Further, if forms constitute numbers, all the sowedby^the' forms will be such as some certain thing or other Idealist. that is good. Notwithstanding, let any one suppose the existence of ideas of any description whatsoever he feels disposed to admit; for, allowing that they are to bo classed amongst things that are good ^ merely, ideas will not constitute substances: but if, also, they are to rank amongst substances, all animals and plants are good, and the parti- cipants of these likewise.
8. Danger of Now, both do thcsc absurdiUes concur with idX'an? fh?* *^^ hypothesis, and what is contrary constitutes rn dfa»6v toge- an element, whether we assimie it to be plurality ther. Qj. inequality; and great and small will amount to what is an actual eviL Wherefore, no doubt, a certain philosopher avoided the connexion of the good with unity, as if, on this hypothesis, it would be what is contrary, since generation arose from contraries, that the nature of plurality should necessarily be evil. Some, however, affirm the unequal to be of the nature of eviL * This reminds one of the doctrines of Plato, in his yearnings after the reai^ticQ of the various virtueii in form.
OH. V.l irO SYSTEM CAN BEST ON A DENUL OF THIS. 407 Therefore do all these entities happen to have « « „. *v** a share m what is eyil, except unity — ^which con- way is the good stitutes actual unity — ^and we find that numbers ^ capacity, participate in a more unmixed state than magnitudes; it also follows that evil is a place of the good^ and that it shares in and desires after that which is subject to decay of itself; for one contrary is corruptive of another contrary. And if it is the case, as we have affirmed, that matter constitutes everything that subsists in capacity^ — as fire in capacity is the matter of fire in energy — evil will constitute the good itself in potentiality.
Now, all these results concur partly in con- ^^ sovaee of sequence of their constituting every first prin- the foregoing ciple as an element, and partly in consequence ®p^*°°*- of their making contraries first principles, and partly because they make unity itself a first principle of things, and partly because they regard numbers as first substances, and such as involve a separable subsistence, and because they take the flame view of the species or forms.
CHAPTER V.
CHAPTER V.
If, therefore, also, the non-positing of the good j^ ^^^^ ^j. in the rank of first principles, and the positing it lows on the nonin the way we have alluded to, be what is impos- the t6 dtaObv sible, it is evident that first principles are not JriSSSils^* correctly assigned, nor the primary substances. Yet one does not form his opinions correctly, either if he should assimilate the first principles of the Universe to the principle belonging to animals and plants; because from things that are indefinite and unfinished there arise always things that are more perfect Wherefore, also, in the case of the Primary Substances, they affirm that it happens in this way, that neither does any particular entity constitute actual unity. For in objects that are here — that is, that fidl under the notice of our senses — ^are the first principles perfect from which these objects derive their original; for man begets nan, and the seed is not that which ia first. But it would be absurd, also^ the making a place along with mathematical 408 THE METAPHTSICS OF ARI8T0TLB. [bOOK Xltt Bolids — for the place of singulars is peculiar to them; where* fore are they topically or locally separable, mathematical «)lid8, however, are not situated in any certain locality; and the assertion that they will be situated, indeed, somewhere^ and at the same time not to say what the place ia^ is absurd.
But it would become those who say that nilmber orip entities are compounded of elements, and that first p^Spiest li^nibers are the first of entities, that they should, by thus making a division as to how one thing derives an existence from another, express themselves in such a way as to make us acquainted after what manner number originates from certain first principles, whether this takes place by means of mixture.
