Many, indeed, therefore, are the sources of the error with respect to these causes; but parti- fhe^'^noif-Jensr cularly does this remark apply to the doubt pre- this dogma valent downwards from Antiquity. For it appeared «^*"^"*«*- t9 the Philosophers of ancient days that all entities will be one — I mean, entity itself — unless one should adduce a solu- tion of the doubt, and at the same time would advance in the investigation in a line parallel with the theory of Parmenides-^ ** For tLis would you never know tc be * non-ens; * * * » For mstanoe, in the " De Ccelo."
* This principle Aristotle establishes in book XI., the way having been prepared for it in book VIII. and the end of book X.
* The Leipsic edition takes these words as uttered by Aristotle him- ■elf; I have followed Didot in making them a quotation from Parmenidea.
SdG THE XETAPHTSIOS OF ABI8TOTLB. [BOOK Xllt • but there is a necessity for showing, in regard of its existence^ that *' non-ens" has an existence; for in t£is way out of entity and something else will entities arise, supposing they are many. Although, in the first place, indeed, will tiiis be truf if entity is denominated multifariously; for one entity sig- nifies that a thing constitutes substance, and another that it is quality, and another that it is quantity, and so of the rest of the categories, therefore. What sort of one will all the entities in such a case be, if non-entity will not have an existence — whether will they be substances, or passive oon-. ditions, and other things, truly, in like manner; or will they constitute all things, and the one will be this particular things and such like, and so much, and such other particulars as signifyone certain entity? But absurd — ^nay, rather, impossible — ^would be the assertion that one certain nature produced should be a cause, and that of this entity, and of the same entity, something should be this particular thing, and some- thing else should be endued with quality, and that this should belong to quantity, and that to the place where. In such a case, may I ask, from what sort of nonentity and entity will entities subsist? for also multi&riously is denominated nonentity, since, likewise, this is the case with entity; and non-man signifies that which is not this, and the non-straiglit the not being a thing of this description, and the being not- three cubits that which does not possess this particular quality of measure. Of what sort, therefore, of entity and nonentity are many classes of entities? 5. The utter ^^^ ^"^ advocate of this opinion is desirous of impossibiuty asserting what is false, and of calling this nature of is scheme. ^Q^Q^^i^jy q^^ ^f which and entity arise th< many classes of entities that are generated. Wherefore, also, it was said that it is requisite that something that is false be supposed in the same manner as also geometricians allow, hypothetically, that a thing is pedal ^ which is not pedal. And it is impossible that these things be so; for neither dc geometricians suppose anything that is false — for that is not what is the object of the proposition in the syllogism — nor are things generated nor corrupted from that which consti- tutes nonentity after this mode. Since, however, nonentity, ^ Tida is Taylor^s traaBlaUon; the word means, ''what is of the niflasuro of a foot."
OB. U.] RELATION AM) PLURALnT. 397 according to its declensions,^ is styled in an equal number 01 ways with the categories, and besides this tbat is denominated nonentity which subsists as what is &'se, and that which subsists according to potentiality, from this generation takes place — fix)m that which is not-man but man in capacity is generated a man, and a thing that is white from that which is not-white in energy but white in capacity; and, in like manner, is it the case whether both one certain thing ia generated, and whether many are.
The inquiry, however, appears to be as to how g jj^,^ ^^^ *'ens," which ispredicated according tosubstances, "ens" consti- should constitute what is plural; for numbers, ^^'•P^^^^^y' and lengths, and bodies, are things that are being produced. Now, absurd is the inquiry as to how, indeed, entity which constitutes the nature of some particular thing is plural, and not also to inquire how it possesses either qualities or quan- tities. For, beyond all doubt, the indefinite duad is not a cause, nor yet the great and the small, that two things are white, or that there are many colours, or tastes, or figures, for these would be numbers and monads. But, really sup- posing that they attended to these inquiries, at least, they would have perceived also in them the cause; for the same thing, and that which is analogous or proportional, would constitute a cause. For the actual deviation is a cause also of the opposition that is under investigation by them, as subsisting between entity and unity, from which and from these such persons seek to generate entities, and have adopted their hypothesis in regard of relation and inequality, because there neither exists a contrary nor negation of these, but one nature of entities as both this particular thing and that particular quality.
