Aristotle · a new plain-English translation from the original language
1| That the one is spoken of in many ways has been said earlier, in the discussions of how many ways a thing is divided; but though it is spoken of in more ways, the modes that sum it up are four, for things spoken of as one primarily and in their own right, and not accidentally. For one thing is the continuous, either simply, or especially that which is continuous by nature and not by contact or by a bond (and among these, more one and prior is that whose motion is more indivisible and more simple); further, of this kind, and more so, is the whole, that which has some shape and form, most of all if something is such by nature and not by force, as things are that are held by glue or a peg or a bond, but rather has in itself the cause of its own being continuous. And a thing is of this kind by having its motion one and indivisible in place and time; so that it is clear that if something has by nature a starting point of motion — the primary starting point of the primary motion, I mean, for instance, of locomotion, circular motion — then this is the primary one magnitude. Some things, then, are one in this way, as continuous or as a whole; others are things whose account is one, and such are things whose thinking is one, and such are things whose thinking is indivisible, and it is indivisible either in species or in number of what is indivisible: in number, then, the indivisible is the particular, while in species it is that which is indivisible with respect to what is knowable and to scientific knowledge; so that what is a cause of the one for substances would be one in the primary sense. The one, then, is spoken of in so many ways: the continuous by nature, and the whole, and the particular, and the universal — and all of these are one by being indivisible, some of them in respect of motion, others in respect of thought or account.
2| [1052b] — And one must understand that it is not to be taken in the same way to say what sorts of things are called one, and what it is to be one and what its account is. For the one is spoken of in so many ways, and each of these things will be one, whatever it is to which any of these modes belongs; but to be one will sometimes belong to it by one of these modes, sometimes by another, which is even closer to the name, while those others belong to it potentially — just as, concerning element and cause too, if one had to speak while both distinguishing among the things and rendering a definition of the name. For fire is in a way an element (and perhaps the unlimited, or something else of that sort, is also an element in its own right), but in a way it is not: for being fire and being an element are not the same thing; rather, as a thing and a nature, fire is an element, while the name signifies that this belongs to it accidentally, namely that there is something composed out of it as a primary constituent. So too with cause and with the one and with all such things; and this is why to be one is to be indivisible, being just this particular thing and separable either in place or in form or in thought — or else to be whole and indivisible; but above all, to be the primary measure of each genus, and most properly the measure of quantity;
3| for it is from this that the notion has come to the others. For a measure is that by which quantity is known; and quantity, insofar as it is quantity, is known either by a unit or by a number, and every number is known by a unit; so that all quantity, insofar as it is quantity, is known by the one, and that by which quantities are primarily known, this itself is one; hence the one is the starting point of number, insofar as it is number. And from this, in the other cases too, that is called a measure by which each thing is primarily known, and the measure of each thing is one — in length, in breadth, in depth, in weight, in speed (for weight and speed are common terms applying to opposites: for each of these is twofold, as weight is said both of whatever has any downward tendency at all, and of what has an excess of downward tendency, and speed both of whatever has any motion at all, and of what has an excess of motion: for there is a certain speed even of the slow thing, and a weight even of the lighter thing). In all these cases, then, the measure and starting point is some one and indivisible thing, since even in the case of lines they use the foot-length as something indivisible. For everywhere they seek as the measure some one and indivisible thing; and this is what is simple, either in quality or in quantity. Now wherever it is thought that nothing can be taken away or added, this is the exact measure (hence the measure of number is the most exact:
4| [1053a] for they posit the unit as indivisible in every way); and in the other cases they imitate this. For from a stade or a talent, and always from the greater quantity, an addition or subtraction would go unnoticed more than from a lesser one; so that the first quantity from which, as far as perception goes, a change is not possible, this is what everyone makes the measure, both of liquids and of dry things, and of weight and of magnitude; and they think they know the quantity when they know it by means of this measure. And indeed they measure motion too by the simple motion and the fastest one (for this takes the least time); hence in astronomy such a one is a starting point and measure (for they suppose the motion of the heavens to be uniform and the fastest, and by reference to it they judge the others), and in music the quarter-tone, because it is the smallest interval, and in speech the letter. And all these are one in this way — not as something common called 'the one', but as has been said. And the measure is not always one in number, but sometimes several — for instance, the quarter-tones are two, not as perceived by hearing but in their ratios, and the vowel sounds by which we measure are several, and the diagonal is measured by two units, and so is the side, and all magnitudes.
