Very similar to the views which we have just mentioned is the dictum of Protagoras¹; for he said that man is the measure of all things, by which he meant simply that each individual’s impressions are positively true. But if this is so, it follows that the same thing is and is not, and is bad and good, and that all the other implications of opposite statements are true; because often a given thing seems beautiful to one set of people and ugly to another, and that which seems to each individual is the measure. This difficulty will be solved if we consider the origin of the assumption. It seems probable that it arose in some cases from the doctrine of the natural philosophers, and in others from the fact that everyone does not form the same opinion about the same things, but to some a given thing seems sweet and to others the contrary. For that nothing comes from what is not, but everything from what is, is a doctrine common to nearly all natural philosophers.² Since, then, a thing does not become white which was before completely white and in no respect not-white, that which becomes white must come from what was not-white. Hence according to this theory there would be generation from what is not, unless the same thing were originally white and not-white. However, it is not hard to solve this difficulty. We have explained in the Physics³ in what sense things which are generated are generated from what is not, and in what sense from what is. But to attach equal importance to the opinions and impressions of opposing parties is foolish, because clearly one side or the other must be wrong.⁴ This is evident from what happens in the sphere of sensation; 1063afor the same thing never seems to some people sweet and to others to the contrary unless one of the parties has the organ of sense which distinguishes the said flavors injured or impaired. Such being the case, the one party should be taken as the “measure,” and the other not. And I hold the same in the case of good and bad, and of beautiful and ugly, and of all other such qualities. For to maintain this view⁵ is just the same as to maintain that what appears to us when we press the finger below the eye and make a thing seem two instead of one must be two because it appears to be so, and then afterwards that it must be one; because if we do not interfere with our sight that which is one appears to be one. And in general it is absurd to form our opinion of the truth from the appearances of things in this world of ours which are subject to change and never remain in the same state⁶; for it is by reference to those things which are always the same state and undergo no change that we should prosecute our search for truth. Of this kind are the heavenly bodies; for these do not appear to be now of one nature and subsequently of another, but are manifestly always the same and have no change of any kind. Again, if there is motion there is also something which is moved; and everything is moved from something and into something. Therefore that which is moved must be in that from which it is to be moved, and must also not be in it; and must be moved into so-and-so and must also come to be in it; but the contradictory statements cannot be true at the same time, as our opponents allege. And if the things of our world are in a state of continuous flux and motion in respect of quantity, and we assume this although it is not true, why should they not be constant in respect of quality?⁷ It appears that not the least reason why our opponents predicate opposite statements of the same thing is that they start with the assumption that quantity is not constant in the case of bodies; hence they say that the same thing is and is not six feet long. But essence depends upon quality, and this is of a determinate, whereas quantity is of an indeterminate nature. Again, when the doctor orders them to adopt some article of diet, why do they adopt it?⁸ For on their view it is no more true that a thing is bread than that it is not; and therefore it would make no difference whether they ate it or not. But as it is, they adopt a particular food as though they knew the truth about it and it were the food prescribed; yet they ought not to do so if there were no fixed and permanent nature in sensible things and everything were always in a state of motion and flux. Again, if we are always changing and never remain the same, is it any wonder that to us, as to the diseased, things never appear the same?⁹ 1063bFor to the diseased, since they are not in the same physical condition as when they were well, sensible qualities do not appear to be the same; although this does not mean that the sensible things themselves partake of any change, but that they cause different, and not the same, sensations in the diseased. Doubtless the same must be true if the change which we have referred to takes place in us. If, however, we do not change but remain always the same, there must be something permanent. As for those who raise the aforesaid difficulties on dialectical grounds,¹⁰ it is not easy to find a solution which will convince them unless they grant some assumption for which they no longer require an explanation; for every argument and proof is possible only in this way. If they grant no assumption, they destroy discussion and reasoning in general. Thus there is no arguing with people of this kind; but in the case of those who are perplexed by the traditional difficulties it is easy to meet and refute the causes of their perplexity. This is evident from what has been already said. Thus from these considerations it is obvious that opposite statements cannot be true of the same thing at one time; nor can contrary statements, since every contrariety involves privation. This is clear if we reduce the formulae of contraries to their first principles.