And one ought, also, to institute this inquiry, 7. xheinqniiy namely, as to how relatives are plural, but not ^ow rei^^^es single. In the present case, however, the inquiry "* ^ is as to how there are numerous monads beside the first one; but they do not also further inquire how there are many unequals beside the unequal. Although they employ and affirm the existence of the great, the small, the much, the few, of which numbers consist — the long, the shorty cf which ^ The Latin is ''casoB." Aristotle, in tke Orgazon, tues nhia word fco mean ** the mood of a syllogism."
398 THE XRTAPHTSICS O^ ABI8I0TLE. [BOOK Xm length (Consists — the hroad, the narrow, of which the surface ii oumpobed — the deep, the low, of which the bulks ^ consist,-— and in* this way, fiirther, they without doubt afl&rm the existen3e of as many species of relatives as they may intro- duce. What, therefore, let me ask, is the cause with theso of their being plural? It is requisite, therefore, indeed, as we have affirmed, that entity in capacity should be supposed as subsisting in each of these; but by one who makes these assertions is this also evinced — ^namely, that this particular thing constitutes an entity in capacity, and a substance, but nonentity in itself, because it constitutes a relative: just as if he should speak of something of such a quality, whidi is neither unity nor entity in capacity, nor a negation of unity nor of entity, but one certain thing which is something belong- ing to entities; and much more will this be the case, as liM been declared, if he prosecuted the inquiry as to the manner how entities are plural, not through the investigation as to the mode those things that belong to the same predicamental line constitute many substances, or many things endued with qualities, but how they are many entities; for some things are substances, but some, passive states, and some^ relations.
I. The inquiry ^Q the casc, therefore, of the rest of the cate- ibout plurality gories, the subsistence of plurality involves the to the other matter also of some other investigation; for, on categoric*. account of their not being separable, as the^ubject becomes, and is plural, and those things that are endued with qualities and quantities are plural likewise: although, at least, it be necessary that there should subsist a certain matter for every genus, save that it is impossible that it should involve an existence separable from substancesi. In the case, however, of those things subsisting as a certain particular thing, there is involved some reason in the inquiry how this particular thing is plural, if it will not be something particular, and this very particular thing, and a certain nature of this description. But rather does thif doubt originate from hence, how quantities are many sub- stances in energy, but not one. However, without doubt, even ^ 6fKovs. The word <^kos means either " a curve^'* and is akin tc ipfKvKot and the Latin "uncus," or'*' a bulk;** and it is then, aooordiiig to Buttmaiii to be referred to the root If7ic«, i¥fyKU¥» ea, IH.] DIFFEJEiEVT FYTHAGOREAK theobies. 399 {hough this particular thing is not the same with ihat which is a certain quantity, it is not expressed how and why entities are plural^ but hew and why quantities are pluitil. For every number signifies a certain quantity, and the monad constitutes nothing else than a measure, because it is, according to quantity, what is indivisible. If, therefore, a quantity be different from that which subsists as a definite particular, from what it is that such definite particular results is not declared, nor how plurality subsists; but, if it is the same, the person who makes the assertion supports many contrarieties.
And one may also prosecute the inquiry, as 9. what regards number, whence are we to obtain our con- ^rSie exist-" fidence as to their existence] For in the doctrine enceof number, of ideas the Idealists furnish a certain cause for OT*mathema?* entities, since each one of the numbers con- ticau stitutes a certain idea; but the idea is the cause of exist- ence to other things, in some way or other, to be sure: for let this be assumed as a supposition of theirs. To one, how- ever, who does not think in this way, on account of discern- ing inherent difficulties independent of the doctrine of ideas, the case is different; so that on this account, at least, he does not constitute them as numbers: but to one who introduces mathematical number, whence, may I ask, is it necessary even to have confidence in the existence of number of such a description, and in what respect will such be serviceable to other things] For neither does such a one sa^ that it is the cause of anything who affirms its existence; but such a one asserts it as being a certain nature which involves an esseu^ tial subsistence: nor does it appear that it is a cause, for all the speculations of arithmeticians, as has been stated, will likewise have an existence as conversant with objects cogni^ sant to our senses.
CHAPTER III.i Those, therefore, that posite the existence of 1. Those who ideas, and say that these are numbers, should identify ideM • make an attempt to inform us how and why they ^ "'^ ' * Arisiotle has already taken notice of these variouB BubdivittonP of tfte theoriw about nnmberi^ in book XII..
