by Aristotle
If on the other hand we set up what are thought to be the most unchangeable principles, being and unity, firstly, if each of these does not indicate a ‘this’ and a [1060b1] substance, how will they be separable and independent? Yet we expect the eternal and primary principles to be so. But if each of them does signify a ‘this’ and a substance, all things that are are substances; for being is predicated of all things [5] (and unity also of some); but that all things that are are substance is false. Further, how can they be right who say that the first principle is unity and this is substance, and generate number as the first product from unity and from matter, and assert that number is substance? How are we to think of two, and each of the other [10] numbers composed of units, as one? On this point neither do they say anything nor is it easy to say anything. But if we suppose lines or what comes after these (I mean the primary plane figures) to be principles, these at least are not separable substances, but sections and divisions—the former of surfaces, the latter of solids [15] (while points are sections and divisions of lines); and further they are limits of these same things; and all these are in other things and none is separable. Further, how are we to suppose that there is a substance of unity and the point? Every substance comes into being, but the point does not; for the point is a division.
[20] A further difficulty is raised by the fact that all knowledge is of universals and of the ‘such’, but substance does not belong to universals, but is rather a ‘this’ and separable, so that if there is knowledge about the first principles, the question arises, how are we to suppose the first principle to be substance?
Further, is there anything apart from the compound thing (by which I mean [25] the matter and that which is joined with matter), or not? If not, all things that are in matter are perishable. But if there is something, it must be the form or shape. It is hard to determine in which cases this exists apart and in which it does not; for in some cases the form is evidently not separable, e.g. in the case of a house.
Further, are the principles the same in kind or in number? If they are one in [30] number, all things will be the same.
3 · Since the science of the philosopher treats of being qua being universally and not of some part of it, and ‘being’ has many senses and is not used in one only, it follows that if it is used homonymously and in virtue of no common nature, it does not fall under one science (for there is no one class in the case of such things); but if [35] it is used in virtue of some common nature, it will fall under one science. The term seems to be used in the way we have mentioned, like ‘medical’ and ‘healthy’. For [1061a1] each of these also we use in many senses; and each is used in this way because the former refers somehow to medical science and the latter to health. Other terms refer to other things, but each term refers to some one thing. For a prescription and a knife are called medical because the former proceeds from medical science, and [5] the latter is useful to it. And a thing is called healthy in the same way; one thing because it is indicative of health, another because it is productive of it. And the same is true in the other cases. Everything that is, then, is said to be in this same way; each thing is said to be because it is a modification of being qua being or a [10] permanent or a transient state or a movement of it, or something else of the sort. And since everything that is may be referred to some one common nature, each of the contrarieties also may be referred to the first differences and contrarieties of being, whether the first differences of being are plurality and unity or likeness and [15] unlikeness, or some other differences; let these be taken as already discussed. It makes no difference whether that which is be referred to being or to unity. For even if they are not the same but different, they are convertible; for that which is one is also somehow being, and that which is being is one.—But as every pair of contraries falls to be examined by one and the same science, and in each pair one term is the [20] privation of the other (though one might regarding some contraries raise the question, how they can be privatively related, viz. those which have an intermediate, e.g. unjust and just; in all such cases one must maintain that the privation is not of the whole formula, but of its extreme form; e.g. if a man is just who is by virtue of [25] some permanent disposition obedient to the laws, the unjust man need not have the whole formula denied of him, but will be in some respect deficient in obedience to the laws, and in this respect the privation will attach to him; and similarly in all other cases); and since, as the mathematician investigates abstractions (for in his investigation he eliminates all the sensible qualities, e.g. weight and lightness, [30] hardness and its contrary, and also heat and cold and the other sensible contrarieties, and leaves only the quantitative and continuous, sometimes in one, sometimes in two, sometimes in three dimensions, and the attributes of things qua quantitative and continuous, and does not consider them in any other respect, and examines the [35] relative positions of some and the consequences of these, and the commensurability and incommensurability of others, and the ratios of others; but yet we say there is [1061b1] one and the same science of all these things—geometry), the same is true with regard to being (for the attributes of this in so far as it is being, and the contrarieties in it qua being, it is the business of no other science than philosophy to investigate; [5] for to natural science one would assign the study of things not qua being, but rather qua sharing in movement; while dialectic and sophistic deal with the attributes of things that are, but not of things qua being, and not with being itself in so far as it is being);—therefore it remains that the philosopher studies the things we have [10] named, in so far as they are being. Since all that is is said to be in virtue of one common character though the term has many meanings, and contraries are in the same case (for they are referred to the first contrarieties and differences of being), and things of this sort can fall under one science, the difficulty we stated at the [15] beginning is solved,—I mean the question how there can be one science of things which are many and different in genus.
