subject of that which is allowable as a subject of perplexity doubt here. ^^ ^j^^ ^^^^^ ^^ spccies viewed in reference to genus, when one may admit the subsistence of universals— namely, whether animal itself may reside in animal, or there be something therein that is different from animal itself) For, on the supposition that this is not separable, it will not create any doubt; but, on the supposition of its being separ- able, as the persons who make these statements afiirm, it would not be easy to decide the question of doubt respecting unity and respecting numbers; and if such be not easy, it is necessary to say what is impossible. For when any one understands unity as involved in the notion of the duad, and, in general, in that of number, the question arises whe- ther does he pero^ve a o^rtain actual thing or something Alse?
CH. IX.] WHAT DOES NUMBER CONSIST FROlCl 383 Some, therefore, generate magnitudes from ^ Different matter of this description, but others from a modes of the point; but a point seems to them not to be an S^Stude/^ unit, but to involve some similar quality with unity, and to belong to a diflferent matter — such as multitude belongs to, but which does not belong to multitude — respect- ing which not a whit the less it happens that one feels the same doubts. For if, in &ct, the matter is one, the same thing will be a line, and a sur&ce, and a solid, for from the same things will be derived that which is one and the same thing: but if the matters are many in number, and there will exist one matter of a line, and another of a surface, and another of a solid, assuredly, they will follow one another, or they will not; so that the same consequences will ensue . likewise in this view of the case. For either the surface will not involve a line, or it will constitute a line.
Further, how it is admissible that number 5. Doesnum- should subsist from unity and plurality, there is ber consist of no attempt made to show; yet, howsoever, there- raiity, or unity fore, they happen to frame their statements, they *°*^ duautyt encounter the same difficulties as those who make number to consist from unity, and from the duad, which is indefinite. For one, indeed, generates number out of that which is pre* dicated universally, and not out of a certain multitude; but the other from a certain multitude — ^yet from that which is primary: for they say that the duad is a certain primary multitude. Wherefore, there is no difference, so to speak, dis- coverable in all this; but the same doubts wiil follow whether we assume it to be mixture, or position, or temperament, or generation, and whatever things of this kind there are.
But one might especially inquire — supposing ^ j^^^ ^^^ that each monad is one — from what does it does each mo- subsist? for, undoubtedly, each will not constitute °"^ *^®°'^* °^* unity itself at least: but it is necessary that it be derived from unity itself, and from plurality, or from a portion of plurality. The assertion, therefore, that the monad consti> tutes a certain multitude is impossible, since, at least, it is indivisible; but the assertion that a monad is from a portion of multitude involves many other difficulties: for it is neces- sary, also, that each of the portions be indivisible, or that it constitute multitude^ and that the monad should be divisible^ 384 THE METAPHTStCB OF ARISTOTLE. fBOClt XH and that unity and the multitude should not be an element^ for each monad is not from multitude and an unit. Further, the person who puts forward this assertion does nothing else than make another number, for multitude is a number of indivisible things.
7. This con- Moreover, also, it is worthy of inquiry, in n'ected with tha respeot of those who make assertions in this way, number^i^ii^ whether number may be infinite or finite? ^ for, as 0nite 01 infl. [t appears, the multitude was also finite out of ' which and imity finite monads were produced, and multitude itself is different from infinite multitude. What sort of multitude, then, and what SGd: of an elementi is unity? And in like manner might ontt inquire, also, and as to a ret^pecting a point and the element, from which dros^ifsubTist* ^^®y make magnitudes; for there is not merely, fr<>mr at least, one actual point. Therefore, at any rate, one might ask the question from what each of the rest of the points will ensue? for, undoubtedly, it is not from a certain interval, at least, and an actual point. But, assuredly, neither is it admissible that indivisible portions constitute the portions of an interval, as they do of the multitude from which the monads consist, for number is composed of . things that are indivisible; but this is not the case with magnitudes.
8. Conclusion Now, all thesc Statements, as well as others of drawn. ^i^jg kin^^ render it evident that it is an impos- sibility for number and for magnitudes to possess a separable subsistence.
