LESSON 8

Other Arguments Against the Foregoing Position

Chapter 4: 1007b 18-1008b 2

             343. Furthermore, if all contradictories are true of the same subject at the same time, it is evident that all things will be one. For the same thing will be a trireme, a wall and a man, if it is possible either to affirm or to deny anything of everything.

             344. And this is what must follow for those who agree with Protagoras' view. For if it appears to anyone that a man is not a trireme, it is evident that he is not a trireme; so that he also is a trireme if contradictories are true. And thus there arises the view of Anaxagoras that all things exist together at the same time, so that nothing is truly one. Hence they seem to be speaking about the indeterminate; and while they think they are speaking about being, they are speaking about non-being; for the indeterminate is what exists potentially and is not complete.

             345. But the affirmation and the negation of every predicate of every subject must be admitted by them; for it would be absurd if each subject should have its own negation predicated of it while the negation of something else which cannot be predicated of it should not be predicated of it. I mean that, if it is true to say that a man is not a man, evidently it is also true to say that he is not a trireme. Therefore, if the affirmation is predicable of him, so also must the negation be. But if the affirmation is not predicable of him, the negation of the other term will be predicable of him to a greater degree than his own negation. If, then, the latter negation is predicable of him, the negation of trireme will also be predicable of him; and if this is predicable of him, the affirmation will be too. This is what follows, then, for those who hold this view.

             346. And it also follows for them that it is not necessary either to affirm or to deny. For if it is true that the same thing is both a man and a not-man, evidently it will be neither a man nor a not-man; for of the two affirmations there are two negations. And if the former is taken as a single proposition composed of the two, the latter also will be a single proposition opposed to the former.

             347. Again, either this is true of all things, and a thing is both white and not-white, and both being and not-being, and the same applies to other affirmations and negations; or it is not true of all but is true of some and not of others. And if not of all, the exceptions will be admitted. But if it is true of all, then either the negation will be true of everything of which the affirmation is, and the affirmation will be true of everything of which the negation is, or the negation will be true of everything of which the affirmation is, but the affirmation will not always be true of everything of which the negation is. And if the latter is true, there will be something that certainly is not, and this will be an unshakeable opinion. And if that it is not is something certain and knowable, more known indeed will be the opposite affirmation than the negation. But if in denying something it is equally possible to affirm what is denied, it is necessary to state what is true about these things, either separately (for example, to say that a thing is white and that it is not-white), or not. And if it is not true to affirm them separately, then an opponent will not be saying what he professes to say, and nothing will exist. But how could non-existent things speak or walk, as he does? Again, [according to this view] all things will be one, as has been said before (336:C 616), and man and God and a trireme and their contradictories will be the same. Similarly, if this is true of each thing, one thing will differ in no respect from another; for if it differs, this difference will be something true and proper to it. And similarly if it is possible for each to be true separately, the results described will follow. And to this we may add that all will speak the truth and all speak falsely; and that each man will admit of himself that he is in error. And at the same time it is evident that up to this point the discussion is about nothing at all, because our opponent says nothing. For he does not say that a thing is so or is not so, but that it is both so and not so; and again he denies both of these and says that it is neither so nor not so. For if this were not the case there would already be some definite statement. Further, if when the affirmation is true the negation is false, and if when the negation is true the affirmation is false, it will be impossible both to affirm and to deny the same thing truly at the same time. But perhaps someone will say that this was the contention from the very beginning.

COMMENTARY

             636. Then he gives a third argument, which involves oneness and difference. The argument runs thus: if an affirmation and a negation are true of the same subject at the same time, all things will be one. But the consequent is false. Hence the antecedent must be false. In regard to this argument he does three things.

             First (343:C 636), he lays down a conditional proposition and gives an example, namely, that if contradictories are true of the same subject at the same time, it will follow that the same thing will be a trireme (i.e., a ship with three banks of oars), a wall and a man.