4 · Since even the mathematician uses the common axioms only in a special application, it must be the business of first philosophy to examine the principles of mathematics also. That when equals are taken from equals the remainders are [20] equal, is common to all quantities, but mathematics marks off a part of its proper matter and studies it separately, e.g. lines or angles or numbers or some other kind of quality—not, however, qua being but in so far as each of them is continuous in one or two or three dimensions; but philosophy does not inquire about particular [25] subjects in so far as each of them has such and such attributes, but considers each subject in relation to being qua being.—Natural science is in the same position as mathematics; for natural science studies the attributes and the principles of the things that are, qua moving and not qua being, whereas the primary science, we [30] have said, deals with these only in so far as the underlying subjects are existent, and not in virtue of any other character. Therefore both natural science and mathematics must be regarded as parts of Wisdom.
5 · There is a principle in things, about which we cannot be deceived, but must always, on the contrary, recognize the truth,—viz. that the same thing cannot at one and the same time be and not be, or admit any other similar pair of opposites. [1062a1] About such matters there is no proof in the full sense, though there is proof ad hominem. For it is not possible to infer this truth itself from a more certain principle, yet this is necessary if there is to be proof of it without qualification. But [5] he who wants to prove to the asserter of opposites that he is wrong must get from him an admission which shall be identical with the principle that the same thing cannot both be and not be at one and the same time, but shall not seem to be identical: for thus alone can he demonstrate his thesis to the man who says that [10] opposite statements can be truly made about the same subject. Those, then, who are to join in argument with one another must to some extent understand one another; for if this does not happen how can they join in argument with one another? Therefore every word must be intelligible and
signify something, and not many [15] things but only one; and if it signifies more than one thing, it must be made plain to which of these the word is being applied. He, then, who says this is and is not denies what he affirms, so that what the word signifies, he says it does not signify; and this is impossible. Therefore if ‘this is’ signifies something, one cannot truly assert the contradictory.
[20] Further, if the word signifies something and this can be truly asserted of it, it necessarily is this; and it is not possible that that which is necessary should ever not be; it is not possible therefore to make the opposed assertions truly of the same subject. Further, if the affirmation is no more true than the negation, he who says [25] ‘man’ will be no more right than he who says ‘not-man’. It would seem also that in saying the man is not a horse we should be either more or not less right than in saying he is not a man, so that we shall be right in saying that the same person is a horse; for it was assumed to be possible to make opposite statements equally truly. It follows then that the same person is a man and a horse, or any other animal. While, [30] then, there is no proof of the axiom without qualification, there is a proof relatively to anyone who will make these suppositions. And perhaps if we had questioned Heraclitus himself in this way we might have forced him to confess that opposite statements can never be true of the same subjects. But, as it is, he adopted his opinion without understanding what his statement involved. But in any case if what [1062b1] is said by him is true, not even this itself is true—viz. that the same thing can at one and the same time both be and not be. For as, when the statements are separated, the affirmation is no more true than the negation, in the same way—the complex [5] statement being like one affirmation—the whole taken as an affirmation will be no more true than its negation. Further, if it is not possible to affirm anything truly, this itself will be false—the assertion that there is no true affirmation. But if a true [10] affirmation exists, this appears to refute what is said by those who raise such objections and utterly destroy rational discourse.
6 · The saying of Protagoras is like the views we have mentioned; he said that man is the measure of all things, meaning simply that that which seems to each man [15] assuredly is. If this is so, it follows that the same thing both is and is not, and is bad and good, and that the contents of all other opposite statements are true, because often a particular thing appears beautiful to some and ugly to others, and that [20] which appears to each man is the measure. This difficulty may be solved by considering the source of the opinion. It seems to have arisen in some cases from the doctrine of the natural philosophers, and in others from the fact that all men have not the same views about the same things, but a particular thing appears pleasant to some and the contrary of pleasant to others.
That nothing comes to be out of that which is not, but everything out of that which is, is a doctrine common to nearly all the natural philosophers. Since, then, a [25] thing can become not-white, having been perfectly white and in no respect not-white, that which becomes white must come from that which is not-white; so that a thing must come to be out of that which is not (so they argue), unless the same thing was at the beginning both not-white and white. But it is not hard to solve [30] this difficulty; for we have said in the Physics1 in what sense things that come to be come to be from that which is not, and in what sense from that which is.
