But there are some, both of those who really hold these convictions and of those who merely profess these views, who raise a difficulty; they inquire who is to judge of the healthy man, and in general who is to judge rightly in each particular case. But such questions are like wondering whether we are at any given moment asleep or awake; and all problems of this kind amount to the same thing. These people demand a reason for everything. They want a starting-point, and want to grasp it by demonstration; while it is obvious from their actions that they have no conviction. But their case is just what we have stated before¹; for they require a reason for things which have no reason, since the starting-point of a demonstration is not a matter of demonstration. The first class, then, may be readily convinced of this, because it is not hard to grasp. But those who look only for cogency in argument look for an impossibility, for they claim the right to contradict themselves, and lose no time in doing so. Yet if not everything is relative, but some things are self-existent, not every appearance will be true; for an appearance is an appearance to someone. And so he who says that all appearances are true makes everything relative. Hence those who demand something cogent in argument, and at the same time claim to make out a case, must guard themselves by saying that the appearance is true; not in itself, but for him to whom it appears, and at, the time when it appears, and in the way and manner in which it appears. And if they make out a case without this qualification, as a result they will soon contradict themselves; for it is possible in the case of the same man for a thing to appear honey to the sight, but not to the taste, and for things to appear different to the sight of each of his two eyes, if their sight is unequal. For to those who assert (for the reasons previously stated²) that appearances are true, and that all things are therefore equally false and true, because they do not appear the same to all, nor always the same to the same person, but often have contrary appearances at the same time (since if one crosses the fingers touch says that an object is two, while sight says that it is only one³), we shall say “but not to the same sense or to the same part of it in the same way and at the same time”; so that with this qualification the appearance will be true. 1011bBut perhaps it is for this reason that those who argue not from a sense of difficulty but for argument’s sake are compelled to say that the appearance is not true in itself, but true to the percipient; and, as we have said before, are compelled also to make everything relative and dependent upon opinion and sensation, so that nothing has happened or will happen unless someone has first formed an opinion about it; otherwise clearly all things would not be relative to opinion. Further, if a thing is one, it is relative to one thing or to something determinate. And if the same thing is both a half and an equal, yet the equal is not relative to the double. If to the thinking subject “man” and the object of thought are the same, “man” will be not the thinking subject but the object of thought; and if each thing is to be regarded as relative to the thinking subject, the thinking subject will be relative to an infinity of specifically different things. That the most certain of all beliefs is that opposite statements are not both true at the same time, and what follows for those who maintain that they are true, and why these thinkers maintain this, may be regarded as adequately stated. And since the contradiction of a statement cannot be true at the same time of the same thing, it is obvious that contraries cannot apply at the same time to the same thing. For in each pair of contraries one is a privation no less than it is a contrary—a privation of substance. And privation is the negation of a predicate to some defined genus. Therefore if it is impossible at the same time to affirm and deny a thing truly, it is also impossible for contraries to apply to a thing at the same time; either both must apply in a modified sense, or one in a modified sense and the other absolutely.

Nor indeed can there be any intermediate between contrary statements, but of one thing we must either assert or deny one thing, whatever it may be. This will be plain if we first define truth and falsehood. To say that what is is not, or that what is not is, is false; but to say that what is is, and what is not is not, is true; and therefore also he who says that a thing is or is not will say either what is true or what is false. But neither what is nor what is not is said not to be or to be. Further, an intermediate between contraries will be intermediate either as grey is between black and white, or as “neither man nor horse” is between man and horse. If in the latter sense, it cannot change (for change is from not-good to good, or from good to not-good); but in fact it is clearly always changing; for change can only be into the opposite and the intermediate. And if it is a true intermediate, in this case too there would be a kind of change into white not from not-white; but in fact this is not seen.⁴ 1012aFurther, the understanding either affirms or denies every object of understanding or thought (as is clear from the definition⁵) whenever it is right or wrong. When, in asserting or denying, it combines the predicates in one way, it is right; when in the other, it is wrong. Again, unless it is maintained merely for argument’s sake, the intermediate must exist beside all contrary terms; so that one will say what is neither true nor false. And it will exist beside what is and what is not; so that there will be a form of change beside generation and destruction. Again, there will also be an intermediate in all classes in which the negation of a term implies the contrary assertion; e.g., among numbers there will be a number which is neither odd nor not-odd. But this is impossible, as is clear from the definition.⁶ Again, there will be an infinite progression, and existing things will be not only half as many again, but even more. For again it will be possible to deny the intermediate in reference both to its assertion and to its negation, and the result will be something⁷; for its essence is something distinct. Again, when a man is asked whether a thing is white and says “no,” he has denied nothing except that it is 〈white〉, and its not-being 〈white〉 is a negation. Now this view has occurred to certain people in just the same way as other paradoxes have also occurred; for when they cannot find a way out from eristic arguments, they submit to the argument and admit that the conclusion is true. Some, then, hold the theory for this kind of reason, and others because they require an explanation for everything. In dealing with all such persons the starting-point is from definition; and definition results from the necessity of their meaning something; because the formula, which their term implies, will be a definition.⁸ The doctrine of Heraclitus, which says that everything is and is not,⁹ seems to make all things true; and that of Anaxagoras¹⁰ seems to imply an intermediate in contradiction, so that all things are false; for when things are mixed, the mixture is neither good nor not-good; and so no statement is true.

It is obvious from this analysis that the one-sided and sweeping statements which some people make cannot be substantially true—some maintaining that nothing is true (for they say that there is no reason why the same rule should not apply to everything as applies to the commensurability of the diagonal of a square¹¹), and some that everything is true. These theories are almost the same as that of Heraclitus. For the theory which says that all things are true and all false also makes each of these statements separately; 1012bso that if they are impossible in combination they are also impossible individually. And again obviously there are contrary statements, which cannot be true at the same time. Nor can they all be false, although from what we have said, this might seem more possible. But in opposing all such theories we must demand, as was said in our discussion above,¹² not that something should be or not be, but some significant statement; and so we must argue from a definition, having first grasped what “falsehood” or “truth” means. And if to assert what is true is nothing else than to deny what is false, everything cannot be false; for one part of the contradiction must be true. Further, if everything must be either asserted or denied, both parts cannot be false; for one and only one part of the contradiction is false. Indeed, the consequence follows which is notorious in the case of all such theories, that they destroy themselves; for he who says that everything is true makes the opposite theory true too, and therefore his own untrue (for the opposite theory says that his is not true); and he who says that everything is false makes himself a liar. And if they make exceptions, the one that the opposite theory alone is not true, and the other that his own theory alone is not false, it follows none the less that they postulate an infinite number of true and false statements. For the statement that the true statement is true is also true; and this will go on to infinity. Nor, as is obvious, are those right who say that all things are at rest; nor those who say that all things are in motion. For if all things are at rest, the same things will always be true and false, whereas this state of affairs is obviously subject to change; for the speaker himself once did not exist, and again he will not exist. And if all things are in motion, nothing will be true, so everything will be false; but this has been proved to be impossible. Again, it must be that which is that changes, for change is from something into something. And further, neither is it true that all things are at rest or in motion sometimes, but nothing continuously; for there is something ¹³ which always moves that which is moved, and the “prime mover” is itself unmoved.¹⁴