Aristotle: Metaphysics Book 10

[1052a] [15]

That “one” has several meanings has been already stated1 in our distinction of the various meanings of terms. But although it has a number of senses, the things which are primarily and essentially called one, and not in an accidental sense, may be summarized under four heads:

(1.) That which is continuous, [20] either absolutely or in particular that which is continuous by natural growth and not by contact or ligature; and of these things those are more strictly and in a prior sense one whose motion is more simple and indivisible.

(2.) Of this kind in a still higher degree is that which is a whole and has a definite shape or form, particularly that which is such by nature and not by constraint (like things which are joined by glue or nails or by being tied together), but which contains in itself the cause of its continuity.A thing is of this kind if its motion is one and indivisible in respect of place and time; so that clearly if a thing has as its principle of motion the primary kind of motion (i.e. locomotion) in its primary form (i.e. circular locomotion), it is in the primary sense one spatial magnitude.2

Some things, then, are one in this sense, qua continuous or whole; the other things which are one are those whose formula is one.Such are the things of which the concept is one, i.e. of which the concept is indivisible; and this is indivisible when the object is indivisible (3.) in form or (4.) in number. Now in number the individual is indivisible, and in form that which is indivisible in comprehension and knowledge; so that that which causes the unity of substances must be one in the primary sense.Such, then, in number are the meanings of “one”: the naturally continuous, the whole, the individual, and the universal. All these are one because they are indivisible; some in motion, and others in concept or formula. [1052b] [1] But we must recognize that the questions, “What sort of things are called one?” and “What is essential unity, and what is the formula?” must not be taken to be the same. “One” has these several meanings, and each thing to which some one of these senses applies will be one; but essential unity will have now one of these senses and now something else, which is still nearer to the term one, whereas they are nearer to its denotation . This is also true of “element” and “cause,” supposing that one had to explain them both by exhibiting concrete examples and by giving a definition of the term. There is a sense in which fire is an element (and no doubt so too is “the indeterminate”3 or some other similar thing, of its own nature), and there is a sense in which it is not; because “to be fire” and “to be an element” are not the same. It is as a concrete thing and as a stuff that fire is an element; but the term “element” denotes that it has this attribute: that something is made of it as a primary constituent. The same is true of “cause” or “one” and all other such terms.

Hence “to be one” means “to be indivisible” (being essentially a particular thing, distinct and separate in place or form or thought), or “to be whole and indivisible”; but especially “to be the first measure of each kind,” and above all of quantity; for it is from this that it has been extended to the other categories. [20] Measure is that by which quantity is known, and quantity qua quantity is known either by unity or by number, and all number is known by unity. Therefore all quantity qua quantity is known by unity, and that by which quantities are primarily known is absolute unity.Thus unity is the starting point of number qua number. Hence in other cases too “measure” means that by which each thing is primarily known, and the measure of each thing is a unit—in length, breadth, depth, weight and speed.(The terms “weight” and “speed” are common to both contraries, for each of them has a double meaning; e.g., “weight” applies to that which has the least amount of gravity and also to that which has excess of it, and speed to that which has the least amount of motion and also to that which has excess of it; for even the slow has some speed, and the light some weight.)

In all these cases, then, the measure and starting-point is some indivisible unit (since even in the case of lines we treat the “one-foot line” as indivisible). For everywhere we require as our measure an indivisible unit; i.e., that which is simple either in quality or in quantity.Now where it seems impossible to take away or add, there the measure is exact. [1053a] [1] Hence the measure of number is most exact, for we posit the unit as in every way indivisible; and in all other cases we follow this example, for with the furlong or talent or in general with the greater measure an addition or subtraction would be less obvious than with a smaller one.Therefore the first thing from which, according to our perception, nothing can be subtracted is used by all men as their measure of wet and dry, weight and magnitude; and they think that they know the quantity only when they know it in terms of this measure. And they know motion too by simple motion and the most rapid, for this takes least time.Hence in astronomy a unit of this kind is the starting point and measure; for they assume that the motion of the heavens is uniform and the most rapid, and by it they judge the others. In music the measure is the quarter tone, because it is the smallest interval; and in language the letter. All these are examples of units in this sense—not in the sense that unity is something common to them all, but in the sense which we have described.The measure is not always numerically one, but sometimes more than one; e.g., there are two quarter tones, distinguished not by our hearing but by their theoretical ratios4; and the articulate sounds by which we measure speech are more than one; and the diagonal of a square is measured by two quantities,5 and so are all magnitudes of this kind. Thus unity is the measure of all things, because we learn of what the substance is composed by dividing it, [20] in respect of either quantity or form.Hence unity is indivisible, because that which is primary in each class of things is indivisible. But not every unit is indivisible in the same sense—e.g. the foot and the arithmetical unit; but the latter is absolutely indivisible, and the former must be classed as indivisible with respect to our power of perception, as we have already stated; since presumably everything which is continuous is divisible.

