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Contents

Chapter 1

Greek Latin English
METHAPHISICE ARISTOTILIS LIBER TERTIUS Aristotle Metaphysics Book 3 (B)
[995α] [24] ἀνάγκη πρὸς τὴν ἐπιζητουμένην ἐπιστήμην ἐπελθεῖν ἡμᾶς [25] πρῶτον περὶ ὧν ἀπορῆσαι δεῖ πρῶτον: ταῦτα δ᾽ ἐστὶν ὅσα τε περὶ αὐτῶν ἄλλως ὑπειλήφασί τινες, κἂν εἴ τι χωρὶς τούτων τυγχάνει παρεωραμένον. > Necesse est ad quesitam scientiam nos aggredi primum de quibus dubitare primum oportet. Haec autem sunt quaecumque de ipsis aliter susceperunt quidam, et si quid extra haec est praetermissum. Chapter 1. WE must, with a view to the science which we are seeking, first recount the subjects that should be first discussed. These include both the other opinions that some have held on the first principles, and any point besides these that happens to have been overlooked.
ἔστι δὲ τοῖς εὐπορῆσαι βουλομένοις προὔργου τὸ διαπορῆσαι καλῶς: ἡ γὰρ ὕστερον εὐπορία λύσις τῶν πρότερον ἀπορουμένων ἐστί, λύειν δ᾽ οὐκ [30] ἔστιν ἀγνοοῦντας τὸν δεσμόν, ἀλλ᾽ ἡ τῆς διανοίας ἀπορία δηλοῖ τοῦτο περὶ τοῦ πράγματος: ᾗ γὰρ ἀπορεῖ, ταύτῃ παραπλήσιον πέπονθε τοῖς δεδεμένοις: ἀδύνατον γὰρ ἀμφοτέρως προελθεῖν εἰς τὸ πρόσθεν. διὸ δεῖ τὰς δυσχερείας τεθεωρηκέναι πάσας πρότερον, τούτων τε χάριν καὶ διὰ τὸ τοὺς [35] ζητοῦντας ἄνευ τοῦ διαπορῆσαι πρῶτον ὁμοίους εἶναι τοῖς ποῖ δεῖ βαδίζειν ἀγνοοῦσι, Inest autem investigare volentibus pre opere bene dubitare; posterior enim copia [investigatio] priorum est solutio dubitatorum, soluere vero non est ignorantis vinculum. Sed mentis dubitatio hoc de re demonstrat. In quantum enim dubitat, in tantum similiter ligatis est passa; impossibile enim utrisque procedere ad quod est ante. Propter quod oportet difficultates speculari omnes prius, horumque causa et quia quaerentes sine dubitatione primo similes sunt quo oportet ire ignorantibus; For those who wish to get clear of difficulties it is advantageous to discuss the difficulties well; for the subsequent free play of thought implies the solution of the previous difficulties, and it is not possible to untie a knot of which one does not know. But the difficulty of our thinking points to a knot in the object; for in so far as our thought is in difficulties, it is in like case with those who are bound; for in either case it is impossible to go forward. Hence one should have surveyed all the difficulties beforehand, both for the purposes we have stated and because people who inquire without first stating the difficulties are like those who do not know where they have to go;
καὶ πρὸς τούτοις οὐδ᾽ εἴ ποτε τὸ ζητούμενον εὕρηκεν ἢ μὴ γιγνώσκειν: [995β] [1] τὸ γὰρ τέλος τούτῳ μὲν οὐ δῆλον τῷ δὲ προηπορηκότι δῆλον. ἔτι δὲ βέλτιον ἀνάγκη ἔχειν πρὸς τὸ κρῖναι τὸν ὥσπερ ἀντιδίκων καὶ τῶν ἀμφισβητούντων λόγων ἀκηκοότα πάντων. et ad haec * neque quando quesitum invenit aut > non, cognoscit; finis enim huic est non manifestus, * predubitanti vero manifestus. Amplius melius necesse est habere ad iudicandum eum qui audivit velut adversariorum et dubitantium omnes rationes. besides, a man does not otherwise know even whether he has at any given time found what he is looking for [95b] or not; for the end is not clear to such a man, while to him who has first discussed the difficulties it is clear. Further, he who has heard all the contending arguments, as if they were the parties to a case, must be in a better position for judging.
ἔστι δ᾽ ἀπορία πρώτη [5] μὲν περὶ ὧν ἐν τοῖς πεφροιμιασμένοις διηπορήσαμεν, πότερον μιᾶς ἢ πολλῶν ἐπιστημῶν θεωρῆσαι τὰς αἰτίας: καὶ πότερον τὰς τῆς οὐσίας ἀρχὰς τὰς πρώτας ἐστὶ τῆς ἐπιστήμης ἰδεῖν μόνον ἢ καὶ περὶ τῶν ἀρχῶν ἐξ ὧν δεικνύουσι πάντες, οἷον πότερον ἐνδέχεται ταὐτὸ καὶ ἓν ἅμα φάναι καὶ ἀποφάναι [10] ἢ οὔ, καὶ περὶ τῶν ἄλλων τῶν τοιούτων: εἴ τ᾽ ἐστι περὶ τὴν οὐσίαν, πότερον μία περὶ πάσας ἢ πλείονές εἰσι, κἂν εἰ πλείονες πότερον ἅπασαι συγγενεῖς ἢ τὰς μὲν σοφίας τὰς δὲ ἄλλο τι λεκτέον αὐτῶν. Est autem dubitatio prima quidem de quibus in prohemialiter dictis dubitavimus, utrum unius aut multarum est scientiarum causas speculari; et utrum substantiae principia prima est scientie huius scire solum aut etiam de principiis ex quibus ostendunt omnes, ut utrum contingit unum et idem simul dicere et negare aut non, et de aliis talibus. Et si est circa substantiam, utrum una circa omnes aut plures sunt, et si plures, utrum omnes cognate aut earum hae quidem sapientie ille vero aliquid aliud dicende sunt. The first problem concerns the subject which we discussed in our prefatory remarks. It is this – (1) whether the investigation of the causes belongs to one or to more sciences, and (2) whether such a science should survey only the first principles of substance, or also the principles on which all men base their proofs, e.g. whether it is possible at the same time to assert and deny one and the same thing or not, and all other such questions; and (3) if the science in question deals with substance, whether one science deals with all substances, or more than one, and if more, whether all are akin, or some of them must be called forms of Wisdom and the others something else.
καὶ τοῦτο δ᾽ αὐτὸ τῶν ἀναγκαίων ἐστὶ ζητῆσαι, πότερον τὰς αἰσθητὰς οὐσίας εἶναι [15] μόνον φατέον ἢ καὶ παρὰ ταύτας ἄλλας, καὶ πότερον μοναχῶς ἢ πλείονα γένη τῶν οὐσιῶν, οἷον οἱ ποιοῦντες τά τε εἴδη καὶ τὰ μαθηματικὰ μεταξὺ τούτων τε καὶ τῶν αἰσθητῶν. περί τε τούτων οὖν, Et hoc idem quoque necessarium est quaerere, utrum sensibiles substantiae esse solum dicende sunt aut praeter has aliae, et utrum unice sunt aut plura genera substantiarum, ut facientes species et mathematica inter istas et sensibilia *. De hiis igitur, ut dicimus, perscrutandum est. And (4) this itself is also one of the things that must be discussed-whether sensible substances alone should be said to exist or others also besides them, and whether these others are of one kind or there are several classes of substances, as is supposed by those who believe both in Forms and in mathematical objects intermediate between these and sensible things. Into these questions, then, as we say, we must inquire,
καθάπερ φαμέν, ἐπισκεπτέον, καὶ πότερον περὶ τὰς οὐσίας ἡ θεωρία μόνον ἐστὶν ἢ καὶ περὶ [20] τὰ συμβεβηκότα καθ᾽ αὑτὰ ταῖς οὐσίαις, πρὸς δὲ τούτοις περὶ ταὐτοῦ καὶ ἑτέρου καὶ ὁμοίου καὶ ἀνομοίου καὶ ἐναντιότητος, καὶ περὶ προτέρου καὶ ὑστέρου καὶ τῶν ἄλλων ἁπάντων τῶν τοιούτων περὶ ὅσων οἱ διαλεκτικοὶ πειρῶνται σκοπεῖν ἐκ τῶν ἐνδόξων μόνων ποιούμενοι τὴν σκέψιν, τίνος [25] ἐστὶ θεωρῆσαι περὶ πάντων: ἔτι δὲ τούτοις αὐτοῖς ὅσα καθ᾽ αὑτὰ συμβέβηκεν, καὶ μὴ μόνον τί ἐστι τούτων ἕκαστον ἀλλὰ καὶ ἆρα ἓν ἑνὶ ἐναντίον: Et utrum circa substantias solum est speculatio aut et circa quae accidunt secundum se substantiis. Adhuc autem de eodem et diverso, simili et dissimili et contrarietate et de priore et posteriore et aliis omnibus talibus de quibuscumque dialetici intendere temptant, ex probabilibus solum perscrutationem facientes, quorum theoria est de omnibus. Amplius autem hiis eisdem quaecumque secundum se accidunt; et non solum quid est horum unumquodque, sed utrum uni est unum contrarium. and also (5) whether our investigation is concerned only with substances or also with the essential attributes of substances. Further, with regard to the same and other and like and unlike and contrariety, and with regard to prior and posterior and all other such terms about which the dialecticians try to inquire, starting their investigation from probable premises only,-whose business is it to inquire [95b 25] into all these? Further, we must discuss the essential attributes of these themselves; and we must ask not only what each of these is, but also whether one thing always has one contrary.
καὶ πότερον αἱ ἀρχαὶ καὶ τὰ στοιχεῖα τὰ γένη ἐστὶν ἢ εἰς ἃ διαιρεῖται ἐνυπάρχοντα ἕκαστον: καὶ εἰ τὰ γένη, πότερον ὅσα ἐπὶ τοῖς ἀτόμοις λέγεται [30] τελευταῖα ἢ τὰ πρῶτα, οἷον πότερον ζῷον ἢ ἄνθρωπος ἀρχή τε καὶ μᾶλλον ἔστι παρὰ τὸ καθ᾽ ἕκαστον. Et utrum principia et elementa genera sunt aut in quae dividitur existentium singulum. Et si genera, utrum quaecumque de individuis dicuntur finalia aut prima, ut utrum animal aut homo principiumque et magis est quam singulare. Again (6), are the principles and elements of things the genera, or the parts present in each thing, into which it is divided; and (7) if they are the genera, are they the genera that are predicated proximately of the individuals, or the highest genera, e.g. is animal or man the first principle and the more independent of the individual instance?
μάλιστα δὲ ζητητέον καὶ πραγματευτέον πότερον ἔστι τι παρὰ τὴν ὕλην αἴτιον καθ᾽ αὑτὸ ἢ οὔ, καὶ τοῦτο χωριστὸν ἢ οὔ, καὶ πότερον ἓν ἢ πλείω τὸν ἀριθμόν, καὶ πότερον ἔστι τι παρὰ τὸ [35] σύνολον (λέγω δὲ τὸ σύνολον, ὅταν κατηγορηθῇ τι τῆς ὕλης) ἢ οὐθέν, ἢ τῶν μὲν τῶν δ᾽ οὔ, καὶ ποῖα τοιαῦτα τῶν ὄντων. Maxime vero quaerendum est et > tractandum utrum est aliquid praeter materiam causa secundum se aut non, et hoc separabile aut non, et utrum unum aut plura numero. Et utrum est aliquid praeter simul totum (dico autem synolon, quando predicatur aliquid de materia) aut nihil, aut horum quidem horum vero non, et qualia talia existentium. And (8) we must inquire and discuss especially whether there is, besides the matter, any thing that is a cause in itself or not, and whether this can exist apart or not, and whether it is one or more in number, and whether there is something apart from the concrete thing (by the concrete thing I mean the matter with something already predicated of it), or there is nothing apart, or there is something in some cases though not in others, and what sort of cases these are.
[996α] [1] ἔτι αἱ ἀρχαὶ πότερον ἀριθμῷ ἢ εἴδει ὡρισμέναι, καὶ αἱ ἐν τοῖς λόγοις καὶ αἱ ἐν τῷ ὑποκειμένῳ; καὶ πότερον τῶν φθαρτῶν καὶ ἀφθάρτων αἱ αὐταὶ ἢ ἕτεραι, καὶ πότερον ἄφθαρτοι πᾶσαι ἢ τῶν φθαρτῶν φθαρταί; ἔτι δὲ τὸ πάντων [5] χαλεπώτατον καὶ πλείστην ἀπορίαν ἔχον, πότερον τὸ ἓν καὶ τὸ ὄν, καθάπερ οἱ Πυθαγόρειοι καὶ Πλάτων ἔλεγεν, οὐχ ἕτερόν τί ἐστιν ἀλλ᾽ οὐσία τῶν ὄντων; ἢ οὔ, ἀλλ᾽ ἕτερόν τι τὸ ὑποκείμενον, ὥσπερ Ἐμπεδοκλῆς φησὶ φιλίαν ἄλλος δέ τις πῦρ ὁ δὲ ὕδωρ ἢ ἀέρα: καὶ πότερον αἱ ἀρχαὶ [10] καθόλου εἰσὶν ἢ ὡς τὰ καθ᾽ ἕκαστα τῶν πραγμάτων, Amplius autem utrum principia numero aut specie determinata, et * in rationibus et * in subiecto, et utrum corruptibilium et incorruptibilium eadem aut diversa, et utrum incorruptibilia omnia aut corruptibilium corruptibilia. Amplius autem quod omnium difficillimum est et plurimam habet dubitationem: utrum unum aut ens, quemadmodum pytagorici et Plato dicebant, non alterum aliquid est sed entium substantia, aut non, sed alterum aliquid ipsum subiectum, ut Empedocles amorem dicit, alius vero ignem, alius aquam aut aerem. [96a] Again (9) we ask whether the principles are limited in number or in kind, both those in the definitions and those in the substratum; and (10) whether the principles of perishable and of imperishable things are the same or different; and whether they are all imperishable or those of perishable things are perishable. Further (11) there is the question which is hardest of all and most perplexing, whether unity and being, as the Pythagoreans and Plato said, are not attributes of something else but the substance of existing things, or this is not the case, but the substratum is something else,-as Empedocles says, love; as some one else says, fire; while another says water or air. Again (12) we ask whether the principles are universal or like individual things,
καὶ δυνάμει ἢ ἐνεργείᾳ: ἔτι πότερον ἄλλως ἢ κατὰ κίνησιν: καὶ γὰρ ταῦτα ἀπορίαν ἂν παράσχοι πολλήν. Et utrum principia sint universalia aut ut singularia rerum; et potestate aut actu. Amplius utrum aliter aut secundum motum; haec enim dubitationem prestant magnam. and (13) whether they exist potentially or actually, and further, whether they are potential or actual in any other sense than in reference to movement; for these questions also would present much difficulty.
πρὸς δὲ τούτοις πότερον οἱ ἀριθμοὶ καὶ τὰ μήκη καὶ τὰ σχήματα καὶ αἱ στιγμαὶ οὐσίαι τινές εἰσιν ἢ οὔ, κἂν εἰ οὐσίαι πότερον [15] κεχωρισμέναι τῶν αἰσθητῶν ἢ ἐνυπάρχουσαι ἐν τούτοις; περὶ γὰρ τούτων ἁπάντων οὐ μόνον χαλεπὸν τὸ εὐπορῆσαι τῆς ἀληθείας ἀλλ᾽ οὐδὲ τὸ διαπορῆσαι τῷ λόγῳ ῥᾴδιον καλῶς. Ad haec autem utrum numeri et longitudines et figure et puncta substantiae quaedam sunt aut non. Et si substantiae, utrum separata a sensibilibus aut in eis. De hiis enim omnibus non solum difficile veritatem ipsam inquirere sed nec dubitare * ratione facile bene. Further (14), are numbers and lines and figures and points a kind of substance or not, and if they are substances are they separate from sensible things or present in them? With regard to all these matters not only is it hard to get possession of the truth, but it is not easy even to think out the difficulties well.