400 THE METAFHTSIGS OF ARI8T0TLB. [bOOK XJTL subsist; since, acoording to the expasition^ of each, every ide$ constitutes one certain thing that is different from what we regard the many as being. Doubtless, howeyer, since these things are neither necessary nor possible, neither is it to be affirmed that mathematical number exists separably, or numbers on accoimt of theso at least But the Pytha*- with things; goreaus, on accoimt of their perceiving many passive qualities of numbers as subsisting in bodies cog- nisant to the senses, made entities to be numbers, I admit, not involving, however, a separable existence; but they regarded entities as compounded from numbers. And why sol be- cause the passive qualities of numbers subsist in Harmony, or mathema- ^^^ *^ *^® Heaven, and in many other things, ticai entities To those, however, who maintain that ma- with numbers, j^^jguj^tical number exists merely, nothing of this kind is it admissible for them to affirm — that is, if they follow their own hypothesis; but it was asserted by them, because of these will there not exist systems of scientific knowledge. We assert, however, that the case stands^ as we affirmed formerly. And it is evident that mathematical numbers do not possess a separated subsistence; for, if they did, the passive qualities of those that have actually been separated would not have been resident in bodies. 2. Aristotle's ^^® Pythagoreans, indeed, therefore, as regards criticism on the a point of this description, are not deserving of pythagorics. reprehension in any way; but so far, however, as they constitute physical or natural bodies out of numbers, or, in other words, from things not possessing gravity nor having lightness, tilings involving lightness and heaviness, — so faXf I say, they seem to speak respecting another heaven, and other bodies, but not of those that &11 under the notioe of our senses.
8 Those Those, howevcr, who constitute number a« Who assert the involving a Separable subsistence because ax- sSenc?©?^ ioms will not exist as inherent in objects cog- numbers, nisant to the senses; the assertions, likewise, ^ This is the way Taylor renders this passage. The Latin version, howeyer, would construe it as follows: — " Those who lay down that ideas exist, in their making an abstraction of every general, independent ol many singulars, in this way make an attempt to declare why, and from what caue&, each is one.** Some copies read wtp\ instead of iropd r^ roXAd ' As he has done in book XIL OB. III.] NUMBEB8 AND M4THEMATI0AL ENTITIES. 401 of the existence of the other, that is, of the mathematical entities, will be true; and these serve to cause a soothing sensation^ in the soul: and they suppose that numbers exist and involve a separable subsistence; and in like manner is it the dase with the magnitudes of the mathematicians. It is evident, therefore, that also the adverse argument will enun- ciate things that are contrary, and the point which just now has been declai'ed a matter of doubt must be decided by those who speak in this way — namely, as to why, on the sup- position of these things not by any means being inherent in objects cognisant to our senses, the passive quaUties of them should be in sensibles.
But there are some who, from the &ct of the ^ «^ ^ ^ existence of boundaries, and extremities — vi&, led to this from a point being the boimdary of a line, Jomef ^**^ and again, a line of a sur&ce, and a sur&ce of a solid — imagine that natures of this description exist necessarily. Therefore one ought also to discover, as r^ards this reason, whether it may not in reality be very weak; for neither are extremities substances, but rather do all these constitute limits or boundaries, since both of walking, and, in general, of motion, there exists a certain limit. Is, therefor^ this limit some particular thing, and a certain substance 1 but to indulge in such a supposition is absurd. Certainly, however, ad- mitting that they have even an existence, all of them would be found amongst those objects that &11 under the notice of our senses, for the argument itself proclaims their existence in these. Why, then, will they involve a separable sub- sistence But, further, would one who was not very 5. why prior credulous investigate respecting, therefore, of gJJ^^'J^^^j' course, every number and mathematical natures, to subsequent as to why such as these as are prior contribute ""^' nothing to those that are subsequent; for, according to those who say that mathematical natures merely exist, though number should not have any existence, yet magnitudes will have a subsistence, and though even these were not in ^ o«/yc«~"adblandii]ntiir.*' The word literally is applied to animab in their fawning; e,g. dogs wagging their tails. I cannot conceive what has given rise to Taylor^s tnmslating, ''causing perturbation;* he, in all Ukelihoody followed some different reading.
402 THB ICBIAPHYaiCB OF ARI8T0TLB. [BOOK ZIII.
exifltenoe, yet still would the soul exist, and such bodies as are cognisant to our senses.