The measure is always akin to the thing measured. The measure of magnitude is magnitude, and in particular the measure of length is a length; of breadth, a breadth; of sounds, a sound; of weight, a weight; of units, a unit; for this is the view that we must take, and not that the measure of numbers is a number. The latter, indeed, would necessarily be true, if the analogy held good; but the supposition is not analogous—it is as though one were to suppose that the measure of units is units, and not a unit; for number is a plurality of units.

We also speak of knowledge or sense perception as a measure of things for the same reason, because through them we come to know something; whereas really they are measured themselves rather than measure other things. But our experience is as though someone else measured us, and we learned our height by noticing to what extent he applied his foot-rule to us.Protagoras says that “man is the measure of all things,” meaning, as it were, the scholar or the man of perception; [1053b] [1] and these because they possess, the one knowledge, and the other perception, which we hold to be the measures of objects. Thus, while appearing to say something exceptional, he is really saying nothing.6

Obviously, then, unity in the strictest sense, if we make our definition in accordance with the meaning of the term, is a measure; particularly of quantity, and secondarily of quality. Some things will be of this kind if they are indivisible in quantity, and others if in quality. Therefore that which is one is indivisible, either absolutely or qua one.

We must inquire, with regard to the substance and nature of unity, in which sense it exists. This is the same question which we approached in our discussion of difficulties7: what unity is, and what view we are to take of it; whether that unity itself is a kind of substance—as first the Pythagoreans, and later Plato, both maintain—or whether rather some nature underlies it, and we should give a more intelligible account of it, and more after the manner of the physicists; for of them one8 holds that the One is Love, another9 Air, and another10 the Indeterminate.

Now if no universal can be a substance (as we have stated in our discussion11 of substance and being), and being itself cannot be a substance in the sense of one thing existing alongside the many (since it is common to them), but only as a predicate, [20] then clearly neither can unity be a substance; because being and unity are the most universal of all predicates.Therefore (a) genera are not certain entities and substances separate from other things; and (b) unity cannot be a genus, for the same reasons that being and substance cannot.12

Further, the nature of unity must be the same for all categories.Now being and unity have the same number of meanings; so that since in the category of qualities unity is something definite, i.e. some definite entity, and similarly in the category of quantity, clearly we must also inquire in general what unity is, just as in the case of being; since it is not enough to say that its nature is simply unity or being.But in the sphere of colors unity is a color, e.g. white; that is if all the other colors are apparently derived from white and black, and black is a privation of white, as darkness is of light. Thus if all existing things were colors, all existing things would be a number; but of what?Clearly of colors. And unity would be some one color, e.g. white. Similarly if all existing things were tunes, there would be a number—of quarter-tones; but their substance would not be a number; and unity would be something whose substance is not unity but a quarter-tone. [1054a] [1] Similarly in the case of sounds, existing things would be a number of letters, and unity would be a vowel;and if existing things were right-lined figures, they would be a number of figures, and unity would be a triangle. And the same principle holds for all other genera. Therefore if in the categories of passivity and quality and quantity and motion there is in every category a number and a unity, and if the number is of particular things and the unity is a particular unity, and its substance is not unity, then the same must be true in the case of substances, because the same is true in all cases.