s. Is it by mix- Neither, however, is everything that has tvef undergone mxiture different fix>m that which is being produced; and nnity will not be a thing that involves a separable subsistence, nor a difierent nature: but they wish that it should be after this manner. Does orbysyn- number, however, we may ask, subsist through thesis? composition as a syllable? But in this case it is requisite that there shoidd be position; and he who employs his understanding thereupon will comprehend unity apart from plurality. Number, then, will constitute this, that is, a monad and plurality, or unity and inequality. And since that body which subsists from certain entities subsists partly as frx)m things that are inherent, and partly that this is not the case, in which, may I ask, will number be found? for those things which do not subsist in this way, as frx)m those that are inherent, are no other than those of nth w which there is generation. Does it, however, a thing is txom then, subsist 88 &x)m Seed 1 But it is not pos- ^' Bible for anything to proceed forth from what is indivisible. Shall we say, however, that it arises from a con- trary that does not involve a permanent subsistence? But whatever things subsist in this manner, are also from some- thing else that does possess a permanent subeastence. 4. Different Since, therefore, as regards unity, one Philotheories of Bophcr, iu &ct, positcs it as & thing that is con- duced^lfferent^ trary to plurality, and another as what is cou- lesuits. trary to inequality, employing unity as if it were equality, number should, therefore, subsist as if it were froxa ok T ' THB GAUSALITT OF NUHBEBS. 409 contraries. There will then be something else from whiok, aa involving a permanent subsistence, a generation of the other is brought about Further, why then, at all, are the other things of this sort subject to decay, as many as have their existence from contraries, or wherein contraries are to be found 1 — why, I say, are they subject to decay, even though they may arise from everything ) and yet that this be not the case with number. For respecting this nothing is de- clared, although a contrary, which is both inherent and not inherent, destroys that which is contrary to itself; as^ for instance, discord, mixture: and yet, at any rate, such ought not necessarily to be the case; for the former is not contrary to the latter, at least.
There has been, however, no determination arrived at either, as to the mode in which num- J; JJ'^^^Iode bers are causative of substances, and of existence, of the eauiauty whether as limits, for example, points of magni- ®'°**™*>«"« tides; and according to the arrangements adopted by Eurytus, that a certain number belongs to a certain thing, as this number belongs to man, and that to horse, just as they who refer numbers to figures, the triangle and the square, thus assimilating the forms of plants to pebbles of calcidation )^ Or, shall we say that this is the case with the ratio or the symphony of numbers? And, in like manner, it is so af regards man, and everything else: but, as regards then the passive states, how, may I ask, are they numbers^ such as the white, and sweet, and hot?
That numbers, however, do not constitute sub- g Numiws do stances, and that they are not causes of form, is not constitute plain; for reason, that is, the formal principle, ***^*"®*»* constitutes substance, but number constitutes matter, as the number or substance of flesh or bone. In this way are there three of fire, and two of earth: and number, whatsoever it may be, is invariably of certain things, and constitutes either what is fiery or earthy, or of the nature of a monad. Sub- stance, however, is that which consists in being so much with relation to so much, according to mixture; but this no longer constitutes number, but a proportion or ratio of the mixture of corporeal numbers, or certain other things. Neither, therefore, does number constitute a cause in respect of pro* ^ For the alluBion contained in these words^ vide note p. 41& 410 THE METAFHTBIOB OF ABISTOTLB. [bOOK XSOk duction, nor does it as number exist at all, nor as such num- ber as is of the nature of a monad, nor as matter, nor as the formal principle, and the form itself of things. But, undoubtedly, neither does it constitute that on accotint of which a thing subsists — I mean, of course, the final cause of things.
CHAPTER VI.
CHAPTER VI.
« wv.*i ♦!. One, however, might also doubt what *'tha ^^r^hltVr'^ weU*' is which originttes from numben, if mix- SlUS'Sr?"" t^re is to be found in number, either in that which is rational, or in that which is odd. For now would nothing more conducive to health arise from water and honey being thrice three times mingled; but it would be of more service in that way supposing liiat there were to subsist no proportion in the condiments, but that it be watery, or, in number that which is an immixed ^ntitf^ Farther, the ratios — I mean those belon^g to the mixtures ^-consequent upon the addition of numbers are not foimd in numbers themselves, as the ratio between 3 and 2 is that of 3: 2, not thrice two, however, for there ought to be the same geuus in the multiplications. Wherefore, it is necessary that both by the A should be measured the order in whid^ the ABG is to be found, and by the D, that which DEZ will assume. Wherefore, there must be the same measure in all things. Therefore, there will be of fire BEGZ, and of water the number twice three.