It does not, howeyer, appear from the pheno- tion^pSSr* na®i"^ *^* Nature is devoid of a connexion with tqvLtiLy to herself, just in the way that a vicious tragedy **** might be. With those, however, who are for establishing the subsistence of ideas, this, no doubt, escapes them j for they constitute magnitudes out of matter and number — ^from the duad, indeed, lengths, and from the triad, surfisuses, perhaps, and from the tetrad, solids, or also from other numbers, for there is no difference. But whether, one may ask, will these exist, at any rate, as ideas, or what, pray, will be the manner of their subsistence, and in what way are they contributors to entities, as to their being? for, as with mathematical entities, so do these neither contribute anything in that way. But, assuredly, neither of these doth there exist, at least, any theorem, unless one should choose to put in motion mathematical entities, and to create certain peculiar opinions of his own: but it is not difficult for those who put forward any description of hypotheses whatsoever to be able to be prolix, and to speak without ceasing.
Those, therefore, who cement together^ matheitiiy icali tors having constituted two numbers, the one of form, and the other of a mathematical nature, by no means either have declared, or would they be able to say, the manner how this is effected, and from what mathematical number will be compounded. For they make it intermediate between formal and sensible number. For, if we suppose that it is composed of the great and small, the same will it be with that which is belonging to the ideas; but if from some other thing that is small and great, this will not be the case, for number produces magnitudes. But if he will speak of any- thing different, he will afi&rm the existence of many elements; and if the first principle of each thing constitutes a certain original unity, there will be in the case of these a something that is common — ^namely, unity. We must likewise investigate how, also, these many are one, and, at the same time, in npoffyXi^X^l'*^^^' ^^ yrord ia akin to yxitrxpcs, which meant "gluey."
identi^^nathe- Hiatical entities with ideas are in this way guilty matic^ entities of error; but the earliest amongst these specula- III.] HATHEHATIOAL ENTITIES AND IDEAS. 403 regard of the fact that it is an impdisibility that number should be produced otherwise than from either unity and an indefinite duad.
Therefore are all these consequences irrational; Jigt^c^^yJ^g"' and they are at yariance both themselves with trated. one another, and with those statements that are reasonable, and there appears to be inherent in them the " long discourse " of Simonides. For a long discourse^ is like that of the slaves, when no wholesome assertion is made. But also they appear with respect to those elements, the great and the smetU, to bawl out as if they were being dragged away with violence, for by no means are they able to generate number without doubling that which proceeds from unity.
But it is absurd — nay, rather, a certain one of 9 ^^^ ^^^ the impossibilities of this system — to introduce these systems generation in the case of entities that are eternal. I^neration't As to the Pythagoreans, indeed, therefore, they ^^ y^ ^^ have no need to labour under doubt whether PytbagoreanA they do not introduce or do introduce genera- ^^^ Physicists, tion; for they manifestly affirm that unity has been esta- blished, and that, accordingly, what is immediately nearest to the Infinite, whether from surfaces, or from colour, or from seed, or from such things as they are at a loss to declare, is so, because it has been dragged forward, and bounded by a limit or termination. Since, however, they frame Cos- mogonies, and wish to express themselves physically, it is just that they should institute some inquiry ccnceming Nature, but as a departure from the present method of in- vestigation; ^ for we are engaged in the investigation of the first principles belonging to things that are immovable: wherefore, also, we must examine into the generation of numbers of this kind.
^ d fuucpos \6yos. As we learn from the oommentators, the allusion hsre is to certain portions of the writings of Simonides, which he styled A^yoi "Araicroif " loose thoughts," as a modem author would style them. In these Simonides mentions ihe sort of language that it would be natural to suppose slaves would employ if questioned by their masters to give an accoimt of themselves as to certain derelictions of duty. " These. would be very tedious, and long, and verbose," says Simonides, ** but nothing to the point, no sound reasoning; not evea would Uie apology contain a probable argument.** ' Ai Aristotle hai already shown repeatedly in this Treatiat.
dd2 404 TBI MBTAFHTSIOS OF ABISTOTLB. |2O0K XlBw CHAPTER IV.