5| So then the one is the measure of all things, because we come to know the substance out of which a thing is composed by dividing it either by quantity or by form. And this is why the one is indivisible—because the first thing in each case is indivisible. But not everything is indivisible in the same way: for instance a foot and a unit are not indivisible in the same way, but the one is indivisible in every respect, while the other must be taken as indivisible relative to perception, as has already been said; for presumably everything continuous is divisible. And the measure is always akin to what it measures: of magnitudes, a magnitude, and in each case a length is measured by a length, a breadth by a breadth, a sound by a sound, a weight by a weight, units by a unit. For this is how we must understand it, and not that number is measured by number—though that would be required if the cases were alike; but the requirement is not the same, but rather as if one required that units be measured by units, and not by a unit; and number is a plurality of units. And we speak of scientific knowledge and of perception as the measure of things for the same reason, because it is by means of them that we come to know something—since they are measured rather than measuring. But it happens with us as it would if someone else were measuring us and we thereby came to know how large we are, by having the cubit-measure applied to us just so many times. Protagoras says that man is the measure of all things, meaning, as it were, the man who knows or the man who perceives:
6| [1053b] and these have it because the one has perception and the other has knowledge, which we say are measures of their underlying subjects. So while they seem to be saying nothing out of the ordinary, they do appear to be saying something. That being one is, above all according to the meaning of the word, in a way a certain measure—most properly a measure of quantity, and secondarily of quality—is clear; and a thing will be such a measure if it is indivisible in respect of quantity, and such if it is indivisible in respect of quality; and this is why the one is indivisible either absolutely or qua one. But as regards substance and nature, we must inquire which way the matter stands, just as we went into it among the puzzles: what the one is and how we must conceive of it—whether the one itself is some substance, as the Pythagoreans say first and Plato afterward, or rather some nature underlies it and it must be stated more intelligibly and more in the manner of the natural philosophers; for among these, one says the one is love, another air, another the unlimited. If, then, none of the universals can be a substance, as has been said in the discussions concerning substance and being, then this itself cannot be a substance either, as being some one thing beside the many (for it is common to them), but can only be a predicate, then clearly the one cannot be a substance either:
7| for being and the one are predicated universally, more than anything else. So neither are the genera certain natures and substances separate from other things, nor can the one be a genus, for the same reasons for which neither being nor substance can be a genus. Further, the same must necessarily hold in all cases alike: being and the one are said in an equal number of ways; so that since among qualities there is some one and some nature, and likewise among quantities, it is clear that we must also inquire generally what the one is, just as what being is, on the ground that it is not enough to say that its nature just is this itself. But indeed among colors the one is a single color, for instance white, and then the others appear to come to be out of this and black, and black is the privation of white, just as darkness is the privation of light: so that if the things that are were colors, the things that are would be a certain number, but a number of what? Clearly of colors, and the one would be some one thing, for instance white. Likewise, too, if the things that are were musical intervals, there would be a number, of quarter-tones indeed, but their substance would not be number:
8| and the one would be something whose substance is not the one but the quarter-tone. [1054a] Likewise also in the case of vocal sounds, the things that are would be a number of letters, and the one would be a vowel letter. And if the things that are were rectilinear figures, there would be a number of figures, and the one would be the triangle. And the same account holds for the other genera as well, so that if indeed among affections too, and among qualities, and among quantities, and in motion there are numbers, and in every case some one thing, and the number is a number of certain things and the one is a certain one, but this is not itself the substance, then the same must necessarily hold in the case of substances too; for the case is alike in all of them. It is clear, then, that the one in every genus is some nature, and that in no case is this itself—the one—the nature of the thing; but just as among colors we must look for the one itself as one color, so too among substances we must look for the one itself as one substance: and that the one and being signify in a way the same thing is clear from the fact that they accompany the categories in an equal number of ways and are present in none of them (for instance neither in the category of what a thing is nor in that of quality, but stand in the same relation as being does), and from the fact that "one man" adds no further predicate beyond "man" (just as being adds nothing beyond what a thing is, or its quality, or its quantity), and from the fact that to be one is just to be a particular thing.
