LESSON 16

No Intermediate between Contradictories. How Heraclitus and Anaxagoras Influenced This Position

Chapter 7: 1011b 23-1012a 28

             383. Neither can there be an intermediate between contradictories, but of each subject it is necessary either to affirm or to deny one thing. This first becomes evident when people define what truth and falsity are; for to say that what is, is not, or that what is not, is, is false; and to say that what is, is, or that what is not, is not, is true. Hence he who affirms that something is or is not will say either what is true or what is false. But neither what is nor what is not is said to be or not to be.

             384. Further, an intermediate between contradictories will be such either in the way that green is an intermediate between white and black, or as what is neither a man nor a horse is an intermediate between a man and a horse. If it is of the latter sort, there will then be no change; for change is from what is good to what is not-good, or from the latter to the former. But that this now occurs is always apparent; for change takes place only between opposites and intermediates. But if it is a true intermediate, then in this case there will be a kind of change to something white, but not from what is not-white. However, this is not now apparent.

             385. Further, the mind either affirms or denies every sensible and intelligible object. This is clear from the definition, because it expresses what is true or what is false. Indeed, when the mind composes in this way by affirming or denying, it says what is true; and when it does it otherwise, it says what is false.

             386. Again, there must be an intermediate in addition to all contradictories, unless one is arguing for the sake of argument. In that case one will say what is neither true nor false. And then there will be something else besides being and non-being; and therefore there will also be some kind of change besides generation and corruption.

             387. Again, there will also be an intermediate in all those classes of things in which the negation of a term implies its contrary; for example, in the class of numbers there will be a number which is neither even nor odd. But this is impossible, as is evident from the definition.

             388. Further, there will be an infinite regress, and there will be things which are related not only as half again as much but even more. For it will also be possible to deny the intermediate both with reference to its affirmation and to its negation; and this again will be something, for its substance is something different.

             389. Again, when one answers "no" to the question whether a thing is white, he has denied nothing except that it is; and its not-being is a negation.

             390. Now some men have formed this opinion in the same way that other unreasonable opinions have been formed; for when they cannot refute eristic arguments, they assent to the argument and claim that the conclusion is true. Some men hold this view, then, for this reason, and others because they seek an explanation for everything.

             391. The starting point to be used against all of these people is the definition, and the definition results from the necessity of their meaning something; for the concept, of which the word is a sign, is a definition.

             392. Now the statement of Heraclitus, which says that all things are and are not, seems to make all things true; and the statement of Anaxagoras that there is an intermediate between contradictories seems to make everything false; for when all things are mixed together, the mixture is neither good nor not good, so that it is impossible to say anything true.

COMMENTARY

             720. Having argued dialectically against those who maintain that contradictories are true at the same time, Aristotle now argues against those who maintain that there is an intermediate between contradictories; for these thinkers do not always say that the one or the other part of a contradiction is true. In regard to this he does two things. First (383:C 720), he argues against this position. Second (393:C 736), he argues against certain other unreasonable questions which follow from this position and from the one above ("With these points").

             In regard to the first he does two things. First, he raises arguments against the position mentioned. Second (390:C 731), he gives the reason why some thinkers have been moved to hold this position ("Now some men").

             In regard to the first part he gives seven arguments. He says, first (383), that, just as contradictories cannot be true at the same time, neither can there be an intermediate between contradictories, but it is necessary either to affirm or deny one or the other.

             721. This first becomes evident from the definition of truth and falsity; for to say what is false is simply to say that what is, is not, or that what is not, is. And to say what is true is simply to say that what is, is, or that what is not, is not. It is clear, then, that whoever says that something is, says either what is true or what is false; and if he says what is true, it must be so, because to say what is true is to say that what is, is. And if he says what is false, it must not be so, because to say what is false is simply to say that what is, is not. The same thing applies if he says that something is not; for if he says what is false, it must be; and if he says what is true, it must not be. Therefore, either the affirmation or the negation is necessarily true. But he who holds that there is an intermediate between contradictories does not claim that it is necessary to say that what is either is or is not; nor does he claim that it is necessary to speak in this way about what is not. Thus neither he who affirms nor he who denies need say what is true or what is false.