9. In the dis- Moreover, the discordancy of the original cordancyof frasncrs of this Theory respecting numbers is an these ^specula- indication that these things, not being true, are iiiow «j"faise- fr*^^^* ^^^^ sourccs of confusion unto them. bood of their For somc of this school constituting matheraa- theories. ^.^ natures merely in addition to those that are cognisant by the senses, when they came to perceive the difficulty and fiction attendant upon forms, have withdrawn their assent from the ideal or formal number,^ and have introduced mathematical number in its stead; but others wishing to make forms to exist at the same time with the ' This point has been discussed in chapter vili. ^ 4nstotle qieans the Pythagoreans.
CB. IX.] DI600RD IN THB PTTHAOOBIO SCHOOLS. S65 numbers,^ but not discerning in what mannei>--on the sup- position of one's admitting tiiese as first principles — nmthe- matical number will subsist independent of that which is ideal, have constituted ideal and mathematical number as the same in definition; since, in point of &ct, at least, mathe- matical number has been done away with in this hypothesis: for they introduce peculiar theories of their own, and such as are not consistent with mathematical science.
The philosopher, however,^ who first sought to establish the existence of both forms and num- took a true ^'^ bers, in obedience to the dictates of reason assigns jibTe^t^^^* a separate subsistence to forms and mathematical entities. Wherefore, it happens that all of this sect express themselves correctly in a certain respect, no doubt, yet not entirely with correctness. And themselves, likewise, acknow- ledge so much, as being persons who do not make the same statements at all times, but such as are contrary with one another.
And a cause of this is the following, that their j^ Theincon- suppositions and first principles are false. But sistencyorthe it would be difficult from things that are not re^uuTnh'e* properly disposed in regard of truth and false- fai«ehood of hood to frame an hypothesis with correctness, «""?""<' p««* according to Epicharmus; for in this case, as soon as the assertion is made, immediately also is apparent that which is not properly disposed in the before-mentioned respect.
Regarding numbers, however, let thus much suffice of the questions that have been started, tion concerning and of the definitions and distinctions that have n«n»b€wended. been framed. For a person who has been brought to a state of acquiescence in a theory would still the more be induced to yield assent fr*om the force of more numerous arguments; but nothing further will prevail towards inducing persuasion in the case of one who has not been prevailed upon to yield his assent already.
With respect, however,^ to first principles, and is. The theories first ca^ and elements, whatever aLrtions ^'^^ ^ Suolx as SpeusippuB and Xenocrates.
' Thif is Plato, who reoognised the existence of both forms and DJmben, but coutended for their subsistence distinctively, wberetf tae Xenocratic dogma was to identify them.
' Some make chapter xii to commenoe here.
00 386 THB XVTAFHTSICB OF ARI8T0TLB. [bQOK fXt vant to onto- those persons put forward, who are engaged ib thMe ^^the^ framing ^ their dbtinctions in regard of a B¥rt)Btaiioe supranattt. merely cognisant by the senses, some of these, indeed, have been declared in our Treatise on Physic; but the remainder of them are omitted, seeing that they do not belong unto the plan of inquiry proposed to be pursued in our present Work. But whaterer assertions are made by those who afi&rm that there exist different substanoes independent of those that fall under the notice of our senses, this is a subject for investigation consecutive to those states ments that have been already made upon this point 14. Amongst Since, therefore, certain persons affirm that naturaSsts there are such like ideas and numbers, and that some put for- the elements of these are elements and first JJid^iSTidSS, principles of entities, with respect to these we as the original' must inquire what it is they say, and how they "**', say it. Those philosophers, then, who are for constitating as such existences numbers^ only, and such as are mathematical numbers, are to form subjects for examina- tion afterwards.
15 Two ftinda- ^^ thosc, howevcr, who affirm the existence of mental mis- the ideas, ouc should at the same time be able to idealists! Mid perceive both the manner of their existence, and the source of the matter of doubt that is prevalent regarding ^^' them; for also do they constitute ideas as existing simultaneously with universal substances, and, again, they view them as involving a separate subsistence even from singulars. But that these statements are not possible has been previously made a matter of doubt. A cause, however, of their connecting these substances into one and the same species — I mean, with those persons who call ideas universals — is because they are not accustomed to constitute them as the same substances with sensibles.