2. conse- But if it be necessary that all things should raakinriSi participate of number, it is requisite, likewise^ things share in that there should be a concurrence of many things numbers. ^^^^ ^^ ^j^^ g^^j^g^ ^^^ ^.j^^^. ^^^^^^ ghoidd be the same number for this and for another. Is this thing, there> fore, a cause, and on account of this is there anything tha* is doue,^ or is it obscure, such, for instance, as is a certait number of the revolutionary movements of the sun; • and, again, of those of the moon; and the life and age of each of the animal creation, at least) What obstruction, then, I may ask, is there to some of these being square, but others of them ^ TpayfM. ifl the thing done, irpd^ts the method of doing it.
CB. VI.] IS THIS tmSSORT SUPPORTED BY FACTS 1 413 cubical and equal to each other, and others twofold. For there is no hindrance to this: but it is necessary that they be intimately connected with these, if all things are wont to participate in common of number; and if it should be admis- sible that things which differ from each other should fall under the same number. Wherefore, if the same number happens to be found in certain things, those will be the same with one another, having the same form of number; as sun and moon will be the same, having the same numeric^ form. But why are these causes of things? There, „ are seven vowels, no doubt, and seven chords or iity of numbers harmonies, and seven Pleiades,^ and within seven JJJnws^^ ^' years some animals cast their teeth — some, at any rate, do so, and some do not — and seven in number were those warriors that undertook the famous.expedition against Thebes.^ Is it, then, the case, because such a particular number is naturally suited for such purposes, that on this account either those chieftains amounted to seven, or that the Pleiades consist of seven stars; or were the " Septem contra Thebas" so on account of the gates of Thebes, or through some other different cause ) If, however, we reckon in this manner, and assign twelve stars to Arcturus, at lea^t, yet others a^ree in assigning a greater number; since XYZ they affirm to constitute symphonies, and that because those are three, these also are three. But that there may be ten thousand things of this sort no one in the least feels any concern; for G and R would be one sign. But if because each of the others is twofold, but another is not so— now the cause is, inasmuch as there being three places, one in each is added to S — on this account there subsist three only, but not because there are three symphonies, since there are, at least, more symphonies than three; yet in the present instance there cannot any longer be more than three. Now, these philoso- phers, also, are not unlike the ancient interpreters of Homer,^ who discover minute, but fail to observe important, similitudes.
* Aristotle himself wrote a work upon astronomy, which has not come down to us.
' This alludes to the well-known defence of Thebes against the Argives, led on by Polynices against his brother Eteocles, who chose six chieftains beside himself— just as Aristotle states— that there might be one commander posted at each of the gates.
' Possibly this sneer may have been leTelled against those phi- 413 THB MBTAPHTSI08 OF ABI8T0TLB. [BOOK THk ♦. Thecypiniont Certain speculators, however, assert that there afothen on are many such like particulars: as, for instanceb •^ •»««•• eveu as regards midia, one medium k r^ whereas another is eight, and a verse of seventeen feet is equal in number to these. Now they say that the verse ascends on the right in nine syllables, but in eight on the left, and that the distance is equal, both in letters from A to Z, and in musical instruments from the most grave sound to the most acute, the number of which constitutes an equality in the all-various melody of the Heaven. One ought not, however, to observe things of this kind (for no one would entertain a shadow of doubt as regards them); nor ought we to make any assertions concerning them, nor to attempt to discover them in things that are eternal; since, also, they are to be discovered in things that are subject to corruption.