9| The one and the many are opposed in several ways, one of which is the one and the plurality as indivisible and divisible: for what is either divided or divisible is called a plurality of some sort, while what is indivisible, or not divided, is called one. Since, then, oppositions are of four kinds, and one of these two is spoken of in terms of privation, they would be contraries, and neither as contradiction nor as things spoken of relatively. Now the one is spoken of, and made clear, from its contrary: the indivisible from the divisible, because plurality and the divisible are more perceptible than the indivisible, so that in account plurality is prior to the indivisible, on account of perception. And to the one belong—just as we set out in the division of the contraries—the same, the similar, and the equal, while to plurality belong the different, the dissimilar, and the unequal. And since the same is spoken of in several ways, in one way we sometimes speak of it numerically; and a thing is one in this sense if it is one both in account and in number, as for instance you are one with yourself both in form and in matter; and further if the account of the primary substance is one,
10| [1054b] as for instance equal straight lines are the same, and equal and equal-angled quadrilaterals are the same, though there are more than one of them; but in these cases equality is a kind of oneness. Things are similar if, without being simply the same, and without being undifferentiated in respect of their composite substance, they are the same in respect of form—as, for instance, the larger square is similar to the smaller, and so are unequal straight lines; for these are similar, but not simply the same. Other things are similar if, having the same form, in cases admitting of more and less, they are neither more nor less. Others are similar if they have the same affection, and are one in form—for instance white—though intensely and less so; these are said to be similar because their form is one. Others are similar if they have more points that are the same than different, either absolutely or in the obvious respects—for instance tin is similar to silver in that it is white, and gold is similar to fire in that it is yellow and reddish. So it is clear that both the different and the dissimilar are spoken of in several ways. And in one sense the different is opposed to the same, so that everything, in relation to everything else, is either the same or different: but in another sense a thing is different if its matter and its account are not both one; hence you and your neighbor are different:
11| The third sense is as things are in mathematics. Now the other and the same are, for this reason, said of everything in relation to everything, of all that is called one and being: for the contradictory is not the contradictory of the same, and so it is not said of things that are not (though "not the same" is said of them), but of everything that is: for whatever is a being and a one is by nature either one or not one with another. The other and the same, then, are opposed in this way, but differentia and otherness are something else. For that which is other, and that from which it is other, need not be other in respect of anything: for whatever is, is either other or the same, no matter what it is. But that which is different is different from something in some respect, so that there must be something the same in respect of which the differing things differ. And this same thing is genus or species: for everything that differs, differs either in genus or in species — in genus, when things have no matter in common and no coming-to-be into one another, as with things whose figure of predication is different; in species, when things share the same genus (a genus being called the same when the differing things are both said to be the same thing in respect of substance). Contraries are different things, and contrariety is a kind of differentia. That we posit this correctly is clear from induction:
12| For all these too are evidently different, and not merely other, but some other in genus, others within the same coordinate series of the category, [1055a] so that they are the same in genus when they are in the same genus. It has been determined elsewhere which things are the same or other in genus. Since things that differ can differ from one another more or less, there is also a greatest difference, and this I call contrariety. That it is the greatest difference is clear from induction. For things that differ in genus have no path into one another, but stand further apart and are not comparable; while for things that differ in species, comings-to-be proceed from the contraries as extremes, and the interval between extremes is the greatest, so that so too is the interval between contraries. But indeed the greatest thing in each genus is complete. For the greatest is that beyond which there is no excess, and the complete is that outside which it is not possible to take anything further: for the complete differentia has an end (just as other things too are called complete by having an end), and outside the end there is nothing — for the end is the extreme in everything, and contains everything else, and so nothing lies outside the end, and the complete needs nothing further. That contrariety, then, is complete difference, is clear from this. Since "contrary" is said in many ways, completeness will follow in whatever way being contraries belongs to the things in question.