             637. And this is what (344).

             Then he shows that the same impossible conclusion follows with regard to two other positions. He does this, first, with regard to the opinion of Protagoras, who said that whatever seems so to anyone is wholly true for him; for if it seems to someone that a man is not a trireme, then he will not be a trireme; and if it seems to someone else that a man is a trireme, he will be a trireme; and thus contradictories will be true.

             638. Second, he does this with regard to the opinion of Anaxagoras, who said that all things exist together, so that nothing which is truly one is distinguished from other things, but all are one in a kind of mixture. For he said that everything is found in everything else, as has been shown in Book I of the Physics. This is the position which Anaxagoras adopted because he seems to be speaking about indeterminate being, i.e., what has not been made actually determinate. And while he thought he was speaking about complete being, he was speaking about potential being, as will become clear below (355:C 667). But the indeterminate is what exists potentially and is not "complete," i.e., actual; for potency is made determinate only by actuality.

             639. But the affirmation (345).

             Third, he proves that the first conditional proposition is true. He does this, first, on the grounds that all things would have to be affirmed to be one; and second (346:C 640), on the grounds that affirmations would not be distinguished from their negations from the viewpoint of truth and falsity ("And it also follows").

             He accordingly says, first (345), that the first conditional proposition must be admitted by them inasmuch as they hold than an affirmation and a negation are true of the same subject at the same time because an affirmation and a negation are true of anything at all. For it is clear that the negation of some other thing seems to be predicable of each thing to a greater degree than its own negation. For it would be absurd if some subject should have its own negation predicated of it and not the negation of something else by which it is signified that this other thing is not predicable of it. For example, if it is true to say that a man is not a man, it is much truer to say that a man is not a trireme. Hence it is clear that anything of which a negation must be predicated must also have an affirmation predicated of it. Therefore a negation will be predicated of it since an affirmation and a negation are true at the same time; or if an affirmation is not predicated of it, the negation of the other term will be predicated of it to a greater degree than its own negation. For example, if the term trireme is not predicable of man, non-trireme will be predicated of him inasmuch as it may be said that a man is not a trireme. But if the affirmation is predicable, so also must the negation be, since they are verified of the same thing. A man, then, must be a trireme, and he must also be anything else on the same grounds. Hence all things must be one. Therefore this is what follows for those who maintain the position that contradictories are true of the same subject.

             640. And it also follows (346).

             He now draws the other impossible conclusion which follows from this view, namely, that a negation will not be distinguished from an affirmation as regards falsity, but each will be false. Thus he says that not only the foregoing impossible conclusions follow from the above-mentioned position, but also the conclusion that it is not necessary "either to affirm or to deny," i.e., it is not necessary that either the affirmation or the negation of a thing should be true, but each may be false; and so there will be no difference between being true and being false. He proves this as follows.

             641. If it is true that something is both a man and a not-man, it is also true that it is neither a man nor a not-man. This is evident. For of these two terms, man and not-man, there are two negations, not man and not not-man. And if one proposition were formed from the first two, for example, if one were to say that Socrates is neither a man nor a not-man, it would follow that neither the affirmation nor the negation is true but that both are false.

             642. Again, either this (347).

             Then he gives a fourth argument, and this is based on certitude in knowing. It runs thus. If an affirmation and a negation are true at the same time, either this is true of all things, or it is true of some and not of others. But if it is not true of all, then those of which it is true will be "admitted"; i.e., they will be conceded simply and absolutely, or according to another translation "they will be certain," i.e., true with certainty; that is, in their case the negation will be true because the affirmation is false, or the reverse.

             643. But if it is true in all cases that contradictories are verified of the same subject, this might happen in two ways. In one way anything of which affirmations are true, negations are true, and the reverse. In another way anything of which affirmations are true, negations are true, but not the reverse.

