airgumenrs of of the arguments that have been brought forward are dtstJuctive ^^ favour of the Ideal Theory, certain speculators, of their own no doubt, make ideas to belong to relatives, of hypothesis. ^hich they do not affirm that there is an essential genus, whereas others assert the existence of a third man. And, in general, the arguments concerning forms overturn the very things wh'.ch those persons who maintain the existence of theae ' I hav^ followed Didct's text, which differs in this passage some* what from Bekker. ludteiii of J/Acgyujuov, some MSS. read^ owupofio^.
OH. IV.] INCONSISTirrniES OF TBE ItlSAt HBltOtLY. 361 forms would desire to exist, in preference to the existotice of the forms themselves. For it happens that the duad is not first, but that the number is; and prior to this is that which is relative, and that which involves an essential subsistence ia prior too; and this will be the case with all those things whatsoever which certain philosophers, in their adherence to these opinions respecting forms, have put forward in oppo* Bition to first principles.
Further, according, indeed, to that supposition ^ ^^ by which these speculators affirm the existence tency in this Of ideas, not only will there be forms of sub- J^JJ^^S^ S. stances, but of many other things besides; for forms to be there is not only the one concept^ about substances p*^*"p*°**- but also concerning those things that are not substances, and there will be systems of scientific knowledge conversant not about substance merely. But there are innumerable other consequences that ensue unto this hypothesis. In accord- ance, however, with what is necessary, and with the opinions that are prevalent concerning the Ideal Theory, on the suppo- sition that the forms are pai*ticipants, it is expedient that there should be ideas of substances merely; for these do not participate according to what is accidental, but it is requisite that they should participate of each thing so far forth as there doth not exist a predication of it of a subject. Now I say, for example, if anything participates of the two- fold itself, this also participates of what is everlasting, but according to accident, for it is an accident for the twofold to be everlasting. Wherefore, forms will constitute substance, and these here and there ^ are in their signification equivalent to substance; or, can we say that there is any existence of anything independent of these? take the case, for instance, of the notion of unity involved in that of plurality.
And, surely, if one establish that there is the 9. There is, or same form of the ideas as of those things that |? not, the same are participants of them, there will subsist some- idea and of the thing that is in commo© to both; for why, may I?"**«!«"**• ask, in the case of corruptible duads, and of duads that are many, I admit, in number, yefc everlasting — ^why, I say, in the 1 v6rifm is the word I have tranfllated " concept." ^ Didot reads, ravrd, and the Leipsic cditiou, ravra; the fiinoM Lftving a full stop after oOc %l 362 THB METAPHTSICS OF AfiTHTOTLB. [bCOK XII case of these is the duad one and the same thing, rather than, in the case both of this and a certain particular duad? If, however, there is not the same form of these, the result would be that entities would be homonymous, and the case would be just as if one should call both Gallias and a piece of wood a man, though at the same time unable to discern any point of communion between them.
10. lUuBtration ^^> however, we shall establish that other things from mathe- — ^qqw, I mean common reasons ^ — are capable of adaptation to the forms, as, for instance, a plain figure to the circle itself, as well as the other portions ot the definition of the circle, and if that, also, to which it oelongs will be annexed in addition — if all this be done, we ought to institute an inquiry as to whether or not this may be entirely an ineffectual proceeding? For, also, to what, it may be asked, will the addition be made — whether to the centre, or to the sur&ce, or to all the parts? for all things that are involved in substance constitute ideas; for instance, animal and biped. Further, it is evident that it is necessary that a thing itself should be something — ^in the same way as a surface must be some nature or other which will be inherent in all the forms — as is the case with the genus.
CHAPTER V.
CHAPTER V.
I Theinsuffl- ^^ °^^®^ especially ^ might one raise the eiency of the questiou as to what at all it is that forms con- BccSuntingToir tribute either to the things that are eternal actual pheno- amongst thosc that figdl under the notice of our senses, or to things that are being generated and corrupted? for neither are these a cause to them of any motion, or of any change whatever. But, certainly, neither do these forms render any assistance towards the advauce- ^ The Latin veraion, by rendeiing this ''communes rationes,** does not throw much light on the meaning of these words. The com- mentators, as well as [ can undei-stand them, consider them equivalent with ** ordinary predications," ' The student will remember how the same objectioDS are urged ii book I. chap. ix.
