Commentary Aristotle Metaphysics
He proves the minor thus. If all attributes which are predicated of the same subject have the same concept and are signified by one term, it follows that all are one, as has been stated and explained. Now if this is impossible, the position we have maintained follows, namely, that being a man and not being a man are different. And for this reason the final conclusion given above will follow, namely, that man is a two-footed animal, and that it is impossible for him to be what is not a two-footed animal.
623. That is to say. He rejects one quibble by which the foregoing process of reasoning could be obstructed. For when an opponent has been asked whether man must be a two-footed animal, he need not reply either affirmatively or negatively, but could say that man must be both a two-footed animal and not a two-footed animal. But the Philosopher rejects this here, saying that the foregoing conclusion follows so long as an opponent wishes to give a simple answer to the question.
But if in giving a simple answer to the question on the side of the affirmative he also wishes to include in his answer the negative aspect, he will not be answering the question. He proves this as follows. One and the same thing can be both a man and white and a thousand other things of this kind. Yet if it is asked here whether a man is white, we must give in our answer only what is signified by one word, and not add all the other attributes.
For example, if one asks whether this is a man, we must answer that it is a man, and not add that it is both a man and white and large and the like. For we must give either all of the accidents of a thing at once or none. But not all accidents can be given at once since they are infinite in number, for there are an infinite number of accidents belonging to one and the same thing by reason of its relationship to an infinite number of antecedents and consequents, and what is infinite in number cannot be traversed.
In answering the question, then, we must not give any of the attributes which are accidental to the thing about which the question is raised but only the attribute which is asked for. Hence, even if it is supposed a thousand times that man and not-man are the same, still, when the question is asked about man, the answer must not include anything about not-man, unless all those things that are accidental to man are given. And if this were done, no dispute would be possible, because it would never reach completion, since an infinite number of things cannot be traversed.
624. And those who. Then he gives the second argument, and it is based on the notion of substantial and accidental predicates. This is his argument. If an affirmation and a negation are verified of the same subject, it follows that no term will be predicated quidditatively, or substantially, but only accidentally. Therefore, there will have to be an infinite regress in accidental predicates. But the consequent is impossible, and thus the antecedent must be impossible.
625. In this argument he does two things.
First, he gives a conditional proposition.
Second, he gives a proof that destroys the consequent, at moreover, if all.
Regarding the first part he proceeds as follows. He says that those who state that an affirmation and a negation may be true at the same time completely do away with substance, that is, with a substantial predicate, or essence, that is, with an essential predicate. For they must say that all attributes are accidents, or accidental predicates, and that there is no such thing as being a man or being an animal, and that what the quiddity of man or the quiddity of animal signifies does not exist.
626. He proves this as follows. If there is something which is being a man, that is, which is the substantial essence of man, which is predicated of man, it will not be not being a man or being a not-man. For these two—not being a man and being a not-man—are the negations of being a man. It is clear, then, that an affirmation and a negation are not verified of the same subject, for not being a man or being a not-man is not verified of being a man.
627. And the assumption made—namely, that if there is such a thing as being a man, this will not be not being a man or being a not-man—he proves in the following way. It was posited and proved above that the thing which a term signifies is one. And it was also posited that the thing which a term signifies is the substance of something, namely, a thing’s quiddity. Hence it is clear that some term signifies a thing’s substance, and that the thing which was signified is not something else. Therefore, if the essence or quiddity of man should be either not being a man or being a not-man, it is quite clear that it would differ from itself. It would be necessary to say, then, that there is no definition signifying a thing’s essence. But from this it would follow that all predicates are accidental ones.
628. For substance is distinguished from accident (that is, a substantial predicate is distinguished from an accidental one) in that each thing is truly what is predicated substantially of it. Thus it cannot be said that a substantial predicate is not one thing, for each thing exists only if it is one. But man is said to be white because whiteness or white is one of his accidents, although not in such a way that he is the very essence of white or whiteness. It is not necessary, then, that an accidental predicate should be one only, but there can be many accidental predicates. A substantial predicate, however, is one only; and thus it is clear that what being a man is, is not what not being a man is. But if a substantial predicate is both, it will no longer be one only, and thus will not be substantial, but accidental.
629. Moreover, if all. He destroys the consequent, showing that it is impossible that all predicates should be accidental and none substantial, for if all were accidental, there would be no universal predicate. (And “universal predicate” here means the same thing as it does in the Posterior Analytics, namely, an attribute which is predicated of something in virtue of itself and in reference to what it itself is.) But this is impossible, for if one attribute is always predicated of another accidentally, there will be an infinite regress in accidental predication, which is impossible for this reason.
630. There are only two ways in which accidental predication occurs.
One way is when one accident is predicated accidentally of another, and this happens because both are accidents of the same subject (for example, when white is predicated of musical because both are accidents of man).
The other way is had when an accident is predicated of a subject (as when Socrates is said to be musical), not because both are accidents of some other subject, but because one of them is an accident of the other.
Hence, even though there are two ways in which accidents may be predicated, in neither way can there be an infinite regress in predication.
631. For it is clear that there cannot be an infinite regress in that way in which one accident is predicated of another, because one must reach some subject. For it has been stated already that the notion of this kind of predication is that both accidents are predicated of one subject. And thus by descending from a predicate to a subject, the subject itself can be found to be the terminus.
632. And there cannot be an infinite regress in an upward direction when an accident is predicated of a subject (as when Socrates is said to be white) by ascending from a subject to a predicate so as to say that white is an accident of Socrates and that some other attribute is an accident of white Socrates. For this could occur only in two ways.
One way would be that one thing would come from white and Socrates; and thus, just as Socrates is one subject of whiteness, in a similar way white Socrates would be one subject of another accident. But this cannot be so, because one thing does not come from all of these predicates. For what is one in an absolute sense does not come from a substance and an accident in the way that one thing comes from a genus and a difference. Hence it cannot be said that white Socrates is one subject.
633. The other way would be that, just as Socrates is the subject of whiteness, in a similar way, some other accident, such as musical, would have whiteness as its subject. But neither can this be so, and for two reasons.
First, there can be no special reason why musical should be said to be an accident of white rather than the reverse; neither white nor musical will be prior to the other, but they will rather be of equal rank.
Second, in conjunction with this, it has been established or determined at the same time that this way of predicating in which an accident is predicated of an accident differs from that in which an accident is predicated of a subject, as when musical is predicated of Socrates. But in the way of which he is now speaking, accidental predication does not mean that an accident is predicated of an accident, but it is to be so taken in the way we first described.
634. It is evident, then, that an infinite regress in accidental predication is impossible, and therefore that not all predications are accidental. And it is also evident that there will be some term which signifies substance, and that contradictories are not true of the same subject.
635. Now with regard to the argument given it must be noted that, even though one accident is not the subject of another, and thus one accident is not related to the other as its subject, still one is related to the other as cause and thing caused. For one accident is the cause of another. Heat and moistness, for example, are the cause of sweetness, and surface is the cause of color. For a subject is receptive of another accident because it is receptive of one.