16. The Ideal- Some singulai-s, indeed, therefore, that are iRts cannot involvcd in objects that fall under the notice of asa^u6?<rf our scnscs they considered to be in a state of their system, fly^^ ^j^^ ^q^ qj^q of them to remain in a condition of permanence; but that the universal subsists both beside these and is something that is different from them. But, as ' Aristotle has likewise eiamined these points in book L, and ia Physics, book L * FtWe book XUl.
OB. X.] IDEALISM NOTICED ONOE MORE. 387 we IiiEiire declared in the foregoing statements, Socrates com- munioated an i npulse, it is true, to this inquiry, by reason of definitions, jet he did not r^dly abstract them, at least, from singulars; and, in thus not assigning them a separate subsistence, he formed his conceptions correctly.
And one could make this assertion evident j^ gocrates in from the actual occurrence of facts; for without this theory is universals, of course, it is not possible to attain SSteM^f fact. Unto scientific knowledge: but the abstraction of them from singulars is a cause of the difi&culties that ensue in regard of ideas.
But some, as if it were necessary that if there are certain substances beside those that are cog- of tMs theory" nisant by sense and are in a state of flux, they »^"* univer- should involye a separate subsistence— some, I say, were not in possession of other natures, but brought forward those that are denominated universals; so that it happens that both universals and singulars are nearly the same natures. This, to be sure, then, would itself amount tp a certain essential difficulty in those statements that have been put forward above.
CHAPTER X.
CHAPTER X.
What it is, however, that is attended with ^ ^^ ^^.^.^^ doubt, both unto those who affirm the existence or statements of ideas, and those who deny their existence, has, JS^^*^^ '^^ likewise, been observed previously,^ in the doubts enumerated at the beginning of this Treatise; let us, however at present, make a repetition of the statements made there. For if, indeed, one will not admit that substances involve a separate subsistence, and that the singulars of entities subsist in that manner as they are declared to do, such a view of things will overturn substance, as we are disposed to allow; yet, should one assume that there are substances possessing a separate subsistence, how will he establish the elements and the first principles of them?
For, supposing them to subsist as a singular, and i. Results of Dot as an universal, entities of this kind will be ekmentt^J*^^ ' Vide book II. chap, ii 388 TTHB HETAPHTSICB OV AKI8T0TL1S. [BOOK ZII.
separable sub- SB numerous OS elements, and the elements will HrtM^a^iU^ not be things capable of being made objects o| jruiar and not scientific knowledge. For let the syllables in a ^illustrated^' ^ovd be granted to be as substances, and let the to *^® «3j|i«We" elements of them be the elements of substances^ in such a case as this it is, therefore, necessary that BA be one, and that each of the syllables should be one, if not, in fact, universally and the same in species, yet each must be one in number, and this certain particiUar thing, and not equivocal; and, further, they regard each one as the very thing itself. If syllables, however, be thus, so also will those things be of which syllables are composed There wiU not, accordingly, be more than one letter A, nor will any of the rest of the elements be more than one according to the very same mode of reasoning, in accordance with whi(£ neither is there any of the other syllables that is the same; but there is'one in one word, and another in another. But^ certainly, if this be the case, there will not exist any different entities beside the elements; but entities will constitute elements merely. And, further, neither will the elements be objects of scientific knowledge, for they are not universals; but scientific knowledge is conversant about universals as objects of investigation.
8. Confirmed Now this is evident both from demonstrations^ S?Sinon"tr»f* ^^^ definitions;2 for a syllogism is not completed tion and defi- bccausc this psurticular triangle has angles equal nition. ^^ ^^Q right angles, unless every triangle has angles equal to two right angles; nor because this man is au animal, unless every man is an animal.
But, undoubtedly, if first principles are tmi- principierbe"* versal, or, also, if substances that are compounds universal, of thcsc are Universal, non-substance in such a substan^ be ' case wiU be a thing that is antecedent to sub* Jtencef*'^^ stance; for, what is universal does not consti* tute substance: whereas the element and the first principle are universal. The element, however, and the first principle are things that are antecedent to those to which a first principle and an element belong. And, there- ^ As might be seen in the course of argument which Aristotle put fues in the Posterior Analytics. ' As is done in book YI. of this Treatise.