             722. Further, an intermediate (384).

             He gives the second argument, which runs thus: an intermediate between any two contradictories can be understood in one way as something that participates in each of the extremes, and this is an intermediate in the same genus, as green or yellow is an intermediate between white and black; or in another way as something that is the negation of each extreme, and such an intermediate is different in genus; for example, a stone, which is neither a man nor a horse, is an intermediate between a man and a horse. Therefore, if there is an intermediate between contradictories, it will be such either in the first way or in the second.

             723. If it is an intermediate in the second way, there will be no change. This becomes clear as follows: every change is from what is not-good to what is good, or from what is good to what is not-good. Hence, since change is between contraries, for example, white and black, change must take place between things which are opposed as contradictories; for black is not white, as is clear from the above statements. But according to the foregoing position there cannot be change from what is not-good to what is good, or the reverse. Hence there will be no change. Yet it always appears or seems that change proceeds from what is not-good to what is good, or the reverse. That every change of this sort would be destroyed if the foregoing position is true becomes clear as follows. Change can take place only between contraries and intermediates which belong to the same genus. But there can be a change from one extreme to another only through an intermediate. Therefore, if there is an intermediate between contradictories as the negation of both, i.e., as something belonging to a different genus, it will be impossible for change to take place between an extreme and an intermediate, and therefore between one extreme and another.

             724. And if it is an intermediate in the first way, so that the intermediate between contradictories belongs to the same genus by participating in both, as yellow is an intermediate between white and black, this impossible conclusion follows: there will be some process of generation which terminates in white and does not come from the not-white, because change proceeds not only from one extreme to another but also from an intermediate. But it does not seem to be true that there is any process of change terminating in the white which does not proceed from the not-white. Thus it is clear that there is no way at all in which there can be an intermediate between contradictories.

             725. Further, the mind (385).

             He gives the third argument, which runs thus: in every one of the conceptions by which the intellect knows or understands, it either affirms or denies something. Now from the definition of truth and falsity it seems that whether one affirms or denies he must say what is true or what is false; because when the intellect composes in this way, either by affirming or denying as the matter stands in reality, it expresses what is true; but when it does it otherwise, it expresses what is false. Thus it is clear that a true statement must always be either an affirmation or a negation, because some opinion must be true, and every opinion is either an affirmation or a negation. Hence it must always be either an affirmation or a negation that is true; and thus there is no intermediate between contradictories.

             726. Again, there must (386).

             Then he gives the fourth argument, which runs thus: if one maintains that there must be an intermediate between contradictories, then it is necessary to say that in the case of all contradictories there must be besides the contradictories themselves something true which is an intermediate between them, unless this person is arguing "for the sake of argument," i.e., without any real reason but only because it pleases him to speak in this way. But this cannot be true in all cases, because the true and the not-true are contradictories. Thus it would follow that there is someone who says what is neither true nor false. But the opposite of this was made clear from the definition of truth and falsity.

             727. Similarly, since being and nonbeing are contradictories, it will follow that there is something besides being and non-being, and thus there will be some kind of change besides generation and corruption; for generation is a change to being, and corruption a change to non-being. Therefore there can be no intermediate between contradictories.

             728. Again, there will (387).

             He gives the fifth argument. He says that in some genera a negation takes the place of a contrary difference; or, according to another text, "negation supplies the contrary," because one of two contraries, which must be in the same genus, derives its definition from negation, as is clear in the case of the even and the odd, and the just and unjust. Therefore, if there is an intermediate between affirmation and negation, there will be some intermediate between all these contraries, since they obviously depend on affirmation and negation; for example, in the case of number, there will be some number which is neither even nor odd. But this is clearly impossible in the light of the definition of the even and the odd; for the even is what can be divided into equal numbers, and the odd is what cannot. Therefore it follows that there cannot be an intermediate between affirmation and negation.

