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wife it would poffefs fome one of these colours. In like manner, it must have been taftelefs: and, from the fame reafoning, it could not have been any thing else of the like kind. For it is not poffible that it could poffefs any quality or quantity, or be any actual thing, fince fomething of those things which are called partial forms would be inherent in it. But this is impoflible, in confequence of all things (according to him) being mingled together; for they would now be separated. But he fays that all things were mingled except intellect; and that this alone was unmingled and pure. Hence it comes to pafs, that he proclaims, as principles, the one (for this is fimple and unmingled), and another thing, as if it were being, fuch as we confider the indefinite to be, before it is bounded and participates of a certain form. So that this is afferted, indeed, neither with rectitude nor perfpicuity; yet he wishes to fay fomething fimilar to what more modern philofophers have said, and more agreeable to the present phænomena. But these philofophers only fpeak in a manner accommodated to the affertions respecting generation, corruption, and motion. For they nearly alone inveftigate an effence, principles

and causes of this kind.

But with respect to fuch, indeed, as make all beings the subject of their speculation, and confider fome beings as fenfible and others as not fenfible, it is evident that they inquire concerning both genera; and on this account any one may be induced to dwell longer on the confideration of what they have faid, well or ill, with respect to our present investigation. Thofe, therefore, who are called Pythagoræans, ufe principles and elements in a more incredible manner than phyfiologifts. But the reafon is, because they do not receive these from fenfibles. For mathematical entities are without motion, except thofe things which pertain to aftronomy. Yet notwithstanding this, they difcourse about and difcufs all things refpecting nature. For they generate the heaven, and observe what happens refpecting its parts, participated properties, and operations; and into thefe they refolve principles and caufes, as agreeing with other physiologists, that whatever is fenfible is being, and is comprehended by that which is called heaven. But, as we have faid, and as they alfo affert, they fpeak fufficiently refpecting caufes and principles, and even afcend to a higher order of beings, and this more than is adapted to difcourfes concerning nature; but they are filent as to the mode in which motion, bound, and infinity, the even and the odd, these being alone the fubjects of hypothefis, fubfift; or

* That is, to incorporeal and immoveable natures.

how

how it is poffible that generation and corruption can exift without motion and mutation; or how the operations of the bodies which revolve in the heavens can be accomplished.

Further ftill, whether any one grants them that magnitude is from these, or whether this is fhown to be the cafe; yet, at the fame time, after what manner will fome bodies poffefs levity, and others gravity, refpealing which their hypothefes and affertions do not lefs accord with mathematical bodies than with fenfibles? Hence they do not fay any thing refpecting fire, or earth, or other bodies of this kind; and this, I think, because they do not affert any thing which is their own concerning fenfible natures. Again, how ought we to receive the affertion, that the participated properties of number, and number itself, are the caufes of things which exift, and are produced in the heavens, both from the beginning, and at prefent, at the fame time that there is no other number befides this number, from which the world is compofed? For fince, according to them, opinion and opportunity are in this part of the world, but a little higher or a little lower, injuftice *, and separation, or mixture, and they adduce demonftration that each of thefe is number, and it happens from this mode of reasoning, that there is now a multitude of constituted magnitudes, because these properties follow the refpective places;-fince this is the case, whether is it owing to that number which is in the heavens that each of these exifts, or to another number befides this? For Plato says it is owing to another number; though he also thought that numbers are these things, and are the caufes of thefe; but that they are indeed intelligible causes, while these are nothing more than fenfibles. Refpecting the Pythagoræans, therefore, we shall speak no further at prefent; for it is fufficient to have thus much touched upon them.

But those who confider ideas as caufes, in the first place exploring the causes of these things, introduce other things equal to these in number: just as if some one, wishing to numerate, fhould think that he cannot accomplish this if there are but a few things, but that he can numerate if he increases

Alexander Aphrodifienfis informs us that in fome copies тo avanтov, the unconquered, is found instead of adinia, injustice. But, fays he, the unconquered was called by the Pythagoræans the number five, because, in a right-angled triangle, of thofe fides containing the right angle, one is as three, and the other as four; and the base is as five. Since, therefore, the base is in power equal to both together, it is called the victor, and the other fides are faid to be vanquished. Hence the number five was denominated by them unconquered, being as it were not furpaffed, but unconquered and superior.

E

their

their number. For nearly forms are equal, or not lefs than thofe things, of which, investigating the causes, they proceed from thefe to thofe ; for, according to each individual thing, there is a certain homonymous form, and befides the effences of other things, there is the one in many, both in thefe, and in eternal entities. Further ftill, forms do not appear to have a fubfiftence, according to any one of those modes by which we have shown them to fubfift. For, from fome, the reasoning does not neceffarily follow; and from others forms are produced of those things, of which we do not think there are forms; for, according to the reasons arising from the fciences, there are forms of all fuch things as there are sciences; and from that argument for ideas, which is founded in confidering the one in the many, it follows, that there are also forms or ideas of negations. Likewise, in confequence of the ability to understand something of things corruptible, there will also be forms of corruptible natures; for there is a certain phantafm of these.