Chapter 2

Greek Latin English
πρῶτον μὲν οὖν περὶ ὧν πρῶτον εἴπομεν, πότερον μιᾶς ἢ πλειόνων ἐστὶν ἐπιστημῶν θεωρῆσαι πάντα τὰ γένη τῶν [20] αἰτίων. μιᾶς μὲν γὰρ ἐπιστήμης πῶς ἂν εἴη μὴ ἐναντίας οὔσας τὰς ἀρχὰς γνωρίζειν; Primum ergo de quibus in primis diximus, utrum unius aut plurium scientiarum sunt speculanda omnia genera causarum. Unius enim scientie quomodo erit non contraria existentia principia cognoscere? Chapter 2. (1) First then with regard to what we mentioned first, does it belong to one or to more sciences to investigate all the kinds of causes? How could it belong to one science to recognize the principles if these are not contrary?
ἔτι δὲ πολλοῖς τῶν ὄντων οὐχ ὑπάρχουσι πᾶσαι: τίνα γὰρ τρόπον οἷόν τε κινήσεως ἀρχὴν εἶναι τοῖς ἀκινήτοις ἢ τὴν τἀγαθοῦ φύσιν, εἴπερ ἅπαν ὃ ἂν ᾖ ἀγαθὸν καθ᾽ αὑτὸ καὶ διὰ τὴν αὑτοῦ φύσιν τέλος ἐστὶν [25] καὶ οὕτως αἴτιον ὅτι ἐκείνου ἕνεκα καὶ γίγνεται καὶ ἔστι τἆλλα, τὸ δὲ τέλος καὶ τὸ οὗ ἕνεκα πράξεώς τινός ἐστι τέλος, αἱ δὲ πράξεις πᾶσαι μετὰ κινήσεως; ὥστ᾽ ἐν τοῖς ἀκινήτοις οὐκ ἂν ἐνδέχοιτο ταύτην εἶναι τὴν ἀρχὴν οὐδ᾽ εἶναί τι αὐτοαγαθόν. διὸ καὶ ἐν τοῖς μαθήμασιν οὐθὲν δείκνυται διὰ [30] ταύτης τῆς αἰτίας, οὐδ᾽ ἔστιν ἀπόδειξις οὐδεμία διότι βέλτιον ἢ χεῖρον, ἀλλ᾽ οὐδὲ τὸ παράπαν μέμνηται οὐθεὶς οὐθενὸς τῶν τοιούτων, ὥστε διὰ ταῦτα τῶν σοφιστῶν τινὲς οἷον Ἀρίστιππος προεπηλάκιζεν αὐτάς: ἐν μὲν γὰρ ταῖς ἄλλαις τέχναις, καὶ ταῖς βαναύσοις, οἷον ἐν τεκτονικῇ καὶ σκυτικῇ, διότι [35] βέλτιον ἢ χεῖρον λέγεσθαι πάντα, τὰς δὲ μαθηματικὰς οὐθένα ποιεῖσθαι λόγον περὶ ἀγαθῶν καὶ κακῶν. Amplius autem multis existentium non insunt omnibus omnia. Quo namque modo possibile est motus principium esse > in immobilibus aut boni naturam, siquidem omne quod est bonum secundum se et propter suam naturam finis est et ita causa quod illius causa et fiunt et sunt cetera, finis autem et cuius causa actus cuiusdam est finis, sed actus omnes cum motu? Quare in immobilibus non continget hoc esse principium nec esse aliquid autoagathon. Unde et in mathematicis nihil per hanc ostenditur causam, nec est demonstratio nulla eo quod melius aut deterius; sed nec omnino nullus talium alicuius reminiscitur. Quapropter et sophistarum quidam, ut aristippus, ipsas preneglexit. In aliis enim artibus et illiberalibus, ut tectonica et coriaria, eo quod * melius vel deterius dici omnia, mathematicas vero nullam de bonis et malis rationem facere. Further, there are many things to which not all the principles pertain. For how can a principle of change or the nature of the good exist for unchangeable things, since everything that in itself and by its own nature is good is an end, and a cause in the sense that for its sake the other things both come to be and are, and since an end or purpose is the end of some action, and all actions imply change? So in the case of unchangeable things this principle could not exist, nor could there be a good itself. This is why in mathematics nothing is proved by means of this kind of cause, nor is there any demonstration of this kind – because it is better, or worse; indeed no one even mentions anything of the kind. And so for this reason some of the Sophists, e.g. Aristippus, used to ridicule mathematics; for in the arts (he maintained), even in the industrial arts, e.g. in carpentry and cobbling, the reason always given is because it is better, or worse, but the mathematical sciences take no account of goods and evils.
[996β] [1] - ἀλλὰ μὴν εἴ γε πλείους ἐπιστῆμαι τῶν αἰτίων εἰσὶ καὶ ἑτέρα ἑτέρας ἀρχῆς, τίνα τούτων φατέον εἶναι τὴν ζητουμένην, ἢ τίνα μάλιστα τοῦ πράγματος τοῦ ζητουμένου ἐπιστήμονα τῶν ἐχόντων [5] αὐτάς; At vero si causarum scientie sunt plures et altera alterius principii, quae earum est dicenda quae quaeritur? Aut quis maxime rem quaesitam est sciens eas habentium? [96b] But if there are several sciences of the causes, and a different science for each different principle, which of these sciences should be said to be that which we seek, or which of the people who possess them has the most scientific knowledge of the object in question?
ἐνδέχεται γὰρ τῷ αὐτῷ πάντας τοὺς τρόπους τοὺς τῶν αἰτίων ὑπάρχειν, οἷον οἰκίας ὅθεν μὲν ἡ κίνησις ἡ τέχνη καὶ ὁ οἰκοδόμος, οὗ δ᾽ ἕνεκα τὸ ἔργον, ὕλη δὲ γῆ καὶ λίθοι, τὸ δ᾽ εἶδος ὁ λόγος. Contingit enim eidem omnes modos causarum inesse, ut domus unde quidem motus ars et edificator, cuius vero causa opus, et materia terra et lapides, species vero ratio. The same thing may have all the kinds of causes, e.g. the moving cause of a house is the art or the builder, the final cause is the function it fulfils, the matter is earth and stones, and the form is the definition.
ἐκ μὲν οὖν τῶν πάλαι διωρισμένων τίνα χρὴ καλεῖν τῶν ἐπιστημῶν σοφίαν ἔχει λόγον ἑκάστην [10] προσαγορεύειν: ᾗ μὲν γὰρ ἀρχικωτάτη καὶ ἡγεμονικωτάτη καὶ ᾗ ὥσπερ δούλας οὐδ᾽ ἀντειπεῖν τὰς ἄλλας ἐπιστήμας δίκαιον, ἡ τοῦ τέλους καὶ τἀγαθοῦ τοιαύτη (τούτου γὰρ ἕνεκα τἆλλα), Igitur ex dudum determinatis quam decet vocare scientiarum sapientiam habet * rationem quamlibet appellari. In quantum enim senior quidem et principalior, cui veluti seruientes non contradicere scientias alias iustum est, quae finis et boni talis est; huius enim causa sunt cetera. To judge from our previous discussion of the question which of the sciences should be called Wisdom, there is reason for applying the name to each of them. For inasmuch as it is most architectonic and authoritative and the other sciences, like slavewomen, may not even contradict it, the science of the end and of the good is of the nature of Wisdom (for the other things are for the sake of the end).
ᾗ δὲ τῶν πρώτων αἰτίων καὶ τοῦ μάλιστα ἐπιστητοῦ διωρίσθη εἶναι, ἡ τῆς οὐσίας ἂν εἴη τοιαύτη: πολλαχῶς γὰρ [15] ἐπισταμένων τὸ αὐτὸ μᾶλλον μὲν εἰδέναι φαμὲν τὸν τῷ εἶναι γνωρίζοντα τί τὸ πρᾶγμα ἢ τῷ μὴ εἶναι, αὐτῶν δὲ τούτων ἕτερον ἑτέρου μᾶλλον, καὶ μάλιστα τὸν τί ἐστιν ἀλλ᾽ οὐ τὸν πόσον ἢ ποῖον ἢ τί ποιεῖν ἢ πάσχειν πέφυκεν. ἔτι δὲ καὶ ἐν τοῖς ἄλλοις τὸ εἰδέναι ἕκαστον καὶ ὧν ἀποδείξεις [20] εἰσί, τότ᾽ οἰόμεθα ὑπάρχειν ὅταν εἰδῶμεν τί ἐστιν (οἷον τί ἐστι τὸ τετραγωνίζειν, ὅτι μέσης εὕρεσις: ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων), In quantum vero primarum causarum et maxime scibilis 95 diffmita est esse, quae substantiae utique erit talis. Multis enim modis idem scientibus magis quidem scire dicimus eum qui novit in ipso esse quid * res * quam in non esse, et horum eorundem alium alio magis, sed maxime qui quid est et non > quantum aut quale aut quid facere aut pati est apta nata. Amplius autem et in aliis scire singula et quorum demonstrationes sunt tunc putamus existere quando scimus quid est, ut tetragonizare quid est, quia medie inventio; similiter autem et in aliis. But inasmuch as it was described as dealing with the first causes and that which is in the highest sense object of knowledge, the science of substance must be of the nature of Wisdom. For since men may know the same thing in many ways, we say that he who recognizes what a thing is by its being so and so knows more fully than he who recognizes it by its not being so and so, and in the former class itself one knows more fully than another, and he knows most fully who knows what a thing is, not he who knows its quantity or quality or what it can by nature do or have done to it. And further [96b 18]in all cases also we think that the knowledge of each even of the things of which demonstration is possible is present only when we know what the thing is, e.g. what squaring a rectangle is, viz. that it is the finding of a mean; and similarly in all other cases.
περὶ δὲ τὰς γενέσεις καὶ τὰς πράξεις καὶ περὶ πᾶσαν μεταβολὴν ὅταν εἰδῶμεν τὴν ἀρχὴν τῆς κινήσεως: τοῦτο δ᾽ ἕτερον καὶ ἀντικείμενον τῷ τέλει, ὥστ᾽ ἄλλης ἂν [25] δόξειεν ἐπιστήμης εἶναι τὸ θεωρῆσαι τῶν αἰτίων τούτων ἕκαστον. Circa generationes vero et actus et circa omnem transmutationem, quando cognoscimus principium motus; hoc autem alterum et oppositum fini. Quapropter videbitur alius esse scientie causarum harum singulas speculari. And we know about becomings and actions and about every change when we know the source of the movement; and this is other than and opposed to the end. Therefore it would seem to belong to different sciences to investigate these causes severally.
ἀλλὰ μὴν καὶ περὶ τῶν ἀποδεικτικῶν ἀρχῶν, πότερον μιᾶς ἐστὶν ἐπιστήμης ἢ πλειόνων, ἀμφισβητήσιμόν ἐστιν (λέγω [28] δὲ ἀποδεικτικὰς τὰς κοινὰς δόξας ἐξ ὧν ἅπαντες δεικνύουσιν) οἷον ὅτι πᾶν ἀναγκαῖον ἢ φάναι ἢ ἀποφάναι, καὶ [30] ἀδύνατον ἅμα εἶναι καὶ μὴ εἶναι, καὶ ὅσαι ἄλλαι τοιαῦται προτάσεις, πότερον μία τούτων ἐπιστήμη καὶ τῆς οὐσίας ἢ ἑτέρα, κἂν εἰ μὴ μία, ποτέραν χρὴ προσαγορεύειν τὴν ζητουμένην νῦν. At vero et de principiis demonstrationis, utrum unius est scientie aut plurium, dubitatio est. Dico autem demonstrativas * comrnunes opiniones ex quibus omnes demonstrant. Ut quoniam omne necessarium aut dicere aut negare, et impossibile simul esse et non esse, et quaecumque aliae tales propositiones: utrum harum una scientia et substantiae aut alia, et si non una est, quam oportet appellare quae nunc est quaesita. But (2), taking the starting-points of demonstration as well as the causes, it is a disputable question whether they are the object of one science or of more (by the starting-points of demonstration I mean the common beliefs, on which all men base their proofs); e.g. that everything must be either affirmed or denied, and that a thing cannot at the same time be and not be, and all other such premisses:-the question is whether the same science deals with them as with substance, or a different science, and if it is not one science, which of the two must be identified with that which we now seek.
μιᾶς μὲν οὖν οὐκ εὔλογον εἶναι: τί γὰρ μᾶλλον γεωμετρίας ἢ ὁποιασοῦν περὶ τούτων ἐστὶν ἴδιον τὸ ἐπαΐειν; [35] εἴπερ οὖν ὁμοίως μὲν ὁποιασοῦν ἐστίν, ἁπασῶν δὲ μὴ ἐνδέχεται, [997α] [1] ὥσπερ οὐδὲ τῶν ἄλλων οὕτως οὐδὲ τῆς γνωριζούσης τὰς οὐσίας ἴδιόν ἐστι τὸ γιγνώσκειν περὶ αὐτῶν. Unius igitur esse non est rationabile; quid enim magis geometrie quam qualiscumque de hiis est proprium obaudire? Si igitur similiter quidem qualiscumque est, omnium vero non contingit, sicut nec aliarum ita nec ipsas substantias cognoscentis proprium est de ipsis cognoscere. -It is not reasonable that these topics should be the object of one science; for why should it be peculiarly appropriate to geometry or to any other science to understand these matters? If then it belongs to every science [97a] alike, and cannot belong to all, it is not peculiar to the science which investigates substances, any more than to any other science, to know about these topics.
ἅμα δὲ καὶ τίνα τρόπον ἔσται αὐτῶν ἐπιστήμη; τί μὲν γὰρ ἕκαστον τούτων τυγχάνει ὂν καὶ νῦν γνωρίζομεν (χρῶνται γοῦν ὡς γιγνωσκομένοις [5] αὐτοῖς καὶ ἄλλαι τέχναι): εἰ δὲ ἀποδεικτικὴ περὶ αὐτῶν ἐστί, δεήσει τι γένος εἶναι ὑποκείμενον καὶ τὰ μὲν πάθη τὰ δ᾽ ἀξιώματ᾽ αὐτῶν (περὶ πάντων γὰρ ἀδύνατον ἀπόδειξιν εἶναι), ἀνάγκη γὰρ ἔκ τινων εἶναι καὶ περί τι καὶ τινῶν τὴν ἀπόδειξιν: ὥστε συμβαίνει πάντων εἶναι γένος ἕν [10] τι τῶν δεικνυμένων, πᾶσαι γὰρ αἱ ἀποδεικτικαὶ χρῶνται τοῖς ἀξιώμασιν. Simul autem et quomodo erit ipsorum scientia? Quid quidem enim et unumquodque horum existit ens et nunc novimus; utuntur igitur eis ut notis artes aliae. Si autem de eis demonstratio est, oportebit aliquod genus esse subiectum et haec quidem passiones illa vero dignitates eorum. Nam de omnibus esse demonstrationem est impossibile. Necesse enim ex aliquibus esse et circa aliquid et aliquorum demonstrationem. Quare accidit omnium esse genus unum aliquid monstratorum1; omnes enim demonstrative * dignitatibus utuntur. -And, at the same time, in what way can there be a science of the first principles? For we are aware even now what each of them in fact is (at least even other sciences use them as familiar); but if there is a demonstrative science which deals with them, there will have to be an underlying kind, and some of them must be demonstrable attributes and others must be axioms (for it is impossible that there should be demonstration about all of them); for the demonstration must start from certain premisses and be about a certain subject and prove certain attributes. Therefore it follows that all attributes that are proved must belong to a single class; for all demonstrative sciences use the axioms.
ἀλλὰ μὴν εἰ ἑτέρα ἡ τῆς οὐσίας καὶ ἡ περὶ τούτων, ποτέρα κυριωτέρα καὶ προτέρα πέφυκεν αὐτῶν; καθόλου γὰρ μάλιστα καὶ πάντων ἀρχαὶ τὰ ἀξιώματά ἐστιν, εἴ τ᾽ ἐστὶ μὴ τοῦ φιλοσόφου, τίνος ἔσται περὶ αὐτῶν ἄλλου τὸ [15] θεωρῆσαι τὸ ἀληθὲς καὶ ψεῦδος; > At vero si alia quae substantiae et quae de hiis, quae earum principalior et prior est earum? Universaliter enim maxime omnium principia sunt dignitates. Et si non est philosophi, cuius erit alius de eis speculari veritatem et falsitatem? But if the science of substance and the science which deals with the axioms are different, which of them is by nature more authoritative and prior? The axioms are most universal and are principles of all things. And if it is not the business of the philosopher, to whom else will it belong to inquire what is true and what is untrue about them?
ὅλως τε τῶν οὐσιῶν πότερον μία πασῶν ἐστὶν ἢ πλείους ἐπιστῆμαι; εἰ μὲν οὖν μὴ μία, ποίας οὐσίας θετέον τὴν ἐπιστήμην ταύτην; Totaliterque substantiarum utrum una omnium est aut plures scientie? Si quidem ergo non una, cuius substantiae ponenda est scientia ista? (3) In general, do all substances fall under one science or under more than one? If the latter, to what sort of substance is the present science to be assigned?