Those natures, however, in numbers that are lity of numben the subjects of applause, and the things contrary proved;** *^ these, and in general those that fell under our notice in the mathematical sciences — as some^ losophers of the very early ages who sought to win assent to their theories by enlistmg in their favour the sanction of the popular Religion. Now, this many of them endeavoured to accomplish by attempting to prove their doctrines to be in harmony with certain systems of science capable of being extracted, as they alleged, from an aUegoricoL interpretation of Homer's poetry. Supposing, however, that Aristotle here directs his attack against the " Critics/' technically so termed, such censure must be received with some latitude, for we have the iiames of, at least, four of these Critics, ^e from the imputation of such extravagances in interpretation, and which, as such, have been indissolubly united with the Iliad and Odyssey, namely, Zenodotus^ Aristophanes of Byzantium, Aristarchus, and Crates. At the same time, we must allow that the complaint uttered in the text has been reiterated by those who have had occasion to examine into the critical labours of Antiquity upon the Homeric writings. Indeed, in a matter of the kind, Aristotle himself was no contemptible authority, for he Eroduced poems from his own pen, one of which has been preserved by dogenes Laertius (p. 183, Bohn's Trans.). In the '* Poetics," too, we can see how completely he has mastered the difficulties of his subject, and we have reason to think that he wrote more at large upon it in other works — e. g. his UepX Uoiiirmv — that have unfortunately perished. In fact, there was no quarter of the regions of knowledge — the " globus iutellectualis," as Bacon would say — so far as they had been explored by mankind at that primitive period of the world's nabtory, but had been fully penetrated by the sagacity of this extraordinorj nan.
OH. VI.] ITS PRACTICAL ABBURDITT CONFIRMED. 413 in &ct, affirm them to be, and constitute them as causes of Nature— appear to persons, at least, who view the matter iii this light, to escape their notice; for according to no one of the modes of those that are defined respecting first principles is any of them causative. And yet they do make manifest that point, namely, that ** the well " has a subsistence, and that to the co-ordination in the case of the fair belong the odd, the straight, the equal, the powers of certain numbers. For at the same time subsist seasons, and such a particular number, and other things, therefore, of this sort — such as they gather from mathematical theorems — these all involve this power or capacity. Wherefore, also, they seem like unto casual coinci- dences; for they are accidents, no doubt, yet all are appro- priate to one another, the analogical, however, is one. For in each category of entity is there the analogical; as the straight in length is analogous to the even in superficies, to, perhaps, the odd in number, and in colour to the white.
Further, numbers which are in the species do ^..
not constitute causes ^ of thmgs harmonic, and the shown in the like; for those that are equals in the species Jumber!''™*^ difier from each other, for likewise do the monads differ. Wherefore, on account of these things, at least, we must not constitute them species. As regards the conse- quences, indeed, then, that ensue, both these, and even still more than these, can be collected. They appear, however, to furnish a proof of the fact that the supporters of the Ideal Hypothesis fall into many errors respecting the generation of them, and that in no way can a connexion be traced in their systems; inasmuch as mathematical species do not involve a subsistence separable from sensibles, as some affirm; nor do these constitute the first principles of things.
^ The causality of numbers Eurytus — its great patron — ^was in the habit of proying to its opponents by the following curious illustration: — Smearing a wall with a substance capable of being impressed with a sketch of the human figure, he would then take numerous small pebbles of various colours, and fix them within the outlines of the face, hands, and BO on, till all of them were exhausted. At other times he would do the same in the case of the picture of a plant. The amount of pebbles thus employed he would assign as the causative number of man or plant in the reality of things. This plainly is the allusion in the words (chap, y), d^ojLtoiotWat tfr^<^oif riis dil>opfids tSp <l>vT»y, ** por- traying the foims of plants by means of pebbles." This Euzytus was a Pythagorean, and a disciple of Philolaus.
QUESTIONS on ARISTOTLE'S METAPHYSICS, BOOK I.
CHAPTER I.
Thebb has prevailed some diversity of opinion as to the import of the word Metaphysics, rd ucr& rd ijiva-iKa, Man's natural thirst for knowledge is indicated by what fiRCt, according to Aristotle P State the Stagyrite's object in reminding us of our natural desire of knowledge.
A graduated scale of intelligence is observable in the animal creation.
Why is this fact in Natural History brought under notice P Amongst the senses, we award the superiority to the sense oi sight. WhyP What distinguishes man from the other animals, in respect of his means of acquiring knowledge P Point out the difference between Art and Experience.
Show that you understand Aristotle's object in noticing this difference.
Why does Aristotle award the superiority to Art compared with Experience, and how does this bear on the science of Ontology P What, in fact, is the distinguishing trait in the scientific man P How does Aristotle account for tne admiration that is bestowed upon the inventor of any art whatsoever P Signify the difference between animate and inanimate things, in regard of the fulfilment of their proper functions.
