Commentary Aristotle Metaphysics
Lecture 7. Contradictories cannot be true at the same time
The starting point of all such discussions is not the desire that someone shall state that something either is or is not, for this might perhaps be thought to be begging the question, but that he shall state something significant both for himself and for someone else; for this he must do if he is to say anything. For if he does not, no discussion will be possible for such a person either with himself or with another. But if anyone will grant this, demonstration will be possible, for there will already be something definite. But this will not have the effect of demonstrating, but of upholding, for he who destroys reason upholds reason.
First of all, then, it is evident that this at least is true, that the term “to be” or “not to be” signifies something, such that not everything will be so and not so.
Again, if the term “man” signifies one thing, let this be a two-footed animal.
Now, by “signifying one thing” I mean this. Granted that man is a two-footed animal, then if something is a man, this will be what being a man is. And it makes no difference even if someone were to say that this term signifies many things, provided that there are a definite number, for a different term might be assigned to each concept.
I mean, for example, that if one were to say that the term “man” signifies not one thing but many, one of which would have a single concept, namely, two-footed animal, there might still be many others, if only there are a limited number. For a particular term might be assigned to each concept.
However, if this were not the case, but one were to say that a term signifies an infinite number of things, evidently reasoning would be impossible; for, not to signify one thing is to signify nothing. And if words signify nothing, there will be no discourse with another or even with ourselves. For it is impossible to understand anything unless one understands one thing, but if this does happen, a term may be assigned to this thing. Let it be assumed, then, as we said at the beginning, that a term signifies something, and that it signifies one thing.
It is impossible, then, that “being a man” should mean “not being a man,” if the term “man” not only signifies something about one subject but also signifies one thing. For we do not think it fitting to identify “signifying one thing” with “signifying something about one subject,” since the terms “musical,” “white,” and “man” would then signify one thing. And therefore all things would be one, because all would be synonymous. And it will be impossible to be and not to be the same thing, except in an equivocal sense, as occurs if one whom we call “man” others call “not-man.” But the problem is not whether the same thing can at the same time be and not be a man in name, but whether it can in fact.
Now if “man” and “not-man” do not signify something different, it is evident that “not being a man” will not differ from “being a man.” Thus “being a man” will be identical with “not being a man,” for they will be one thing. For being one means this: being related as “clothing” and “garment” are if they are taken in the same sense. And if “being a man” and “not being a man” are to be one, they must signify one thing. But it has been shown that they signify different things.
Therefore, if it is true to say that something is a man, it must be a two-footed animal, for this is what the term “man” signifies. But if this is necessary, it is impossible for this very thing not to be a two-footed animal; for this is what “to be necessary” means, namely, unable not to be. Hence it cannot be true to say that the same thing is and is not a man at the same time. The same argument also applies to “not being a man.”
For “being a man” and “not being a man” signify different things, since “being white” and “being a man” are different; for there is much greater opposition in the former case, so that they signify different things. And if one were to say also that “white” signifies the same thing as “man” and is one in concept, we shall say the same thing as was said before, namely, that all things are one, and not merely opposites. But if this is impossible, then what has been said will follow.
That is to say, it will follow if our opponent answers the question. And if, in giving a simple answer to the question, he also adds the negations, he is not answering the question. For there is nothing to prevent the same thing from being man and white and a thousand other things numerically.
Still, if one asks whether it is or is not true to say that this is a man, his opponent should reply by stating something that means one thing and not add that it is also white or black or large. Indeed, it is impossible to enumerate the accidents of being, which are infinite in number; so therefore let him enumerate either all or none.
Similarly, even if the same thing is a thousand times a man and a not-man, he must not, in answering the question of whether this is a man, add that it is also at the same time a not-man, unless he also gives all the other corresponding accidents, whatever are so or are not so. And if he does not do this, there will be no debate with him.
And those who say this do away completely with substance or essence, for they must say that all attributes are accidents, and that there is no such thing as “being a man” or “being an animal.” For if there is to be such a thing as “being a man,” this will not be “being a not-man” or “not being a man”; in fact, these are the negations of it. For there was one thing which the term signified, and this was the substance of something. And to signify the substance of a thing is to signify that its being is not something else. And if being essentially a man is being essentially a not-man, then the being of man will be something else. Hence they are compelled to say that nothing will have such a concept as this, but that all attributes are accidental. For this distinguishes substance from accident; for white is an accident of man, because, while some man is white, he is not the essence of whiteness.
Moreover, if all attributes are accidental predicates, there will be no first universal. And if the accidental always implies a predication about some subject, the process must go on to infinity. But this is impossible, for no more than two terms are combined in accidental predication.
For an accident is an accident of an accident only because both are accidents of the same subject. I mean, for example, that white is an accident of musical and musical of white only because both are accidental to man; but Socrates is not musical in the sense that both are accidental to something else.
Therefore, since some accidents are predicated in the latter sense and some in the former sense, all those that are predicated in the same way as white is predicated of Socrates cannot form an infinite series in an upward direction so that there should be another accident of white Socrates. For no one thing results from all of these.
Nor again will white have another accident, such as musical, for this is no more an accident of that than that of this. And at the same time it has been established that some things are accidents in this sense and some in the sense that musical is an accident of Socrates.
And whatever attributes are predicated accidentally in the latter sense are not accidents of accidents but only those predicated in the former sense. Not all attributes, then, are said to be accidents; and thus there must be some term which also signifies substance. And if this is so, then we have proved that contradictories cannot be predicated at the same time of the same subject.
611. Here he begins to argue by means of refutation against those who deny the foregoing principle, and this is divided into two parts.
In the first, he argues against those who say that contradictories are true at the same time;
in the second, against those who say that they are false at the same time, at neither can there be.
First, he argues in a general way against those who make the aforesaid errors.
Second, he shows how we must argue specifically against different positions, at but the same method.
First, he argues dialectically against the reasoning of those who deny the foregoing principle.
Second, he shows that Protagoras’ opinion is fundamentally the same as the one just mentioned, at the doctrine of Protagoras.
In regard to the first point he gives seven arguments.
He gives the second at the words, and those who;
the third at, furthermore, if all;
the fourth at, again, either this;
the fifth at, again, how;
the sixth at, it is most evident;
and the seventh at, further, even if all.
In regard to the first he does two things.
First, he indicates the starting point from which one must proceed to argue against those who deny the first principle.
Second, he proceeds to argue from that starting point, at first of all, then.
He therefore first says that, with respect to all such unreasonable positions, there is no need for us to take as a starting point that someone wishes to suppose that this thing definitely is or is not. In other words, it is not necessary to take as a starting point some proposition in which some attribute is either affirmed or denied of a subject (for this would be a begging of the question, as was said above). But it is necessary to take as a starting point that a term signifies something both to the one who utters it, inasmuch as he himself understands what he is saying, and to someone else who hears him.