τὸ δὲ μίαν πασῶν οὐκ εὔλογον: καὶ γὰρ ἂν ἀποδεικτικὴ μία περὶ πάντων εἴη τῶν συμβεβηκότων, εἴπερ πᾶσα ἀποδεικτικὴ περί [20] τι ὑποκείμενον θεωρεῖ τὰ καθ᾽ αὑτὰ συμβεβηκότα ἐκ τῶν κοινῶν δοξῶν. περὶ οὖν τὸ αὐτὸ γένος τὰ συμβεβηκότα καθ᾽ αὑτὰ τῆς αὐτῆς ἐστὶ θεωρῆσαι ἐκ τῶν αὐτῶν δοξῶν. περί τε γὰρ ὃ μιᾶς καὶ ἐξ ὧν μιᾶς, εἴτε τῆς αὐτῆς εἴτε ἄλλης, ὥστε καὶ τὰ συμβεβηκότα, εἴθ᾽ αὗται θεωροῦσιν εἴτ᾽ [25] ἐκ τούτων μία. Unam vero omnium non est rationabile. Et enim demonstrativa una de omnibus erit utique * accidentibus, siquidem omnis demonstrativa circa aliquod subiectum speculatur per se accidentia ex communibus opinionibus. Circa idem igitur genus accidentia per se eiusdem est speculari ex eisdem opinionibus. Nam circa ipsum quia unius et ex quibus unius, sive eiusdem sive alius; quare et accidentia deinde hae speculabuntur aut ex hiis una. -On the other hand, it is not reasonable that one science should deal with all. For then there would be one demonstrative science dealing with all attributes. For ever demonstrative science investigates with regard to some subject its essential attributes, starting from the common beliefs. Therefore to investigate the essential attributes of one class of things, starting from one set of beliefs, is the business of one science. For the subject belongs to one science, and the premisses belong to one, whether to the same or to another; so that the attributes do so too, whether they are investigated by these sciences or by one compounded out of them.
ἔτι δὲ πότερον περὶ τὰς οὐσίας μόνον ἡ θεωρία ἐστὶν ἢ καὶ περὶ τὰ συμβεβηκότα ταύταις; λέγω δ᾽ οἷον, εἰ τὸ στερεὸν οὐσία τίς ἐστι καὶ γραμμαὶ καὶ ἐπίπεδα, πότερον τῆς αὐτῆς ταῦτα γνωρίζειν ἐστὶν ἐπιστήμης καὶ τὰ συμβεβηκότα περὶ ἕκαστον γένος περὶ ὧν αἱ μαθηματικαὶ [30] δεικνύουσιν, ἢ ἄλλης. Amplius autem utrum circa substantias solum theoria est aut et circa ipsis accidentia? Dico autem ut si solidum quaedam substantia est et lineae et superficies, utrum eiusdem scientie est ea cognoscere et accidentia circa unumquodque genus de quibus mathematice ostendunt, aut alius. (5) Further, does our investigation deal with substances alone or also with their attributes? I mean for instance, if the solid is a substance and so are lines and planes, is it the business of the same science to know these and to know the attributes of each of these classes (the attributes about which the mathematical sciences offer proofs), or of a different science?
εἰ μὲν γὰρ τῆς αὐτῆς, ἀποδεικτική τις ἂν εἴη καὶ ἡ τῆς οὐσίας, οὐ δοκεῖ δὲ τοῦ τί ἐστιν ἀπόδειξις εἶναι: Nam si eiusdem, demonstrativa quaedam erit et quae est substantiae; non autem videtur eius quod quid est demonstratio esse. If of the same, the science of substance also must be a demonstrative science, but it is thought that there is no demonstration of the essence of things.
εἰ δ᾽ ἑτέρας, τίς ἔσται ἡ θεωροῦσα περὶ τὴν οὐσίαν τὰ συμβεβηκότα; τοῦτο γὰρ ἀποδοῦναι παγχάλεπον. Si vero diverse, quae erit speculans circa substantiam accidentia? Hoc enim reddere est valde difficile. And if of another, what will be the science that investigates the attributes of substance? This is a very difficult question.
ἔτι δὲ πότερον τὰς αἰσθητὰς οὐσίας μόνας εἶναι [35] φατέον ἢ καὶ παρὰ ταύτας ἄλλας, καὶ πότερον μοναχῶς ἢ πλείω γένη τετύχηκεν ὄντα τῶν οὐσιῶν, [997β] [1] οἷον οἱ λέγοντες τά τε εἴδη καὶ τὰ μεταξύ, περὶ ἃ τὰς μαθηματικὰς εἶναί φασιν ἐπιστήμας; Amplius autem utrum sensibiles substantiae sole esse sint dicende aut praeter eas aliae? Et utrum unice aut plura genera substantiarum sunt, ut dicentes species et intermedia, circa quae mathematicas dicunt esse scientias? (4) Further, must we say that sensible substances alone exist, or that there are others besides these? And are substances of one kind or are there in fact several kinds of [97b] substances, as those say who assert the existence both of the Forms and of the intermediates, with which they say the mathematical sciences deal?
ὡς μὲν οὖν λέγομεν τὰ εἴδη αἴτιά τε καὶ οὐσίας εἶναι καθ᾽ ἑαυτὰς εἴρηται ἐν τοῖς πρώτοις λόγοις περὶ [5] αὐτῶν: Quomodo ergo dicimus species causasque et substantias secundum se, dictum est in pri>mis de ipsis sermonibus. -The sense in which we say the Forms are both causes and self-dependent substances has been explained in our first remarks about them;
πολλαχῇ δὲ ἐχόντων δυσκολίαν, οὐθενὸς ἧττον ἄτοπον τὸ φάναι μὲν εἶναί τινας φύσεις παρὰ τὰς ἐν τῷ οὐρανῷ, ταύτας δὲ τὰς αὐτὰς φάναι τοῖς αἰσθητοῖς πλὴν ὅτι τὰ μὲν ἀΐδια τὰ δὲ φθαρτά. αὐτὸ γὰρ ἄνθρωπόν φασιν εἶναι καὶ ἵππον καὶ ὑγίειαν, ἄλλο δ᾽ οὐδέν, παραπλήσιον [10] ποιοῦντες τοῖς θεοὺς μὲν εἶναι φάσκουσιν ἀνθρωποειδεῖς δέ: οὔτε γὰρ ἐκεῖνοι οὐδὲν ἄλλο ἐποίουν ἢ ἀνθρώπους ἀϊδίους, οὔθ᾽ οὗτοι τὰ εἴδη ἄλλ᾽ ἢ αἰσθητὰ ἀΐδια. Multis autem modis habentibus difficultatem, nullo minus absurdum dicere quidem aliquas esse naturas praeter eas quae sunt in celo, has autem easdem dicere sensibilibus nisi quia haec quidem sempiterna illa vero corruptibilia. Nam per se hominem dicunt esse et equum et sanitatem, aliud autem nihil, simile facientes deos esse dicentibus et humane speciei esse. Nihil enim aliud illi fecerunt quam homines sempiternos, nec hii species nisi sensibiles sempiternas. while the theory presents difficulties in many ways, the most paradoxical thing of all is the statement that there are certain things besides those in the material universe, and that these are the same as sensible things except that they are eternal while the latter are perishable. For they say there is a man-himself and a horse-itself and health-itself, with no further qualification,-a procedure like that of the people who said there are gods, but in human form. For they were positing nothing but eternal men, nor are the Platonists making the Forms anything other than eternal sensible things.
ἔτι δὲ εἴ τις παρὰ τὰ εἴδη καὶ τὰ αἰσθητὰ τὰ μεταξὺ θήσεται, πολλὰς ἀπορίας ἕξει: δῆλον γὰρ ὡς ὁμοίως γραμμαί τε παρά τ᾽ αὐτὰς καὶ [15] τὰς αἰσθητὰς ἔσονται καὶ ἕκαστον τῶν ἄλλων γενῶν: ὥστ᾽ ἐπείπερ ἡ ἀστρολογία μία τούτων ἐστίν, ἔσται τις καὶ οὐρανὸς παρὰ τὸν αἰσθητὸν οὐρανὸν καὶ ἥλιός τε καὶ σελήνη καὶ τἆλλα ὁμοίως τὰ κατὰ τὸν οὐρανόν. καίτοι πῶς δεῖ πιστεῦσαι τούτοις; οὐδὲ γὰρ ἀκίνητον εὔλογον εἶναι, κινούμενον δὲ [20] καὶ παντελῶς ἀδύνατον: ὁμοίως δὲ καὶ περὶ ὧν ἡ ὀπτικὴ πραγματεύεται καὶ ἡ ἐν τοῖς μαθήμασιν ἁρμονική: καὶ γὰρ ταῦτα ἀδύνατον εἶναι παρὰ τὰ αἰσθητὰ διὰ τὰς αὐτὰς αἰτίας: εἰ γὰρ ἔστιν αἰσθητὰ μεταξὺ καὶ αἰσθήσεις, δῆλον ὅτι καὶ ζῷα ἔσονται μεταξὺ αὐτῶν τε καὶ τῶν φθαρτῶν. Amplius autem si quis praeter species et sensibilia * intermedia ponat, multas habebit dubitationes. Palam enim quia similiter lineae * praeter ipsas et sensibiles erunt et unumquodque aliorum generum. Igitur quoniam astrologia harum una est, erit quoddam celum praeter sensibile celum et sol et luna et alia similiter celestia. Et quomodo hiis credere oportet? Neque enim immobile rationabile * esse, mobile vero omnino impossibile. — Similiter autem et de quibus perspectiva tractat et in mathematicis armonica; et enim haec impossibile * esse praeter sensibilia propter easdem causas. Nam si sunt sensibilia intermedia et sensus, palam quia et animalia erunt intermedia ipsorum et corruptibilium. Further, if we are to posit besides the Forms and the sensibles the intermediates between them, we shall have many difficulties. For clearly on the same principle there will be lines besides the lines-themselves and the sensible lines, and so with each of the other classes of things; so that since astronomy is one of these mathematical sciences there will also be a heaven besides the sensible heaven, and a sun and a moon (and so with the other heavenly bodies) besides the sensible. Yet how are we to believe in these things? It is not reasonable even to suppose such a body immovable, but to suppose it moving is quite impossible.-And similarly with the things of which optics and mathematical harmonics treat; for these also cannot exist apart from the sensible things, for the same reasons. For if there are sensible things and sensations intermediate between Form and individual, evidently there will also be animals intermediate between animals-themselves and the perishable animals.
[25] ἀπορήσειε δ᾽ ἄν τις καὶ περὶ ποῖα τῶν ὄντων δεῖ ζητεῖν ταύτας τὰς ἐπιστήμας. εἰ γὰρ τούτῳ διοίσει τῆς γεωδαισίας ἡ γεωμετρία μόνον, ὅτι ἡ μὲν τούτων ἐστὶν ὧν αἰσθανόμεθα ἡ δ᾽ οὐκ αἰσθητῶν, δῆλον ὅτι καὶ παρ᾽ ἰατρικὴν ἔσται τις ἐπιστήμη καὶ παρ᾽ ἑκάστην τῶν ἄλλων μεταξὺ αὐτῆς τε ἰατρικῆς [30] καὶ τῆσδε τῆς ἰατρικῆς: καίτοι πῶς τοῦτο δυνατόν; καὶ γὰρ ἂν ὑγιείν᾽ ἄττα εἴη παρὰ τὰ αἰσθητὰ καὶ αὐτὸ τὸ ὑγιεινόν. — Dubitabit autem aliquis et circa quae existentium quaerere oportet has scientias. Nam si in hoc differt geometria a geodesia solum, quia haec quidem horum est quae sentimus illa vero non sensibilium, palam quia et praeter medicinalem et alia erit scientia (et praeter unamquamque aliarum) inter ipsam medicinalem et hanc medicinalem. Sed quomodo hoc possibile? Et enim rsalubria quaedam utique erunt praeter sensibilia et autosanum. -We might also raise the question, with reference to which kind of existing things we must look for these sciences of intermediates. If geometry is to differ from mensuration only in this, that the latter deals with things that we perceive, and the former with things that are not perceptible, evidently there will also be a science other than medicine, intermediate between medical-science-itself and this individual medical science, and so with each of the other sciences. Yet how is this possible? There would have to be also healthy things besides the perceptible healthy things and the healthy-itself.
ἅμα δὲ οὐδὲ τοῦτο ἀληθές, ὡς ἡ γεωδαισία τῶν αἰσθητῶν ἐστὶ μεγεθῶν καὶ φθαρτῶν: ἐφθείρετο γὰρ ἂν φθειρομένων. Simul autem nec hoc verum quia geodesia sensibilium est magnitudinum et corruptibilium; corrupta enim utique esset corruptis. And at the same time not even this is true, that mensuration deals with perceptible and perishable magnitudes; for then it would have perished when they perished.
ἀλλὰ μὴν οὐδὲ τῶν αἰσθητῶν ἂν εἴη μεγεθῶν [35] οὐδὲ περὶ τὸν οὐρανὸν ἡ ἀστρολογία τόνδε. [998α] [1] οὔτε γὰρ αἱ αἰσθηταὶ γραμμαὶ τοιαῦταί εἰσιν οἵας λέγει ὁ γεωμέτρης (οὐθὲν γὰρ εὐθὺ τῶν αἰσθητῶν οὕτως οὐδὲ στρογγύλον: ἅπτεται γὰρ τοῦ κανόνος οὐ κατὰ στιγμὴν ὁ κύκλος ἀλλ᾽ ὥσπερ Πρωταγόρας ἔλεγεν ἐλέγχων τοὺς γεωμέτρας), οὔθ᾽ αἱ κινήσεις καὶ [5] ἕλικες τοῦ οὐρανοῦ ὅμοιαι περὶ ὧν ἡ ἀστρολογία ποιεῖται τοὺς λόγους, οὔτε τὰ σημεῖα τοῖς ἄστροις τὴν αὐτὴν ἔχει φύσιν. > At vero nec sensibilium erit magnitudinum nec * circa caelum hoc astrologia. Nec enim sensibiles lineae tales sunt quales dicit geometer. Nihil enim rectum sensibilium ita nec rotundum; tangit enim regulam non secundum punctum circulus, sed ut Protagoras ait geometras redarguens. Nec motus nec revolutiones celi similes de quibus astrologia facit sermones, nec astris puncta naturam habent eandem. But on the other hand astronomy cannot be dealing with perceptible magnitudes nor with this heaven above us. For neither are perceptible lines such lines as the [98a]geometer speaks of (for no perceptible thing is straight or round in the way in which he defines straight and round ; for a hoop touches a straight edge not at a point, but as Protagoras used to say it did, in his refutation of the geometers), nor are the movements and spiral orbits in the heavens like those of which astronomy treats, nor have geometrical points the same nature as the actual stars.
εἰσὶ δέ τινες οἵ φασιν εἶναι μὲν τὰ μεταξὺ ταῦτα λεγόμενα τῶν τε εἰδῶν καὶ τῶν αἰσθητῶν, οὐ μὴν χωρίς γε τῶν αἰσθητῶν ἀλλ᾽ ἐν τούτοις: οἷς τὰ συμβαίνοντα ἀδύνατα πάντα [10] μὲν πλείονος λόγου διελθεῖν, ἱκανὸν δὲ καὶ τὰ τοιαῦτα θεωρῆσαι. — Sunt autem aliqui qui dicunt esse quidem intermedia haec * dicta * infra species et sensibilia, non tamen sine sensibilibus sed in hiis. Quibus accidentia impossibilia omnia quidem pluris est orationis pertransire, sufficit autem et talia speculari. -Now there are some who say that these so-called intermediates between the Forms and the perceptible things exist, not apart from the perceptible things, however, but in these; the impossible results of this view would take too long to enumerate, but it is enough to consider even such points as the following:
οὔτε γὰρ ἐπὶ τούτων εὔλογον ἔχειν οὕτω μόνον, ἀλλὰ δῆλον ὅτι καὶ τὰ εἴδη ἐνδέχοιτ᾽ ἂν ἐν τοῖς αἰσθητοῖς εἶναι (τοῦ γὰρ αὐτοῦ λόγου ἀμφότερα ταῦτά ἐστιν), Non enim in talibus congruum est habere sic solum, sed palam quia et species convenit in sensibilibus esse; eiusdem enim rationis utraque haec sunt. -It is not reasonable that this should be so only in the case of these intermediates, but clearly the Forms also might be in the perceptible things; for both statements are parts of the same theory.
ἔτι δὲ δύο στερεὰ ἐν τῷ αὐτῷ ἀναγκαῖον εἶναι τόπῳ, Amplius autem duo solida in eodem necesse est esse loco, Further, it follows from this theory that there are two solids in the same place,
καὶ μὴ εἶναι ἀκίνητα [15] ἐν κινουμένοις γε ὄντα τοῖς αἰσθητοῖς. et non esse immobilia in motis existentia sensibilibus. and that the intermediates are not immovable, since they are in the moving perceptible things.
ὅλως δὲ τίνος ἕνεκ᾽ ἄν τις θείη εἶναι μὲν αὐτά, εἶναι δ᾽ ἐν τοῖς αἰσθητοῖς; ταὐτὰ γὰρ συμβήσεται ἄτοπα τοῖς προειρημένοις: ἔσται γὰρ οὐρανός τις παρὰ τὸν οὐρανόν, πλήν γ᾽ οὐ χωρὶς ἀλλ᾽ ἐν τῷ αὐτῷ τόπῳ: ὅπερ ἐστὶν ἀδυνατώτερον. [20] Totaliter autem cuius causa quis ponet utique esse quidem ipsa, esse autem in sensibilibus? Eadem enim contingent inconvenientia eis quae predicta sunt; erit enim celum aliquod preter celum, tamen non extra sed in eodem loco, quod magis est impossibile. And in general to what purpose would one suppose them to exist indeed, but to exist in perceptible things? For the same paradoxical results will follow which we have already mentioned; there will be a heaven besides the heaven, only it will be not apart but in the same place; which is still more impossible.

