Authors/Aristotle/metaphysics/l3/c5

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 ↵ ƿ 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 qui↵dem 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;	ƿ Videtur enim substantia non ens prius nunc esse aut prius exis↵tens 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 corrum↵puntur, 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.