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 (1006a18), 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 (1006a32), 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 (1006a18; [611]), he argues against those who say that contradictories are true at the same time;

in the second (1011b23; [720]), against those who say that they are false at the same time, at neither can there be.

In regard to the first, he does two things.

First, he argues in a general way against those who make the aforesaid errors.

Second (1009a16; [663]), he shows how we must argue specifically against different positions, at but the same method.

In regard to the first he does two things.

First, he argues dialectically against the reasoning of those who deny the foregoing principle.

Second (1009a6; [661]), 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 (1007a20; [624]) at the words, and those who;

the third (1007b18; [636]) at, furthermore, if all;

the fourth (1008a8; [642]) at, again, either this;

the fifth (1008b2; [652]) at, again, how;

the sixth (1008b12; [654]) at, it is most evident;

and the seventh (1008b31; [659]) 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 (1006a26; [612]), he proceeds to argue from that starting point, at first of all, then.

He therefore first says (1006a18) 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 (1006a11; [609]). 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.

But if such a person does not admit this, he will not say anything meaningful, either for himself or for someone else, and it will then be idle to dispute with him. But when he has admitted this, a demonstration will at once be possible against him; for there is straightway found to be something definite and determinate which is signified by the term distinct from its contradictory, as will become clear below. Yet this will not strictly be a demonstration of the foregoing principle, but only an argument upholding this principle against those who deny it. For he who destroys reason (that is, his own intelligible expression) by saying that a term signifies nothing, must uphold its significance, because he can express what he denies only by speaking and by signifying something.

612. First of all, then (1006a26). He proceeds from the assumption he had made to prove what he intends.

First, he deals with one particular case;

second (1006a31), he treats all cases in a general way, at again, if the term.

He accordingly first says (1006a26) that, if a term signifies something, it will be evident first of all that this proposition will be true, and that its contradictory, which he denies, will be false. Thus this at least will be true: not every affirmation is true together with its negation.

613. Now by “signifying”** (1006a32). Then he shows that this applies universally to all cases, namely, that contradictories are not true at the same time. In regard to this he does four things.

First, he makes certain assumptions which are necessary for drawing his intended conclusion.

Second (1006b28; [620]), he draws his conclusion, at therefore, if it is true.

Third (1007a1; [622]), he proves one assumption which he had made, at for “being a man”.

Fourth (1007a8; [623]), he rejects a quibble, at that is to say.

In regard to the first he does three things.

First, he shows that a term signifies one thing;

second (1006b13; [616]), he shows from this that the term man signifies what being a man is, but not what it is not, at it is impossible, then.

Third (1006b22; [619]), he shows that the term man signifies one thing, at now if “man”.

He accordingly first says (1006a32) that, if the term “man” signifies one thing, let this be two-footed animal. For a term is said to signify this one thing which is the definition of the thing signified by the term, so that if two-footed animal is the being of “man” (that is, if this is what the essence of man is), this will be what is signified by the term man.

614. But if one were to say that a term signifies many things, it will signify either a finite or an infinite number of them. But if it signifies a finite number, it will differ in no way, according to another translation, from the term which is assumed to signify one thing; for it signifies many finite concepts of different things and different terms can be fitted to each single concept.

For example, if the term “man” were to signify many concepts, and the concept two-footed animal is one of them, one term is assigned to the concept man. And if there are many other concepts, many other terms may be assigned so long as those concepts are finite in number. Thus he will be forced back to the first position, that a term signifies one thing.

615. But if a term does not signify a finite number of concepts, but rather an infinite number, evidently neither reasoning nor debate will be possible. This becomes clear as follows.

Any term that does not signify one thing signifies nothing. This is proved thus. Terms signify something understood, and therefore if nothing is understood, nothing is signified. But if one thing is not understood, nothing is understood, because anyone who understands anything must distinguish it from other things. If a term does not signify one thing, then it signifies nothing at all; if terms signify nothing, discourse will be impossible, both the kind which establishes truth and the kind which refutes an assertion.

Hence it is clear that, if terms signify an infinite number of things, neither reasoning nor dispute will be possible. But if it is possible to understand one thing, a term may be given to it. So let it be held then that a term signifies something.