Chapter 3

Greek Latin English
περί τε τούτων οὖν ἀπορία πολλὴ πῶς δεῖ θέμενον τυχεῖν τῆς ἀληθείας, καὶ περὶ τῶν ἀρχῶν πότερον δεῖ τὰ γένη στοιχεῖα καὶ ἀρχὰς ὑπολαμβάνειν ἢ μᾶλλον ἐξ ὧν ἐνυπαρχόντων ἐστὶν ἕκαστον πρώτων, De hiis ergo dubitatio multa quomodo oportet positum habere veritatem. Et de principiis, utrum oportet genera elementa et principia suscipere aut magis ex quibus cum insint est unumquodque primis. Chapter 3. (6) Apart from the great difficulty of stating the case truly with regard to these matters, it is very hard to say, with regard to the first principles, whether it is the genera that should be taken as elements and principles, or rather the primary constituents of a thing;
οἷον φωνῆς στοιχεῖα καὶ ἀρχαὶ δοκοῦσιν εἶναι ταῦτ᾽ ἐξ ὧν σύγκεινται αἱ φωναὶ [25] πρώτων, ἀλλ᾽ οὐ τὸ κοινὸν ἡ φωνή: καὶ τῶν διαγραμμάτων ταῦτα στοιχεῖα λέγομεν ὧν αἱ ἀποδείξεις ἐνυπάρχουσιν ἐν ταῖς τῶν ἄλλων ἀποδείξεσιν ἢ πάντων ἢ τῶν πλείστων, Ut vocis elementa et principia videntur esse ea ex quibus componuntur voces omnes primis, sed non commune vox; et diagramatum ea dicimus elementa quorum demonstrationes insunt in aliorum demonstrationibus aut omnium aut plurimorum. e.g. it is the primary parts of which articulate sounds consist that are thought to be elements and principles of articulate sound, not the common genus-articulate sound; and we give the name of elements to those geometrical propositions, the proofs of which are implied in the proofs of the others, either of all or of most.
ἔτι δὲ τῶν σωμάτων καὶ οἱ πλείω λέγοντες εἶναι στοιχεῖα καὶ οἱ ἕν, ἐξ ὧν σύγκειται καὶ ἐξ ὧν συνέστηκεν ἀρχὰς λέγουσιν [30] εἶναι, οἷον Ἐμπεδοκλῆς πῦρ καὶ ὕδωρ καὶ τὰ μετὰ τούτων στοιχεῖά φησιν εἶναι ἐξ ὧν ἐστὶ τὰ ὄντα ἐνυπαρχόντων, ἀλλ᾽ οὐχ ὡς γένη λέγει ταῦτα τῶν ὄντων. Amplius autem corporum qui dicunt esse plura elementa et qui unum, ex quibus componuntur et constant principia esse dicunt, ut Empedocles ignem et aquam et quae * cum hiis ele>menta dicit esse ex quibus sunt entia inexistentibus, sed non ut genera dicit ea eorum quae sunt. Further, both those who say there are several elements of corporeal things and those who say there is one, say the parts of which bodies are compounded and consist are principles; e.g. Empedocles says fire and water and the rest are the constituent elements of things, but does not describe these as genera of existing things.
πρὸς δὲ τούτοις καὶ τῶν ἄλλων εἴ τις ἐθέλει τὴν φύσιν ἀθρεῖν, [998β] [1] οἷον κλίνην ἐξ ὧν μορίων συνέστηκε καὶ πῶς συγκειμένων, τότε γνωρίζει τὴν φύσιν αὐτῆς. ἐκ μὲν οὖν τούτων τῶν λόγων οὐκ ἂν εἴησαν αἱ ἀρχαὶ τὰ γένη τῶν ὄντων: * ad haec autem et * aliorum si quis vult naturam speculari, ut lectum ex quibus partibus est et quomodo compositis, tunc cognoscet eius naturam. * Ex hiis quidem igitur rationibus non utique erunt principia genera existentium; Besides this, if we want to examine the nature of anything else, we [98b]examine the parts of which, e.g. a bed consists and how they are put together, and then we know its nature. To judge from these arguments, then, the principles of things would not be the genera;
εἰ δ᾽ ἕκαστον μὲν [5] γνωρίζομεν διὰ τῶν ὁρισμῶν, ἀρχαὶ δὲ τὰ γένη τῶν ὁρισμῶν εἰσίν, ἀνάγκη καὶ τῶν ὁριστῶν ἀρχὰς εἶναι τὰ γένη. in quantum autem cognoscimus unumquodque per diffinitiones, principia autem diffinitionum sunt ipsa genera, necesse et diffinitorum principia genera esse. but if we know each thing by its definition, and the genera are the principles or starting-points of definitions, the genera must also be the principles of definable things.
κἂν [7] εἰ ἔστι τὴν τῶν ὄντων λαβεῖν ἐπιστήμην τὸ τῶν εἰδῶν λαβεῖν καθ᾽ ἃ λέγονται τὰ ὄντα, τῶν γε εἰδῶν ἀρχαὶ τὰ γένη εἰσίν. Et si est eorum quae sunt accipere scientiam specierum scientiam accipere secundum quas dicuntur entia, specierum autem principia genera sunt. And if to get the knowledge of the species according to which things are named is to get the knowledge of things, the genera are at least starting-points of the species.
φαίνονται δέ τινες καὶ τῶν λεγόντων στοιχεῖα τῶν ὄντων τὸ [10] ἓν ἢ τὸ ὂν ἢ τὸ μέγα καὶ μικρὸν ὡς γένεσιν αὐτοῖς χρῆσθαι. Videntur autem quidam dicentium elementa existentium unum aut ens aut magnum aut parvum ut generibus eis uti. And some also of those who say unity or being, or the great and the small, are elements of things, seem to treat them as genera.
ἀλλὰ μὴν οὐδὲ ἀμφοτέρως γε οἷόν τε λέγειν τὰς ἀρχάς. ὁ μὲν γὰρ λόγος τῆς οὐσίας εἷς: ἕτερος δ᾽ ἔσται ὁ διὰ τῶν γενῶν ὁρισμὸς καὶ ὁ λέγων ἐξ ὧν ἔστιν ἐνυπαρχόντων. At vero neque utrobique possibile dicere principia *. Ratio namque substantiae est una; diversa vero erit quae est per genera diffinitio et quae dicit ex quibus est inexistentibus. But, again, it is not possible to describe the principles in both ways. For the formula of the essence is one; but definition by genera will be different from that which states the constituent parts of a thing.
πρὸς δὲ τούτοις εἰ καὶ ὅτι μάλιστα ἀρχαὶ τὰ γένη εἰσί, [15] πότερον δεῖ νομίζειν τὰ πρῶτα τῶν γενῶν ἀρχὰς ἢ τὰ ἔσχατα κατηγορούμενα ἐπὶ τῶν ἀτόμων; καὶ γὰρ τοῦτο ἔχει ἀμφισβήτησιν. Ad haec autem si quam maxime principia genera sunt, quae oportet existimare: prima generum principia aut ultima predicata de individuis? Et enim hoc dubitationem habet. (7) Besides this, even if the genera are in the highest degree principles, should one regard the first of the genera as principles, or those which are predicated directly of the individuals? This also admits of dispute.
εἰ μὲν γὰρ ἀεὶ τὰ καθόλου μᾶλλον ἀρχαί, φανερὸν ὅτι τὰ ἀνωτάτω τῶν γενῶν: ταῦτα γὰρ λέγεται κατὰ πάντων. τοσαῦται οὖν ἔσονται ἀρχαὶ τῶν ὄντων ὅσαπερ [20] τὰ πρῶτα γένη, ὥστ᾽ ἔσται τό τε ὂν καὶ τὸ ἓν ἀρχαὶ καὶ οὐσίαι: ταῦτα γὰρ κατὰ πάντων μάλιστα λέγεται τῶν ὄντων. οὐχ οἷόν τε δὲ τῶν ὄντων ἓν εἶναι γένος οὔτε τὸ ἓν οὔτε τὸ ὄν: ἀνάγκη μὲν γὰρ τὰς διαφορὰς ἑκάστου γένους καὶ εἶναι καὶ μίαν εἶναι ἑκάστην, ἀδύνατον δὲ κατηγορεῖσθαι ἢ τὰ εἴδη τοῦ [25] γένους ἐπὶ τῶν οἰκείων διαφορῶν ἢ τὸ γένος ἄνευ τῶν αὐτοῦ εἰδῶν, ὥστ᾽ εἴπερ τὸ ἓν γένος ἢ τὸ ὄν, οὐδεμία διαφορὰ οὔτε ὂν οὔτε ἓν ἔσται. ἀλλὰ μὴν εἰ μὴ γένη, οὐδ᾽ ἀρχαὶ ἔσονται, εἴπερ ἀρχαὶ τὰ γένη. Nam si quia universalia sunt magis principia, palam quia supprema generum; haec namque dicuntur de omnibus. Tot igitur erunt entium principia quot genera prima, quare erunt ens et unum principia et substantiae; haec namque de omnibus maxime dicuntur existentibus. Non est autem possibile genus existentium unum esse neque unum neque ens. Nam necesse differentias cuiuslibet generis et esse et unam esse quamlibet, impossibile autem predicari aut species generis de propriis differentiis aut genus sine suis speciebus; quare si unum genus aut ens, nulla differentia nec unum nec ens erit. At vero si non > genera, nec principia erunt, si principia genera. For if the universals are always more of the nature of principles, evidently the uppermost of the genera are the principles; for these are predicated of all things. There will, then, be as many principles of things as there are primary genera, so that both being and unity will be principles and substances; for these are most of all predicated of all existing things. But it is not possible that either unity or being should be a single genus of things; for the differentiae of any genus must each of them both have being and be one, but it is not possible for the genus taken apart from its species (any more than for the species of the genus) to be predicated of its proper differentiae; so that if unity or being is a genus, no differentia will either have being or be one. But if unity and being are not genera, neither will they be principles, if the genera are the principles.
ἔτι καὶ τὰ μεταξὺ συλλαμβανόμενα μετὰ τῶν διαφορῶν ἔσται γένη μέχρι τῶν ἀτόμων [30] (νῦν δὲ τὰ μὲν δοκεῖ τὰ δ᾽ οὐ δοκεῖ): πρὸς δὲ τούτοις ἔτι μᾶλλον αἱ διαφοραὶ ἀρχαὶ ἢ τὰ γένη: εἰ δὲ καὶ αὗται ἀρχαί, ἄπειροι ὡς εἰπεῖν ἀρχαὶ γίγνονται, ἄλλως τε κἄν τις τὸ πρῶτον γένος ἀρχὴν τιθῇ. — Amplius et intermedia coaccepta cum differentiis erunt genera usque ad individua; nunc autem haec quidem videntur illa vero non videntur. Ad haec autem adhuc magis differentie * principia quam genera; si autem et hae * principia, infinita ut si ita dicatur erunt principia, aliterque et si quis primum genus principium ponat. Again, the intermediate kinds, in whose nature the differentiae are included, will on this theory be genera, down to the indivisible species; but as it is, some are thought to be genera and others are not thought to be so. Besides this, the differentiae are principles even more than the genera; and if these also are principles, there comes to be practically an infinite number of principles, especially if we suppose the [99a] highest genus to be a principle.
[999α] [1] ἀλλὰ μὴν καὶ εἰ μᾶλλόν γε ἀρχοειδὲς τὸ ἕν ἐστιν, ἓν δὲ τὸ ἀδιαίρετον, ἀδιαίρετον δὲ ἅπαν ἢ κατὰ τὸ ποσὸν ἢ κατ᾽ εἶδος, πρότερον δὲ τὸ κατ᾽ εἶδος, τὰ δὲ γένη διαιρετὰ εἰς εἴδη, μᾶλλον ἂν ἓν τὸ [5] ἔσχατον εἴη κατηγορούμενον: οὐ γάρ ἐστι γένος ἅνθρωπος τῶν τινῶν ἀνθρώπων. At vero et si magis principii speciem habens est unum, unum autem indivisibile, indivisibile vero omne aut secundum quantitatem aut secundum speciem, prius autem quod * secundum speciem, genera vero divisibilia in species: magis utique unum ultimum erit predicatum. -But again, if unity is more of the nature of a principle, and the indivisible is one, and everything indivisible is so either in quantity or in species, and that which is so in species is the prior, and genera are divisible into species for man is not the genus of individual men), that which is predicated directly of the individuals will have more unity.
ἔτι ἐν οἷς τὸ πρότερον καὶ ὕστερόν ἐστιν, οὐχ οἷόν τε τὸ ἐπὶ τούτων εἶναί τι παρὰ ταῦτα (οἷον εἰ πρώτη τῶν ἀριθμῶν ἡ δυάς, οὐκ ἔσται τις ἀριθμὸς παρὰ τὰ εἴδη τῶν ἀριθμῶν: ὁμοίως δὲ οὐδὲ σχῆμα παρὰ τὰ εἴδη [10] τῶν σχημάτων: εἰ δὲ μὴ τούτων, σχολῇ τῶν γε ἄλλων ἔσται τὰ γένη παρὰ τὰ εἴδη: τούτων γὰρ δοκεῖ μάλιστα εἶναι γένη): ἐν δὲ τοῖς ἀτόμοις οὐκ ἔστι τὸ μὲν πρότερον τὸ δ᾽ ὕστερον. Non enim est genus homo aliquorum hominum. — Amplius in quibus et prius et posterius est, non est possibile * in hiis * aliquid esse praeter haec; ut si prima numerorum est dualitas, non erit numerus aliquis praeter species numerorum, similiter autem nec figura aliqua praeter species figurarum. Si autem non horum, schola * aliorum erunt genera praeter species; horum enim maxime genera esse videntur. In individuis vero non est hoc prius et illud posterius. — -Further, in the case of things in which the distinction of prior and posterior is present, that which is predicable of these things cannot be something apart from them (e.g. if two is the first of numbers, there will not be a Number apart from the kinds of numbers; and similarly there will not be a Figure apart from the kinds of figures; and if the genera of these things do not exist apart from the species, the genera of other things will scarcely do so; for genera of these things are thought to exist if any do). But among the individuals one is not prior and another posterior.
ἔτι ὅπου τὸ μὲν βέλτιον τὸ δὲ χεῖρον, ἀεὶ τὸ βέλτιον πρότερον: ὥστ᾽ οὐδὲ τούτων ἂν εἴη γένος. ἐκ μὲν οὖν τούτων [15] μᾶλλον φαίνεται τὰ ἐπὶ τῶν ἀτόμων κατηγορούμενα ἀρχαὶ εἶναι τῶν γενῶν: Amplius autem ubi hoc quidem melius illud vero vilius, semper quod est melius prius; quare neque horum erit utique genus. Ex hiis quidem igitur magis videntur quae de individuis sunt predicata esse principia generum. Further, where one thing is better and another worse, the better is always prior; so that of these also no genus can exist. From these considerations, then, the species predicated of individuals seem to be principles rather than the genera.
πάλιν δὲ πῶς αὖ δεῖ ταύτας ἀρχὰς ὑπολαβεῖν οὐ ῥᾴδιον εἰπεῖν. τὴν μὲν γὰρ ἀρχὴν δεῖ καὶ τὴν αἰτίαν εἶναι παρὰ τὰ πράγματα ὧν ἀρχή, καὶ δύνασθαι εἶναι χωριζομένην αὐτῶν: τοιοῦτον δέ τι παρὰ τὸ καθ᾽ ἕκαστον [20] εἶναι διὰ τί ἄν τις ὑπολάβοι, πλὴν ὅτι καθόλου κατηγορεῖται καὶ κατὰ πάντων; ἀλλὰ μὴν εἰ διὰ τοῦτο, τὰ μᾶλλον καθόλου μᾶλλον θετέον ἀρχάς: ὥστε ἀρχαὶ τὰ πρῶτ᾽ ἂν εἴησαν γένη. Iterum autem quomodo oportet haec existimare principia, non * facile dicere. Principium enim et causam oportet esse praeter res quarum principium est, et possibile ab eis separatum esse; tale vero aliquid praeter sin>gularia esse propter quid utique aliquis suscipiet, nisi quia universaliter et de omnibus predicatur? At vero si propter hoc, magis universalia magis ponenda sunt principia; quare principia prima erunt genera. But again, it is not easy to say in what sense these are to be taken as principles. For the principle or cause must exist alongside of the things of which it is the principle, and must be capable of existing in separation from them; but for what reason should we suppose any such thing to exist alongside of the individual, except that it is predicated universally and of all? But if this is the reason, the things that are more universal must be supposed to be more of the nature of principles; so that the highest genera would be the principles.