CH. v.] IRRELKYANOT OF THIS HYPOTHESIS. 363 xnent of the science of other things. For neither are thoso the substance of these — for, in such a case, they would he inherent in them— nor do they contribute to the exist- ence of anything at all, inasmuch as they are not, at least, inherent in those things that are participants; for if they were so they might perhaps seem to be equivalent with causes, as in the case of what is. white when it has been mixed with what is white.
But, undoubtedly, may this reason be very 2. The idealists easily overturned — a tenet, to be sure, which Anax- cannot estaWuft agoms, in the first instance, and, subsequently to anyof t?e^ ^ his age, Eudoxus,^ and certain other speculators, Jh^™a?e*put from time to time, maintained whilst labour- forward in its ing under doubts: the theory itself, however, I *^pp^^' say, is capable of refutation; for it would be easy to collect together many antagonistic arguments as well as many impossible consequences in reference to such an opinion. But the fact is, that neither do other things subsist from the forms according to any of the modes which are accustomed to be put forward by the advocates of tlie Ideal Hypothesis.
And the assertion that ideas are models or.,,, _ exemplars, and that other things participate m not the models these, is to speak quite at random, and to assert ®^ ***"*«*• what is tantamount with mere poetic metaphoi*s. For what, allow me to ask, is that which operates having an eye, so to say, or looking towards the ideas? for anything whatsoever admits of coming into existence, and of being generated; and yet there is no consequent necessity that it should be a thing that is modelled after some form or image. So that, even though we should suppose Socrates to exist, and not to exists there yet would be generated some such thing as Socrates actually is. And in like manner is it evident that this would be the case even though Socrates were eternal.^ Also will there subsist many paradigms or models of the same thing; so that this will hold good of the forms, likewise: as, in the instance of man^ animal and biped will subsist as forms in ' This tenet of Eudoxus has been examined into, in the earlier por^ tions of the Metaphysies, as one professed by Anaxagoras, as is stated in the text.
* I have followed Didot's reading and punctuation of this sentenoOi in prefereice to fiekker's.
S64 tnn «STAPHTBIC8 09 ARtStOTLB. [uOOfe Xlt eonjunotion also with ideal man. Further, not onlj will the forms oonstltute the paradigms of sensibles, but also those of themselves; as genus might be regarded a paradigm ot species that are generic. Wherefore, the exemplar and the image will be the same thing.
4. How wiu Further, it would appear an impossibility that tie idealists Bubstance and that to which the substance belongs nSmtjv pf'*^^ should be separate. Wherefore, how would ideas forms f which are said to constitute the substances of things involve a separable subsistence 1 In the Phsedo, how- ever, is an assertion made to this effect — I mean, to the effect that forms are the causes both of existence and of generation. Nevertheless, on the supposition of the existence of these forms, entities, notwithstanding, are not being produced, if also there should not subsist something that is likely to be an efficient cause; and to this we may add that different other things are generated, as a house and a ring, of which they do not say that there are forms at all.
5. Aristotle's Wherefore, it is evident that those things, general objec- ajgo, of which thesc advocatcs of the Ideal Theory ideafiinK^- ^ B&j that there are ideas, may both exist and be thesis. generated on accoimt of such causes as we may eonsider the things, also, to be that have been just now men- tioned,^ but not on account of forms. But, certainly, as far as regards the subject of the Ideal Hypothesis, it is possible, both in the manner now adopted, as well as by means of argu- ments that are more logical and accurate, to collect together many similar points with those that already have been made subjects of inquiry.
CHAPTER VI.
1. The Pytha- Now, sincc WO have thus far arrived at some foric system of settlement of the controversy concerning these mimbers. upholders of the Ideal Theory, it is well once more to examine into the com>equences in respect of num- ^ This I conceive to be the literal meaning of these words; the Latin vordon is as follows: ** Propter teles causas quales eorum s*inl q^ias nunc dicta sunt."
CH. TI.] PTTHAGOBIO SYSTEM OF 5UMBXBS. 360 bers,^ that happen in the systems of those who assert that they are substances that involve a separable subsistence, anci the primary causes of entities.
It is necessary^ however, on the supposition that number oonstitutes a certain nature, and that somethLg' ^ there is not any other substance of it, but this prfm^y "»* very thing, as certain affirm-it la. I say, un- "~"'^- doubtedly necessary in this case that something belong- ing to it should be classed as what is primary, whereas that something as consequential to this be in every instance different in form. And this directly resides either in monads^ and then every monad whatsoever is incapable of comparison with any monad whatsoever, or all of these are directly in order consequent, and any whatsoever are comparable with any monads whatsoever, as scientific men afi&nn to be the case with mathematical number.
