METAPHYSICS
BOOK XI

ARISTOTLE’S TEXT Chapter 1: 1059a 18-1060a 2
[1059α] [18] ὅτι μὲν ἡ σοφία περὶ ἀρχὰς ἐπιστήμη τίς ἐστι, δῆλον ἐκ τῶν πρώτων ἐν οἷς διηπόρηται πρὸς τὰ ὑπὸ τῶν ἄλλων [20] εἰρημένα περὶ τῶν ἀρχῶν:	899. That wisdom is a science of principles, then, is evident from the first chapters (45-143) of this work, in which problems were raised concerning the statements of other philosophers about the principles of things.
ἀπορήσειε δ᾽ ἄν τις πότερον μίαν ὑπολαβεῖν εἶναι δεῖ τὴν σοφίαν ἐπιστήμην ἢ πολλάς: εἰ μὲν γὰρ μίαν, μία γ᾽ ἐστὶν ἀεὶ τῶν ἐναντίων, αἱ δ᾽ ἀρχαὶ οὐκ ἐναντίαι: εἰ δὲ μὴ μία, ποίας δεῖ θεῖναι ταύτας;	900. But one might raise the question whether wisdom must be understood to be one science or many (181, 190). For if it is one, then the objection might be raised that one science always deals with contraries; but principles are not contraries. And if it is not one but many, what kind of sciences must they be assumed to be (190-197)?
ἔτι τὰς ἀποδεικτικὰς ἀρχὰς θεωρῆσαι μιᾶς ἢ πλειόνων; εἰ μὲν γὰρ [25] μιᾶς, τί μᾶλλον ταύτης ἢ ὁποιασοῦν; εἰ δὲ πλειόνων, ποίας δεῖ ταύτας τιθέναι;	901. Further, one might raise the question whether it is the office of one science or of many to study the principles of demonstration? For if it is the office of one science, why should it be the office of this science rather than of another? And if it is the office of many, what kind of sciences must these be admitted to be (198-201)?
ἔτι πότερον πασῶν τῶν οὐσιῶν ἢ οὔ; εἰ μὲν γὰρ μὴ πασῶν, ποίων χαλεπὸν ἀποδοῦναι: εἰ δὲ πασῶν μία, ἄδηλον πῶς ἐνδέχεται πλειόνων τὴν αὐτὴν ἐπιστήμην εἶναι.	902. Further, there is the question whether it is the office of wisdom to deal with all substances or not (182)? And if not with all, it is difficult to say with what kind it does deal. But if there is one science of all substances, the problem arises how one science can deal with many subjects (202-204).
ἔτι πότερον περὶ τὰς οὐσίας μόνον ἢ καὶ τὰ [30] συμβεβηκότα [ἀπόδειξίς ἐστιν]; εἰ γὰρ περί γε τὰ συμβεβηκότα ἀπόδειξίς ἐστιν, περὶ τὰς οὐσίας οὐκ ἔστιν: εἰ δ᾽ ἑτέρα, τίς ἑκατέρα καὶ ποτέρα σοφία; ᾗ μὲν γὰρ ἀποδεικτική, σοφία ἡ περὶ τὰ συμβεβηκότα: ᾗ δὲ περὶ τὰ πρῶτα, ἡ τῶν οὐσιῶν.	903. Again, there is the question whether this science is a demonstration of substances alone, or also of accidents (184, 205-207); for if it is a demonstration of accidents, it is not a demonstration of substances. But if there is a different science of accidents, what is the character of each, and which of the two is wisdom? For a demonstrative science of accidents is wisdom; but that which deals with primary things is the science of substances.
ἀλλ᾽ οὐδὲ περὶ τὰς ἐν τοῖς φυσικοῖς εἰρημένας αἰτίας [35] τὴν ἐπιζητουμένην ἐπιστήμην θετέον: οὔτε γὰρ περὶ τὸ οὗ ἕνεκεν (τοιοῦτον γὰρ τὸ ἀγαθόν, τοῦτο δ᾽ ἐν τοῖς πρακτοῖς ὑπάρχει καὶ ταῖς οὖσιν ἐν κινήσει: καὶ τοῦτο πρῶτον κινεῖ—τοιοῦτον γὰρ τὸ τέλος—τὸ δὲ πρῶτον κινῆσαν οὐκ ἔστιν ἐν τοῖς ἀκινήτοις):	904. But the science which we are seeking must not be assumed to be the one which deals with the causes mentioned in the Physics. For it does not deal with the final cause, because such is the good, and this is found in the sphere of practical affairs and in things which are in motion. And it is the first thing which causes motion (for the end is such a nature); but there is no first mover in the realm of immobile things (192).
ὅλως δ᾽ ἀπορίαν ἔχει πότερόν ποτε περὶ τὰς αἰσθητὰς οὐσίας ἐστὶν ἡ ζητουμένη νῦν ἐπιστήμη ἢ οὔ, περὶ δέ τινας ἑτέρας. [1059β] [1] εἰ γὰρ περὶ ἄλλας, ἢ περὶ τὰ εἴδη εἴη ἂν ἢ περὶ τὰ μαθηματικά. τὰ μὲν οὖν εἴδη ὅτι οὐκ ἔστι, δῆλον	905. And in general there is the question whether the science which is now being sought is concerned with sensible substances, or whether it is not concerned with these but with certain others (183). For, if it deals with other substances, it must be concerned with either the separate Forms or with the objects of mathematics. Now it is evident that separate Forms do not exist.
