a first principle and a measure — for their hypothesis is, that the motion of the heavens is equable, and that it is of the utmost velocity; and, in accordance with this, astronomers adjust the other motions — ^and in music diesis is adopted as a measure, because it constitutes the least perceptible sound;3 and in the case of vocal sounds it is an element of speech that is such. And all these things in this way are a certain one, not in such a manner as that the one is a thing common to tl^em, but in such a way as has been declared. A measure is not, however, invariably one in, ^ uumber, but sometimes more than one; as, for siderations set iiistance, two dieses such as are not understood?°!L1o'»?i*°^ ' to measure.
according to hearing, but are contained in the definitions; and the vocal sounds by which we measure are more numerous, and the diameter of the square, likewise, is And hence it is that the mathematicel sciences are characterised fcr so much of certainty and precision.
^ Vide Locke's Essay, book I. chap. xiv.
' The woM ^Utris has been already explained, in a note, p. 124, as a term in music, meaning something the same as our demi-semi-quayer. It occurs in the Posterior Audytics, book I. chap. xxiiL 256 THE METAPHYSICS OF ARISTOTLE. [bOOK IX.
measured by two things, and this is the case with the side and with all magnitudes. Thus, therefore, is unity a measure of all things, because we thereby know those things of which substance consists, by making a division of it either according to quantity or according to form; and on this account is unity indivisible, because the original of everything is that which is indivisible. But each thing is not indivisible in the same manner as a foot and the monad; but the latter is indivisible in every respect, and the former has a tendency towards things that art) indivisible according to sense, as just now has been remarked; for, perhaps, everything continuous is divisible. The measure, however, is always a thing of a kindred nature; for of magnitudes is magnitude the measure: and, in regard of an individual thing, length is a measure of length, breadth of breadth, of vocal sounds voice is a measure, weight a measure of weight, a monad of monads. For in this way must we receive this assertion, but not to the effect that number is a measure of numbers. Although this ought to be the case, if measure, in like manner, in this case is to be kindred with what is measured; * but he who entertains this opinion does not think similarly of this instance, but just as if one would suppose that monads are a measure of monads, but not a monad; number, however, is a multitude of monads.
6 Transferred ^"^ scicuce wc pronouucc to be the measure meaning of the of things and sense,^ likewise, for this very reason, word measure, jje^a^ge ^g attain unto some knowledge through the instrumentality of these, since rather are they measured than are they standards of measure. But it happens unto us just as if another were measuring us we should know how large we were by reason of the cubital measure being extended over us thus far. Protagoras, however, says that man is the measure of all things; just as if he should say that one who possesses scientific knowledge, or who goes through an act of perception by sense, is a measure, and that this is so with these because the one possesses sense, but the other scientific knowledge, which we affirm to be measures of those things * I have added these words to complete the sense.
' The remarks foUowmg draw our attention to what Bacon would sail the "idola tribus." Vide Nov. Org. lib. I. aph. 41 -46; and Da A.iLgm. lib. V. chap. iv.
that are subjects to either one or the other. Doubtlefs, such persons, in their assertion of nothing that is extraordinary appear to say something pertinent to the matter in hand That therefore, indeed, the being or essence of 7. Recapituia- anity subsists in an eminent degree, according ^^°^ to the name which they determine upon, as a certain measure — ^and the most impoilaut measure— of quantity, and, in the next place, of quality, this is evident. Now, a measure of this sort will be of one kind, if it may be indivisible as far as r^ards quantity, but of another, if it be so as regards quality. Wherefore, unity is indivisible either simply or so tJEu: forth as it is unity.
CHAPTER II.
CHAPTER II.
But as regards Substance and Nature ^ we, _. ^. must institute an inquiry how they are dispoBed, L^b t^e in like manner as in the doubts ^ mooted in the Jf?thtog"^* earlier portions of this work we have taken a review of what unity is, and how one ought to take up his opinions respecting the same, — ^whether as though this imity were to be considered as a certain substance (as both the Pythagorics^ affirm in the first instance, and Plato subse- quently), or rather, whether some nature is subjected to it, and in what manner this ought to be more intelligibly discoursed of, and whether rather is it the case that we should look at unity from the point of view that some of the natural philosophers do? for of those a certain one says that unity is harmony, but another air, and a third the Infinite. Now, if it is not possible for any of the imi- versals to be substance,^ as has been declared in our disquisi- tions concerning substance, and in those concerning entity, * ov<r(a and <f>v<rts are terms that already have been explained— 01)0-^0, in books IV. and V 11., and m the opening chapters of the Categories; piitru in book IV., and in the first book of the Physics.