Chapter 4

Greek Latin English
ἔστι δ᾽ ἐχομένη τε τούτων ἀπορία καὶ πασῶν χαλεπωτάτη [25] καὶ ἀναγκαιοτάτη θεωρῆσαι, περὶ ἧς ὁ λόγος ἐφέστηκε νῦν. Est autem habita hiis dubitatio et omnium difficillima et ad considerandum maxime necessaria, de qua ratio nunc extitit. Chapter 4. (8) There is a difficulty connected with these, the hardest of all and the most necessary to examine, and of this the discussion now awaits us.
εἴτε γὰρ μὴ ἔστι τι παρὰ τὰ καθ᾽ ἕκαστα, τὰ δὲ καθ᾽ ἕκαστα ἄπειρα, τῶν δ᾽ ἀπείρων πῶς ἐνδέχεται λαβεῖν ἐπιστήμην; ᾗ γὰρ ἕν τι καὶ ταὐτόν, καὶ ᾗ καθόλου τι ὑπάρχει, ταύτῃ πάντα γνωρίζομεν. Nam si non est aliquid praeter singularia, singularia vero infinita, infinitorum quomodo contingit accipere scientiam? Nam in quantum unum aliquid et idem et in quantum universale aliquid est, in tantum omnia cognoscimus. If, on the one hand, there is nothing apart from individual things, and the individuals are infinite in number, how then is it possible to get knowledge of the infinite individuals? For all things that we come to know, we come to know in so far as they have some unity and identity, and in so far as some attribute belongs to them universally.
ἀλλὰ μὴν εἰ τοῦτο [30] ἀναγκαῖόν ἐστι καὶ δεῖ τι εἶναι παρὰ τὰ καθ᾽ ἕκαστα, ἀναγκαῖον ἂν εἴη τὰ γένη εἶναι παρὰ τὰ καθ᾽ ἕκαστα, ἤτοι τὰ ἔσχατα ἢ τὰ πρῶτα: τοῦτο δ᾽ ὅτι ἀδύνατον ἄρτι διηπορήσαμεν. At vero si hoc est necesse et oportet aliquid esse praeter singularia, necesse utique erit genera esse praeter singularia, aut ujtima aut prima; hoc autem quia impossibile nunc dubitavimus. But if this is necessary, and there must be something apart from the individuals, it will be necessary that the genera exist apart from the individuals, either the lowest or the highest genera; but we found by discussion just now that this is impossible.
ἔτι εἰ ὅτι μάλιστα ἔστι τι παρὰ τὸ σύνολον ὅταν κατηγορηθῇ τι τῆς ὕλης, πότερον, εἰ ἔστι, παρὰ πάντα δεῖ εἶναί τι, ἢ παρὰ μὲν ἔνια εἶναι παρὰ δ᾽ ἔνια μὴ εἶναι, ἢ παρ᾽ οὐδέν; Amplius autem si quam maxime est aliquid praeter simul totum quando predicatur aliquid de materia, utrum, si est * aliquid, praeter omnia oportet aliquid esse, aut praeter quaedam esse et praeter quaedam non esse, aut praeter nihil? Further, if we admit in the fullest sense that something exists apart from the concrete thing, whenever something is predicated of the matter, must there, if there is something apart, be something apart from each set of individuals, [99b] or from some and not from others, or from none?
[999β] [1] εἰ μὲν οὖν μηδέν ἐστι παρὰ τὰ καθ᾽ ἕκαστα, οὐθὲν ἂν εἴη νοητὸν ἀλλὰ πάντα αἰσθητὰ καὶ ἐπιστήμη οὐδενός, εἰ μή τις εἶναι λέγει τὴν αἴσθησιν ἐπιστήμην. Si quidem igitur nihil est praeter singularia, nil utique erit intellectuale sed omnia sensibilia et scientia nullius, nisi quis dicat esse sensum scientiam. (A) If there is nothing apart from individuals, there will be no object of thought, but all things will be objects of sense, and there will not be knowledge of anything, unless we say that sensation is knowledge.
ἔτι δ᾽ οὐδ᾽ ἀΐδιον οὐθὲν οὐδ᾽ ἀκίνητον (τὰ γὰρ αἰσθητὰ [5] πάντα φθείρεται καὶ ἐν κινήσει ἐστίν): — Amplius autem nec sempiternum est aliquid nec immobile; nam sensibilia omnia corrumpuntur et in motu sunt. Further, nothing will be eternal or unmovable; for all perceptible things perish and are in movement.
μὴν εἴ γε ἀΐδιον μηθέν ἐστιν, οὐδὲ γένεσιν εἶναι δυνατόν. ἀνάγκη γὰρ εἶναί τι τὸ γιγνόμενον καὶ ἐξ οὗ γίγνεται καὶ τούτων τὸ ἔσχατον ἀγένητον, εἴπερ ἵσταταί τε καὶ ἐκ μὴ ὄντος γενέσθαι ἀδύνατον: At vero si sempiternum nihil est, nec generationem esse possibile est; necesse est enim aliquid esse quod fit et ex quo fit et horum ultimum ingenitum, si stat et ex non ente generari impossibile. But if there is nothing eternal, neither can there be a process of coming to be; for there must be something that comes to be, i.e. from which something comes to be, and the ultimate term in this series cannot have come to be, since the series has a limit and since nothing can come to be out of that which is not.
ἔτι δὲ γενέσεως οὔσης καὶ κινήσεως ἀνάγκη καὶ πέρας εἶναι (οὔτε [10] γὰρ ἄπειρός ἐστιν οὐδεμία κίνησις ἀλλὰ πάσης ἔστι τέλος, γίγνεσθαί τε οὐχ οἷόν τε τὸ ἀδύνατον γενέσθαι: Amplius autem, cum sit generatio et motus, finem esse est necesse; motus enim nullus est infinitus sed omnis est finis, generarique non possibile quod impossibile est * factum esse; quod autem est generatum est esse necesse quando primum factum est. Further, if generation and movement exist there must also be a limit; for no movement is infinite, but every movement has an end, and that which is incapable of completing its coming to be cannot be in process of coming to be; and that which has completed its coming to be must he as soon as it has come to be.
τὸ δὲ γεγονὸς ἀνάγκη εἶναι ὅτε πρῶτον γέγονεν): ἔτι δ᾽ εἴπερ ἡ ὕλη ἔστι διὰ τὸ ἀγένητος εἶναι, πολὺ ἔτι μᾶλλον εὔλογον εἶναι τὴν οὐσίαν, ὅ ποτε ἐκείνη γίγνεται: εἰ γὰρ μήτε τοῦτο ἔσται [15] μήτε ἐκείνη, οὐθὲν ἔσται τὸ παράπαν, εἰ δὲ τοῦτο ἀδύνατον, ἀνάγκη τι εἶναι παρὰ τὸ σύνολον, τὴν μορφὴν καὶ τὸ εἶδος. Amplius autem si materia est quia est ingenita, multo rationabilius est esse substantiam, * > quando illa fit esse; nam si nec haec erit nec illa, nihil erit omnino. Sed si hoc est impossibile, necesse est aliquid esse praeter sinolon: formam et speciem. Further, since the matter exists, because it is ungenerated, it is a fortiori reasonable that the substance or essence, that which the matter is at any time coming to be, should exist; for if neither essence nor matter is to be, nothing will be at all, and since this is impossible there must be something besides the concrete thing, viz. the shape or form.
εἰ δ᾽ αὖ τις τοῦτο θήσει, ἀπορία ἐπὶ τίνων τε θήσει τοῦτο καὶ ἐπὶ τίνων οὔ. ὅτι μὲν γὰρ ἐπὶ πάντων οὐχ οἷόν τε, φανερόν: οὐ γὰρ ἂν θείημεν εἶναί τινα οἰκίαν παρὰ τὰς τινὰς [20] οἰκίας. Sed si hoc iterum quis ponit, dubitatio in quibus hoc ponet et in quibus non. Nam quod in omnibus non sit possibile, manifestum; non enim utique ponemus domum aliquam praeter domos aliquas. But again (B) if we are to suppose this, it is hard to say in which cases we are to suppose it and in which not. For evidently it is not possible to suppose it in all cases; we could not suppose that there is a house besides the particular houses.
πρὸς δὲ τούτοις πότερον ἡ οὐσία μία πάντων ἔσται, οἷον τῶν ἀνθρώπων; ἀλλ᾽ ἄτοπον: ἓν γὰρ πάντα ὧν ἡ οὐσία μία. ἀλλὰ πολλὰ καὶ διάφορα; Ad haec autem utrum substantia una erit omnium, ut hominum? Sed inconveniens est; non enim unum omnia quorum substantia una. Sed multa et differentia? -Besides this, will the substance of all the individuals, e.g. of all men, be one? This is paradoxical, for all the things whose substance is one are one. But are the substances many and different?
ἀλλὰ καὶ τοῦτο ἄλογον. Sed et hoc extra rationem. This also is unreasonable.
ἅμα δὲ καὶ πῶς γίγνεται ἡ ὕλη τούτων ἕκαστον καὶ ἔστι τὸ σύνολον ἄμφω ταῦτα; Simul autem et quomodo fit materia horum singulum et est sinolon ambo haec? -At the same time, how does the matter become each of the individuals, and how is the concrete thing these two elements?
ἔτι δὲ περὶ τῶν ἀρχῶν [25] καὶ τόδε ἀπορήσειεν ἄν τις. εἰ μὲν γὰρ εἴδει εἰσὶν ἕν, οὐθὲν ἔσται ἀριθμῷ ἕν, οὐδ᾽ αὐτὸ τὸ ἓν καὶ τὸ ὄν: καὶ τὸ ἐπίστασθαι πῶς ἔσται, εἰ μή τι ἔσται ἓν ἐπὶ πάντων; Amplius autem et de principiis et hoc dubitabit aliquis.Nam si specie sunt unum, nihil erit numero unum, nec * iterum unum ipsum et ens. Et scire quomodo erit, si non aliquid erit unum in omnibus? (9) Again, one might ask the following question also about the first principles. If they are one in kind only, nothing will be numerically one, not even unity-itself and being-itself; and how will knowing exist, if there is not to be something common to a whole set of individuals?