For in mathematical number there is no differ- ^ ^^^^. ence as regards any monad one from another: or, this on its com. shall we say that, as far as the monads are con- 5!*^®?n Sathl** cemed, that some of them are capable of compari- maticai num- son with one another, whereas some are not? just '' as if the first duad were to subsist after unity, and next in order the triad; and so, therefore, another number. But the monads in each number are capable of being compared one with another, as the monads contained in the first duad are with themselves, and those in the first triad with them- selves;'^ and so, therefore, is it in the case of the rest of the numbers. Those monads, however, that are contained in the duad itself are incapable of comparison with those that are contained in the triad itself; and the case is the same with the other consecutive numbers.
Wherefore, also, the mathematician reckons 4 Digferent two after the one, along with the one before, modes of nu- another one; and after the numeration of the '°®'^**°"' three, in addition to these two, he subjoins another one, and the rest in like manner. But this philosopher — I mean Plato ^ — after the one reckons two others without the first one, and the triad without the duad; and the * This inquiry he pursues Id chaps, vi., vii., viii. pad ix. ' Bekker reads, adrris. Aristotle plaiuly is alluding to Plato 1 96^6 THB UETAFHT8ICB OF ABISIOTLB.' [2X>K XIL case stands the same with the other number: or shall we say that one sort of numbers should subsist as that which has been mentioned first, but another, such as the mathematicians put forward, and a tliird which has been •(K>ken of as last?
5. Numbers Further, it is evident that these numbers are ^te*o *SIe a- ®^^^®^ separable from things or are not separable, table firom but are resident in objects that fall under the fihingi. notice of our senses; yet not in these in such a manner as we have considered at the first, but as subsisting in sensibles^ through inherent numbers; or, at any rate, one kind of these must have a subsistence thus, and another not 80, or all of them must exist thus.
6. Confirmation '^^® modcs, indeed, therefore, according to in&Tourof which it is possible that these should exist are lions to regaSd necessarily only these. In general, however, of numbers, those philosophers who affirm unity to be a first principle, and a substance and element of all things, and that number derives its existence from this and from a certain other one, almost each of them has declared his adherence to some one of these modes, with the exception of that one where all the monads are assumed as being incapable of comparison one with another. And this has happened con- sistently with rational principles, for it is not admissible that there should be further another mode of the subsistence of number beside those that have been enumerated.
Some, therefore, assert that both are num« miiate number bcrs,* and that one of these modes which in- ^or ''^d' **b- ^^^^®s what is antecedent and what is subsequent sequent— that accords with idcas, but that mathematical num^ and^Jome^wur ^^^ ^® different from ideas and sensibles, and merely mathe- that both ideas and mathematical number possess mat c num- ^ sei)arable subsistence from sensibles; whereas others assert that mathematical number only it is that is the original of entities, and that it has been actually separated from sensibles.
8. Some con- -^^^ *^® Pythagoreans say that there exists tend for a ma- the mathematical imit, but not one which haa ^ (diTBiiroTs. Bekker reads, Hura rd ouadrird I have followed Didot. ' The thr^ opinioos set down here by Arl:totle bslong severally to PUiio, Xenocratoi, aud Pythaf^oras.
int tl.] QUESTIONS BEBFEOrnrS NTJHBERS. 367 been separated; but they affirm that sensible thematicai, and substances consist from this. For the entire PlJ^"'"'"* heaven they construct out of numbers — with the ' exception of those that are not monadic numbers — ^but they suppose that the monads invoWe magnitude; yet.as to how the first unit consists, possessed of magnitude, they seem to be involved in perplexity. A certain other philo- sopher,^ however, affirms that the first number is that one which ranks amongst forms; and others say that mathe- matical number is this first number.
And in like manner, also, is it the case i^ 9 ^h f r^ard both of lengths and surfaces, and in going nius-: regard of solids; for some say that those which S^og? of ma- are mathematical are different from those that thematicai • subsist after ideas. But, in the case of those who ^'*** say otherwise, some, it is time, speak of mathematical natures even mathematically — ^as many. I meail, as do not constitute the ideas as numbers, or say that the ideas exist; but others speak of the mathematical number, yet not mathematically, however; for what they maintain is this, that neither is every magnitude divided into magnitudes, nor that any monads whatsoever can compose a duad.