Further ftill, with respect to the most accurate of reasons, some make ideas of things relative, of which we do not fay there is an effential genus, and fome affert that there is a third man; and, in short, the reasons respecting forms fubvert those things which, the afferters of forms are of opinion, have a subsistence prior to ideas themfelves. For it happens that the duad is not first, but number, and that which has a relative is prior to that which has an effential fubfiftence. All fuch particulars likewife happen, as, being confequent to the opinions respecting forms, are adverse to principles. Again, from the notion according to which we fay there are ideas, there will not only be forms of effences, but also of many other things: for there is one conception not only respecting effences, but also respecting other things; and sciences are not only sciences of effence, but alfo of other things; and ten thousand such like particulars happen. But, from neceffity, and the opinions respecting forms, it fol

*It appears from the commentary of Alexander, that in this place we fhould read de deixauer, and not devrai; for the authority of Alexander's copy is certainly to be preferred to that of any now exifting. I have accordingly adopted deduxausy in my verfion.

It is remarkable too, that Alexander, who was no friend to the Platonic doctrine of ideas, and who, though on the whole an excellent interpreter of Ariftotle, did not fee his true meaning on that fubject, should in this place obferve "that Aristotle fays we have shown, as if he profeffed, while relating the opinion of Plato respecting ideas, to relate it also as his own, and as if he did not oppofe it as a foreign dogma, but difcuffed and examined it as his own." Indeed it appears to me that this very paffage is fufficient to prove that the objections of Ariftotle to Plato's theory of ideas are rather pretended than real.

lows,

lows, that, if forms are participable, there are only ideas of effences: for they are not participated according to accident; but it is requifite that things should participate each idea, fo far as each idea is not predicated of a fubject. I mean, just as if any thing participates of the double, this alfo participates of the perpetual, but according to accident. For it happens to the double to be eternal; so that forms will be effences; and thefe both here and there will fignify effence. Or what will be the meaning of that affertion, that the one in many is fomething different from fenfible things? And if there is the fame form, both of ideas and their participants, there will be fomething common. For why, in duads, which are corruptible, and in many but eternal duads, is the duad faid to be more one and the fame than in this, and in fome particular thing? But if there is not the fame form, the name only will be common; and it will be just as if fome one fhould call both Clinias and a piece of wood a man, at the same time that he perceives no communion whatever between them.

But fome one may, in the most eminent degree, doubt what it is that forms contribute to fuch things as are eternal among fenfibles, or to things which are generated and corrupted: for neither are they the causes of any motion, nor of any mutation whatever to these. Nor yet do they afford any affiftance to the science of other things (for they are not the effence of these, fince in this cafe they would refide in them); nor do they contribute to the being of other things, fince they are not inherent in their participants. For thus, perhaps, they might be confidered as causes, as a white colour mixed with a body may be said to be the cause that the body is white. But that assertion, which was firft made by Anaxagoras, and afterwards by Eudoxus and others, refpecting the temperament of things from fimilar natures, may be easily confuted; for it is easy to collect for it is easy to collect many and impoffible confequences in oppofition to this opinion. But, indeed, neither do other things fubsist from forms, according to any of those modes which are generally adduced. And to fay that forms are paradigms, and that they are participated by other things, is to speak vainly, and to utter poetical metaphors. For, what is that which operates looking to ideas? for it is poffible that any thing may both be, and be generated fimilar, without being affimilated to that to which it is similar; so that, Socrates both fubfifting and not fubfifting, fome other may be generated fuch as Socrates is: and, in like manner, it is evident that this will follow, although Socrates fhould be eternal. Befides, there will also be many paradigms of the

fame thing; and confequently forms, as man, animal, biped; and at the fame time, man himself, or the ideal man, will have a fubfiftence.

it

Further ftill, forms will not only be paradigms of sensibles, but also of forms themselves; as, for instance, genus, fo far as genus, will be the paradigm of fpecies: fo that the fame thing will be both paradigm and image. Again, may seem to be impoffible that effence fhould be feparated from that of which it is the effence. So that how will ideas, fince they are the effences of things, be feparated from them? But, in the Phædo, forms are faid to be the causes, both that things are, and that they are generated; though, at the fame time, participants will not be generated, even admitting the subsistence of forms, unless that which is motive fubfifts. And befides this, many other things are made, fuch as a house and a ring, of which we do not say there are forms: fo that it is evident that other things may be, and may be generated, through fuch caufes as we have juft now mentioned.

Again, if forms are numbers, how will they be caufes? Whether because beings are different numbers? as, for instance, man is this number, Socrates another, and Callias a number different from both. Why, therefore, are those the causes of these? For it is of no confequence, if those are eternal, but these not. But if it is because fenfible natures are the reafons of numbers, as a fymphony, it is evident that there will be one certain thing, of which they are reasons or ratios. If, therefore, this one thing is matter, it is evident that numbers themselves alfo will be certain ratios of another thing to another thing. I fay, for inftance, if Callias is a ratio in numbers of fire and earth, water and air, and of certain other fubjects, man himself also, whether this idea is a certain number or not, will be a ratio of certain things in numbers, without being himself number, and will not through these things be fome particular number.

Further ftill: from many numbers one number is produced; but how is one form produced from forms? But if form is not produced from forms, but from the unities which are in number, after what manner will the unities fubfift? For, if they are of the fame fpecies, many abfurd confequences * will enfue; and if they are not of the fame fpecies, nor the fame with each

* These confequences he enumerates in the thirteenth book, to the notes on which we refer the reader. In these too (as we have already obferved) the reader will find a folution of the preceding and subsequent objections.

other,