' The doubts cocjiected with ontology are stated and examined into in book II.
' ArifltoUe thus reprehends all efforts on the part of those philo- ■ophers who sought to discover either unity in matter — that is, somt jirimary element— or unity in an idealistic sense.
* Tlui question is discussed in book YI. chap. xiii.
'25% THB mtTAPHTiilCS OF ARISTOTLE. [DOCK IX nor that this very thing be substance so as to be enduei with the papacity of subsisting as a certain one thing separatf from plurality, (for a thing of this kind is what is common, but alone may be ranked as a category, it is evident, if tht foregoing be true, that neither is unity itself a substance, for entity and unity, in an eminent degree above other things, are predicated universally of all things. Wherefore, neither are genera certain natures and substances capable of a separable subsistence from other things, nor does unity admit of being a genus, on account of the same causes, through, which neither does unity or substance admit of being a genua And, further, in like manner it is expedient that the ^ase stand in regard of all things. Now, unity and entity are predicated in an equal number of ways: wherefore, since in quantities there is a certain unity and a certain nature, and since, in like manner, both of these reside in quantities, it is plain that likewise, in general, we must investigate what unity is, as well as what entity is also; as if it were not sufficient to determine that this very thing is the nature of it. s. Illustrated ^^*» Unquestionably, in colours, at least, there is by the case of the One colour, — for example, whiti), — afterwards CO ours; ^j^^ ^.^^ appear to be produced from this and black; but black is a privation of white, as darkness also is of light, but this is a privation of light. Wherefore, if entities were colours, entities would constitute a certain number — ^but of what 1 let me ask — without doubt, manifestly of colours; and unity would be a certain one thing, as, for example, white. and of music ^^^ ^^ ^^^® manner, also, if entities were me- and Tocai lodics there would be a number of dieses,^ how- tounds. ever; but the substance of them would not be number, and unity would be something the substance of which would not be unity, but diesis. In like manner, also, in the case of the elements of sounds, if all entities wero sounds they would constitute the number of the elemental and unity would be a vocal element; and if entities were right-lined figures they would constitute the number of figures, and unity would be a triangle: and the same reason- ing stands good, likewise, in the case of the other genera of things. Wherefore, if also in passive properties, and in qualities, and in quantities, and in motion, there subsist ^ The Leipsic edition reads this in the Bingular.
OB. m.] UNITY AS OPPOSED TO PLURALITY. 259 numbers, and a certain one thing in all these, unity would be both a number of certain things, and it would constitute a certain entity; ^ but by no means would this be the sub- stance of that thing: and as regards substances the case must needs be the same; for in like manner is it in the case of all things. That, therefore, unity in eveiy genus is a sort of nature, and that this very thing — namely, unity— is ^ not the nature of anything, is evident; but as in colours there is one colour to be sought for as unity itself, so, also, in sub- stances is one substance to be sought for as unity itself.
But that somehow unity and entity are ^ unity and squivalent in their meaning is evident from the entity equipoi- fact that unity follows upon the categories in an {JJ^* "* °^®*"" equal number of ways with entity, and yet does not subsist in any of them; as, for example, neither m quiddity nor in quality, but it subsists in like manner as entity. And from this &ct it follows that there is not any- thing different from man additionally predicated in the pre- ' dication of one man, as neither is entity^ anything inde- pendent of quiddity, or quality, or quantity, and that tho being of unity is the same thing as the being of some indi^ vidual thing.
CHAPTER III.
Unity, however, and plurality are opposed in j opposition many ways; in one of whioh modes the unity between unity and the multitude are opposed as what is in- "°*^ P^^'*^**y- divisible and what is divisible: for that which has been divided, or is actually divisible, is styled a certain multitude; but what is indivisible, or that which has not been di- vided, is styled one. Since, therefore, the oppositions are fourfold,^ and one of these is expressed according to priva- tion, there would subsist what is contrary, and neither would they be denominated as contradictions, nor as things predi- ^ Some copies read Iv instead of 6y, ' This sentence is not quite intelligible.