             729. Further, there will (388).

             He now gives the sixth argument: those who claim that there is an intermediate between an affirmation and a negation hold some third thing besides these two, which all posit in common, saying that there is nothing intermediate between them. But three is related to two "as half again as much," i.e., in a proportion of one and a half to one. Therefore, according to the opinion of those who hold an intermediate between an affirmation and a negation it appears at first sight that all things "will be related as half again as much," i.e., in a proportion of one and a half to one to the things which are given, because there will be not only affirmations and negations but also intermediates. And this is not the only conclusion that follows, but it also follows that there will be many more things in infinite regression. For it is evident that everything which can be affirmed can also be denied. But if it is possible to affirm that the following three things exist: an affirmation, a negation and an intermediate, it is then also possible to deny these three. And just as a negation differs from an affirmation, in a similar way there will also be some fourth thing which differs from the three mentioned; for it will have a different substance and intelligible structure than those just mentioned, in the same way that a negation has a different substance and intelligible structure from an affirmation. And it is possible to deny these four, and the negations of these will be true; and so on to infinity. Hence there will be infinitely more things than have just been posited. This seems absurd.

             730. Again, when one (389).

             He gives the seventh argument, and it runs as follows: if someone were to ask whether a man or some other thing is white, the one answering him must say either "yes" or "no." If he says "yes," it is plain that he says that the affirmation is true; but if he does not affirm this but says "no," it is clear that he denies this. Now the only thing which he denies is what he was asked, and the negation of this is non-being because it is negative. Therefore it follows that, when he answers this question, he must of necessity either admit the affirmative or assert the negative. Hence there is no intermediate between these two.

             731. Now some men (390).

             He gives the reason why some men adopt this opinion, and in regard to this he does three things. First, he shows why some men have held this opinion. Second (391:C 733), he explains how one can argue dialectically against them ("The starting point"). Third (392:C 734), he notes the philosophical views on which the foregoing opinions depend ("Now the statement").

             He accordingly says, first (390), that the foregoing opinion, like other unreasonable opinions, is adopted by certain thinkers for one of two reasons. The first is this: when some men cannot refute "eristic arguments," i.e., disputatious or sophistical arguments, which are presented to them either by others or by themselves, they agree with the one giving the argument and assent to the conclusion, saying that what has been shown is true. And then they try to confirm this by devising other arguments.

             732. The second reason why men adopt this position is that some men want to discover an argument to prove everything, and therefore whatever cannot be proved they do not want to affirm but deny. But first principles, which are the common conceptions of all men, cannot be proved. Hence these men deny them and thereby adopt unreasonable views.

             733. The starting point (391).

             He indicates the starting point from which one must proceed to argue against such opinions. He says that the starting point is derived from the definitions of truth and falsity, or from the definitions of other terms, as is clear from the arguments given above. For men must admit the definitions of things if they hold that words signify something; for the intelligible expression of a thing which a word signifies is a thing's definition. But if they do not admit that all words signify something, they do not differ from plants, as has been said above (348:C 652).

             734. Now the statement (392).

             Here he gives the opinion on which the foregoing opinions depend. He says that these opinions stem from the position of Heraclitus, who said that all things are in motion, and therefore that they both are and are not at the same time. And since what is being moved has non-being mixed with being, it follows that everything is true.

             735. And from the position of Anaxagoras it follows that there is an intermediate between contradictories; for he held that everything is mixed with everything, because everything comes from everything. But neither of the extremes can be predicated of the mixture; for example, intermediate colors are neither whiteness or blackness. Hence the mixture is neither good nor not-good, neither white nor not-white; and thus there is an intermediate between contradictories. It follows, then, that everything is false; for according to the common opinion we posit nothing but affirmation and negation. Hence, if both an affirmation and its negation are false, it follows that everything is false.