13| Given this, it is clear that a thing cannot have more than one contrary (for nothing could be more extreme than the extreme, and one interval cannot have more than two extremes), and in general, if contrariety is a difference, and difference is between two terms, then so is complete difference. The other definitions of contraries must hold true as well. For the complete difference is the greatest difference (since among things that differ in genus nothing can be taken further out, nor among things that differ in species — for it has been shown that there is no difference with respect to things outside the genus, and within the genus this is the greatest difference), and things within the same genus that differ most are contraries (for the greatest difference among them is the complete one), and things within the same recipient that differ most are contraries (for the matter is the same for contraries), and things falling under the same capacity that differ most are contraries (for the science of one genus is one science): in all these cases the complete difference is the greatest. The primary contrariety is that of possession and privation — not privation in every sense (for privation is said in many ways), but whichever privation is complete. The other contraries will be spoken of by reference to these: some by having the state or its privation, others by producing it or being capable of producing it, others by being acquisitions or losses of these or of other contraries.
14| If, then, contradiction, privation, contrariety, and relative terms are opposed each to its own correlate, [1055b] and of these contradiction is primary, and there is nothing between the terms of a contradiction, while between contraries there can be something, it is clear that contradiction and contraries are not the same thing. Privation is a kind of contradiction: for either a thing is wholly incapable of having an attribute, or, being naturally disposed to have it, does not have it — either altogether or in some defined respect (for we already use this word in many senses, as has been distinguished elsewhere for us) — so that privation is a kind of contradiction, or an incapacity that has been defined, or one taken together with its recipient. Hence there is nothing between the terms of a contradiction, but there is something between the terms of a given privation: for everything is either equal or not equal, but not everything is equal or unequal — rather this holds, if at all, only within what is capable of receiving equality. If, then, comings-to-be in matter proceed from contraries, and things come to be either from the form and the possession of the form, or from some privation of the form and the shape, it is clear that every contrariety would be a privation, though perhaps not every privation is a contrariety (the reason being that what has been deprived can be deprived in many ways): for the things from which changes proceed, taken as extremes, are the contraries. This is clear also from induction. For every contrariety involves privation in one of its two terms, though not all in the same way:
15| For inequality is a privation of equality, unlikeness a privation of likeness, vice a privation of virtue — but they differ as has been said: in the one case the privation holds only if it is total, in the other it holds if it obtains at some time or in some respect, for instance at a certain age or in the governing part, or throughout. Hence for some of these there is something in between, and a person can be neither good nor bad, while for others there is not, but a thing must be either odd or even. Again, some have a determinate underlying subject, others do not. So it is clear that one of the two contraries is always spoken of in terms of privation. It is enough, too, to consider the primary contraries and the genera of contraries, such as the one and the many, for the others are reduced to these. But since one thing is contrary to one thing, one might raise the difficulty of how the one and the many are opposed, and the equal to the large and the small. For if we always use "which of the two" within an opposition — as in "which, white or black?" and "which, white or not white?" (we do not say "which, man or white?" except by supposition, when we are inquiring, for instance, "which came, Cleon or Socrates?" — though this is not necessary in any genus; yet even this usage has come from the same source):
16| For it is only opposites that cannot hold at once, and this is what is being drawn on here too, in "which of the two came?" [1056a] — for if both could hold at once, the question would be absurd; and if it is not the case that both can hold at once, then even this falls likewise into an opposition, into the one or the many, as in "did both come, or one of the two?" If, then, in the case of opposites the inquiry is always "which of the two," and we say "which, greater or smaller or equal," what is the opposition to these terms on the side of the equal? For it is contrary neither to one of them alone nor to both together: for why should it be contrary to the greater any more than to the smaller? Further, the equal is contrary to the unequal, so that it would turn out contrary to more than one thing. But if "unequal" signifies the same thing said of both at once, it would be opposed to both together (and this difficulty supports those who say that the unequal is a dyad), but then it follows that one thing is contrary to two things, which is impossible. Further, the equal evidently lies between the large and the small, but no contrariety appears to lie between its own terms, nor is this possible by definition: for a contrariety that lay between two things would not be complete, but rather a contrariety always has something of itself in between. It remains, then, that the equal is opposed either as a negation or as a privation. It cannot be opposed to one of the two alone (for why should it be opposed to the large any more than to the small?): it is, therefore, a privative negation of both together, and this is why "which of the two" is said with reference to both together, but not with reference to just one of them (for instance, "which, greater or equal?" or "which, equal or smaller?"), but there are always three terms.