(ὅμως δὲ ἀπορίαν ἔχει, κἂν εἶναί τις αὐτὰ θῇ, διὰ τί ποτ᾽ οὐχ ὥσπερ ἐπὶ τῶν μαθηματικῶν, [5] οὕτως ἔχει καὶ ἐπὶ τῶν ἄλλων ὧν ἔστιν εἴδη: λέγω δ᾽ ὅτι τὰ μαθηματικὰ μὲν μεταξύ τε τῶν εἰδῶν τιθέασι καὶ τῶν αἰσθητῶν οἷον τρίτα τινὰ παρὰ τὰ εἴδη τε καὶ τὰ δεῦρο, τρίτος δ᾽ ἄνθρωπος οὐκ ἔστιν οὐδ᾽ ἵππος παρ᾽ αὐτόν τε καὶ τοὺς καθ᾽ ἕκαστον:	906. But nevertheless even if one were to assume that these separate Forms exist, the problem would arise why the same thing should not be true of the other things of which there are Forms as is true of the objects of mathematics. I mean that they place the objects of mathematics between the Forms and sensible things as a kind of third class of entities besides the Forms and the things which exist here. But there is no third man or horse over and above man-in-himself and horse-in-itself and singular men and horses.
εἰ δ᾽ αὖ μὴ ἔστιν ὡς λέγουσι, [10] περὶ ποῖα θετέον πραγματεύεσθαι τὸν μαθηματικόν; οὐ γὰρ δὴ περὶ τὰ δεῦρο: τούτων γὰρ οὐθέν ἐστιν οἷον αἱ μαθηματικαὶ ζητοῦσι τῶν ἐπιστημῶν): οὐδὲ μὴν περὶ τὰ μαθηματικὰ ἡ ζητουμένη νῦν ἐστὶν ἐπιστήμη (χωριστὸν γὰρ αὐτῶν οὐθέν): ἀλλ᾽ οὐδὲ τῶν αἰσθητῶν οὐσιῶν: φθαρταὶ γάρ.	907. If, however, the situation is not as they say, with what kind of things must the mathematician be assumed to deal? For he is not concerned with the things which exist here, because none of these are the kind of things which the mathematical sciences study. Nor is the science which we are now seeking concerned with the objects of mathematics; for no one of these is capable of existing separately. Nor does it deal with sensible substances, for these are corruptible (208-219).
ὅλως δ᾽ ἀπορήσειέ [15] τις ἂν ποίας ἐστὶν ἐπιστήμης τὸ διαπορῆσαι περὶ τῆς τῶν μαθηματικῶν ὕλης. οὔτε γὰρ τῆς φυσικῆς, διὰ τὸ περὶ τὰ ἔχοντα ἐν αὑτοῖς ἀρχὴν κινήσεως καὶ στάσεως τὴν τοῦ φυσικοῦ πᾶσαν εἶναι πραγματείαν, οὐδὲ μὴν τῆς σκοπούσης περὶ ἀποδείξεώς τε καὶ ἐπιστήμης: περὶ γὰρ αὐτὸ τοῦτο τὸ [20] γένος τὴν ζήτησιν ποιεῖται. λείπεται τοίνυν τὴν προκειμένην φιλοσοφίαν περὶ αὐτῶν τὴν σκέψιν ποιεῖσθαι.	908. And in general one might raise the question to what science it belongs to consider the problem about the matter of the mathematical sciences (627). It is not the office of the philosophy of nature, for this science is wholly concerned with things which have in themselves a principle of rest and of motion. Nor is it the office of the science which investigates demonstration and scientific knowledge, for it is about this class of things that it makes its investigations. It follows, then, that it pertains to the philosophy which we have proposed to investigate these things.
διαπορήσειε δ᾽ ἄν τις εἰ δεῖ θεῖναι τὴν ζητουμένην ἐπιστήμην περὶ τὰς ἀρχάς, τὰ καλούμενα ὑπό τινων στοιχεῖα: ταῦτα δὲ πάντες ἐνυπάρχοντα τοῖς συνθέτοις τιθέασιν. μᾶλλον δ᾽ ἂν δόξειε [25] τῶν καθόλου δεῖν εἶναι τὴν ζητουμένην ἐπιστήμην: πᾶς γὰρ λόγος καὶ πᾶσα ἐπιστήμη τῶν καθόλου καὶ οὐ τῶν ἐσχάτων, ὥστ᾽ εἴη ἂν οὕτω τῶν πρώτων γενῶν.	909. And one might raise the question whether the science which is now being sought must deal with the principles which are called elements by some thinkers (184). But all men suppose these to be present in composite things. And it would seem rather that the science which is now being sought ought to deal with universals, for every intelligible nature and every science is of universals and not of extremes (228), so that in this way they would deal with the primary genera.