All speculators, however — with the exception ^^ ^^^ of such of the Pythagorics as assert that unity opinion in constitutes, as it may be said, an element and n^terlis firet principle of entities— seek to establish the that they are dogma that numbers partake of the nature of "*°" *°' monads; yet those, undoubtedly, speak of monads as involving magnitude,^ as has been stated previously. In what number of ways it is admissible, therefore, that statements should have been made respecting numbers, and that all such me- tliods have been enumerated, is evident from these foregoing assertions: all these assertions, however, are, to be sure^ impossible, but perhaps one more than another.
* A certain philosopher belonging to the Pythagorean seat. ' T^iis was tiie tenet of the PytbagoreaDS.
U8 THB METAPHTSIOS OF ABI8T0TL1L [BOOK XII.
CHAPTER VII.
In the first place, then, we must examine touching the whether monads are capable of mutual com- Smonads"^^ parisou, or are incapable of such comparison; and, on the supposition of their being incapable of comparison, whether^ they are to be viewed in the manner that we have divided. For, indeed, it is possible that any taooad whatsoever should not admit of being compared^ with any whatsoever; and it is possible that those monads that are resident in the actual duad should not be capable of a comparison with those that are in the actual triad; and so, therefore, that those be incapable of comparison with one another which are contained in each primary number. 2. If the mo- If, therefore, all the monads are capable of nads are ^^ comparison, and devoid of any mutual diflference, ideas will not mathematical number, and one number alone, be numbers, come into being, and it is not admissible that ideas should constitute number. For what sort of a number will an ideal man be, or an ideal animal, or any other species whatsoever 1 for there is one idea of each, as one idea of man himself, and of animal itself there is another one. Numbers, however, that are similar and devoid of difference are infinite. Wherefore, in no respect will this triad constitute ideal man more than any other one whatever. 3 If the ideas ^^ ^^® Supposition, however, that the ideas are not num- are not numbers, neither is it possible that these njrex?8?aran. ^^^^^ ^^ ^^^ f^ ^^^ ^^^^ ^^^^ ^^^^ principles, may I ask, will the ideas be derived? For number is derivable from unity and the duad, which is indefinite; and these are said to be the first principles and the elements of number, and it is not admissible to arrange them in classes either as prior or subsequent to numbers.
* troripas or irorepov.
■ avufiKriToi and d<r{/u$\riTcu — " commensurable " and " incommen- surable; " this is the translation in Liddell and Scott.
* This, then, would amount to a simultaneous overthrow of Platonism ttkd Py thagoricism; and also, as is shown in the next sentence, to th» iy^t^t|oi^ of tl^e theory of Xeaocmte^, CH. Tn.J THE INC0MMEXSURA6ILITT OF MONADS. 3()B If, howetsr, monads are incapable of com- ^ ifmonadt paiison^ and;ncapable of companson after this are incom]»r mode, 80 that everything whatever is diflferent fgn®v7mSht* from everything whatever, neither is it admis- maticai Bible that this can constitute mathematical """^ '* number — for, in feet, mathematical number is derived from monads which are devoid of difiference, and things that are demonstrated thereby are found to harmonize with monads of this description — nor yet can this number belgng to forms, for the firet duad v/ill not be derived from unity and the indefinite duad. In the next place, the consecutive numbers, as it is affirmed, are duad, triad, tetmd; for at the same time are the monads produced which are contained in the first duad, whether after the same manner as the Philoso- pher was for maintaining who first made the assertion of their subsistence from unequal monads — for from things reduced to a state of equality they have been actually produced — or whether they have a subsistence in another way.
In the next place, on the supposition that 5. other argu- there will be one monad that is prior to another, ^^}^ against it will also be prior to the duad that is derived biutyofmo- from these. For in case of the subsistence of any- "*^^- thing, there is something prior, and something subsequent; likewise will that which subsists from these be a thing that is antecedent to the one, but subsequent to the other. Fur- ther, whereas this actual unity is first, then doth there belong a certain first unit to the others, and a second after that, and again a third; there will be a second, of course, after the second, and a third after the first one: wherefore, the monads would be antecedent to the numbers of which they are composed; as, to give an instance, in the duad there will reside a third monad antecedent to the existence of the number three, and in the triad a fourth, and in the tetrad a fifth, before the existence of these numbers.