17| But privation is not necessarily present: for not everything that is neither greater nor less is thereby equal, but only among things whose nature admits of greater and less. The equal, then, is that which is neither large nor small, though its nature is to be either large or small: and it is opposed to both as a privative negation, and that is why it is also an intermediate. So too what is neither good nor bad is opposed to both, but is nameless: for each of the two is said in many ways, and there is not a single receptive subject, but rather it is whatever is neither white nor black. Nor is even this said as one thing, but the things of which this privative negation is said are in a way determinate: for it must be either gray or sallow or something else of that sort. So those who complain that everything is spoken of alike are not right, on the ground that there would then be, between a shoe and a hand, something that is neither shoe nor hand, just as there is between the good and the bad something that is neither good nor bad, as though there would have to be an intermediate in every case. But this does not necessarily follow. For the joint negation of opposites applies to those between which there is by nature some intermediate and some interval:
18| [1056b] but for others there is no such joint negation; for the things whose joint negations these are belong to a different genus, so that the underlying subject is not one. Similarly one might raise a puzzle about the one and the many. For if the many is opposed to the one without qualification, certain impossibilities result. For then the one will be few, or a few thing: for the many is opposed to the few as well. Further, two will be many, if indeed the double is a case of the manifold, and manifold is said with reference to two: so that the one will be few. For in relation to what is two many, if not in relation to one and to the few? For nothing is fewer. Further, if, as in length there is the long and the short, so in plurality there is the much and the little, and whatever is much is also many, and the many is much (unless indeed there is some difference in the case of a continuum easily bounded), the little will be some plurality. So the one will be some plurality, if indeed it is also few: and this must be so, if two is many. But perhaps the many is in a sense also said of the much, though as a distinct notion—for example water is much, but not many. But wherever things are divisible, the term applies; in one way, if there is a plurality having excess either absolutely or relatively to something (and the little likewise is a plurality having deficiency), in another way as number, which alone is opposed to the one.
19| For it is in this way that we speak of one or many, just as one might say one and ones, or white and whites, and the things measured in relation to the measure and the measurable: it is in this way too that the manifold is spoken of; for each number is many because it is composed of ones and because each is measurable by one, and as the opposite of the one, not of the few. In this sense, then, two also is many, but as a plurality having excess either relatively or absolutely it is not, but is the first case of plurality. But two is few without qualification: for it is the first plurality that has deficiency (hence Anaxagoras did not do right in leaving the matter as it stood when he said that all things were together, unlimited both in plurality and in smallness—he ought to have said, instead of 'and in smallness,' 'and in fewness'; for they are not unlimited), since the little exists not on account of the one, as some say, but on account of two. The one and the many that belong to numbers, then, are opposed as measure to measurable; and these are opposed as things that are relative are opposed, namely as many as are not relatives in their own right. We have distinguished elsewhere that the relative is spoken of in two ways: in one way as contraries, in another as knowledge is related to the knowable, by the fact that something else is spoken of in relation to it.
20| [1057a] But nothing prevents the one from being less than something, for instance than the two: for it does not follow that if it is less it is also few. But plurality is, so to speak, a genus of number: for number is a plurality measurable by one, and the one and number are in a way opposed, not as contrary, but, as has been said, as some relatives are opposed; for insofar as the one is a measure and the other is measurable, in this respect they are opposed. That is why not everything that is one is a number—for instance, if something is indivisible. Knowledge, though spoken of in a similar way in relation to the knowable, does not work out in a similar way. For knowledge would seem to be the measure, and the knowable the thing measured, but it turns out that while every knowledge is knowable, not everything knowable is knowledge, because knowledge is in a way measured by the knowable. But plurality is opposed neither to the few—rather the much is opposed to this, as an excessive plurality to a plurality that is exceeded—nor to the one in every way; but the one is opposed to it, as has been said, in that the one is indivisible and it is divisible, and it is opposed to it also as a relative, as knowledge is to the knowable, if it is a number and the one is a measure. Now since it is possible for there to be something intermediate between contraries, and in some cases there is, the intermediates must be composed out of the contraries.