• T^ «Tvoi, that is, the " esse."
* This subject was examined into by Aristotle in a Treatise Tltpi kydeov, mentioned in book XXL of the Metaphysics. Vide note in chap li. of that book, p. 84.
82 260 THB nXAFHTBIOB OF ABISTOTLB |^BOOK IS cated relatively. But unity is predicated from its contraiy, and thereby made evident, — y'lz. that whioh is indivi»ble from that which is divisible, — from the fact that multitude, and thai which is divisible, are rather cognisable by sense than that which is indivisible. Wherefore, in the definition the multi- tude is prior to that which is indivisible by reason of per- ception by sense.
s. coneomi- There also belong to unity — as we have likewise taatt of unity, described iu our division of oontraries ' — same- 8imUarit7,and uoss, and similarity, and equality; but to multi- equaiity. ^^^^ beloug diversity, and dissimilarity, and in^ equality. Seeing, however, that sameness is predicated in many ways, after one mode also — ^namely, according to numbei>— subsists that which we denominate occasionidly as this, and after another mode if a thing be one both in definition and in number; for instance, you are the same with yourself both in form and matter. Further, are those things said to be the same to the primary substance of whioh there may belong one definition; as, for instance, equal right lines are the same, and equal and equal-angled quadrangular figures, notwithstanding that they are many in number; but in these the equality is unity. And things are said to be similar if they be not the same simply considered, nor without a difierence in regard of subject-substance, but yet may be the same as regards form; for example, the greater square is similar to a less: and so it is with unequal right lines, for these are similar, no doubt, but not the same absolutely. And some things are called similar if they possess the same form wherein reside the more and less, as properties ingenerated, while the things themselves are neither greater nor less. And other things are so styled if there belong to them the same plEissive condition, and such as is one in species; as, for instance, that which is exceedingly white, and what is so in a less degree, they say that such are similar because the form of them is one. And other things are so called if they possess more of sameness than of diversity, either considered simply, or provided they be more obvious to perception as possessing such; for instance, tin is * For the subject of contraries, vide the Categories, chap, x.; Topka, book IL chap. vii. Aristotle is thought to have written a distinct treatise on contraries, entitled *£kAo7^ rwv hatvrlwp, mentioned in th« Metaphysics, book IU. chap. iL CB. in.J C0K00MITAI7TB OF UNITY AND PLURALITY. 261: more similar to silver than to gold, and gold is similar to fire^ 80 &r forth as it is ruddy and brilliant.
Wherefore, it is evident that both diversity s. Concomi- and dissimilarity are denominated in many Syl^unm^" waya; and that which is another thing is ex- larity.diversity: pressed in opposition to that which is the same. •"* difference. Wherefore, everything in relation to everything is either the same or different; but that is said to take plaoQ if the matter and the definition be not one: wherefore, you and your neighbour are different But a third signification of the foregoing is when things subsist as in mathematical entities. Therefore, indeed, on this account, everything of those, as many as are denominated unity and entity, are so deno- minated in reference to everything as different or the same. For neither is there any contradiction of sameness. Where- fore, the assertion is not made in the case of nonentities, but of all entities, — the "not-same," however, is predicated of entities, — for sameness and diversity being constituted by nature an entity and one thing, are either one or not one. That, then, which is diversity, and that which is sameness, are in this way opposed. Difference, however, and diversity are something else; for it is not requisite that a thing which is diverse, and that in reference to, or because of which, a thing is diverse, should be a diverse thing by reason of something common;^ for everything whatsoever, in regard of its being an entity, is either diverse or the same. That, however, which is different from something is different by something, or in some respect, so that it is necessary that something wherein they differ should be the same, and this something which is thus the same is either genus or species; for everything that is different differs either in genus or in species; those things differ in genus of which neither the matter is common nor their generation into one another — for instance, take the case of those things of at many as there is another figure of predication — ^but things are different in species of whish the genus may be the same, and that is called a genus in respect of which both of the things that are different are styled the same according to substance. But contraries are things different, and con* tranety is a certain difference.
' Taylor supplies this word.
