The Basic Works of Aristotle (Modern Library Classics)

by Mckeon, Richard

  But the measure is not always one in number—sometimes there are several; e. g. the quarter-tones (not to the ear, (15) but as determined by the ratios) are two, and the articulate sounds by which we measure are more than one, and the diagonal of the square and its side are measured by two quantities, and all spatial magnitudes reveal similar varieties of unit. Thus, then, the one is the measure of all things, because we come to know the elements in the substance by dividing the things either in respect of quantity or in respect of kind. (20) And the one is indivisible just because the first of each class of things is indivisible. But it is not in the same way that every ‘one’ is indivisible, e. g. a foot and a unit; the latter is indivisible in every respect, while the former must be placed among things which are undivided to perception, as has been said already5—only to perception, for doubtless every continuous thing is divisible.

  The measure is always homogeneous with the thing measured; the measure of spatial magnitudes is a spatial magnitude, (25) and in particular that of length is a length, that of breadth a breadth, that of articulate sound an articulate sound, that of weight a weight, that of units a unit. (For we must state the matter so, and not say that the measure of numbers is a number; we ought indeed to say this if we were to use the corresponding form of words, but the claim does not really correspond—it is as if one claimed that the measure of units is units, (30) and not a unit; number is a plurality of units.)

  Knowledge, also, and perception, we call the measure of things for the same reason, because we come to know something by them—while as a matter of fact they are measured rather than measure other things. But it is with us as if some one else measured us and we came to know how big we are by seeing that he applied the cubit-measure to such and such a fraction of us. But Protagoras says ‘man is the measure of all things’, (35) as if he had said ‘the man who knows’ or ‘the man who perceives’; and these because they have respectively knowledge and perception, which we say are the measures of objects. [1053b] Such thinkers are saying nothing, then, while they appear to be saying something remarkable.

  Evidently, then, unity in the strictest sense, if we define it according to the meaning of the word, is a measure, and most properly of quantity, (5) and secondly of quality. And some things will be one if they are indivisible in quantity, and others if they are indivisible in quality; and so that which is one is indivisible, either absolutely or qua one.

  2 With regard to the substance and nature of the one we must ask in which of two ways it exists. (10) This is the very question that we reviewed6 in our discussion of problems, viz. what the one is and how we must conceive of it, whether we must take the one itself as being a substance (as both the Pythagoreans say in earlier and Plato in later times), or there is, rather, an underlying nature and the one should be described more intelligibly and more in the manner of the physical philosophers, (15) of whom one says the one is love, another says it is air, and another the indefinite.7

  If, then, no universal can be a substance, as has been said8 in our discussion of substance and being, and if being itself cannot be a substance in the sense of a one apart from the many (for it is common to the many), (20) but is only a predicate, clearly unity also cannot be a substance; for being and unity are the most universal of all predicates. Therefore, on the one hand, genera are not certain entities and substances separable from other things; and on the other hand the one cannot be a genus, for the same reasons for which being and substance cannot be genera.

  Further, the position must be similar in all the kinds of unity. Now ‘unity’ has just as many meanings as ‘being’; so that since in the sphere of qualities the one is something definite—some particular kind of thing—and similarly in the sphere of quantities, (25) clearly we must in every category ask what the one is, as we must ask what the existent is, since it is not enough to say that its nature is just to be one or existent. But in colours the one is a colour, e. g. white, and then the other colours are observed to be produced out of this and black, (30) and black is the privation of white, as darkness of light. Therefore if all existent things were colours, existent things would have been a number, indeed, but of what? Clearly of colours; and the ‘one’ would have been a particular ‘one’, i. e. white. And similarly if all existing things were tunes, they would have been a number, (35) but a number of quarter-tones, and their essence would not have been number; and the one would have been something whose substance was not to be one but to be the quarter-tone. [1054a] And similarly if all existent things had been articulate sounds, they would have been a number of letters, and the one would have been a vowel. And if all existent things were rectilinear figures, they would have been a number of figures, and the one would have been the triangle. And the same argument applies to all other classes. Since, therefore, while there are numbers and a one both in affections and in qualities and in quantities and in movement, (5) in all cases the number is a number of particular things and the one is one something, and its substance is not just to be one, the same must be true of substances also; for it is true of all cases alike.

  That the one, then, in every class is a definite thing, (10) and in no case is its nature just this, unity, is evident; but as in colours the one-itself which we must seek is one colour, so too in substance the one-itself is one substance. That in a sense unity means the same as being is clear from the facts that its meanings correspond to the categories one to one, and it is not comprised within any category (e. g. it is comprised neither in ‘what a thing is’ nor in quality, (15) but is related to them just as being is); that in ‘one man’ nothing more is predicated than in ‘man’ (just as being is nothing apart from substance or quality or quantity); and that to be one is just to be a particular thing.