But to lend oneself equally to the opinions and the fancies of disputing parties is foolish; for clearly one of them must be mistaken. And this is evident from what happens in sensation; for the same thing never appears sweet to some and bitter to [1063a1] others, unless in the one case the sense-organ which discriminates the aforesaid flavours has been perverted and injured. And if this is so the one party must be taken to be the measure, and the other must not. And I say the same of good and [5] bad, and beautiful and ugly, and all other such qualities. For to maintain the view we are opposing is just like maintaining the truth of what appears to people who put their finger under their eye and make the object appear two instead of one, i.e. like saying that it is two (because it appears to be of that number) and again one (for to those who do not interfere with their eye the one object appears one). [10]
In general, it is absurd to make the fact that the things of this earth are observed to change and never to remain in the same state, the basis of our judgements about the truth. For in pursuing the truth one must start from the things that are always in the same state and suffer no change. Such are the heavenly [15] bodies; for these do not appear to be now of one nature and again of another, but are manifestly always the same and share in no change.
Further, if there is movement, and something moved, and everything is moved out of something and into something, it follows that that which is moved must first be in that out of which it is to be moved, and then not be in it, and move into the [20] other and come to be in it, and that the contradictory statements are not true at the same time, as our opponents assert they are.
And if the things of this earth continuously flow and move in respect of quantity—if one were to suppose this, although it is not true—why should they not endure in respect of quality? For the assertion of contradictory statements about the same thing seems to have arisen largely from the belief that the quantity of [25] bodies does not endure, so that the same thing both is and is not four cubits long. But the substance depends on quality, and this is of determinate nature, though quantity is indeterminate.
Further, when the doctor orders people to take some particular food, why do they take it? For why is this bread rather than not bread?—so that it would make [30] no difference whether one ate or not. But as a matter of fact they take it, assuming that they know the truth about it and that what has been prescribed is bread. Yet they should not, if there were no fixed constant nature in sensible things, but all moved and flowed for ever.
[35] Again, if we are always changing and never remain the same, what wonder is it if to us, as to the sick, things never appear the same? For to them also, because they [1063b1] are not in the same condition as when they were well, sensible qualities do not appear like; yet, for all that, the sensible things themselves need not share in any change, though they produce different, and not identical, sensations in the sick. And [5] the same must surely happen to the healthy if the aforesaid change takes place. But if we do not change but remain the same, there will be something that endures.
As for those to whom these difficulties are suggested by reason, it is not easy to solve the difficulties unless they will posit something and no longer demand a reason [10] for it; for it is thus that all reasoning and all proof is accomplished; if they posit nothing, they destroy discussion and all reasoning. Therefore with such men there is no reasoning. But as for those who are perplexed by the traditional difficulties, it is easy to meet them and to dissipate the causes of their perplexity. This is evident from what has been said.
[15] It is manifest, therefore, from these arguments that contradictory statements cannot be truly made about the same subject at one time, nor can contrary statements, because every contrariety depends on privation. This is evident if we reduce the formulae of contraries to their principle.
[20] Similarly, no intermediate between contraries can be predicated of one and the same subject. If the subject is white we shall be wrong in saying it is neither white nor black, for it would follow that it is and is not white; for the first of the two terms we have put together would be true of it, and this is the contradictory of white.
[25] We could not be right, then, in accepting the views either of Heraclitus or of Anaxagoras. If we were, it would follow that contraries would be predicated of the same subject, for when Anaxagoras says a portion of everything is in everything, he says nothing is sweet any more than it is bitter, and so with any other pair of contraries, since in everything everything is present not potentially only, but [30] actually and separately. And similarly all statements cannot be false nor all true, both because of many other difficulties which
might be deduced as arising from this position, and because if all are false it will not be true even to say all are false, and if [35] all are true it will not be false to say all are false.
7 · Every science seeks certain principles and causes for each of its [1064a1] objects—e.g. medicine and gymnastics and each of the other sciences, whether productive or mathematical. For each of these marks off a certain class of things for itself and busies itself about this as about something that exists and is—not however qua being; the science that does this is another distinct from these. Of the sciences [5] mentioned each gets somehow the ‘what’ in some class of things and tries to prove the other truths, whether loosely or accurately. Some get the ‘what’ through perception, others by hypothesis; so that it is clear from an induction of this sort that there is no demonstration of the substance, i.e. of the ‘what’.
There is a science of nature, and evidently it must be different both from [10] practical and from productive science. For in the case of productive science the principle of production is in the producer and not in the product, and is either an art or some other capacity. And similarly in practical science the movement is not in the thing done, but rather in the doers. But the science of the natural philosopher [15] deals with the things that have in themselves a principle of movement. It is clear from these facts, then, that natural science must be neither practical nor productive, but theoretical (for it must fall into one of these classes). And since each of the sciences must somehow know the ‘what’ and use this as a principle, we must not fail [20] to observe how the natural philosopher should define things and how he must state the formula of the substance—whether as akin to snub or rather to concave. For of these the formula of the snub includes the matter of the thing, but that of the concave is independent of the matter; for snubness is found in a nose, so that its [25] formula includes the nose—for the snub is a concave nose. Evidently then the formula of flesh and the eye and the other parts must always be stated without eliminating the matter.