269 THE METAPHTSIOB OF JJU8I0TL1. [BOOK H, 4 coof rma- ^^^ ^^^ ^® ^^^ made this foregoiiig snppo- iton of the sition coirectlj is evident from induction; for aU ta3l]Sl'^ those things that are different their di£forenoe ii even apparent: and not merely so vrhen thej are diverse; but some things are diverse in genus, bat others are diverse which belong to the same coordination of predication. Wherefore, also, those same things that an contained in the same genus are also involved in the same species. Now, it has been determined in the case of other things what sort of entities are the same or different in the genus.
CHAPTER IV.i 1. Contrariety BuT since it is admissible that things which JS2?tSt*dift?. are different should differ one from another «nce. more and less, there is, likewise, a certain greatest difference; and I mean by this contrariety: and that thei» does exist this greatest difference is evident from induc- tion. For some things that are different in genus do not possess a way one towards another, but are distant to a con- siderable extent, and are not things that may be comparea together. To those things, however, that differ in species belong generations that take their rise frt)m contraries as from extremes, but the last interval is the greatest Where- fore, also, is this the case with that which lies between the con- 2 Deductions traries. But, surely, this which is the greatest therefrom. jq gach genus, at any rate, is that which is perfect; for greatest is that of which there is no excess, or superabun- dancy, and finished is that beyond' which there is no possi- bility of assuming anything, for the perfect difference involves an end: in like manner as other things are called perfect, or finished in respect of their involving an end. But to the end there is nothing extrinsic; for it is the ultimate thing in everything, and comprises those things of which it is the end. Wherefore, nothing is extrinsic to the end, nor does the perfect require anything of the sort That therefore, ^ The logical questions discussed in this and the following bhapten would appear somewhat out of place. Perhaps the subject of tiis opposition between unity and plurality suggested them to Aristotle^ mind.
cm. IV. J CONTRABIETT THK GREATEST DIFFERENCE. 265 indeed, contrariety constitutes a perfect difference is evident from these statements. And whereas contraries^ are denomi- nated in many ways, subsistence in a perfect manner will follow in such a way as that the subsistence also of contraries would be inherent in them. Now, seeing that these things are so, it is plain that there is no possibility of one thing involving many contraries; for neither could there be anything more ultimate, or final, than the extreme, nor of one interval would there be more than two extremes. And, in general, if con- trariety be a difference, yet difference is the difference be- tween two things: wherefore, also, this will be the case with the perfect difference.
It is necessary, however, that the rest of the s. The troth of definitions also of the contraries be correct; an dcflnitions for likewise doth the perfect difference evince dei>endent on the greatest amount of difference: for of things ftJSJe?ta*ac- that differ in genus and in species there is no cordancewith possibility of assuming anything that is more *^® *°"^«°»°8- external; for it has been demonstrated that, respecting things extrinsic to the genus, there subsists not a difference, and of these this is the greatest difference: and those things that belong to the same genus, and involve the greatest difference, are contraries, for the greatest difference of these is the perfect difierence. And those things that involve the greatest amount of difference in the same recipient are con- traries, for there is the same matter for the contraries; and things that rank under the same potentiality, and involve the greatest difference, are also contraries; for also the science is one concerning one genus of those things in which the perfect difference is the greatest The first or chief contrariety, however, consists ^ ^^ ^., in habit and privation; yet not every privation contrariety (for privation 2 is predicated in many ways), but JjJJoiJ"** ^"" whatsoever such as may be perfect. And the other contraries will be denominated according to these, some, on the one hand, in respect of possession, and others from action, or from being fit subjects for action; and, on the other hand, some in respect of their being recipients, and rejections of these, or of other contraries.