             644. And if the second is true, this impossible conclusion will follow: there will be something that firmly or certainly is not; and so there will be an unshakeable opinion regarding a negative proposition. And this will be the case because a negation is always true since whenever an affirmation is true its negation is also true. But an affirmation will not always be true, because it was posited that an affirmation is not true of anything at all of which a negation is true; and thus a negation will be more certain and knowable than an affirmation. But this seems to be false because, even though non-being is certain and knowable, an affirmation will always be more certain than its opposite negation; for the truth of a negation always depends on that of some affirmation. Hence a negative conclusion can be drawn only if there is some kind of affirmation in the premises. But an affirmative conclusion can never be drawn from negative premises.

             645. Now if one were to speak in the first way and say that of anything of which an affirmation is true the negation is also true, and similarly that of anything of which the negation is true the affirmation is also true, inasmuch as affirmation and negation are interchangeable, this might happen in two ways. For if an affirmation and a negation are both true at the same time, either it will be possible to state what is true of each separately, for example, to say that each of these propositions is true separately--"Man is white" and "Man is not white"; or it will not be possible to state that each is true separately but only both together. For example, if we were to say that this copulative proposition is true--"Man is white and man is not white."

             646. And if we were to speak in the second way and say that neither one is true separately but only both together, two impossible conclusions would then follow. The first is that "an opponent will not be saying what he professes to say," i.e., he will assert neither the affirmation nor the negation of something, and "neither will exist," i.e., both will be false; or according to another text, "nothing will exist," i.e., it will follow that nothing is true, neither the affirmation nor the negation. And if nothing is true it will be impossible to understand or to express anything. For how can anyone understand or express non-being? Implied is the reply: in no way.

             647. The second impossible conclusion would be that all things are one, as has been stated in a previous argument (345:C 639). For it would follow that a man and God and a trireme, and also their contradictories, a not-man, not-God and not-trireme, are the same. Thus it is clear that, if an affirmation and a negation are true of any subject at the same time, one thing will not differ from another. For if one were to differ from another, something would have to be predicated of the one which is not predicated of the other; and so it would follow that something is definitely and properly true of this thing which does not fit the other. Therefore an affirmation and a negation will not be true of anything whatever. But it is clear that things which differ in no way are one. Thus it would follow that all things are one.

             648. But if one were to speak in the first way and say that it is possible for an affirmation and a negation to be true, not only together but also separately, four impossible conclusions will follow. The first is that this position "indicates that this statement is true"; i.e., it proves that the statement just made is true. Hence another text reads, "the results described will follow," i.e., all things will be one, because it will then be possible both to affirm and to deny each thing, and one will not differ from the other.

             649. A second impossible conclusion is that all will speak the truth, because anyone at all must make either an affirmation or a negation, and each will be true. And each man will also admit of himself that he is wrong when he says that the affirmation is true; for, since he says that the negation is true, he admits that he was in error when he made the affirmation.

             650. A third impossible conclusion is that up to this point there obviously could not be any investigation or dispute. For it is impossible to carry on a dispute with someone who admits nothing, because such a person really says nothing since he does not say absolutely that something is so or is not so; but he says that it is both so and not so. And again he denies both of these, for he says that it is neither so nor not so, as is evident from the preceding argument. For if he does not deny all of these he will know that something is definitely true, and this is contrary to his original position. Or according to another translation which expresses this more clearly, "there would already be some definite statement."

             651. A fourth impossible conclusion will follow because of the definition of the true and the false. For truth exists when one says that what is, is, or that what is not, is not. But falsity exists when one says that what is, is not, or that what is not, is. Hence from the definition of the true and the false it is clear that, when an affirmation is true, its negation is false; for one then says that what is, is not. And when a negation is true, its affirmation is false; for what is not is then said to be. Therefore it is impossible both to affirm and to deny the same thing truly. But perhaps an opponent could say that this last argument is begging the question; for he who claims that contradictories are true at the same time does not accept this definition of the false: the false is to say that what is not, is, or that what is, is not.