The wonder evoked by clever discoveries is entirely independent of their utility. Show this to be the fact.
Historical proof of this.
In what part of Aristotle*s works are we to look for his distinctioi between Art and Soieni^ \ OH. III.] <)UESTIONS ON ARI8T0TLB*S METAFHTSICS. 415 As regards the experienced, why do we find them compassing their objects more successfully than the mere theorist?
Aristotle illustrates this from the science of Medicine.
When do we award the superiority to Experience over Art? And when do we the iame to Art over Experience?
State Aristotle's object, that he has in yiew, in undertaking his present Treatise on Metaphysics.
CHAPTER II.
Allowing Metaphysics to be conversant with causes, as such, what inquiry presents itself next in order?
What determines this precbe order?
Give an analysis of Aristotle's Sophos, or " Wise Man," as well as of his Sophia, or Wisdom?
Mr. Maurice well points out in what respect Aristotle in these Analyses departed from his predecessors.
Gould you show how these Analyses bear on the subject of meta- physeal science P What do we term Science " par excellence P" Knowledge after all is eligible for its own sake. Gould you prove thisP The purely speculative character of the higher sciences is mani- fested-in the earliest systems of Philosophy.
Now, this fact bears immensely on the question of the dignity of Metaphysical Science.
What object has Aristotle in his mention of Simonides, in tliis second chapter P Why is it not correct to ascribe Philosophy to an origin merely human P Aristotle mentions the general sense of mankind on the nature of a cause.
Would not this determine the origin of Metaphysical Science P Aristotle censures a certain view of the Divine nature prevalent amount the poets.
This view, however, seems supported by what is often observed actually to take place.
Begarding Metaphysics as a science of causes, determine the order of its development r Now, does this order correspond with that assumed by the rest of the sciences P Illustrate this from Geometry.
GHAPTER nL Wht has Aristotle occasion to examine into how many genera fauses may be reduced P Has he made a similar redaction in any other part of his writings i 416 4)UESII01IB ON ARISTOTLlTb XETAFHTBIOa. [BOOK U Point out from the History of Philosophy any fact that testifies to the permanence of this fourfold division of causes.
It is the nature of Metaphysics as a science that forces on Aristotle his review of the Greek Philosophy* WhyP This review, however, will be serviceable to the Metaphysioia]^ WhvP Now, what is the Stagyrite's general objection— stated almost &om the start — against the entire Greek Philosophy?
He proceeds to make good this objection from the mention of particular systems.
Gould you state — as given by Aristotle— the notion of the ancient Philosophers about the nature of " an element "?
Whom does the Stagyrite specify as the author of the Materialistic Philosophy?
Do Gicero and Aristotle agree in their view of the system of ThalesP We can find traces according to Aristotle of the Thaletian Philo- sophy, amongst the very ancient Theologians in their Theogonies.
The Philosophy, however, of Thales does not entirely contradiel experience.
Aristotle states what he considers to be the origin in Nature of the principles put forward by Thales.
Aristotle mentions water as ui object of adjuration amongst the gods. What object has he in this P What Philosophers does the Stagyrite bring under review next P These ancient Philosophers unconsciously adopted correct prin- ciples.
This exemplified, in the most eminent degree, in the philosophy of Parmenides.
But, after all, what was the real difficulty that obviously presented itself to the mind of these speculators P How, for example, did ^axagoras endeavour to get over this difficulty P Does Aristotle consider Anaxagoras as the discoverer of the " efficient cause " P The efficient cause, put forward by the early Philosophers, uncon- sciously to themselves, really involved the solution of two sets of phenomena.
Do Gicero and Aristotle agree in their view of the Anaxagoreaa Philosophy?
GHAPTER IV.
How comes Aristotle to mention the system of Hesiod P The same difficulty presented itself in the way of Hesiod^ as cf the rest of the early speculators. Now, Aristotle states, that if you really compare the system of CH. v.] QUESTIONS ON AfilSTOTLE S XSTAPHTBIOS. 417 Empedocles with the actual phenomena, this same difficulty will pre* sent itself here also.