  3 The one and the many are opposed in several ways, (20) of which one is the opposition of the one and plurality as indivisible and divisible; for that which is either divided or divisible is called a plurality, and that which is indivisible or not divided is called one. Now since opposition is of four kinds, and one of these two terms is privative in meaning, they must be contraries, and neither contradictory nor correlative in meaning.9 (25) And the one derives its name and its explanation from its contrary, the indivisible from the divisible, because plurality and the divisible is more perceptible than the indivisible, so that in definition plurality is prior to the indivisible, because of the conditions of perception.

  To the one belong, as we indicated graphically in our distinction of the contraries,10 (30) the same and the like and the equal, and to plurality belong the other and the unlike and the unequal. ‘The same’ has several meanings; (1) we sometimes mean ‘the same numerically’; again, (2) we call a thing the same if it is one both in definition and in number, e. g. you ate one with yourself both in form and in matter; and again, (35) (3) if the definition of its primary essence is one; e. g. equal straight lines are the same, and so are equal and equal-angled quadrilaterals; there are many such, but in these equality constitutes unity. [1054b]

  Things are like if, not being absolutely the same, nor without difference in respect of their concrete substance, (5) they are the same in form; e. g. the larger square is like the smaller, and unequal straight lines are like; they are like, but not absolutely the same. Other things are like, if, having the same form, and being things in which difference of degree is possible, they have no difference of degree. Other things, if they have a quality that is in form one and the same—e. g. whiteness—in a greater or less degree, (10) are called like because their form is one. Other things are called like if the qualities they have in common are more numerous than those in which they differ—either the qualities in general or the prominent qualities; e. g. tin is like silver, qua white, and gold is like fire, qua yellow and red.

  Evidently, then, ‘other’ and ‘unlike’ also have several meanings. And the other in one sense is the opposite of the same (so that everything is either the same as or other than everything else). (15) In another sense things are ot
her unless both their matter and their definition are one (so that you are other than your neighbour). The other in the third sense is exemplified in the objects of mathematics. ‘Other or the same’ can therefore be predicated of everything with regard to everything else—but only if the things are one and existent, for ‘other’ is not the contradictory of ‘the same’; which is why it is not predicated of non-existent things (while ‘not the same’ is so predicated). (20) It is predicated of all existing things; for everything that is existent and one is by its very nature either one or not one with anything else.

  The other, then, and the same are thus opposed. But difference is not the same as otherness. For the other and that which it is other than need not be other in some definite respect (for everything that is existent is either other or the same), (25) but that which is different is different from some particular thing in some particular respect, so that there must be something identical whereby they differ. And this identical thing is genus or species; for everything that differs differs either in genus or in species, in genus if the things have not their matter in common and are not generated out of each other (i. e. if they belong to different figures of predication), and in species if they have the same genus (‘genus’ meaning that identical thing which is essentially predicated of both the different things). (30)

  Contraries are different, and contrariety is a kind of difference. That we are right in this supposition is shown by induction. (35) For all of these too are seen to be different; they are not merely other, but some are other in genus, and others are in the same line of predication, and therefore in the same genus, and the same in genus. [1055a] We have distinguished11 elsewhere what sort of things are the same or other in genus.

  4 Since things which differ may differ from one another more or less, there is also a greatest difference, and this I call contrariety. (5) That contrariety is the greatest difference is made clear by induction. For things which differ in genus have no way to one another, but are too far distant and are not comparable; and for things that differ in species the extremes from which generation takes place are the contraries, and the distance between extremes—and therefore that between the contraries—is the greatest.

  But surely that which is greatest in each class is complete. (10) For that is greatest which cannot be exceeded, and that is complete beyond which nothing can be found. For the complete difference marks the end of a series (just as the other things which are called complete are so called because they have attained an end), and beyond the end there is nothing; for in everything it is the extreme and includes all else, (15) and therefore there is nothing beyond the end, and the complete needs nothing further. From this, then, it is clear that contrariety is complete difference; and as contraries are so called in several senses, their modes of completeness will answer to the various modes of contrariety which attach to the contraries.

  This being so, it is clear that one thing cannot have more than one contrary (for neither can there be anything more extreme than the extreme, (20) nor can there be more than two extremes for the one interval), and, to put the matter generally, this is clear if contrariety is a difference, and if difference, and therefore also the complete difference, must be between two things.