CH. Z.] FIRST PBINCIPLRS AS UNIYEBSALS 38V fore, do all these consequences ensue reasonably, when both certain philosophers constitute ideas as out of elements, ami when, beside ideas and substances involving the same form, they may be of opinion that there is some one thing that has actually a separate subsistence. I^ however, there is no hindrance, but that, as in the case of the elements of speech, there should be a multitude of the letters A and the letters B, and that A itself and B itself should be nothing beside the multitude of these, on this account, at least, there will be infinite similar syllables.
But the fact that all seientifio knowledge is, ^^^^ ^^^ conversant about what is imiversal, so that it is deny their uni- necessary that both the first principles of entities Si"Sey'be°^ should be universal,and not separable substances — objecu of this feet, I say, most especially is attended with ■*'*®°^® doubtfulness above any of the assertions already mada The assertion that is made is, notwithstanding, in a manner true, and in a manner it is not true; for scientific knowledge, as also the act of scientific cognition, is twofold^ of which one subsists in capacity, but the other in energy.
Capacity, then, I mean that which subsists as 6. How it!• the matter of that which is universal and is in- ^^Jjjj^t® *' definite, belongs to what is universal and indefinite, about the uni- The energy, however, being definite, is likewise JfJ^e'rSS ^** this certain particular thing belonging to this tense it is not certain definite particular thing. But according '*'• to accident it is that the power of vision beholds universal colour, because this particular colour which it beholds is a colour; and what the grammarian speculates into as this par- ticular letter A is a letter A; since, if it be necessary that the firat principles should be imiversal, it is also necessary that those things which subsist from these should be universal: as is shown in the instance of demonstrations. And, if this be the case, there will be nothing that involves a separate subsistence, nor will thero be in existence actual substance. It is evident, however, that in a manner scientific knowledge is conversant about what is universal as an object of its in- vestigations, but that in a manner this is not the case.
BOOK xra.»
CHAPTER I.
. Are con- Resfeotino, indeed, then, this sobstanoe' Itl dpietorth£gsr ^^^ much suffice to have been spoken; bat that all constitute first principles as contraries — as we have observed in our Physics* — ^this is also the case in like manner respecting immoyable substances. Kit is not admis- sible, howeyer, that there should be anything prior to the first principle of all things, it would be impossible that the prin- ciple being anything else should be the first principle of all things; as if one should say that a thing that is wlute was a first principle, not so £ax forth as it is something else, bat so far forth as it is white, and that this, notwithstanding, belong- ing to its subject is white, and is something different at the same time, for that will be antecedent. But, certainly, all things are generated from contraries as from a certain sub- ject; it is requisite, then, that especially this should take place in contraries. Always, therefore, will all contraries belong to a subject, and none of them will be separable. But, as also it appears, nothing is contrary to substance, and reason certifies to the truth of this statement. Not one, therefore, of contraries is strictly a first principle of all things^ bat a principle that is different from these. 2 Different Some, however, make one of the contraries as theories on this matter; certain of them, on the one hand, consti- point. tuting the unequal as contrary to unity, that is, to * This book, which some reckon as book XIV., is somewhat obBcnre, It is not at all times easy to understand what particular set of opinioiis Aristotle is here setting forth: even Taylor, who is seldom baffled on such occasions, is doubtful too, and sesms to think that Aristotle is not expressing his sentiments seriously.
' That is, the Immovable and Eternal Substance which he mentions in the beginning of book XII. Some regard books XII. and XIIL AS one.
' Vide Physics, book I. chap. ir.
OH.L] CONTRARIES AS FIRST FBIKOIPLES. 391 equality, as if this were the nature of multitude; but some, ou the other hand, making multitude or plurality contrary to unity. For niunbers are generated by some, no dcubt; from the unequal duad — I mean, the great and small; yet a certain philosopher generates them from plurality: by both, however, this is done from the substance of unity. For the person who says that the unequal and the one constitute elements, but that the unequal, as a compound from great and small, constitutes the duad, speaks of inequality, and greatness, and smallness, as if they were one; and he does /lot clearly determine that they are so in definition, but not in number. Yet, certainly, oven the first principles, which they call elements, they haye not correctly furnished an explanation o^: some speculators amongst them, introducing along with unity the great and the small, affirm that these three are elements of numbers, the two first, as matter, but unity as form; yet, according to others, the much and the few are elements, because the great and the small are naturally more peculiar properties of magnitude; but, according to the systems of others, elements are things that are more uni- versal in the case of these— I mean, the exceeding and the exceeded.