Even granting, however, that the efficient cause wa£i recognised by Empedocles, show that his treatment of it is incomplete.
What other Philosophers does Aristotle mention in this chapter?
Does not the same objection lie against these, likewise, as thct»i? already mentioned P Aristotle gives us a sketch of part of the Democritic Philosophy.
Cicero, for example, amongst others, notices a fundamental pnn« ciple in the philosophy of Democritus, quite overlooked by Aristotle.
Who is the best exponent in modern times of the Democritic Philosophy P Do all philosophers agree with Aristotle and Cicero in the ascrip- tion of the Atomic hypothesis to Leucippus and Democritus P CHAPTER V.
How does Aristotle account for the rise of such a School as that of the Pythagoreans P Could you state the grounds upon which the Pythagoreans them- selves rested their theory of Numbers P What was the precise object which the Pythagoric Philosophers had in view in their introduction of a Co-ordinate Series — trvirroixia?
What are probably the best sources for obtaining information upon the Philosophy of Pythagoras P What Philosopher does Aristotle mention as adopting a system similar to that oi the Pythagoreans P In what respect does Aristotle consider Pythagoras as contributing most to Metaphysical Science P Is there no other Philosopher that can contend with Pythagoras for the credit of inventing the Philosophy of the Italic Schools P Was Parmenides really the originator of the Philosophy of Unity — ther3?vP Could you state the difference between the systems of Parmenides and Melissus P In the enunciation of his theories, Parmenides was more circum- spect than others of his school.
At the end of this chapter Aristotle furnishes his readers with the conclusion suggested by the review of thus much of the Greek Philosophy.
Even in the Pythagorean treatment of the rh ri cori, there was imperfection inherent. How so P is there any trace of the Pvthagorean Philosophy to be found dsewhere, save in the schools of Italy f BB CHAPTER VL Weat famous system is brought under review in this ehapterf Is there any connexion between the Platonic and the Pythagoreas Philosophies, according to AristoUe P What part has Cratylus in the rise and progress of Platoninn P Is there any system from which Platonism may be considered as a reaction, according to Aristotle P To what extent are we to admit the influence of the Socratie on the Platonic Philosophy P According to Mr. Maurice, in his Analysis of the Metaphysics, Aristotle is ungenerous towards the fame of Socrates on this Tery point.
In some respects the difference between the systems of Plato and Pythagoras was merely nominal.
C!ould you point out some particulars where the Pythagoreans agreed, and some others where they differed with the PliSonists P To what extent does Plato go in the number of his causes P What particuhir Science does Aristotle allow the Platonists the credit of oringing forward P CHAPTER VIL One point Aristotle considers as positively settled by reasmi of the foregoing review.
This is exemplified in the case of the PUtonics, and Italics, and others.
What is the chief value of Platonism in regard of the theory of Causation P In Chapter YII. Aristotle indicates the completeness of his four- fold division of causes.
This chapter is a repetition of what has gone before, but is not, on that account, the less aeserving of attention, according to Mr. Maurice.
CHAPTER VHL What system is noticed by Aristotle in the b^;inning of this chapter P What may be considered as the general fault of those who put forward a material cause only P: What systems of material causes are attacked in this chapter by i Aristotle P The system of Anax&goras is partly true, and partly false, in the j opinion of Aristotle.
The Pythagoreans agree and differ with the Materiaista, in what respect P now do you account for the divergence of the Pythagoreans frun the Natural Philosophers in their several systems P OB. I.] QUBSTIONft ON ARISTOTLE*S HBTAPHTSICe. 419 The absurdities of the Pythagoric theoiy of Nomben are again exposed by Aristotle. Where P CHAPTER IX.
This chapter opens with an attack on what famona hypothesis?
Boes Anstoib repeat this attack in any other portion of bis writings P Gomd you point ont the general arguments employed for the overthrow of Plato's Ideal theory P What seems to be Aristotle's leading; objection to this hypothesis P Why does the Ideal theory destroy its own pretensions to truth P Show that it pro?es too much.
Can these ideas, as the Platonists contend, constitute the models of created things P What erroneous principle laid down in the Phndo is stigmatized nere by Aristotle P