence than the material things known to us. For the latter are particular and material, but the former universal and immaterial. For they are premonstrations, that is, certain exemplars, of material things (taking 'premonstrations' here as above, when we spoke of something being shown beforehand in order to prove something). Therefore, since they are the premonstrations or exemplars of natural things, it is necessary that in these natural things there be found certain participations of those Forms which pertain to the essences of these natural things. And thus, if such separated Forms exist, as the Platonists contend, they have nothing to do with the present matter. For we are concerned with things, the science of which is produced in us through demonstration. And these are things existing in matter and known to us and concerning which demonstrations deal. Consequently, if it be granted that “animal” is something separated, an existing premonstration, as it were, of natural animals, then when I say, “Man is an animal,” in the sense that we use this proposition in demonstrating, 'animal' signifies the essence of the natural thing concerning which the demonstration is made.