^ Vide note on oontrariei, chap, iii ' The term orhri<ru is defined in book IV. chap, zxiii 264 THB METAFHYSICS OF ABISTOTLK. [BCOIL A B. Contrariety Now, if they are opposed — I mean, contr» Is not contra- diction and privation, and contrariety and rela- ®*®^ tions — and if of these contradiction is the first, and of contradiction there is nothing intermediate but if of contraries this is admissible, it is evident that contradiction is not the same thing with contrariety, and that privation constitates a certain contradiction; for pri- vation belongs either to what is entirely devoid of a capacity of possessing, or to that which, even though adapted by nature for possession, may yet not actually possess either entirely or in a certain definite manner; for we now express this in many ways, just as the dibtinctions have been drawn by us elsewhere. Wherefore, privation is a certain contradiction, or a defined impotentiality, or one which is conjoined along with what is receptive. Wherefore, of contradiction there is not anything that is intermediate; but of a certain privation there is, for everything is either equal or not equal; but not everything is equal or unequal, but only if it be contained in that whidi is receptive of equality. 6. Contrariety ^i i^ow, there are generations in matter from is privation, contraries, and these are produced either from form but not everv but not everv privation is and tlio habit of the species, or from a certain contrariety. pnvatiou of the spccies and of the form, it is evi- dent that every contrariety would constitute a certain priva- tion, but not every privation, perhaps, would constitute con- trariety. And a cause of this is the following: that whatever is a subject of the privation admits of being a subject of privation in many ways; for those things from the extremities of which changes are generated, these are contraries. ^ ^^, And this is evident, likewise, from induction; going view con- for cvery coutranety involves a privation of hiduSioS™ either of the contraries. Not similarly, however^ is it the case with all things; for inequality us a privation of equality, but dissimilarity of similarity, and vice of virtue.^ But there is the same difiference as has been * To make evil a mere negation of good is to be expected in a Pagan, whose mind was in the dark as to those various sources of evil whicfe our Redeemer has put us on our guard against. Vide Dean Trench's " Notes on the Parables/' where, in his exposition of the '* Parable of thd Tares/' the influence of the Devil, viewed as a pergonal influence over frail humanity, is most beautifully extracted from the iFymbol ol •Ihetaret."
U9. T.] OPPOSITION OF ORBATNBSS TO 8MALLX£SS. 260 stated; for one thing is a subject of privation if it may happen to be deprived of anything, but another if it may be so at any time, or in any subject; as, for example, would be the case at a certain age either in that which is the principal age, or altogether so, Wherefore, of some contraries is there a medium, and there is a man who iH neither good nor evil; but of others there is not a medium, but a number must needs be either odd or even: further, do some things involve a definite subject, but others do not. Wherefore^ it is evident that invariably either of the con- traries is denominated according to privation: it is sufficient, however, if there are in existence the primaries atid the genera of contraries; as, for instance, unity and plurality are styled such, for the rest are referred or reduced to these.
CHAPTER V.i CHAPTER V.i But since one thing is contrary to one thing, i. Question la a person would feel perplexed as to how unity J*«jni j' the and plurality are opposed, and how the equal is fition betwe^ opposed to the great and the small. For there SS^ms^m is the question whether invariably we speak of weu as equality a thing in the way of opposition— for example, "*•* «"»»»"»<»•• whether it is white or black, and whether it is white or not white— but we do not say whether such is a man or a thing that is white, unless hypothetically, and in such an inquiry, as, for instance, whether Cleon came or Socrates? but there is no necessity for this inquiry being found in any geuus; but this, likewise, has proceeded from thence. For things in opposition do not admit of subsisting alone at the same time; which aforesaid mode of speaking of a thing one employs in the present instance, — I mean, in the inquiry, which of the two came first? for if both could do so at the same time, the question would be ridiculous. And if this were possible in this way also, in like manner would the person who ^ In this chapter A ristotle, by the mention of the opposition between unity and plurality, is led into discussions purely logicaL The subject of opposition is Inreated of in the seventh and following chapters df Aristotle's Treatise '* On Interpretation,*' and by Archbii^op Whately Ib book n. chap. y. of his Log! u Vide note, p. 129.
266 THB mSTAPHTEIOS OF ARISTOTLE. [bOOK IX makes the inquiry fall into opposition, viz. into unity, ot plurality; as, for example, whether both came, or either of the two \ If, therefore, in things that are opposed the question whether a thing " is so and so " is to be found invariably— now, we speak of a thing as to whether it is greater, or less^ or equal — what opposition is there of equality in respect of these, for neither is it contrary to either only, nor to bcthi for why should it be contrary to the greater more than to the less? Further, is the equal contrary to that which is unequal; wherefore, it will be contrary to more than ona If, however, inequality signifies the same thing with both of these at the same time, it would be in opposition to both, and the doubt renders assistance to those who say that inequality constitutes the duad; it happens, however, that one is contrary to two, which is impossible. ' Moreover, equality seems to be a medium between the great and the small; but no contrariety seems to be either of the nature of a medium, nor from the definition is it a thing possible that it should; for it would not be perfect if it were a mean between anything: yet it rather invariably involves some- thing that is a medium with respect to itself.