ἀλλὰ μὴν εἰ ἀριθμῷ ἓν καὶ μία ἑκάστη τῶν ἀρχῶν, καὶ μὴ ὥσπερ ἐπὶ τῶν αἰσθητῶν ἄλλαι ἄλλων (οἷον τῆσδε τῆς συλλαβῆς [30] τῷ εἴδει τῆς αὐτῆς οὔσης καὶ αἱ ἀρχαὶ εἴδει αἱ αὐταί: καὶ γὰρ αὗται ὑπάρχουσιν ἀριθμῷ ἕτεραι), εἰ δὲ μὴ οὕτως ἀλλ᾽ αἱ τῶν ὄντων ἀρχαὶ ἀριθμῷ ἕν εἰσιν, οὐκ ἔσται παρὰ τὰ στοιχεῖα οὐθὲν ἕτερον: τὸ γὰρ ἀριθμῷ ἓν ἢ τὸ καθ᾽ ἕκαστον λέγειν διαφέρει οὐθέν: οὕτω γὰρ λέγομεν τὸ καθ᾽ ἕκαστον, τὸ ἀριθμῷ ἕν, καθόλου δὲ τὸ ἐπὶ τούτων. [1000α] [1] ὥσπερ οὖν εἰ τὰ τῆς φωνῆς ἀριθμῷ ἦν στοιχεῖα ὡρισμένα, ἀναγκαῖον ἦν ἂν τοσαῦτα εἶναι τὰ πάντα γράμματα ὅσαπερ τὰ στοιχεῖα, μὴ ὄντων γε δύο τῶν αὐτῶν μηδὲ πλειόνων. At vero si numero unum et unum quodlibet principiorum, et non quemadmodum in sensibilibus alia aliorum (ut in hac sillaba specie eadem existente et principia specie eadem; et enim haec sunt numero diversa), si autem non ita sed quae sunt existentium numero unum sunt, non erit praeter elementa nihil aliud. Nam * numero unum aut singulare dicere nihil differt. Sic enim dicimus singulare: numero unum; universale vero quod in hiis est. Sicut igitur si quae vocis unum numero essent elementa determinata, tot omnes litteras esse necesse esset quot elementa, non existentibus quidem duobus eisdem nec pluribus. But if there is a common element which is numerically one, and each of the principles is one, and the principles are not as in the case of perceptible things different for different things (e.g. since this particular syllable is the same in kind whenever it occurs, the elements it are also the same in kind; only in kind, for these also, like the syllable, are numerically different in different contexts),-if it is not like this but the principles of things are numerically one, there will be nothing else besides the elements (for there is no difference of meaning between numerically one and individual ; for this is just what we mean by the individual-the numerically one, and by the universal we [00a] mean that which is predicable of the individuals). Therefore it will be just as if the elements of articulate sound were limited in number; all the language in the world would be confined to the ABC, since there could not be two or more letters of the same kind.
οὐθενὸς δ᾽ ἐλάττων ἀπορία παραλέλειπται καὶ τοῖς νῦν καὶ τοῖς πρότερον, πότερον αἱ αὐταὶ τῶν φθαρτῶν καὶ τῶν ἀφθάρτων ἀρχαί εἰσιν ἢ ἕτεραι. Non minor autem dubitatio modernis et prioribus relinquitur, utrum eadem corruptibilium et incorruptibilium sunt principia aut diversa. (10) One difficulty which is as great as any has been neglected both by modern philosophers and by their predecessors-whether the principles of perishable and those of imperishable things are the same or different.
εἰ μὲν γὰρ αἱ αὐταί, πῶς τὰ μὲν φθαρτὰ τὰ δὲ ἄφθαρτα, καὶ διὰ τίν᾽ αἰτίαν; Nam si eadem sunt, quomodo haec quidem incorruptibilia illa vero corruptibilia, et propter quam causam? If they are the same, how are some things perishable and others imperishable, and for what reason?
οἱ μὲν οὖν περὶ Ἡσίοδον καὶ πάντες ὅσοι θεολόγοι [10] μόνον ἐφρόντισαν τοῦ πιθανοῦ τοῦ πρὸς αὑτούς, ἡμῶν δ᾽ ὠλιγώρησαν (θεοὺς γὰρ ποιοῦντες τὰς ἀρχὰς καὶ ἐκ θεῶν γεγονέναι, τὰ μὴ γευσάμενα τοῦ νέκταρος καὶ τῆς ἀμβροσίας θνητὰ γενέσθαι φασίν, > Qui quidem igitur circa Esyodum et omnes quicumque theologi * solum ad ipsos persuasionem curaverunt, nos autem neglexerunt. Deos enim facientes principia et ex deis esse facta, quae non gustaverunt nectar * et manna mortalia facta esse dicunt. The school of Hesiod and all the theologians thought only of what was plausible to themselves, and had no regard to us. For, asserting the first principles to be gods and born of gods, they say that the beings which did not taste of nectar and ambrosia became mortal;
δῆλον ὡς ταῦτα τὰ ὀνόματα γνώριμα λέγοντες αὑτοῖς: καίτοι περὶ αὐτῆς τῆς προσφορᾶς [15] τῶν αἰτίων τούτων ὑπὲρ ἡμᾶς εἰρήκασιν: εἰ μὲν γὰρ χάριν ἡδονῆς αὐτῶν θιγγάνουσιν, οὐθὲν αἴτια τοῦ εἶναι τὸ νέκταρ καὶ ἡ ἀμβροσία, εἰ δὲ τοῦ εἶναι, πῶς ἂν εἶεν ἀΐδιοι δεόμενοι τροφῆς): Palam quod haec nomina sibi nota dicentes; equidem de allatione harum causarum super nos dixerunt. Nam si gratia voluptatis ipsa tangunt, non est causa existendi nectar et manna. Si vero existendi, quomodo erunt sempiterni cibo egentes? and clearly they are using words which are familiar to themselves, yet what they have said about the very application of these causes is above our comprehension. For if the gods taste of nectar and ambrosia for their pleasure, these are in no wise the causes of their existence; and if they taste them to maintain their existence, how can gods who need food be eternal?
ἀλλὰ περὶ μὲν τῶν μυθικῶς σοφιζομένων οὐκ ἄξιον μετὰ σπουδῆς σκοπεῖν: Sed de fabulose sophizantibus non est dignum cum studio intendere; -But into the subtleties of the mythologists it is not worth our while to inquire seriously;
παρὰ δὲ τῶν δι᾽ [20] ἀποδείξεως λεγόντων δεῖ πυνθάνεσθαι διερωτῶντας τί δή [21] ποτ᾽ ἐκ τῶν αὐτῶν ὄντα τὰ μὲν ἀΐδια τὴν φύσιν ἐστὶ τὰ δὲ φθείρεται τῶν ὄντων. ἐπεὶ δὲ οὔτε αἰτίαν λέγουσιν οὔτε εὔλογον οὕτως ἔχειν, δῆλον ὡς οὐχ αἱ αὐταὶ ἀρχαὶ οὐδὲ αἰτίαι αὐτῶν ἂν εἶεν. a dicentibus vero per demonstrationem oportet sciscitari interrogantes quare ex eisdem existentia haec quidem sempiterna secundum naturam sunt, illa vero corrumpuntur existentium. Quoniam autem nec causam dicunt nec rationabile est sic habere, palam quod nec eadem principia nec cause ipsorum erunt. those, however, who use the language of proof we must cross-examine and ask why, after all, things which consist of the same elements are, some of them, eternal in nature, while others perish. Since these philosophers mention no cause, and it is unreasonable that things should be as they say, evidently the principles or causes of things cannot be the same.
καὶ γὰρ ὅνπερ οἰηθείη λέγειν [25] ἄν τις μάλιστα ὁμολογουμένως αὑτῷ, Ἐμπεδοκλῆς, καὶ οὗτος ταὐτὸν πέπονθεν: τίθησι μὲν γὰρ ἀρχήν τινα αἰτίαν τῆς φθορᾶς τὸ νεῖκος, Et enim quem existimabit utique aliquis dicere maxime ipsi confesse, Empedocles *, et hic idem passus est. Ponit enim principium quoddam causam corruptionis odium, Even the man whom one might suppose to speak most [00a 25]consistently-Empedocles, even he has made the same mistake; for he maintains that strife is a principle that causes destruction,
δόξειε δ᾽ ἂν οὐθὲν ἧττον καὶ τοῦτο γεννᾶν ἔξω τοῦ ἑνός: ἅπαντα γὰρ ἐκ τούτου τἆλλά ἐστι πλὴν ὁ θεός. λέγει γοῦν ἐξ ὧν πάνθ᾽ ὅσα τ᾽ ἦν ὅσα τ᾽ [30] ἔσθ᾽ ὅσα τ᾽ ἔσται ὀπίσσω, δένδρεά τ᾽ ἐβλάστησε καὶ ἀνέρες ἠδὲ γυναῖκες, θῆρές τ᾽ οἰωνοί τε καὶ ὑδατοθρέμμονες ἰχθῦς, καί τε θεοὶ δολιχαίωνες. videbitur * nihil minus et hoc generare extra unum; nam omnia ex hoc alia sunt praeter deum. Dicit ergo: “ex quibus omnia et quaecumque erant et quaecumque erunt, et arbores pullulaverunt et viri et femine, bestieque et vultures et aqua nutriti pisces, et dei longevi”. but even strife would seem no less to produce everything, except the One; for all things excepting God proceed from strife. At least he says:
From which all that was and is and will be hereafter
Trees, and men and women, took their growth,
And beasts and birds and water-nourished fish,
And long-aged gods.
καὶ χωρὶς δὲ τούτων δῆλον: [1000β] [1] εἰ γὰρ μὴ ἦν ἐν τοῖς πράγμασιν, ἓν ἂν ἦν ἅπαντα, ὡς φησίν: ὅταν γὰρ συνέλθῃ, "τότε δ᾽ ἔσχατον ἵστατο νεῖκος." Et praeter haec palam quia si non esset in rebus, essent unum omnia, ut ait; nam quando convenerunt, tunc “ ultimum stabat odium”. The implication is evident even apart from these words; [00b] for if strife had not been present in things, all things would have been one, according to him; for when they have come together, "then strife stood outermost".
διὸ καὶ συμβαίνει αὐτῷ τὸν εὐδαιμονέστατον θεὸν ἧττον φρόνιμον εἶναι τῶν ἄλλων: οὐ γὰρ γνωρίζει [5] ἅπαντα: τὸ γὰρ νεῖκος οὐκ ἔχει, ἡ δὲ γνῶσις τοῦ ὁμοίου τῷ ὁμοίῳ. γαίῃ μὲν γάρ, (φησί,) γαῖαν ὀπώπαμεν, ὕδατι δ᾽ ὕδωρ, αἰθέρι δ᾽ αἰθέρα δῖον, ἀτὰρ πυρὶ πῦρ ἀΐδηλον, στοργὴν δὲ στοργῇ, νεῖκος δέ τε νείκεϊ λυγρῷ. Propter quod et accidit ipsi felicissimum deum minus prudentem esse aliis; non enim cognoscit elementa omnia; nam odium non habet, notitia vero similis > simili. “Terram namque”, ait, “per terram cognovimus, et per aquam aquam, et per affectum affectum, et adhuc odium per odium difficile”. Hence it also follows on his theory that God most blessed is less wise than all others; for he does not know all the elements; for he has in him no strife, and knowledge is of the like by the like. "For by earth", he says,
we see earth, by water water,
By ether godlike ether, by fire wasting fire,
Love by love, and strife by gloomy strife.
ἀλλ᾽ ὅθεν δὴ ὁ λόγος, τοῦτό γε φανερόν, ὅτι [10] συμβαίνει αὐτῷ τὸ νεῖκος μηθὲν μᾶλλον φθορᾶς ἢ τοῦ εἶναι αἴτιον: Sed unde ratio, hoc etiam palam quia accidit ei odium non magis corruptionis quam existendi causam. But-and this is the point we started from this at least is evident, that on his theory it follows that strife is as much the cause of existence as of destruction.
ὁμοίως δ᾽ οὐδ᾽ ἡ φιλότης τοῦ εἶναι, συνάγουσα γὰρ εἰς τὸ ἓν φθείρει τὰ ἄλλα. similiter autem nec amor existendi; colligens enim in unum corrumpit alia. And similarly love is not specially the cause of existence; for in collecting things into the One it destroys all other things.
καὶ ἅμα δὲ αὐτῆς τῆς μεταβολῆς αἴτιον οὐθὲν λέγει ἀλλ᾽ ἢ ὅτι οὕτως πέφυκεν: Simul quoque ipsius transmutationis causam nullam dicit, nisi quia sic aptum natum fuit: And at the same time Empedocles mentions no cause of the change itself, except that things are so by nature.
ἀλλ᾽ ὅτε δὴ μέγα νεῖκος ἐνὶ μελέεσσιν ἐθρέφθη, εἰς τιμάς [15] τ᾽ ἀνόρουσε τελειομένοιο χρόνοιο ὅς σφιν ἀμοιβαῖος πλατέος παρ᾽ ἐλήλαται ὅρκου:


“alias itaque magnum odium in membris nutritum est, et ad honorem intendebat perfecto tempore, qui mutabilis dissolvit sacramentum”. But when strife at last waxed great in the limbs of the Sphere,
And sprang to assert its rights as the time was fulfilled
Which is fixed for them in turn by a mighty oath.
ὡς ἀναγκαῖον μὲν ὂν μεταβάλλειν: αἰτίαν δὲ τῆς ἀνάγκης οὐδεμίαν δηλοῖ. ἀλλ᾽ ὅμως τοσοῦτόν γε μόνος λέγει ὁμολογουμένως: οὐ γὰρ τὰ μὲν φθαρτὰ τὰ δὲ ἄφθαρτα ποιεῖ τῶν ὄντων ἀλλὰ πάντα [20] φθαρτὰ πλὴν τῶν στοιχείων. ἡ δὲ νῦν λεγομένη ἀπορία ἐστὶ διὰ τί τὰ μὲν τὰ δ᾽ οὔ, εἴπερ ἐκ τῶν αὐτῶν ἐστίν. Quasi necessarium ens transmutari; causam vero necessitatis nullam ostendit. At tamen tantum solum dicit confesse; non enim existentium haec quidem corruptibilia illa vero incorruptibilia facit, sed omnia corruptibilia praeter elementa. Dicta vero nunc dubitatio est cur haec quidem illa vero non, si ex eisdem sunt. This implies that change was necessary; but he shows no cause of the necessity. But yet so far at least he alone speaks consistently; for he does not make some things perishable and others imperishable, but makes all perishable except the elements. The difficulty we are speaking of now is, why some things are perishable and others are not, if they consist of the same principles.
ὅτι μὲν οὖν οὐκ ἂν εἴησαν αἱ αὐταὶ ἀρχαί, τοσαῦτα εἰρήσθω: εἰ μὲν γὰρ φθαρταί, δῆλον ὡς [25] ἀναγκαῖον καὶ ταύτας ἔκ τινων εἶναι (πάντα γὰρ φθείρεται εἰς ταῦτ᾽ ἐξ ὧν ἔστιν), ὥστε συμβαίνει τῶν ἀρχῶν ἑτέρας ἀρχὰς εἶναι προτέρας, τοῦτο δ᾽ ἀδύνατον, καὶ εἰ ἵσταται καὶ εἰ βαδίζει εἰς ἄπειρον: ἔτι δὲ πῶς ἔσται τὰ φθαρτά, εἰ αἱ ἀρχαὶ ἀναιρεθήσονται; εἰ δὲ ἄφθαρτοι, διὰ [30] τί ἐκ μὲν τούτων ἀφθάρτων οὐσῶν φθαρτὰ ἔσται, ἐκ δὲ τῶν ἑτέρων ἄφθαρτα; τοῦτο γὰρ οὐκ εὔλογον, ἀλλ᾽ ἢ ἀδύνατον ἢ πολλοῦ λόγου δεῖται. Quod quidem igitur non utique erunt eadem principia, tot dicta sint. Si vero diversa principia, una quidem dubitatio utrum incorruptibilia et haec erunt aut corruptibilia. Nam si corruptibilia, manifestum quia necessarium et ea ex aliquibus esse; omnia enim corrumpuntur in ea ex quibus sunt. Quare contingit principiorum alia principia esse priora. Hoc autem impossibile, sive stet sive in infmitum vadat. — Amplius autem quomodo erunt ipsa corruptibilia, si destruentur principia? Si vero incorruptibilia, cur ex hiis quidem incorruptibilibus existentibus corruptibilia erunt, ex diversis vero incorruptibilia? Hoc enim non rationabile est, sed aut impossibile aut multa ratione eget. Let this suffice as proof of the fact that the principles cannot be the same. But if there are different principles, one difficulty is whether these also will be imperishable or perishable. For if they are perishable, evidently these also must consist of certain elements (for all things that perish, perish by being resolved into the elements of which they consist); so that it follows that prior to the principles there are other principles. But this is impossible, whether the process has a limit or proceeds to infinity. Further, how will perishable things exist, if their principles are to be annulled? But if the principles are imperishable, why will things composed of some imperishable principles be perishable, while those composed of the others are imperishable? This is not probable, but is either impossible or needs much proof.
ἔτι δὲ οὐδ᾽ ἐγκεχείρηκεν οὐδεὶς ἑτέρας, ἀλλὰ τὰς αὐτὰς ἁπάντων λέγουσιν ἀρχάς. [1001α] [1] ἀλλὰ τὸ πρῶτον ἀπορηθὲν ἀποτρώγουσιν ὥσπερ τοῦτο μικρόν τι λαμβάνοντες. Amplius autem nec conatus est aliquis diversa dicere, sed eadem omnium dicunt principia. Verum primum dubitatum corrodunt tamquam hoc parvum aliquid accipientes. Further, no one has even tried to maintain different principles; they maintain the same principles for all things. [01a] But they swallow the difficulty we stated first as if they took it to be something trifling.
πάντων δὲ καὶ θεωρῆσαι χαλεπώτατον καὶ πρὸς τὸ [5] γνῶναι τἀληθὲς ἀναγκαιότατον πότερόν ποτε τὸ ὂν καὶ τὸ ἓν οὐσίαι τῶν ὄντων εἰσί, καὶ ἑκάτερον αὐτῶν οὐχ ἕτερόν τι ὂν τὸ μὲν ἓν τὸ δὲ ὄν ἐστιν, ἢ δεῖ ζητεῖν τί ποτ᾽ ἐστὶ τὸ ὂν καὶ τὸ ἓν ὡς ὑποκειμένης ἄλλης φύσεως. οἱ μὲν γὰρ ἐκείνως οἱ δ᾽ οὕτως οἴονται τὴν φύσιν ἔχειν. Omnium autem ad considerandum difficillimum et ad cognoscendum veritatem maxime necessarium est, utrum unum > et ens substantiae existentium sunt, et utrumque ipsorum non alterum aliquid ens, hoc quidem unum hoc autem ens est, aut oportet quaerere quid est ipsum ens et unum quasi subiecta alia natura. (11) The inquiry that is both the hardest of all and the most necessary for knowledge of the truth is whether being and unity are the substances of things, and whether each of them, without being anything else, is being or unity respectively, or we must inquire what being and unity are, with the implication that they have some other underlying nature.
Πλάτων [10] μὲν γὰρ καὶ οἱ Πυθαγόρειοι οὐχ ἕτερόν τι τὸ ὂν οὐδὲ τὸ ἓν ἀλλὰ τοῦτο αὐτῶν τὴν φύσιν εἶναι, ὡς οὔσης τῆς οὐσίας αὐτοῦ τοῦ ἑνὶ εἶναι καὶ ὄντι: οἱ δὲ περὶ φύσεως, οἷον Ἐμπεδοκλῆς ὡς εἰς γνωριμώτερον ἀνάγων λέγει ὅ τι τὸ ἕν ἐστιν: δόξειε γὰρ ἂν λέγειν τοῦτο τὴν φιλίαν εἶναι (αἰτία [15] γοῦν ἐστὶν αὕτη τοῦ ἓν εἶναι πᾶσιν), ἕτεροι δὲ πῦρ, οἱ δ᾽ ἀέρα φασὶν εἶναι τὸ ἓν τοῦτο καὶ τὸ ὄν, ἐξ οὗ τὰ ὄντα εἶναί τε καὶ γεγονέναι. ὣς δ᾽ αὔτως καὶ οἱ πλείω τὰ στοιχεῖα τιθέμενοι: ἀνάγκη γὰρ καὶ τούτοις τοσαῦτα λέγειν τὸ ἓν καὶ τὸ ὂν ὅσας περ ἀρχὰς εἶναί φασιν. Hii namque illo modo illi hoc modo putant naturam se habere. Plato namque et pytagorici non aliud aliquid ens nec unum sed hoc ipsorum naturam esse, quasi existente substantia * ipsum unum esse et ens aliquid. Alii vero de natura, ut Empedocles ut ad notius reducens dicit quia unum ens est; videbitur enim utique dicere hoc amorem esse; causa namque est hic unum omnibus esse. Alii vero ignem, alii aerem dicunt esse unum hoc et ens, ex quo entia esse et facta esse. Similiter et qui plura ponunt elementa; necesse namque et hiis tot dicere ens et unum quot principia dicunt esse. For some people think they are of the former, others think they are of the latter character. Plato and the Pythagoreans thought being and unity were nothing else, but this was their nature, their essence being just unity and being. But the natural philosophers take a different line; e.g. Empedocles-as though reducing to something more intelligible-says what unity is; for he would seem to say it is love: at least, this is for all things the cause of their being one. Others say this unity and being, of which things consist and have been made, is fire, and others say it is air. A similar view is expressed by those who make the elements more than one; for these also must say that unity and being are precisely all the things which they say are principles.
συμβαίνει [20] δέ, εἰ μέν τις μὴ θήσεται εἶναί τινα οὐσίαν τὸ ἓν καὶ τὸ ὄν, μηδὲ τῶν ἄλλων εἶναι τῶν καθόλου μηθέν (ταῦτα γάρ ἐστι καθόλου μάλιστα πάντων, εἰ δὲ μὴ ἔστι τι ἓν αὐτὸ μηδ᾽ αὐτὸ ὄν, σχολῇ τῶν γε ἄλλων τι ἂν εἴη παρὰ τὰ λεγόμενα καθ᾽ ἕκαστα), ἔτι δὲ μὴ ὄντος τοῦ ἑνὸς οὐσίας, [25] δῆλον ὅτι οὐδ᾽ ἂν ἀριθμὸς εἴη ὡς κεχωρισμένη τις φύσις τῶν ὄντων (ὁ μὲν γὰρ ἀριθμὸς μονάδες, ἡ δὲ μονὰς ὅπερ ἕν τί ἐστιν): Accidit autem, si quidem quis non ponit esse quandam substantiam unum et ens, nec aliorum esse universalium nullum; haec namque universalia sunt maxime omnium. Si vero non est aliquid unum ipsum neque ipsum ens, neque aliorum aliquid erit praeter ea quae dicta sunt singularia. Amplius autem non existente unius substantia, palam quia nec numerus erit quasi natura aliqua ab existentibus separata; numerus enim unitates, unitas vero quod vere unum aliquid est. (A) If we do not suppose unity and being to be substances, it follows that none of the other universals is a substance; for these are most universal of all, and if there is no unity itself or being-itself, there will scarcely be in any other case anything apart from what are called the individuals. Further, if unity is not a substance, evidently number also will not exist as an entity separate from the individual things; for number is units, and the unit is precisely a certain kind of one.
εἰ δ᾽ ἔστι τι αὐτὸ ἓν καὶ ὄν, ἀναγκαῖον οὐσίαν αὐτῶν εἶναι τὸ ἓν καὶ τὸ ὄν: οὐ γὰρ ἕτερόν τι καθόλου κατηγορεῖται ἀλλὰ ταῦτα αὐτά. Si autem aliquid est ipsum unum et ens, necesse est substantiam ipsorum esse ens et unum; non enim aliquid aliud universaliter predicatur sed haec ipsa. But (B) if there is a unity-itself and a being itself, unity and being must be their substance; for it is not something else that is predicated universally of the things that are and are one, but just unity and being.
ἀλλὰ μὴν εἴ γ᾽ ἔσται [30] τι αὐτὸ ὂν καὶ αὐτὸ ἕν, πολλὴ ἀπορία πῶς ἔσται τι παρὰ ταῦτα ἕτερον, λέγω δὲ πῶς ἔσται πλείω ἑνὸς τὰ ὄντα. τὸ γὰρ ἕτερον τοῦ ὄντος οὐκ ἔστιν, ὥστε κατὰ τὸν Παρμενίδου συμβαίνειν ἀνάγκη λόγον ἓν ἅπαντα εἶναι τὰ ὄντα καὶ τοῦτο εἶναι τὸ ὄν. At vero si erit aliquid ens ipsum et ipsum unum, multa erit dubitatio quomodo erit diversum aliquid praeter haec. Dico autem quomodo erunt uno plura entia. Quod enim diversum est ab ente non est; quare secundum Parmenidis rationem acci>dere est necesse unum omnia esse entia et hoc esse ens. But if there is to be a being-itself and a unity-itself, there is much difficulty in seeing how there will be anything else besides these,-I mean, how things will be more than one in number. For what is different from being does not exist, so that it necessarily follows, according to the argument of Parmenides, that all things that are are one and this is being.
[1001β] [1] ἀμφοτέρως δὲ δύσκολον: ἄν τε γὰρ μὴ ᾖ τὸ ἓν οὐσία ἄν τε ᾖ τὸ αὐτὸ ἕν, ἀδύνατον τὸν ἀριθμὸν οὐσίαν εἶναι. ἐὰν μὲν οὖν μὴ ᾖ, εἴρηται πρότερον δι᾽ ὅ: ἐὰν δὲ ᾖ, ἡ αὐτὴ ἀπορία καὶ περὶ τοῦ ὄντος. ἐκ τίνος γὰρ [5] παρὰ τὸ ἓν ἔσται αὐτὸ ἄλλο ἕν; ἀνάγκη γὰρ μὴ ἓν εἶναι: ἅπαντα δὲ τὰ ὄντα ἢ ἓν ἢ πολλὰ ὧν ἓν ἕκαστον. Utrobiquae vero difficile; sive namque non sit unum substantia sive sit ipsum unum, substantiam esse numerum est impossibile. Si quidem igitur non sit, dictum est prius propter quod; si autem fuerit, eadem est dubitatio et de ente. Ex aliquo namque et praeter ens erit ipsum aliud unum. Nihil enim esse est necesse; omnia autem entia aut unum aut multa quorum * unum unumquodque. [01b] There are objections to both views. For whether unity is not a substance or there is a unity-itself, number cannot be a substance. We have already said why this result follows if unity is not a substance; and if it is, the same difficulty arises as arose with regard to being. For whence is there to be another one besides unity-itself? It must be not-one; but all things are either one or many, and of the many each is one.
ἔτι εἰ ἀδιαίρετον αὐτὸ τὸ ἕν, κατὰ μὲν τὸ Ζήνωνος ἀξίωμα οὐθὲν ἂν εἴη (ὃ γὰρ μήτε προστιθέμενον μήτε ἀφαιρούμενον ποιεῖ μεῖζον μηδὲ ἔλαττον, οὔ φησιν εἶναι τοῦτο τῶν ὄντων, [10] ὡς δηλονότι ὄντος μεγέθους τοῦ ὄντος: καὶ εἰ μέγεθος, σωματικόν: τοῦτο γὰρ πάντῃ ὄν: τὰ δὲ ἄλλα πὼς μὲν προστιθέμενα ποιήσει μεῖζον, πὼς δ᾽ οὐθέν, οἷον ἐπίπεδον καὶ γραμμή, στιγμὴ δὲ καὶ μονὰς οὐδαμῶς): Amplius si indivisibile est ipsum unum, secundum Zenonis dignitatem nihil utique erit. Quod enim nec additum nec ablatum facit maius nec minus, non ait esse hoc existentium, tamquam palam quod existente magnitudine ipso ente. Et si magnitudo, corporalis; hoc enim omnino ens, alia vero aliqualiter quidem addita facient maius, aliqualiter autem nihil, ut superficies et linea, punctum vero et unitas nullatenus. Further, if unity-itself is indivisible, according to Zeno's postulate it will be nothing. For that which neither when added makes a thing greater nor when subtracted makes it less, he asserts to have no being, evidently assuming that whatever has being is a spatial magnitude. And if it is a magnitude, it is corporeal; for the corporeal has being in every dimension, while the other objects of mathematics, e.g. a plane or a line, added in one way will increase what they are added to, but in another way will not do so, and a point or a unit does so in no way.
ἀλλ᾽ ἐπειδὴ οὗτος θεωρεῖ φορτικῶς, καὶ ἐνδέχεται εἶναι ἀδιαίρετόν τι [15] ὥστε [καὶ οὕτως] καὶ πρὸς ἐκεῖνόν τιν᾽ ἀπολογίαν ἔχειν (μεῖζον μὲν γὰρ οὐ ποιήσει πλεῖον δὲ προστιθέμενον τὸ τοιοῦτον): Sed quoniam hic speculatur onerose et non contingit esse indivisibile, ut et sic ad illum aliqua habeatur responsio: maius enim non faciet sed plus additum tale. But, since his theory is of a low order, and an indivisible thing can exist in such a way as to have a defence even against him (for the indivisible when added will make the number, though not the size, greater),
ἀλλὰ πῶς δὴ ἐξ ἑνὸς τοιούτου ἢ πλειόνων τοιούτων ἔσται μέγεθος; Sed quomodo ex uno tali aut pluribus erit magnitudo? Simile namque est et lineam ex punctis esse dicere. -yet how can a magnitude proceed from one such indivisible or from many? It is like saying that the line is made out of points.
ὅμοιον γὰρ καὶ τὴν γραμμὴν ἐκ στιγμῶν εἶναι φάσκειν. ἀλλὰ μὴν καὶ εἴ τις οὕτως ὑπολαμβάνει ὥστε [20] γενέσθαι, καθάπερ λέγουσί τινες, ἐκ τοῦ ἑνὸς αὐτοῦ καὶ ἄλλου μὴ ἑνός τινος τὸν ἀριθμόν, οὐθὲν ἧττον ζητητέον διὰ τί καὶ πῶς ὁτὲ μὲν ἀριθμὸς ὁτὲ δὲ μέγεθος ἔσται τὸ γενόμενον, εἴπερ τὸ μὴ ἓν ἡ ἀνισότης καὶ ἡ αὐτὴ φύσις ἦν. οὔτε γὰρ ὅπως ἐξ ἑνὸς καὶ ταύτης οὔτε ὅπως ἐξ ἀριθμοῦ [25] τινὸς καὶ ταύτης γένοιτ᾽ ἂν τὰ μεγέθη, δῆλον. At vero et si quis ita putat ut factus sit, ut quidam dicunt, ex uno ipso et alio non uno aliquo numerus, nihil minus est quaerendum quare et quomodo quandoque quidem numerus quandoque autem magnitudo erit quod factum est, si non unum inequalitas et eadem natura erat. Nec enim quomodo ex uno et hac nec quomodo ex numero aliquo et hac fient utique magnitudines, palam. But even if one supposes the case to be such that, as some say, number proceeds from unity-itself and something else which is not one, none the less we must inquire why and how the product will be sometimes a number and sometimes a magnitude, if the not-one was inequality and was the same principle in either case. For it is not evident how magnitudes could proceed either from the one and this principle, or from some number and this principle.