It is obvious, then, that in every genus one is a definite entity, and that in no case is its nature merely unity; but as in the sphere of colors the One-itself which we have to seek is one color, so too in the sphere of substance the One-itself is one substance.And that in a sense unity means the same as being is clear (a) from the fact that it has a meaning corresponding to each of the categories, and is contained in none of them—e.g., it is contained neither in substance nor in quality, but is related to them exactly as being is; (b) from the fact that in “one man” nothing more is predicated than in “man”13(just as Being too does not exist apart from some thing or quality or quantity); and © because “to be one” is “to be a particular thing.”

[20] “One” and “Many” are opposed in several ways. Unity and Plurality are opposed as being indivisible and divisible; for that which is divided or divisible is called a plurality, and that which is indivisible or undivided is called one. Then since opposition is of four kinds, and one of the present pairs of opposites is used in a privative sense, they must be contraries, and neither contradictories nor relative terms.Unity is described and explained by its contrary—the indivisible by the divisible—because plurality, i.e. the divisible, is more easily perceptible than the indivisible; and so in formula plurality is prior to the indivisible, on account of our powers of perception.

To Unity belong (as we showed by tabulation in our distinction of the contraries14) Identity, Similarity and Equality; and to Plurality belong Otherness, Dissimilarity and Inequality.

“Identity”15 has several meanings. (a) Sometimes we speak of it in respect of number. (b) We call a thing the same if it is one both in formula and in number, e.g., you are one with yourself both in form and in matter; [1054b] [1] and again © if the formula of the primary substance is one, e.g., equal straight lines are the same, and equal quadrilaterals with equal angles, and there are many more examples; but in these equality means unity.

Things are “similar”16(a) if, while not being the same absolutely or indistinguishable in respect of their concrete substance, they are identical in form; e.g the larger square is similar to the smaller, and unequal straight lines are similar. These are similar, but not absolutely the same. (b) If, having the same form, and being capable of difference in degree, they have no difference of degree.© If things have an attribute which is the same and one in form—e.g. white—in different degrees, we say that they are similar because their form is one. (d) If the respects in which they are the same are more than those in which they differ, either in general or as regards their more prominent qualities; e.g., tin is similar to silver, as being white; and gold to fire, as being yellow or flame-colored.

Thus it is obvious that “Other”17 and “Unlike” also have several meanings. (a) In one sense “other” is used in the sense opposite to “the same”; thus everything in relation to every other thing is either “the same” or “other.” (b) In another sense things are “other” unless both their matter and their formula are one; thus you are “other” than your neighbor. © The third sense is that which is found in mathematics.18 Therefore everything in relation to everything else is called either “other” or “the same”; that is, in the case of things of which unity and being are predicated; [20] for “other” is not the contradictory of “the same,” and so it is not predicated of non-existent things (they are called “not the same”), but it is predicated of all things which exist; for whatever is by nature existent and one is either one or not one with something else.

“Other” and “same,” then, are opposed in this way; but “difference”19 is distinct from “otherness.”For that which is “other” than something need not be other in a particular respect, since everything which is existent is either “other” or “the same.” But that which is different from something is different in some particular respect, so that that in which they differ must be the same sort of thing; i.e. the same genus or species.For everything which is different differs either in genus or in species—in genus, such things as have not common matter and cannot be generated into or out of each other, e.g. things which belong to different categories; and in species, such things as are of the same genus (genus meaning that which is predicated of both the different things alike in respect of their substance).

The contraries20 are different, and contrariety is a kind of difference. That this is rightly premissed is made clear by induction; for the contraries are obviously all different, since they are not merely “other,” but some are other in genus, and others are in the same line of predication, [1055a] [1] and so are in the same genus and the same in genus. We have distinguished elsewhere21 what sort of things are the same or other in genus.