There is not, after all, any difference, however, 3 j,^^ ^.^^^ between them, so to say, in regard of certain con- ence between sequences that ensue, unless in respect of logical SaterSS! difficulties merely, which they try to guard against, by themselves introducing logical demonstrations. Never- theless, it rests on the same mode of reasoning, at any rate — namely, the assertion of the exceeding and the exceeded being first principles, but not the great and the small, and that from the elements number is prior to the duad, for both are more universal. But now do they make an assertion of the one, but do not make an assertion of the other.
Others, however, have opposed diversity and ^ ^^^^ ^^^ difference to unity; but some introduce, as prin- oppose diver- dples, plurality and unity. But if entities— as Sift^toSlSty. they are disposed that they should be — are generated from contraries, but to unity either nothing is con- trary, or if, then, there is likely to be anything, it is pliuality; and if the unequal is contrary to the equal, and the diverse to the same^ and t«he different to the same— if all this be the casCi 392 THE HETAFHT8ICS OF ABISTOTLB. [bOOK XIIL most especially are those persons who oppose unity to pla«» rality in possession of a certain opinion that may be urged in their defence; nor, howeyer, haye eyen these speculators adequately proyed their hypothesis. For imity will constitute, what is fewness; for plurality is oppo&3d to paucity, but the much to the few.
5. Unity signi- Now, as regards unity, that it signifies a measure^ «cant of mea- is eyidcnt: and in eyery thing is there some* *^^' thing different that may be clasBed as a subjeo^--'- as in harmony the diesis, and in magnitude a finger or foot, or something else of this description, but in rhythm the basis' or syllable. And in like manner, also, in weight there is a certain definite standard of measure, and according to the same manner, also, it is with all things: in qualities there is found a certain definite quality, but in quantities a certain definite quantity, and that which is indiyisible constitutes the measure; for one sort of measure subsists according to the form, and another according to sense: so that there does iot exist any substance that is essentially one.
6 The fore- "^^^ ^^ assumptiou rests on what is in aog'oing rests on cordaucc with reason; for unity signifies that it grounds. Constitutes a measure of a certain plurality or multitude, and number that it is plurality mea- sured, and a multitude of measures. Wherefore, also, it may be concluded, reasonably enough, that unity is not number; for neither is the measure a standard of measure,^ but a first principle, and the measure, and unity. It is necessary, how- eyer, always that measure should subsist as something that is the same in all things: as, for instance, if a horse is the meajsure, that such should be horses, and if a man, men; but if man, and horse, and a god, are measures, they will perhaps be animal, and the number of them will be animals: but if man, and white, and walking be such, by no means of these will there be number, from the fact of all subsisting in one and the same subject according to number; yet, neyerthe- less, there will exist a number of the genera of these, or of some other such category.
' This Aristotle shows to be the sase in book IX., where he treats of unity.
^ fidffis literally means ** stepping," and then is transferred to meiia * the rhythmical close in a sentence."