No one, indeed, therefoiie, of these aforesaid „, 6 1 nconsMi* philosophers hath asserted that the monads are tency,thereforo, incapable of comparison after this mode. But, in gL'temsIn ^"' accordance, to be sure, with the principles of those regard of speculators, it is reasonable that the case should °"*"'^®'^- be even so; though, according to reality, such is impossible For 'Jtio that monads should be prior and subsequent il D B 870 THB MKTJLFHTSICS OF ABISTOTLE. [BOOK xA reasonablo enough, provided there may be in existence both a certain first monad and first unit; and that in like manner, also, this should be the case in r^ard of duads^ on the supposition that there is a first duad likewise. For after that which is first it is rational and necessary that there should be a something that is second, and if a something that is second, a third, and so, therefore, of the rest in order. At the same time, however, to assert the existence of both— even the existence of a first monad, and of a second after unity^ and of a first duad — this is impossible. But they introduce a monad, I admit, and a first one, but no longer do they bring forward a second and a third; and they introduce a first duad, but no longer do they bring forward a second and a third. But it is evident, also, that such is not admissible on the supposition that all the monads are incapable of com« parison — I mean, that an actual duad, and a triad, and so the other numbers, should have a subsistence. For whether the monads be devoid of difference, and whether they are severally different one from another, it is necessary that number be reckoned according to addition; as, for instance, the duad by the addition of one to another one, and the triad by the addition of another one to the two, and the tetrad in like manner.
Inasmuch as these things, however, are so, it iB the^genS^ratfon iiopossible that there should be a generation o ' of number* numbers after this mode, that is, in the same man* does not take,.,,.. i /• xn place after a ucr as ccrtam speculators generate them from the **!"""?,®^® duad and from unity. For the duad becomes a generation portion of the tnad, and the triad of the tetrad; anTfromunUy. ^^^ ^^ *^® Same manner does it happen in the case of those numbers, also, that follow next in order. But from the first duad, and from the duad that is indefinite, is formed the tetrad, being two duads in addition to the actual duad; but, on the supposition that the actual duad is not a portion, there will exist still another single duad, and the duad will be derived from unity itself, and another one. And, if this be the case, it is not possible that also an indefinite duad should constitute the other element, for it produces one monad, but not a definite duad. Further, beside the aotaal triad, and the actual duad, how, may I aedc, will there exist Mber triads and duads^ and in what manner are they com* Cfi. YII.] ABSUBDITIES OF THIS DOGMA. 371 pounded of prior tind subsequent monads? for all these assumptions are even fictitious, and it is impossible that there be a first duad, then an actual triad; and it would be necessary that this should be the case on ^e supposition that unity and the indefinite duad will constitute elements of numbers. If, however, consequences that are impossibilities ensue, it is likewise impossible that these should be first principles.
If, indeed, therefore, the monads are dif- g. These, then, ferent, any one whatsoever from any one what- ^ *^« results soever, these and such other results necessarily the monads^ ensue. incomparable.
But if the monads^ that are resident in another 9, Another number are difierent, and others that are inherent theory on this in the same number are alone devoid of any such ^thequ^ mutual difference, even in this case not a whit the difficulties, less do consequences ensue that are attended with difficulty. As. for instance, in the decade itself are involved ten monads, and the decade is composed both of these and of two pentads. Since, however, the decade itself is not an niustrated by ordinary number, and since ^ it is not compounded the case of the of ordinary pentads, as neither of ordinary ®^ ®* monads, it is necessary that the monads should involve a mutual difference — I mean, those that are contained in this decade. For, if they do not involve this difference, neither will the pentads be different of which the decade is composed; yet, since they do involve this difference, the monads, likewise, will differ. And, on the supposition that they differ, whether does it follow that there will not be inherent different other pentads, but merely those two, or that there will be inherent such? and if we do not suppose this to be the case, namely, that they will be inherent, it is absurd; or, if they will be inherent, what sort will be the decade that is composed of those? for there is not another decade resident in the decade beside itself. But, assuredly, also it is necessary a^a of the that the tetrad, at any rate, be not compounded ^trad. of the ordinary or casual duads; for the indefinite duad, as they say, receiving the definite duad, has produced two duads, for it causes the duad it has received to become two.
^ Some commentators make chapter viii to commence with these kordB. * Bekker reads oM '^dp, I have followed the Pant edition.
bb;} 372 TH« XBTAPHTSIGB OF ARI8T0TLK. [BOOK SOL