Since things which differ can differ from one another in a greater or less degree, there is a certain maximum difference, and this I call contrariety. That it is the maximum difference is shown by induction. For whereas things which differ in genus have no means of passing into each other, and are more widely distant, and are not comparable, in the case of things which differ in species the contraries are the extremes from which generation takes place;and the greatest distance is that which is between the extremes, and therefore also between the contraries. But in every class the greatest thing is complete. For (a) that is greatest which cannot be exceeded, and (b) that is complete outside which nothing proper to it can be found. For complete difference implies an end, just as all other things are called complete because they imply an end.And there is nothing beyond the end; for in everything the end is the last thing, and forms the boundary. Thus there is nothing beyond the end, and that which is complete lacks nothing.

From this argument, then, it is clear that contrariety is maximum difference; and since we speak of contraries in various senses, the sense of completeness will vary in accordance with the sense of contrariety which applies to the contraries.

[20] This being so, evidently one thing cannot have more than one contrary (since there can be nothing more extreme than the extreme, nor can there be more than two extremes of one interval); and in general this is evident, if contrariety is difference, and difference (and therefore complete difference) is between two things.

The other definitions of contraries must also be true, for (1.) complete difference is the maximum difference; since (a) we can find nothing beyond it, whether things differ in genus or in species (for we have shown that difference in relation to things outside the genus is impossible; this is the maximum difference between them); and (b) the things which differ most in the same genus are contraries; for complete difference is the maximum difference between these.(2.) The things which differ most in the same receptive material are contraries; for contraries have the same matter. (3.) The most different things which come under the same faculty are contraries; for one science treats of one class of things, in which complete difference is the greatest.

“Positive state” and “Privation” constitute primary contrariety—not every form of privation (for it has several senses), but any form which is complete. All other contraries must be so called with respect to these; some because they possess these, others because they produce them or are productive of them, and others because they are acquisitions or losses of these or other contraries.Now if the types of opposition are contradiction, privation, contrariety and relation, [1055b] [1] and of these the primary type is contradiction, and an intermediate is impossible in contradiction but possible between contraries, obviously contradiction is not the same as contrariety; and privation is a form of contradiction;for it is either that which is totally incapable of possessing some attribute,22 or that which would naturally possess some attribute but does not, that suffers privation—either absolutely or in some specified way. Here we already have several meanings, which we have distinguished elsewhere. Thus privation is a kind of contradiction or incapacity which is determinate or associated with the receptive material.This is why though there is no intermediate in contradiction there is one in some kinds of privation. For everything is either equal or not equal, but not everything is either equal or unequal; if it is, it is only so in the case of a material which admits of equality. If, then, processes of material generation start from the contraries, and proceed either from the form and the possession of the form, or from some privation of the form or shape, clearly all contrariety must be a form of privation, although presumably not all privation is contrariety.This is because that which suffers privation may suffer it in several senses; for it is only the extremes from which changes proceed that are contraries.

This can also be shown by induction. Every contrariety involves privation as one of its contraries, but not always in the same way: [20] inequality involves the privation of equality, dissimilarity that of similarity, evil that of goodness.And the differences are as we have stated: one case is, if a thing is merely deprived; another, if it is deprived at a certain time or in a certain part—e.g. at a certain age or in the important part—or entirely. Hence in some cases there is an intermediate (there are men who are neither good nor bad), and in others there is not—a thing must be either odd or even.Again, some have a determinate subject, and others have not. Thus it is evident that one of a pair of contraries always has a privative sense; but it is enough if this is true of the primary or generic contraries, e.g. unity and plurality; for the others can be reduced to them.

Since one thing has one contrary, it might be asked in what sense unity is opposed to plurality, and the equal to the great and to the small. For if we always use the word “whether” in an antithesis—e.g., “whether it is white or black,” or “whether it is white or not” (but we do not ask “whether it is a man or white,” unless we are proceeding upon some assumption, and asking, for instance, whether it was Cleon who came or Socrates.This is not a necessary disjunction in any class of things, but is derived from the use in the case of opposites—for it is only opposites that cannot be true at the same time—and we have this same use here in the question “which of the two came?” [1056a] [1] for if both alternatives were possible, the question would be absurd; but even so the question falls into an antithesis: that of “one” or “many”—i.e., “whether both came, or one”)— if, then, the question “whether” is always concerned with opposites, and we can ask “whether it is greater or smaller, or equal,” what is the nature of the antithesis between “equal” and “greater or smaller”? It is contrary neither to one only, nor to both: for (a) it is no more contrary to the greater than to the smaller; (b) “equal” is contrary to “unequal,” and thus it will be contrary to more than one thing;© if “unequal” means the same as both “greater” and “smaller” at the same time, “equal” must still be opposed to them both: This difficulty supports the theory23 that “the unequal” is a duality. But the result is that one thing is contrary to two; which is impossible.