21| For all intermediates are in the same genus as the things between which they are intermediate. For we call intermediates those things into which what is changing must first change (for example, if something moving from the lowest note to the highest were to change by the smallest interval, it will arrive first at the intermediate notes, and in the case of colors, if it is to move from white to black, it will arrive first at crimson and gray before it arrives at black; and similarly in other cases): but to change from one genus into another genus is not possible, except accidentally, as for instance from color into shape. The intermediates, then, must be in the same genus both as one another and as the things between which they are intermediate. But indeed all intermediates are between certain opposites: for it is only out of these, in their own right, that change is possible (which is why it is impossible for there to be an intermediate between things that are not opposites: for then there would be change even not from opposites). Of opposites, there is no intermediate for contradiction (for this is what contradiction is, an opposition of which either one or the other part is present in anything whatever, having no intermediate); but of the rest, some are relatives, some are privations, and some are contraries. Of relatives, as many as are not contraries have no intermediate:
22| the reason being that they are not in the same genus. For what is intermediate between knowledge and the knowable? But there is something intermediate between large and small. [1057b] But if the intermediates are in the same genus, as has been shown, and are intermediate between contraries, they must be composed out of these contraries. For either there will be some genus of them, or there will be none. And if there is a genus, in such a way that something is prior to the contraries, the differentiae will be prior contraries, which will make the contrary species as differentiae of a genus: for it is out of the genus and the differentiae that the species come (for example, if white and black are contraries, and one is a color that separates the sight and the other a color that concentrates it, these differentiae, the separating and the concentrating, are prior: so that these are contraries to one another, and prior). But indeed those things that differ in a contrary way are more truly contraries: and the remaining cases, the intermediates too, will be composed out of the genus and the differentiae (for example, as many colors as are intermediate between white and black must be spoken of both from the genus—and the genus is color—and from certain differentiae: but these will not be the primary contraries; otherwise each thing would be either white or black: they are therefore other differentiae; these, then, will be intermediate between the primary contraries, and the primary differentiae are the separating and the concentrating).
23| So the first things to investigate are those contraries that are not within a genus, and what the intermediates between them are composed of (for what is within the same genus must either be composed out of things that are not compounds within that genus, or be itself uncompounded). Now the contraries are uncompounded out of each other, and so are starting points; but the intermediates are either all compound or none are. But something comes to be out of the contraries, so that there will be a change into this before there is a change into the contraries themselves; for of each contrary there will be a lesser and a greater degree. So this too will be an intermediate between the contraries. And so all the other intermediates as well are compound; for what is more of one thing and less of another is in some way compounded out of the things of which it is said to be more of the one and less of the other. And since there are no other things prior to the contraries and of the same genus as they, all the intermediates would be composed out of the contraries, so that everything lower down as well — both the contraries and the intermediates — will be composed out of the primary contraries. It is clear, then, that the intermediates are all within the same genus, and are intermediate between contraries, and are all composed out of the contraries. But a thing that is different in species from something is different in some respect, and this must belong to both of them; for instance, if an animal is different in species, both are animals.