1. Generation Thbt do not speak of the generation of th^ In the system odd number, therefore, as if it were a thing of Pythagoras, gyi^jgjj^ ^)^q^ ^f ^^q gy^^ there 18 in existence a generation; but the even, in the first instance, certain specu- lators constitute from unequals — I mean, the great and small equalised. It is, then, with them necessary that in- equality should be prior to the equalisation of these. I( however, there always existed things in a state of equalisa- tion, they would not haye been unequal at a prior period; for of that always existing there is not anything prior. Wherefore, it is evident that it is not for the purpose of speculation that they make the generation of numbers. 2 The relation ^* involves, howovor, a doubt,^ and a subject- between ele- matter for reprehension, to one who acquires ™®2yoS??. **^* knowledge judiciously, how disposed, in respect of the good and the fair are elements and first principles. The doubt I mean is as follows: namely, whether any of those is such as we are disposed to denominate the good itself and the best, or whether they are not of this sort, but are of subsequent growth? for the difficulty appears to be acknowledged by Theologians — ^by certain amongst those of the present day — who do not actually make an assertion of this description, but who maintain that from the principle of progression found in the nature of entities, the good and the fair make their appearance on the stage of Creation. This, however, they do, cautious about falling into a real difficulty which ensues unto the systems of those who affirm, as some do, that unity constitutes a first prmciple of things, s Where th ^^* * ® difficulty to which I allude is not difficulty lies in Started on accouut of this — ^namely, their ascribing this contro. u ^y^^ ^^^ ». ^^^ ^ first principle as a thing that ia implanted in it — ^but firom th0 fact of their making unity a first principle, and a first principle as an element, * Some make chapter iv. to commence with these words, bot I havl followed Bekker mi Didot OH. lY.] THE GOOD A PARAMOUMT FBINOIPLBi 400 and number as consisting from imitj. But the poets — ^those of the early ages^ — acted in a way similar to this, so far as they assert the dominion and the rule not of these first principles, such as Night, and Hearen, or Chaos, or even Oceanus, but of Jupiter.
Notwithstanding, to these persons does it 4. Antiquity, happen that they assert things of this description ^^^^® ^^^j on account of their changing the dominative antecedence of principles of the Universe; because those of ^^ r6 dtaesu, these speculators that, at any rate, were for adopting prin- ciples of a mingled description,^ and in respect of their not broaching their theories in a £a.bulous garb---for example, as Pherecydes ^ and certain others — ^have, in point of feet, esta- blished " the best " as the earliest principle of generation. And this is the case also with the Magi,^ and with the Sophoi or sages of a subsequent period, such as both Empedodes and Anaxagoras; one of whom constituted Harmony as an element, and the other made Mind a first principle of things. Of those Philosophers, however, who asserted the existence of immovable substances, some, I admit, affirm unity to con- stitute the actual good; they, however, in the most eminent degree regarded unity to constitute the gid>8tance of the good. The matter of doubt, of course, therefore, comes to this — as to what way scientific men ought to express themselves on this subject.
It would, however, be surprising if in that - mj^,. which is original, and eternal, and most self- elvn^m^* ' ^ The speculationB in this chapter are moat remarkable, indeed, and well worthy of the attention of the student. The meaning plainly ia Uiis, that the poets recognised in the element of good apparent in things, a paramount principle of creation.
^ This word perhaps applies to ol ipxoprts; that is, the domlnatiye principles which were of a mingled description, were put forward by Anaxagoras and Empedocles.
^ Pherecydes was a very ancient philosopher, and a very enlightened one according to Cicero, Tusc Qusest. lib i. c. 16. Diogenes Laertiua makes him one of the ** wise men of Greece." As to his philosophy, we are given to understand that he coincided with his contemporary Anaximander in most points.
* As to the Magi, the student will do well to consult, amongst many other sources of information. Gibbon's Decline and Fall, c viii.; Stanley's History of Chaldaic Philosophy, pu't 16; Diogenes LaertiuJk book I., Introduction; and Hyde, De Religione Persarum.
406 THB METAFHTSIOS OP ABISTOTLB. [bOOK ZUI.
"ie^*crwSion. sufficient for its own subsistence, this rery origi* nal attribute — I mean> the self-sufficiency and the conservation of itself — should not be discovered as that which constitutes what is good. But, undoubtedly, not on account of anything else is it incorruptible or sufficient to itself, than on account of its existence or condition of sub- sistence after an excellent mode. Wherefore, indeed, the assertion of the existence of a first principle of this descrip- tion appears reasonable, as &r as its reality is concerned. 6. Doei the ^^^ *^^s» howevcr, to be unity, or, if not unity, TO dyaBop eon- both an element and an element of numbers^ is stitute unity t impQggjjjiQ. f^j, much difficulty is coincident with an hypothesis of this kind, and certain speculators, in their attempts to avoid this, have lost sight of the point in ques- tion, when they acknowledged unity to constitute an original first principle and an element of things, but a principle and an element of number, however— I mean, mathematical number. For, supposing this to be the case, all the monads would become a something that is good, and there would exist a certain fair supply of things which are good.