Further, it is apparent that “equal” is intermediate between “great” and “small,” but it is not apparent that any contrariety is intermediate, nor can it be, by definition; for it could not be complete if it were the intermediate of something, but rather it always has something intermediate between itself and the other extreme.

It remains, then, that it is opposed either as negation or as privation. Now it cannot be so opposed to one of the two, for it is no more opposed to the great than to the small.Therefore it is a privative negation of both. For this reason we say “whether” with reference to both, and not to one of the two—e.g., “whether it is greater or equal,” or “whether it is equal or smaller”; [20] there are always three alternatives. But it is not a necessary privation; for not everything is equal which is not greater or smaller, but only things which would naturally have these attributes.

The equal, then, is that which is neither great nor small, but would naturally be either great or small; and it is opposed to both as a privative negation, and therefore is intermediate between them. And that which is neither good nor bad is opposed to both, but it has no name (for each of these terms has several meanings, and there is no one material which is receptive of both); that which is neither white nor black is better entitled to a name,although even this has no single name, but the colors of which this negation is privatively predicated are to a certain extent limited; for it must be either grey or buff or something similar.

Therefore those persons are wrong in their criticism who imagine that all terms are used analogously, so that that which is neither a shoe nor a hand will be intermediate between “shoe” and “hand,” because that which is neither good nor bad is intermediate between good and bad—as though there must be an intermediate in all cases; but this does not necessarily follow.For the one is a joint negation of opposites where there is an intermediate and a natural interval; [1056b] [1] but in the other case there is no question of difference, since the joint negation applies to things which are in different genera, and therefore the substrate is not one.24

A similar question might be raised about “one” and “many.” For if “many” is absolutely opposed to “one,” certain impossibilities result. (1) One will be few; for “many” is also opposed to “few.”(2) Two will be many; since “twofold” is “manifold,” and “twofold” is derived from two. Therefore one will be few; for in what relation can two be many if not in relation to one, which must therefore be few? for there can be nothing less. (3) If “much” and “little” are in plurality what “long” and “short” are in length, and if whatever is “much” is also “many,”and “many” is “much” (unless indeed there is a difference in the case of a plastic continuum25), “few” will be a plurality. Therefore one will be a plurality, if it is few; and this necessarily follows if two is many. Presumably, however, although “many” in a sense means “much,” there is a distinction; e.g., water is called “much” but not “many.”To all things, however, which are divisible the term “many” is applicable: in one sense, if there is a plurality which involves excess either absolutely or relatively (and similarly “few” is a plurality involving defect); and in another in the sense of number, in which case it is opposed to “one” only. [20] For we say “one or many” just as if we were to say “one and ones,” or “white thing and white things,” or were to compare the things measured with the measure.Multiples, too, are spoken of in this way; for every number is “many,” because it consists of “ones,” and because every number is measurable by one; and also as being the opposite of one, and not of few. In this sense even two is many; but as a plurality involving excess either relatively or absolutely it is not many, but the first plurality. Two is, however, absolutely few; because it is the first plurality involving defect(hence Anaxagoras26 was not right in leaving the subject by saying “all things were together, infinite both in multitude and in smallness”; instead of “in smallness” he should have said “in fewness,”27 for things cannot be infinite in fewness), since fewness is constituted not by one, as some hold, but by two.