Chapter 5

Greek Latin English
τούτων δ᾽ ἐχομένη ἀπορία πότερον οἱ ἀριθμοὶ καὶ τὰ σώματα καὶ τὰ ἐπίπεδα καὶ αἱ στιγμαὶ οὐσίαι τινές εἰσιν ἢ οὔ. Hiis autem habita * dubitatio utrum numeri et corpora et superficies et puncta substantiae alique sunt aut non. Chapter 5. (14) A question connected with these is whether numbers and bodies and planes and points are substances of a kind, or not.
εἰ μὲν γὰρ μή εἰσιν, διαφεύγει τί τὸ ὂν καὶ τίνες αἱ οὐσίαι τῶν ὄντων: τὰ μὲν γὰρ πάθη καὶ αἱ κινήσεις [30] καὶ τὰ πρός τι καὶ αἱ διαθέσεις καὶ οἱ λόγοι οὐθενὸς δοκοῦσιν οὐσίαν σημαίνειν (λέγονται γὰρ πάντα καθ᾽ ὑποκειμένου τινός, καὶ οὐθὲν τόδε τι): ἃ δὲ μάλιστ᾽ ἂν δόξειε σημαίνειν οὐσίαν, ὕδωρ καὶ γῆ καὶ πῦρ καὶ ἀήρ, ἐξ ὧν τὰ σύνθετα σώματα συνέστηκε, [1002α] [1] τούτων θερμότητες μὲν καὶ ψυχρότητες καὶ τὰ τοιαῦτα πάθη, οὐκ οὐσίαι, τὸ δὲ σῶμα τὸ ταῦτα πεπονθὸς μόνον ὑπομένει ὡς ὄν τι καὶ οὐσία τις οὖσα. Nam si non sunt, diffugit aliquid ipsum ens et quaedam entium substantiae. Passiones enim et motus et ad aliquid et dispositiones > et orationes nullius videntur substantiam significare; dicuntur enim omnia de subiecto aliquo, et nihil hoc aliquid. Quae vero maxime substantiam significare videntur, aqua et ignis et terra looiai ex quibus composita corpora constant, horum calores quidem et frigiditates et similes passiones non sunt substantiae. Corpus vero haec patiens solum remanet ut ens aliquod et substantia aliqua existens. If they are not, it baffles us to say what being is and what the substances of things are. For modifications and movements and relations and dispositions and ratios do not seem to indicate the substance of anything; for all are predicated of a subject, and none is a this . And as to the things which might seem most of all to indicate substance, water and earth and fire and air, of which composite bodies [02a] consist, heat and cold and the like are modifications of these, not substances, and the body which is thus modified alone persists as something real and as a substance.
ἀλλὰ μὴν τό γε σῶμα ἧττον οὐσία τῆς ἐπιφανείας, [5] καὶ αὕτη τῆς γραμμῆς, καὶ αὕτη τῆς μονάδος καὶ τῆς στιγμῆς: τούτοις γὰρ ὥρισται τὸ σῶμα, καὶ τὰ μὲν ἄνευ σώματος ἐνδέχεσθαι δοκεῖ εἶναι τὸ δὲ σῶμα ἄνευ τούτων ἀδύνατον. At vero corpus est minus substantia superficie, et haec linea, et haec unitate et puncto. Hiis enim diffmitur corpus, et haec quidem sine corpore contingere videntur esse corpus vero sine hiis * impossibile. But, on the other hand, the body is surely less of a substance than the surface, and the surface than the line, and the line than the unit and the point. For the body is bounded by these; and they are thought to be capable of existing without body, but body incapable of existing without these.
διόπερ οἱ μὲν πολλοὶ καὶ οἱ πρότερον τὴν οὐσίαν καὶ τὸ ὂν ᾤοντο τὸ σῶμα εἶναι τὰ δὲ ἄλλα [10] τούτου πάθη, ὥστε καὶ τὰς ἀρχὰς τὰς τῶν σωμάτων τῶν ὄντων εἶναι ἀρχάς: οἱ δ᾽ ὕστεροι καὶ σοφώτεροι τούτων εἶναι δόξαντες ἀριθμούς. καθάπερ οὖν εἴπομεν, εἰ μὴ ἔστιν οὐσία ταῦτα, ὅλως οὐδὲν ἐστὶν οὐσία οὐδὲ ὂν οὐθέν: οὐ γὰρ δὴ τά γε συμβεβηκότα τούτοις ἄξιον ὄντα καλεῖν. Propter quod multi quidem et priores substantiam et ens putabant corpus esse alia vero huius passiones, quare et principia corporum entium esse principia; posteriores vero et sapientiores hiis esse opinabantur numeros. Quemadmodum ergo dicebamus, si non sunt substantia haec, omnino nulla substantia est nec ens nullum; non enim horum accidentia dignum est vocare entia. This is why, while most of the philosophers and the earlier among them thought that substance and being were identical with body, and that all other things were modifications of this, so that the first principles of the bodies were the first principles of being, the more recent and those who were held to be wiser thought numbers were the first principles. As we said, then, if these are not substance, there is no substance and no being at all; for the accidents of these it cannot be right to call beings.
[15] —ἀλλὰ μὴν εἰ τοῦτο μὲν ὁμολογεῖται, ὅτι μᾶλλον οὐσία τὰ μήκη τῶν σωμάτων καὶ αἱ στιγμαί, ταῦτα δὲ μὴ ὁρῶμεν ποίων ἂν εἶεν σωμάτων (ἐν γὰρ τοῖς αἰσθητοῖς ἀδύνατον εἶναι), οὐκ ἂν εἴη οὐσία οὐδεμία. At vero si hoc quidem confessum est, quia magis sunt substantia longitudines corporibus et puncta, haec autem non videmus qualium utique erunt corporum (nam in sensibilibus impossibile esse), non utique erit substantia nulla. But if this is admitted, that lines and points are substance more than bodies, but we do not see to what sort of bodies these could belong (for they cannot be in perceptible bodies), there can be no substance.
ἔτι δὲ φαίνεται ταῦτα πάντα διαιρέσεις ὄντα τοῦ σώματος, τὸ μὲν εἰς πλάτος [20] τὸ δ᾽ εἰς βάθος τὸ δ᾽ εἰς μῆκος. Amplius haec omnia videntur divisiones esse corporis, hoc quidem ad latitudinem, hoc vero ad profunditatem, aliud ad longitudinem. -Further, these are all evidently divisions of body,-one in breadth, another in depth, another in length.
πρὸς δὲ τούτοις ὁμοίως ἔνεστιν ἐν τῷ στερεῷ ὁποιονοῦν σχῆμα: ὥστ᾽ εἰ μηδ᾽ ἐν τῷ λίθῳ Ἑρμῆς, οὐδὲ τὸ ἥμισυ τοῦ κύβου ἐν τῷ κύβῳ οὕτως ὡς ἀφωρισμένον: οὐκ ἄρα οὐδ᾽ ἐπιφάνεια (εἰ γὰρ ὁποιαοῦν, κἂν αὕτη ἂν ἦν ἡ ἀφορίζουσα τὸ ἥμισυ), ὁ δ᾽ [25] αὐτὸς λόγος καὶ ἐπὶ γραμμῆς καὶ στιγμῆς καὶ μονάδος, ὥστ᾽ εἰ μάλιστα μὲν οὐσία τὸ σῶμα, τούτου δὲ μᾶλλον ταῦτα, μὴ ἔστι δὲ ταῦτα μηδὲ οὐσίαι τινές, διαφεύγει τί τὸ ὂν καὶ τίς ἡ οὐσία τῶν ὄντων. Ad haec autem similiter inest in solido quaecumque figura. Quare si nec in lapide Mercurius, nec medietas cubi in cubo sic ut segregata; non igitur * nec superficies. Nam si quaecumque, et utique haec * erat determinans medietatem. eadem autem ratio est et in linea et in puncto et in unitate. quare si maxime quidem substantia est corpus, hoc autem magis haec, nec sunt autem haec nec substantiae alique, diffugit * quid ipsum ens et quae substantia entium. Nam cum dictis et * circa generationem et corruptionem accidunt irrationabilia. Besides this, no sort of shape is present in the solid more than any other; so that if the Hermes is not in the stone, neither is the half of the cube in the cube as something determinate; therefore the surface is not in it either; for if any sort of surface were in it, the surface which marks off the half of the cube would be in it too. And the same account applies to the line and to the point and the unit. Therefore, if on the one hand body is in the highest degree substance, and on the other hand these things are so more than body, but these are not even instances of substance, it baffles us to say what being is and what the substance of things is.
πρὸς γὰρ τοῖς εἰρημένοις καὶ τὰ περὶ τὴν γένεσιν καὶ τὴν φθορὰν συμβαίνει ἄλογα. [30] δοκεῖ μὲν γὰρ ἡ οὐσία, ἐὰν μὴ οὖσα πρότερον νῦν ᾖ ἢ πρότερον οὖσα ὕστερον μὴ ᾖ, μετὰ τοῦ γίγνεσθαι καὶ φθείρεσθαι ταῦτα πάσχειν: τὰς δὲ στιγμὰς καὶ τὰς γραμμὰς καὶ τὰς ἐπιφανείας οὐκ ἐνδέχεται οὔτε γίγνεσθαι οὔτε φθείρεσθαι, ὁτὲ μὲν οὔσας ὁτὲ δὲ οὐκ οὔσας. ὅταν γὰρ ἅπτηται ἢ διαιρῆται τὰ σώματα, [1002β] [1] ἅμα ὁτὲ μὲν μία ἁπτομένων ὁτὲ δὲ δύο διαιρουμένων γίγνονται: ὥστ᾽ οὔτε συγκειμένων ἔστιν ἀλλ᾽ ἔφθαρται, διῃρημένων τε εἰσὶν αἱ πρότερον οὐκ οὖσαι (οὐ γὰρ δὴ ἥ γ᾽ ἀδιαίρετος στιγμὴ διῃρέθη εἰς δύο), εἴ τε γίγνονται καὶ [5] φθείρονται, ἐκ τίνος γίγνονται; > Videtur enim substantia non ens prius nunc esse aut prius existens posterius non, * cum fieri et corrumpi haec pati; puncta vero et lineas et superficies non contingit neque fieri neque corrumpi, quandoque quidem existentes quandoque vero non existentes. Nam quando copulantur aut dividuntur corpora simul, quandoque quidem una copulatorum quandoque due divisorum fiunt; quare non compositorum est sed corruptum est, divisorumque sunt prius non existentes (non enim indivisibile punctum divisum est in duo). Et si generantur et corrumpuntur, ex aliquo generantur. -For besides what has been said, the questions of generation and instruction confront us with further paradoxes. For if substance, not having existed before, now exists, or having existed before, afterwards does not exist, this change is thought to be accompanied by a process of becoming or perishing; but points and lines and surfaces cannot be in process either of becoming or of perishing, when they at one time exist and at another do not. For when bodies come into contact or [02b] are divided, their boundaries simultaneously become one in the one case when they touch, and two in the other-when they are divided; so that when they have been put together one boundary does not exist but has perished, and when they have been divided the boundaries exist which before did not exist (for it cannot be said that the point, which is indivisible, was divided into two). And if the boundaries come into being and cease to be, from what do they come into being?
παραπλησίως δ᾽ ἔχει καὶ περὶ τὸ νῦν τὸ ἐν τῷ χρόνῳ: οὐδὲ γὰρ τοῦτο ἐνδέχεται γίγνεσθαι καὶ φθείρεσθαι, ἀλλ᾽ ὅμως ἕτερον ἀεὶ δοκεῖ εἶναι, οὐκ οὐσία τις οὖσα. ὁμοίως δὲ δῆλον ὅτι ἔχει καὶ περὶ τὰς στιγμὰς καὶ τὰς γραμμὰς καὶ τὰ ἐπίπεδα: ὁ γὰρ [10] αὐτὸς λόγος: ἅπαντα γὰρ ὁμοίως ἢ πέρατα ἢ διαιρέσεις εἰσίν. Similiter autem se habet circa * nunc * in tempore; non enim hoc contingit fieri et corrumpi, at tamen aliud videtur semper esse, non substantia aliqua * existens. Similiter autem palam quia se habet et circa puncta et lineas et superficies; eadem enim ratio, nam omnia similiter aut termini aut divisiones sunt. A similar account may also be given of the now in time; for this also cannot be in process of coming into being or of ceasing to be, but yet seems to be always different, which shows that it is not a substance. And evidently the same is true of points and lines and planes; for the same argument applies, since they are all alike either limits or divisions.

Chapter 6

Greek Latin English
ὅλως δ᾽ ἀπορήσειεν ἄν τις διὰ τί καὶ δεῖ ζητεῖν ἄλλ᾽ ἄττα παρά τε τὰ αἰσθητὰ καὶ τὰ μεταξύ, οἷον ἃ τίθεμεν εἴδη. Omnino vero dubitabit aliquis quare et oportet quaerere alia quaedam praeter sensibilia et intermedia, ut quas ponimus species. Chapter 6. In general one might raise the question why after all, besides perceptible things and the intermediates, we have to look for another class of things, i.e. the Forms which we posit.
εἰ γὰρ διὰ τοῦτο, ὅτι τὰ μὲν μαθηματικὰ [15] τῶν δεῦρο ἄλλῳ μέν τινι διαφέρει, τῷ δὲ πόλλ᾽ ἄττα ὁμοειδῆ εἶναι οὐθὲν διαφέρει, ὥστ᾽ οὐκ ἔσονται αὐτῶν αἱ ἀρχαὶ ἀριθμῷ ἀφωρισμέναι (ὥσπερ οὐδὲ τῶν ἐνταῦθα γραμμάτων ἀριθμῷ μὲν πάντων οὐκ εἰσὶν αἱ ἀρχαὶ ὡρισμέναι, εἴδει δέ, ἐὰν μὴ λαμβάνῃ τις τησδὶ τῆς συλλαβῆς [20] ἢ τησδὶ τῆς φωνῆς: τούτων δ᾽ ἔσονται καὶ ἀριθμῷ ὡρισμέναι—ὁμοίως δὲ καὶ ἐπὶ τῶν μεταξύ: ἄπειρα γὰρ κἀκεῖ τὰ ὁμοειδῆ), ὥστ᾽ εἰ μὴ ἔστι παρὰ τὰ αἰσθητὰ καὶ τὰ μαθηματικὰ ἕτερ᾽ ἄττα οἷα λέγουσι τὰ εἴδη τινές, οὐκ ἔσται μία ἀριθμῷ ἀλλ᾽ εἴδει οὐσία, οὐδ᾽ αἱ ἀρχαὶ τῶν [25] ὄντων ἀριθμῷ ἔσονται ποσαί τινες ἀλλὰ εἴδει: εἰ οὖν τοῦτο ἀναγκαῖον, καὶ τὰ εἴδη ἀναγκαῖον διὰ τοῦτο εἶναι τιθέναι. καὶ γὰρ εἰ μὴ καλῶς διαρθροῦσιν οἱ λέγοντες, ἀλλ᾽ ἔστι γε τοῦθ᾽ ὃ βούλονται, καὶ ἀνάγκη ταῦτα λέγειν αὐτοῖς, ὅτι τῶν εἰδῶν οὐσία τις ἕκαστόν ἐστι καὶ οὐθὲν κατὰ συμβεβηκός. Nam si ideo, quia mathematica a presentibus in alio quodam differunt, in esse vero plura similis speciei nihil differunt. Quare non erunt ipsorum principia numero determinata, quemadmodum nec presentium litterarum numero quidem omnium non sunt principia determinata sed specie, si non lateat quis huius sillabe aut huius vocis, harum enim erunt et numero determinata. Similiter autem et in intermediis; infinita namque et illic * quae eiusdem speciei. Quare si non sunt praeter sensibilia et mathematica alia quaedam qualia dicunt species ipsas quidam, non erit una numero et specie substantia, nec principia entium numero erunt quanta aliqua sed specie. > Ergo si hoc est necessarium, et species necessarium est propter hoc esse. Et enim si non bene dearticulant dicentes, sed hoc est quod volunt, et necesse * haec ipsos dicere, quia specierum substantia quaedam unumquodque est et nihil secundum accidens. If it is for this reason, because the objects of mathematics, while they differ from the things in this world in some other respect, differ not at all in that there are many of the same kind, so that their first principles cannot be limited in number (just as the elements of all the language in this sensible world are not limited in number, but in kind, unless one takes the elements of this individual syllable or of this individual articulate sound-whose elements will be limited even in number; so is it also in the case of the intermediates; for there also the members of the same kind are infinite in number), so that if there are not-besides perceptible and mathematical objects-others such as some maintain the Forms to be, there will be no substance which is one in number, but only in kind, nor will the first principles of things be determinate in number, but only in kind:-if then this must be so, the Forms also must therefore be held to exist. Even if those who support this view do not express it articulately, still this is what they mean, and they must be maintaining the Forms just because each of the Forms is a substance and none is by accident.
ἀλλὰ μὴν εἴ γε θήσομεν τά τε εἴδη εἶναι καὶ ἓν ἀριθμῷ τὰς ἀρχὰς ἀλλὰ μὴ εἴδει, εἰρήκαμεν ἃ συμβαίνειν ἀναγκαῖον ἀδύνατα. At vero si ponimus species esse et * numero principia et non specie, diximus quae contingere necesse est impossibilia. But if we are to suppose both that the Forms exist and that the principles are one in number, not in kind, we have mentioned the impossible results that necessarily follow.
σύνεγγυς δὲ τούτων ἐστὶ τὸ διαπορῆσαι πότερον δυνάμει ἔστι τὰ στοιχεῖα ἤ τιν᾽ ἕτερον τρόπον. Hiis autem affine est quaerere utrum potestate sunt elementa aut aliquo ajio modo. (13) Closely connected with this is the question whether the elements exist potentially or in some other manner.
εἰ μὲν γὰρ ἄλλως πως, πρότερόν τι ἔσται τῶν ἀρχῶν ἄλλο (πρότερον [1003α] [1] γὰρ ἡ δύναμις ἐκείνης τῆς αἰτίας, τὸ δὲ δυνατὸν οὐκ ἀναγκαῖον ἐκείνως πᾶν ἔχειν): Nam si aliter aliqualiter, prius aliquid erit principiis aliud; prior enim * potestas causa illa, possibile autem non est necessarium illo modo omne se habere. If in some other way, there will be something else prior to the first [03a] principles; for the potency is prior to the actual cause, and it is not necessary for everything potential to be actual.
εἰ δ᾽ ἔστι δυνάμει τὰ στοιχεῖα, ἐνδέχεται μηθὲν εἶναι τῶν ὄντων: δυνατὸν γὰρ εἶναι καὶ τὸ μήπω ὄν: γίγνεται μὲν γὰρ τὸ [5] μὴ ὄν, οὐθὲν δὲ γίγνεται τῶν εἶναι ἀδυνάτων. Si vero potestate sunt elementa, nihil entium esse contingit. Nam possibile est esse et quod nondum * ens; fit enim non ens, nihil autem fit impossibilium esse. -But if the elements exist potentially, it is possible that everything that is should not be. For even that which is not yet is capable of being; for that which is not comes to be, but nothing that is incapable of being comes to be.
ταύτας τε οὖν τὰς ἀπορίας ἀναγκαῖον ἀπορῆσαι περὶ τῶν ἀρχῶν, καὶ πότερον καθόλου εἰσὶν ἢ ὡς λέγομεν τὰ καθ᾽ ἕκαστα. Has igitur dubitationes necessarium est dubitare de principiis, et utrum universalia sint aut ut dicimus singularia. (12) We must not only raise these questions about the first principles, but also ask whether they are universal or what we call individuals.
εἰ μὲν γὰρ καθόλου, οὐκ ἔσονται οὐσίαι (οὐθὲν γὰρ τῶν κοινῶν τόδε τι σημαίνει ἀλλὰ τοιόνδε, ἡ δ᾽ οὐσία τόδε τι: Nam si universalia, non erunt substantiae; nihil enim communium hoc aliquid significat sed tale *, substantia vero hoc aliquid est. If they are universal, they will not be substances; for everything that is common indicates not a this but a such , but substance is a this .
δ᾽ [10] ἔσται τόδε τι καὶ ἓν θέσθαι τὸ κοινῇ κατηγορούμενον, πολλὰ ἔσται ζῷα ὁ Σωκράτης, αὐτός τε καὶ ὁ ἄνθρωπος καὶ τὸ ζῷον, εἴπερ σημαίνει ἕκαστον τόδε τι καὶ ἕν): εἰ μὲν οὖν καθόλου αἱ ἀρχαί, ταῦτα συμβαίνει: Sed si est hoc aliquid et ponitur quod communiter predicatur, multa erit animalia Socrates, ipseque homo et animal, si significat singulum hoc aliquid et unum. And if we are to be allowed to lay it down that a common predicate is a this and a single thing, Socrates will be several animals-himself and man and animal , if each of these indicates a this and a single thing.
εἰ δὲ μὴ καθόλου ἀλλ᾽ ὡς τὰ καθ᾽ ἕκαστα, οὐκ ἔσονται ἐπιστηταί (καθόλου [15] γὰρ ἡ ἐπιστήμη πάντων), ὥστ᾽ ἔσονται ἀρχαὶ ἕτεραι πρότεραι τῶν ἀρχῶν αἱ καθόλου κατηγορούμεναι, ἄνπερ μέλλῃ ἔσεσθαι αὐτῶν ἐπιστήμη. Si igitur universalia sunt principia, haec contingunt. Si autem non universalia sed quasi singularia, non erunt scibilia; universales enim sunt omnium scientie. Quare erunt principia diversa priora principiis universaliter predicata, si futura est esse eorum scientia. If, then, the principles are universals, these universal. Therefore if there is to be results follow; if they are not universals but of knowledge of the principles there must be the nature of individuals, they will not be other principles prior to them, namely those knowable; for the knowledge of anything is that are universally predicated of them.


Notes


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