24| Things that differ in species must therefore be within the same genus; for I call a genus of this sort one of which both are said to be one and the same thing, having a differentia not accidentally, [1058a] whether the genus is a kind of matter or something else. For it is not enough that the common element be present — for instance, that both are animals — but this same thing, the animal, must also be different for each of them, as being for the one a horse and for the other a man; hence this common element is different in species as between the two. So in their own right the one will be an animal of this sort and the other an animal of that sort, for instance the one a horse and the other a man. This differentia, then, must be an otherness of the genus. For by a differentia of a genus I mean an otherness that makes the genus itself something other. This otherness, then, will be a contrariety (this is also clear from induction); for everything is divided by opposites, and it has been shown that contraries fall within the same genus; for contrariety was a complete differentia, and every differentia in species is a differentia of something in some respect, so that this something is the same and is the genus for both of the contraries (which is why all the contraries in a single line of predication, so far as they differ in species and not in genus, that fall under the same category, are the most different from each other — for the differentia is complete — and do not occur together in the same subject at the same time). The differentia, then, is a contrariety. This, then, is what it is to be different in species: for things that are within the same genus and are indivisible to possess a contrariety (and things are the same in species when, being indivisible, they possess no contrariety):
25| For in the process of division contrarieties arise even in the intermediate stages, before one reaches the indivisibles; so it is clear that, relative to what is called the genus, none of the things that are species of it is either the same in species or different in species (and reasonably so: for matter is made evident by negation, and the genus is the matter of that of which it is called the genus — not in the sense of the genus of the Heraclids, but in the sense of what is meant in the natural world), nor is any species the same or different in species relative to things not within the same genus, but it will differ in genus from those, and in species from things within the same genus. For the differentia by which a thing differs in species must be a contrariety; and this belongs only to things that are within the same genus. One might raise the difficulty why a woman does not differ in species from a man, given that female and male are contrary and their differentia is a contrariety, and why a female animal and a male animal are not different in species; and yet this differentia belongs to the animal in its own right, and does not belong to it the way whiteness or blackness does, but rather female and male belong to it precisely as animal. This difficulty is nearly the same as the question why one contrariety makes things different in species and another does not — for instance, footed and winged do so, but whiteness and blackness do not.
26| Or is it because some affections belong to the genus in its own right, while others belong to it less so? And since one element is the account and the other the matter, [1058b] whatever contrarieties are present in the account produce a differentia in species, while those present in what is taken together with the matter do not. Hence whiteness in a man does not produce a differentia, nor does blackness, and there is no differentia in species between a white man and a black man, not even if one name were assigned to each. For man here functions as matter, and matter does not produce a differentia; and it is for this reason that individual men are not species of man, even though the flesh and bones out of which this man and that man are made are different: rather the composite whole is different, but not different in species, because there is no contrariety in the account. And this account is the ultimate indivisible: Callias is the account together with the matter; and so is the white man, because Callias is white; man, then, belongs to him accidentally. Nor, likewise, is a bronze circle different in species from a wooden one; nor a bronze triangle from a wooden circle — they do not differ in species on account of the matter, but because there is a contrariety in the account. But does matter, being in some way different, fail to produce things different in species, or is there a sense in which it does? For why is this horse different in species from this man? Yet their accounts are bound up with matter.
27| Or is it because there is a contrariety in the account? For that is also true of the white man and the black horse, and they are indeed different in species, though not insofar as the one is white and the other black, since even if both were white, they would still be different in species. Male and female are affections proper to the animal, but not in respect of its substance, but in the matter and the body; hence the same seed becomes female or male by undergoing a certain affection. What it is, then, to be different in species, and why some things differ in species and others do not, has now been stated. And since contraries are different in species, and the perishable and the imperishable are contraries (for privation is a determinate incapacity), the perishable and the imperishable must be different in genus. Now we have so far been speaking of these in terms of the universal names themselves, so that it might seem not necessary for any perishable thing and any imperishable thing whatever to be different in species, just as white and black need not be either (for the same thing can be both, even at the same time, if it is taken universally — just as man may be both white and black — and the same holds for particulars: for the same individual could be, though not at the same time, both white and black);
28| and yet white is contrary to black). But among contraries, some belong to certain things accidentally — as with the cases just mentioned, and many others — while for others this is impossible, and among these are the perishable and the imperishable; [1059a] for nothing is perishable accidentally: for what is accidental admits of not belonging, whereas the perishable belongs, to whatever it belongs to, among the things that belong of necessity; otherwise the very same one thing would be both perishable and imperishable, if it were possible for perishability not to belong to it. So the perishable must belong to the substance, or within the substance, of each perishable thing. And the same account holds for the imperishable as well: for both belong of necessity to what they belong to. So insofar as, and in virtue of that primary respect in which, the one thing is perishable and the other imperishable, there is an opposition, so that they must be different in genus. It is clear, then, that there cannot be Forms of the kind some people speak of; for then there would be a man who is perishable and one who is imperishable. And yet the Forms are said to be the same in species as particular things, and not merely homonymous with them; but things different in genus are further apart than things different in species.