In the sphere of numbers “one” is opposed to many as the measure to the measurable, i.e., as relative terms are opposed which are not of their own nature relative. We have distinguished elsewhere28 that things are called relative in two senses—either as being contraries, or as knowledge is related to the knowable, A being related to B because B is described in relation to A. [1057a] [1]

There is no reason why one should not be fewer than something, e.g. two; for if it is fewer it is not therefore few. Plurality is, as it were, a genus of number, since number is a plurality measurable by one. And in a sense one and number are opposed; not, however, as being contrary, but as we have said some relative terms to be; for it is qua measure and measurable that they are opposed.(Hence not everything which is one is a number—e.g., a thing which is indivisible.) But although the relation between knowledge and the knowable is said to be similar to this, it turns out not to be similar. For it would seem that knowledge is a measure, and the knowable that which is measurable by it; but it happens that whereas all knowledge is knowable, the knowable is not always knowledge, because in a way knowledge is measured by the knowable.29

Plurality is contrary neither to the few (whose real contrary is the many, as an excessive plurality to an exceeded plurality) nor in all senses to one; but they are contrary in one sense (as has been said) as being the one divisible and the other indivisible; and in another as being relative (just as knowledge is relative to the knowable) if plurality is a number and one is the measure.

Since there can be, and in some cases is, an intermediate between contraries, intermediates must be composed of contraries; [20] for all intermediates are in the same genus as the things between which they are intermediate.By intermediates we mean those things into which that which changes must first change. E.g., if we change from the highest string to the lowest by the smallest gradations we shall first come to the intermediate notes; and in the case of colors if we change from white to black we shall come to red and grey before we come to black; and similarly in other cases.But change from one genus into another is impossible except accidentally; e.g., from color to shape. Therefore intermediates must be in the same genus as one another and as the things between which they are intermediate.

But all intermediates are between certain opposites, for it is only from these per se that change is possible.Hence there can be no intermediate between things which are not opposites; for then there would be change also between things which are not opposites. Of things which are opposites, contradiction has no intermediate term (for contradiction means this: an antithesis one term of which must apply to any given thing, and which contains no intermediate term); of the remaining types of opposites some are relative, others privative, and others contrary.Those relative opposites which are not contrary have no intermediate. The reason for this is that they are not in the same genus— [1057b] [1] for what is intermediate between knowledge and the knowable?—but between great and small there is an intermediate. Now since intermediates are in the same genus, as has been shown, and are between contraries, they must be composed of those contraries. For the contraries must either belong to a genus or not. And if there is a genus in such a waythat it is something prior to the contraries, then the differentiae which constitute the contrary species (for species consist of genus and differentiae) will be contraries in a prior sense.E.g., if white and black are contraries, and the one is a penetrative30 and the other a compressive color, these differentiae, “penetrative” and “compressive,” are prior, and so are opposed to each other in a prior sense.But it is the species which have contrary differentiae that are more truly contraries; the other, i.e. intermediate, species will consist of genus and differentiae. E.g., all colors which are intermediate between white and black should be described by their genus (i.e. color) and by certain differentiae.But these differentiae will not be the primary contraries; otherwise every thing will be either white or black. Therefore they will be different from the primary contraries. Therefore they will be intermediate between them, and the primary differentiae will be “the penetrative” and “the compressive.” [20] Thus we must first investigate the contraries which are not contained in a genus, and discover of what their intermediates are composed.For things which are in the same genus must either be composed of differentiae which are not compounded with the genus, or be incomposite. Contraries are not compounded with one another, and are therefore first principles; but intermediates are either all incomposite or none of them. Now from the contraries something is generated in such a way that change will reach it before reaching the contraries themselves (for there must be something which is less in degree than one contrary and greater than the other). Therefore this also will be intermediate between the contraries.Hence all the other intermediates must be composite; for that which is greater in degree than one contrary and less than the other is in some sense a compound of the contraries of which it is said to be greater in degree than one and less than the other. And since there is nothing else homogeneous which is prior to the contraries, all intermediates must be composed of contraries.Therefore all the lower terms, both contraries and intermediates, must be composed of the primary contraries. Thus it is clear that intermediates are all in the same genus, and are between contraries, and are all composed of contraries.