' I h&ve followed the reading rb lUrpov luvrptu CH. 1.] UaiTY, INF^UALITT, AND PLURALITY. 898 But those who make the unequal as a cer- j Those who lain unity, but the indefinite duad from great snake ineqn*. and small, put forward an assertion very far ^^^''^^^y* from the truth cf things that are apparent and possible; fol these are both piussious and accidents rather than subjects of numbers and magnitudes.^ For the much and few consti- tute passive states of number, and great and small of mag- nitude, just as even and odd, and smooth &nd rough, and straight and curved. Moreover, also, in addition to this error, it is necessary, likewise, that the great and the small, and all things of this kind, should be relatives; but relation, least of all the categories, constitutes a certain nature or sub* stance, and is subsequent both to quality and quantity; and is a certain passive condition of quantity which subsists in relation to something, as has been declared, but does not con- stitute matter or anything else, and, in general, subsists in regard of what is common in relation to something, and in the parts and species of this. For there is nothing that is either great or small, or much or few, and, in short, which subsists as a relative, which is not much or few, or great or small, or a relative, at the same time that it is something else.2 That relation, however, in the smallest degree s. confirmation constitutes a certain substance, and a certain jf^gJ^lP'^^v entity, is indicated by the &.ct of there belonging nature of reia- to it alone neither generation, nor corruption,^ **®°* nor motion; just as with respect to quantity there is increase and diminution, with respect to quality, alteration, with respect to place, motion, with respect to substance, gene- ration simply, and corruption. But this is not the case with respect to relation; for, without being put in motion, at one time it will be greater, and at another time less or equal, so &r forth as the other is put in motion according to quantity. And it is necessary that the matter of everything ^ould be such as the thing itself in capacity: wherefore, also, will this be the case with the matter of substance; but rela* ^ In making a full stop at '^magnitudes,** and inserting the word yhp to commence the next sentence, I have followed Bekker, and differed from Taylor, who follows the same text as Didot. - ' Tl^ rendering, I conceive, explains the sense of the pasMge, * Vide concluding chapters of book X.
894 THE METAPHTSIC8 OF ABIBIOTLa. [SOOK ZUl tion constitutes substance neither in capacity nor in eneigja Therefore,^ it would be absurd — nay, rather, impossible — ^the constituting non-substance an element of substance, and a' thing that is antecedent to it, for all the categoiiies are what is subsequent.
9. Further rea- ^^^ further, elements are not predicated -aa son from the elements of each of the things of which they aife Si'^tf *" elements; but the much and few, both sepa- rately and simultaneously, are predicated of number, and the long and the short of a line, and a suriaoa is both broad and narrow. But i£ doubtless, also, there exists a certain midtitude of things to which always there belongs something, indeed, that is few — as, for example, the duad; for, if this were much, unity would constitute fewness, and, if it were much absolutely, it would be much, after the same manner as the decade, and, if this be not the case, it will be more than this, nay eyen than ten thousand — how,, then, will number, on supposition of the foregoing, in this way consist of few and much, for either both ought to be predicated, or neither? but in the present instance only one of these is predicated.
CHAPTER II.
CHAPTER II.
1. Can things ^^^ it is neccssary absolutely to examine an, eternal be com- to whether, then, it is admissible that things posite natures ^jj^pj^ ^^e eternal should be composed from elements, for they will, in such a case, involve matter; for everything that is compounded of elements constitutes a composite nature. If, therefore, it is necessary that a thing be generated from that of which it consists, (both if it exists invariably, and if it were invariably generated,) but every- thing is generated from that which subsists in capacity ^ — I mean, the thing which is being generated, (for it could no* have been produced from that which is impossible, nor had it any existence before it was generated,) but that which is possible admits of subsisting in energy, and not of subsisting in this way; — now, if this be the case, that number also, most eminently above all things, always subsists, or anytliing ^ This is established in book YIIL CH. II.] ARE THINGS ETERNAL DISCE|IFTIBLE 1 B95 else that inyolves matter, it would admit of non-existence, just as that also which involves the space of one day, and that which possesses any amount of years whatsoever. Now, if this be so, thus much will be true of time also, when it is extended so iis to be without limit.
There would not then exist things eternal, since that is not a thing eternal which admits of i^ore the^ex- non-existence — ^as it has come in our way to treat [hingsTeternai of this subject in other portions of our philo- sophic Discourses.^ If that, however, which is now asserted be true universally, that no one substance is eternal unless it subsist in energy,^ and that the elements are the matter of sub- stance, there will not exist elements of any eternal substance from which, as inherent, this substance is composed.
But there are some persons who make an 3 Di^^ent indefinite duad the element, together with unity; theories on this but as to the unequal, they reasonably enough ^° °** encounter difficulties, on account of coincident impossibilities, from whom so many merely of the difficulties are removed as necessarily arise — on account of the making inequality and; relation an element — to those who make assertions in this way. As many difficulties, however, as ensue independent of this opinion, these it is necessary should exist for those also both whether they constitute out of them ideal number, and whether they do so with mathematical number likewise.