¹¹ Similarly no middle term can be predicated of one and the same thing of which one of the contraries is predicated.¹² If, when the subject is white, we say that it is neither white nor black, we shall be in error; for it follows that it is and is not white, because the first of the two terms in the complex statement will be true of the subject, and this is the contradictory of white. Thus we cannot be right in holding the views either of Heraclitus¹³ or of Anaxagoras.¹⁴ If we could, it would follow that contraries are predicable of the same subject; for when he¹⁵ says that in everything there is a part of everything, he means that nothing is sweet any more than it is bitter, and similarly with any of the other pairs of contraries; that is, if everything is present in everything not merely potentially but actually and in differentiation. Similarly all statements cannot be false, nor all true. Among many other difficulties which might be adduced as involved by this supposition there is the objection that if all statements were false, not even this proposition itself would be true; while if they were all true it would not be false to say that they are all false.

Every science inquires for certain principles and causes with respect to every knowable thing which comes within its scope¹⁶; 1064ae.g., the sciences of medicine and physical culture do this, and so does each of the other productive and mathematical sciences. Each one of these marks out for itself some class of objects, and concerns itself with this as with something existent and real, but not qua real; it is another science distinct from these which does this. Each of the said sciences arrives in some way at the essence in a particular class of things, and then tries to prove the rest more or less exactly. Some arrive at the essence through sense-perception, and some by hypothesis; hence it is obvious from such a process of induction that there is no demonstration of the reality or essence. Now since there is a science of nature, clearly it must be different from both practical and productive science. In a productive science the source of motion is in the producer and not in the thing produced, and is either an art or some other kind of potency; and similarly in a practical science the motion is not in the thing acted upon but rather in the agent. But the science of the natural philosopher is concerned with things which contain in themselves a source of motion. From this it is clear that natural science must be neither practical nor productive, but speculative; since it must fall under one of these classes. And since every science must have some knowledge of the essence and must use it as a starting-point, we must be careful to observe how the natural philosopher should define, and how he should regard the formula of essence—whether in the same way as the term “snub,” or rather as the term “concave.” For of these the formula of “snub” is stated in conjunction with the matter of the object, whereas that of “concave” is stated apart from the matter; since snubness is only found in the nose, which is therefore included in the formula, for “the snub” is a concave nose . Thus it is obvious that the formula of “flesh” and “eye” and the other parts of the body must always be stated in conjunction with their matter. Since there is a science of Being qua Being and separately existent, we must inquire whether this should be regarded as identical with natural science or rather as a distinct branch of knowledge. Physics deals with things which contain a source of motion in themselves, and mathematics is speculative and is a science which deals with permanent things, but not with things which can exist separately. Hence there is a science distinct from both of these, which deals with that which exists separately and is immovable; that is, if there really is a substance of this kind—I mean separately existent and immovable—as we shall endeavor to prove.¹⁷ And if there is an entity of this kind in the world of reality, here surely must be the Divine, and this must be the first and most fundamental principle. 1064bEvidently, then, there are three kinds of speculative science: physics, mathematics, and theology. The highest class of science is the speculative, and of the speculative sciences themselves the highest is the last named, because it deals with the most important side of reality; and each science is reckoned higher or lower in accordance with the object of its study. The question might be raised as to whether the science of Being qua Being should be regarded as universal or not. Each of the mathematical sciences deals with some one class of things which is determinate, but universal mathematics is common to all alike. If, then, natural substances are the first of existing things, physics will be the first of the sciences; but if there is some other nature and substance which exists separately and is immovable, then the science which treats of it must be different from and prior to physics, and universal because of its priority.