That which is “other in species” than something else is “other” in respect of something and that something must apply to both. E.g., if an animal is other in species than something else, they must both be animals. Hence things which are other in species must be in the same genus. The sort of thing I mean by “genus” is that in virtue of which two things are both called the same one thing; [1058a] [1] and which is not accidentally differentiated, whether regarded as matter or otherwise.For not only must the common quality belong to both, e.g., that they are both animals, but the very animality of each must be different; e.g., in one case it must be equinity and in the other humanity. Hence the common quality must for one be other in species than that which it is for the other. They must be, then, of their very nature, the one this kind of animal, and the other that ; e.g., the one a horse and the other a man.Therefore this difference must be “otherness of genus” (I say “otherness of genus” because by “difference of genus” I mean an otherness which makes the genus itself other); this, then, will be a form of contrariety. This is obvious by induction.31 For all differentiation is by opposites, and we have shown32 that contraries are in the same genus, because contrariety was shown to be complete difference. But difference in species is always difference from something in respect of something; therefore this is the same thing, i.e. the genus, for both.(Hence too all contraries which differ in species but not in genus are in the same line of predication,33 and are other than each other in the highest degree; for their difference is complete, and they cannot come into existence simultaneously.) Hence the difference is a form of contrariety.

To be “other in species,” then, means this: to be in the same genus and involve contrariety, while being indivisible(and “the same in species” applies to all things which do not involve contrariety, while being indivisible); [20] for it is in the course of differentiation and in the intermediate terms that contrariety appears, before we come to the indivisibles.34 Thus it is evident that in relation to what is called genus no species is either the same or other in species (and this is as it should be, for the matter is disclosed by negation, and the genus is the matter of that of which it is predicated as genus; not in the sense in which we speak of the genus or clan of the Heraclidae,35 but as we speak of a genus in nature); nor yet in relation to things which are not in the same genus. From the latter it will differ in genus, but in species from things which are in the same genus. For the difference of things which differ in species must be a contrariety; and this belongs only to things which are in the same genus.

The question might be raised as to why woman does not differ in species from man, seeing that female is contrary to male, and difference is contrariety; and why a female and a male animal are not other in species, although this difference belongs to “animal” per se, and not as whiteness or blackness does; “male” and “female” belong to it qua animal.This problem is practically the same as “why does one kind of contrariety (e.g. “footed” and “winged”) make things other in species, while another (e.g. whiteness and blackness) does not?” The answer may be that in the one case the attributes are peculiar to the genus, and in the other they are less so; [1058b] [1] and since one element is formula and the other matter, contrarieties in the formula produce difference in species, but contrarieties in the concrete whole do not.Hence the whiteness or blackness of a man does not produce this, nor is there any specific difference between a white man and a black man; not even if one term is assigned to each. For we are now regarding “man” as matter, and matter does not produce difference; and for this reason, too, individual men are not species of “man,” although the flesh and bones of which this and that man consist are different. The concrete whole is “other,” but not “other in species,” because there is no contrariety in the formula, and this is the ultimate indivisible species.But Callias is definition and matter. Then so too is “white man,” because it is the individual, Callias, who is white. Hence “man” is only white accidentally. Again, a bronze circle and a wooden one do not differ in species; and a bronze triangle and a wooden circle differ in species not because of their matter, but because there is contrariety in their formulae.

But does not matter, when it is “other” in a particular way, make things “other in species”? Probably there is a sense in which it does. Otherwise why is this particular horse “other in species” than this particular man, although the definitions involve matter? Surely it is because there is contrariety in the definition, for so there also is in “white man” and “black horse”; [20] and it is a contrariety in species, but not because one is white and the other black; for even if they had both been white, they would still be “other in species.”

“Male” and “female” are attributes peculiar to the animal, but not in virtue of its substance; they ar material or physical. Hence the same semen may, as the result of some modification, become either female or male.

We have now stated what “to be other in species” means, and why some things differ in species and others do not.