616. It is impossible (1006b13). He proves the second point, namely, that the term “man” does not signify “not being a man.” For a term that signifies one thing signifies not only what is one in subject (and is therefore said to be one because it is predicated of one subject), but what is one absolutely, that is, in concept. For if we wanted to say that a term signifies one thing because it signifies the attributes which are verified of one thing, it would then follow that the terms “musical,” “white,” and “man” all signify one thing, since all are verified of one thing. And from this it would follow that all things are one.

For if white is predicated of man and is therefore identical with him, then when it is also predicated of a stone it will be identical with a stone. And, since those things that are identical with one and the same thing are identical with each other, it would follow that a man and a stone are one thing and have one concept. Thus the result would be that all terms are univocal, that is, one in concept, or synonymous, as another text says, that is, meaning absolutely the same thing in subject and in concept.

617. Now, although being and non-being are verified of the same subject according to those who deny the first principle, still being a man and not being a man must differ in concept, just as white and musical differ in concept even though they are verified of the same subject. Hence it is evident that being and non-being cannot be the same in concept and in subject in the sense that they are signified by one univocal term.

618. Now it must be noted that the expression “being a man” or “to be a man” or “having the being of a man” is taken here for the quiddity of man, and therefore it is concluded from this that the term “man” does not signify not being a man as its proper concept. But because he had said above (1006a32; [614]) that the same term can signify many things according to different concepts, he therefore adds except in an equivocal sense, in order to make clear that the term “man” does not signify in a univocal sense both being a man and not being a man, but it can signify both in an equivocal sense (that is, in the sense that what we call man in one language others might call not-man in another language). For we are not debating whether the same thing can both be and not be man in name, but whether it can in fact.

619. Now if “man” (1006b22). Then he proves the third point. That the terms “man” and “not-man” do not signify the same thing, and he uses the following argument. The term “man” signifies being a man or what man is, and the term “not-man” signifies not being a man or what man is not. If, then, “man” and “not-man” do not signify something different, being a man will not differ from not being a man, or being a not-man, and therefore one of these will be predicated of the other. And they will also have one concept, for when we say that some terms signify one thing, we mean that they signify one concept, as the terms “clothing” and “garment” do. Hence, if being a man and not being a man are one in this way, that is, in concept, there will then be one concept which will signify both being a man and not being a man. But it has been granted or demonstrated that the term which signifies each is different; for it has been shown that the term “man” signifies man and does not signify not-man. Thus it is clear that being a man and not being a man do not have a single concept, and therefore the thesis that “man” and “not-man” signify different things becomes evident.

620. Therefore, if it is true (1006b28). Here he proves his main thesis from the assumptions made earlier, and he uses the following argument. A man must be a two-footed animal, as is true from the foregoing, for this is the concept which the term “man” signifies. But what is necessary cannot not be, for this is what the term necessary means—namely, unable not to be, or incapable of not being, or impossible not to be. Hence it is not possible, or incapable, or impossible for man not to be a two-footed animal. Therefore, it is evident that the affirmation and the negation cannot both be true—that is, it cannot be true that man is both a two-footed animal and not a two-footed animal. The same reasoning based on the meanings of terms can be understood to apply to what is not-man, because what is not-man must be not a two-footed animal, since this is what the term signifies. Therefore, it is impossible that a not-man should be a two-footed animal.

621. Now the things demonstrated above are useful to his thesis, because if someone were to think that the terms “man” and “not-man” might signify the same thing, or that the term “man” might signify both being a man and not being a man, his opponent could deny the proposition that man must be a two-footed animal. For he could say that it is no more necessary to say that man must be a two-footed animal than to say that he is not a two-footed animal, granted that the terms “man” and “not-man” signify the same thing, or granted that the term “man” signifies both of these, being a man and not being a man.

622. For “being a man” (1007a1). Then he proves one of the assumptions which he had made, for in order to prove that the term “man” does not signify not being a man, he assumed that being a man and not being a man are different, even though they might be verified of the same subject. His aim here is to prove this by the following argument. There is greater opposition between being a man and not being a man than between “man” and “white”; but “man” and “white” have different concepts, although they may be the same in subject. Therefore, being a man and not being a man also have different concepts.

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 (1006b13; [616]). 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 (1007a8). 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 (1007a20). 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 (1007a33; [629]), 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 (1007a33). 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.