  And the other commonly accepted definitions of contraries are also necessarily true. For not only is (1) the complete difference the greatest difference (for we can get no difference beyond it of things differing either in genus or in species; for it has been shown12 that there is no ‘difference’ between anything and the things outside its genus, (25) and among the things which differ in species the complete difference is the greatest); but also (2) the things in the same genus which differ most are contrary (for the complete difference is the greatest difference between species of the same genus); and (3) the things in the same receptive material which differ most are contrary (for the matter is the same for contraries); and (4) of the things which fall under the same faculty the most different are contrary (for one science deals with one class of things, (30) and in these the complete difference is the greatest).

  The primary contrariety is that between positive state and privation—not every privation, however (for ‘privation’ has several meanings), (35) but that which is complete. And the other contraries must be called so with reference to these, some because they possess these, others because they produce or tend to produce them, others because they are acquisitions or losses of these or of other contraries. Now if the kinds of opposition are contradiction and privation and contrariety and relation, and of these the first is contradiction, and contradiction admits of no intermediate, while contraries admit of one, clearly contradiction and contrariety are not the same. [1055b] But privation is a kind of contradiction; for what suffers privation, either in general or in some determinate way, is either that which is quite incapable of having some attribute or that which, (5) being of such a nature as to have it, has it not; here we have already a variety of meanings, which have been distinguished13 elsewhere. Privation, therefore, is a contradiction or incapacity which is determinate or taken along with the receptive material. This is the reason why, (10) while contradiction does not admit of an intermediate, privation sometimes does; for everything is equal or not equal, but not everything is equal or unequal, or if it is, it is only within the sphere of that which is receptive of equality. If, then, the comings-to-be which happen to the matter start from the contraries, and proceed either from the form and the possession of the form or from a privation of the form or shape, clearly all contrariety must be privation, (15) but presumably not all privation is contrariety (the reason being that that which has suffered privation may have suffered it in several ways); for it is only the extremes from which changes proceed that are contraries.

  And this is obvious also by induction. For every contrariety involves, as one of its terms, a privation, but not all cases are alike; inequality is the privation of equality and unlikeness of likeness, (20) and on the other hand vice is the privation of virtue. But the cases differ in a way already described;14 in one case we mean simply that the thing has suffered privation, in another case that it has done so either at a certain time or in a certain part (e. g. at a certain age or in the dominant part), or throughout. This is why in some cases there is a mean (there are men who are neither good nor bad), and in others there is not (a number must be either odd or even). Further, (25) some contraries have their subject defined, others have not.—Therefore it is evident that one of the contraries is always privative; but it is enough if this is true of the first—i. e. the generic—contraries, e. g. the one and the many; for the others can be reduced to these.

  5 Since one thing has one contrary, we might raise the question how the one is opposed to the many, (30) and the equal to the great and the small. For if we use the word ‘whether’ only in an antithesis such as ‘whether it is white or black’, or ‘whether it is white or not white’ (we do not ask ‘whether it is a man or white’), unless we are proceeding on a prior assumption and asking something such as ‘whether it was Cleon or Socrates that came’—but this is not a necessary disjunction in any class of things; yet even this is an extension from the case of opposites; for opposites alone cannot be present together; and we assume this incompatibility here too in asking which of the two came; for if they might both have come, (35) the question would have been absurd; but if they might, even so this falls just as much into an antithesis, that of the ‘one or many’, i. e. ‘whether both came or one of the two’:—if, then, the question ‘whether’ is always concerned with opposites, and we can ask ‘whether it is greater or less or equal’, what is the opposition of the equal to the other two? It is not contrary either to one alone or to both; for why should it be contrary to the greater rather than to the less? [1056a] Further, (5) the equal is contrary to the unequal. Therefore if it is contrary to the greater and the less, it will be contrary to more things than one. But if the unequal means the same as both the greater and the less together, the equal wi
ll be opposite to both (and the difficulty supports those who say the unequal is a ‘two’15), (10) but it follows that one thing is contrary to two others, which is impossible. Again, the equal is evidently intermediate between the great and the small, but no contrariety is either observed to be intermediate, or, from its definition, can be so; for it would not be complete16 if it were intermediate between any two things, but rather it always has something intermediate between its own terms.

  It remains, then, that it is opposed either as negation or as privation. (15) It cannot be the negation or privation of one of the two; for why of the great rather than of the small? It is, then, the privative negation of both. This is why ‘whether’ is said with reference to both, not to one of the two (e. g. ‘whether it is greater or equal’ or ‘whether it is equal or less’); there are always three cases. But it is not a necessary privation; for not everything which is not greater or less is equal, (20) but only the things which are of such a nature as to have these attributes.