Since contraries are other in form,36 and “the perishable” and “imperishable” are contraries (for privation is a definite incapacity), “the perishable” must be “other in kind” than “the imperishable.” But so far we have spoken only of the universal terms; and so it might appear to be unnecessary that anything perishable and imperishable should be “other in form,” just as in the case of white and black.For the same thing may be both at the same time, if it is a universal (e.g, “man” may be both white and black); and it may still be both if it is a particular, for the same person may be white and black, although not at the same time. Yet white is contrary to black. But although some contraries(e.g. those which we have just mentioned, and many others) can belong to certain things accidentally, others cannot; [1059a] [1] and this applies to “the perishable” and “the imperishable.” Nothing is accidentally perishable; for that which is accidental may not be applicable; but perishability is an attribute which applies necessarily when it is applicable at all. Otherwise one and the same thing will be imperishable as well as perishable, if it is possible for perishability not to apply to it.Thus perishability must be either the substance or in the substance of every perishable thing. The same argument also applies to the imperishable; for both perishability and imperishability are attributes which are necessarily applicable. Hence the characteristics in respect of which and in direct consequence of which one thing is perishable and another imperishable are opposed; and therefore they must be other in kind.Thus it is obvious that there cannot be Forms such as some thinkers maintain; for then there would be both a perishable and an imperishable “man.”37 Yet the Forms are said to be the same in species as the particulars, and not merely to share a common predicate with them; but things which are other in genus differ more widely than things which are other in species.

1 Aristot. Met. 5.6.

2 This description applies to the celestial spheres.

3 The reference is undoubtedly to Anaximander.

4 i.e., the enharmonic (or quarter-tone proper) and the chromatic, which was 1/3 of a tone (Aristoxenus 1.21, 2.51). There was also the δίεσις ἡμιολία, which was 3/8 of a tone.

5 The meaning seems to be that the diameter consists of two parts, one equal to the side, and the other representing its excess over the side; the two parts being incommensurate are measured by different units (Ross). καὶ ἡ πλευρά must, I think, be a gloss.

6 What Protagoras really meant was (apparently) that appearances are true relatively to the percipient. Cf. Aristot. Met. 4.4.27, and see Burnet, Greek Philosophy (Part I. Thales to Plato), 92.

7 Aristot. Met. 3.4.24-27.

8 Empedocles.

9 Anaximenes.

10 Anaximander.

11 Aristot. Met. 7.13.

12 Cf. Aristot. Met. 3.3.7.

13 Cf. Aristot. Met. 4.2.6-8.

14 Cf. Aristot. Met. 4.2.9.

15 Or “the same.” Cf. Aristot. Met. 5.9.

16 Or “like.” Cf. Aristot. Met. 5.9.5.

17 Cf. Aristot. Met. 5.9.4.

18 sc. as opposed to “same” in sense (a); 3 above.

19 Cf. Aristot. Met. 5.9.4.

20 Cf. Aristot. Met. 5.10.

21 Aristot. Met. 5.28.4.

22 This is not a proper example of privation. Cf. Aristot. Met. 5.22.

23 Held by the Platonists. Cf. Aristot. Met. 14.1.4, 5.

24 Cf. Aristot. Met. 10.3.8

25 i.e., a fluid, which cannot be described as “many.”

26 Cf. Aristot. Met. 1.3.9.

27 sc. “and then the absurdity of his view would have been apparent, for,” etc. Aristotle assumes the Anaxagoras meant “smallness” (μικρότης) to be the opposite of “multitude” (πλῆθος); but he meant just what he said—that the particles of which things consist are infinitely many and infinitely small. See Bowman in Classical Review 30, 42-44.

28 Aristot. Met. 5.15.8, 9.

29 Cf. Aristot. Met. 10.1.19.

30 This is Plato's definition. Cf. Plat. Tim. 67d, e.

31 Aristotle does not use induction to prove his point; indeed he does not prove it at all.

32 In ch. 4.

33 Or “category.”

34 i.e., indivisible species and individuals.

35 Cf. Aristot. Met. 5.28.1.

36 It appears that in this chapter (apart from 5, which may be a later addition) the terms εἶδος and γένος are used in a non-technical sense. Cf. Ross on Aristot. Met. 1058b 28.

37 i.e., the individual man is perishable and the Idea of man imperishable; and these must be other in kind (γένει non-technical). But the Platonists hold that the Idea is the same in species as the particular. This is impossible if it is other in genus (γένει technical).