true or always false. But with regard to incomposite things, what is being or not-being, and truths or falsity? Such a thing is not composite, so as to be when it is united and not to be when it is divided, like the proposition that "the wood is white," or "the diagonal is incommensurable"; nor will truth and falsity apply in the same way to these cases as to the previous ones. In point of fact, just as truth is not the same in these cases, so neither is being. Truth and falsity are as follows: contact i.e. direct and accurate apprehension. and assertion are truth (for assertion is not the same as affirmation), and ignorance is non-contact. I say ignorance, because it is impossible to be deceived with respect to what a thing is, except accidentally i.e. we cannot be mistaken with regard to a simple term X. We either apprehend it or not.
Mistake arises when we either predicate something wrongly of X, or analyze X wrongly.; and the same applies to incomposite substances, for it is impossible to be deceived about them. And they all exist actually, not potentially; otherwise they would be generated and destroyed; but as it is, Being itself is not generated (nor destroyed); if it were, it would be generated out of something. With respect, then, to all things which are essences and actual, there is no question of being mistaken, but only of thinking or not thinking them. Inquiry as to what they are takes the form of inquiring whether they are of such-and-such a nature or not. As for being in the sense of truth, and not-being in the sense of falsity, a unity is true if the terms are combined, and if they are not combined it is false. Again, if the unity exists, it exists in a particular way, and if it does not exist in that way, it does not exist at all. Truth means to think these objects, and there is no falsity or deception, but only ignorance—not, however, ignorance such as blindness is; for blindness is like a total absence of the power of thinking. And it is obvious that with regard to immovable things also, if one assumes that there are immovable things, there is no deception in respect of time. E.g., if we suppose that the triangle is immutable, we shall not suppose that it sometimes contains two right angles and sometimes does not, for this would imply that it changes; but we may suppose that one thing has a certain property and another has not; e.g., that no even number is a prime, or that some are primes and others are not. But about a single number we cannot be mistaken even in this way, for we can no longer suppose that one instance is of such a nature, and another not, but whether we are right or wrong, the fact is always the same.
That "one" has several meanings has been already stated Aristot. Met. 5.6. 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, 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. This description applies to the celestial spheres. 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.
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" The reference is undoubtedly to Anaximander. 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. 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. 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 ratios 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 DI/ESIS H(MIOLI/A, which was 3/8 of a tone.; and the articulate sounds by which we measure speech are more than one; and the diagonal of a square is measured by two quantities, 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).
think, be a gloss. 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, 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; 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. 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. 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 difficulties Aristot. Met. 3.4.24-27.: 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 one Empedocles. holds that the One is Love, another Anaximenes. Air, and another Anaximander. the Indeterminate.
Now if no universal can be a substance (as we have stated in our discussion Aristot. Met. 7.13.
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, 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. Cf.
Aristot. Met. 3.3.7. 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.
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" Cf. Aristot. Met. 4.2.6-8. (just as Being too does not exist apart from some thing or quality or quantity); and (c) because "to be one" is "to be a particular thing." "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 contraries Cf. Aristot. Met.
4.2.9. ) Identity, Similarity and Equality; and to Plurality belong Otherness, Dissimilarity and Inequality. "Identity" Or "the same." Cf. Aristot. Met. 5.9. 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; and again (c) 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" Or "like." Cf. Aristot. Met.
5.9.5. (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. (c) 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" Cf.
Aristot. Met. 5.9.4. 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. (c) The third sense is that which is found in mathematics. sc. as opposed to "same" in sense (a); 3 above. 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; 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" Cf. Aristot. Met.
5.9.4. 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 contraries Cf. Aristot. Met. 5.10.
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, and so are in the same genus and the same in genus. We have distinguished elsewhere Aristot. Met.
5.28.4. 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. 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, 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, This is not a proper example of privation. Cf.
Aristot. Met.
5.22. 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: 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?" 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; (c) 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 theory Held by the Platonists. Cf. Aristot. Met. 14.1.4, 5. 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"; 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; 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. Cf. Aristot. Met. 10.3.8 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 continuum i.e., a fluid, which cannot be described as "many." ), "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. 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 Anaxagoras Cf. Aristot. Met.
1.3.9. 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," sc. "and then the absurdity of his view would have been apparent, for," etc.
Aristotle assumes the Anaxagoras meant "smallness" ( MIKRO/THS ) to be the opposite of "multitude" ( PLH=QOS ); 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. 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 elsewhere Aristot. Met. 5.15.8, 9. 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. 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. Cf. Aristot. Met. 10.1.19.
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; 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— 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 way that it is something prior to the contraries, then the differentiae which constitute the contrary species (for species consist of genus and differentiae) will be