ταῦτα δὲ γίγνοιτ᾽ ἂν τό τε ὂν καὶ τὸ ἕν: ταῦτα γὰρ μάλιστ᾽ ἂν ὑποληφθείη περιέχειν τὰ ὄντα πάντα καὶ μάλιστα ἀρχαῖς ἐοικέναι διὰ [30] τὸ εἶναι πρῶτα τῇ φύσει: φθαρέντων γὰρ αὐτῶν συναναιρεῖται καὶ τὰ λοιπά: πᾶν γὰρ ὂν καὶ ἕν. ᾗ δὲ τὰς διαφορὰς αὐτῶν ἀνάγκη μετέχειν εἰ θήσει τις αὐτὰ γένη, διαφορὰ δ᾽ οὐδεμία τοῦ γένους μετέχει, ταύτῃ δ᾽ οὐκ ἂν δόξειε δεῖν αὐτὰ τιθέναι γένη οὐδ᾽ ἀρχάς.	910. And these would become being and unity; for these most of all might be thought to contain all existing things and to be principles in the highest degree, because they are first by nature; for when they have been destroyed, everything else is destroyed, since everything is a being and one. But if one supposes them to be genera, then inasmuch as it is necessary for differences to participate in them, and no difference participates in a genus, it would seem that they must not be regarded either as genera or as principles.
ἔτι δ᾽ εἰ μᾶλλον [35] ἀρχὴ τὸ ἁπλούστερον τοῦ ἧττον τοιούτου, τὰ δ᾽ ἔσχατα τῶν ἐκ τοῦ γένους ἁπλούστερα τῶν γενῶν (ἄτομα γάρ, τὰ γένη δ᾽ εἰς εἴδη πλείω καὶ διαφέροντα διαιρεῖται), μᾶλλον ἂν ἀρχὴ δόξειεν εἶναι τὰ εἴδη τῶν γενῶν. ᾗ δὲ συναναιρεῖται τοῖς γένεσι τὰ εἴδη, τὰ γένη ταῖς ἀρχαῖς ἔοικε μᾶλλον: ἀρχὴ γὰρ τὸ συναναιροῦν. [1060α] [1] τὰ μὲν οὖν τὴν ἀπορίαν ἔχοντα ταῦτα καὶ τοιαῦτ᾽ ἐστὶν ἕτερα.	911. Further, if what is more simple is more of a principle than what is less simple, and the ultimate members resulting from the subdivision of different genera are more simple than the genera themselves (for these members are indivisible, whereas genera are divided into many different species), it would seem that species are principles to a greater degree than genera. But since species are involved in the destruction of their genera, genera are like principles to a greater degree; for whatever involves something else in its destruction is a principle of that thing (229-234). These and other such points, then, are the ones which cause difficulties.

ARISTOTLE’S TEXT Chapter 2: 1060a 3-1060b 3
ἔτι πότερον δεῖ τιθέναι τι παρὰ τὰ καθ᾽ ἕκαστα ἢ οὔ, ἀλλὰ τούτων ἡ ζητουμένη ἐπιστήμη; ἀλλὰ ταῦτα ἄπειρα: [5] τά γε μὴν παρὰ τὰ καθ᾽ ἕκαστα γένη ἢ εἴδη ἐστίν, ἀλλ᾽ οὐδετέρου τούτων ἡ ζητουμένη νῦν ἐπιστήμη. διότι γὰρ ἀδύνατον τοῦτο, εἴρηται.	912. Further, there is the question whether or not we must posit the existence of something besides singular things; and if not, then the science which we are now seeking must deal with these things. But they are infinite in number. And what exists apart from singular things are genera and species; but the science which we are now seeking deals with neither of these. The reason why this is impossible has already been stated (909-911).
καὶ γὰρ ὅλως ἀπορίαν ἔχει πότερον δεῖ τινὰ ὑπολαβεῖν οὐσίαν εἶναι χωριστὴν παρὰ τὰς αἰσθητὰς οὐσίας καὶ τὰς δεῦρο, ἢ οὔ, ἀλλὰ ταῦτ᾽ εἶναι τὰ ὄντα καὶ [10] περὶ ταῦτα τὴν σοφίαν ὑπάρχειν. ζητεῖν μὲν γὰρ ἐοίκαμεν ἄλλην τινά, καὶ τὸ προκείμενον τοῦτ᾽ ἔστιν ἡμῖν, λέγω δὲ τὸ ἰδεῖν εἴ τι χωριστὸν καθ᾽ αὑτὸ καὶ μηδενὶ τῶν αἰσθητῶν ὑπάρχον.	913. And in general the problem is whether one must suppose that there is some substance which is separable from sensible substances (i.e., the things which exist here and now), or that the latter are beings and the things with which wisdom deals. For we seem to be looking for another kind of substance, and this constitutes the object of our study: I mean, to know whether there is something which is separable in itself and belongs to no sensible thing.
ἔτι δ᾽ εἰ παρὰ τὰς αἰσθητὰς οὐσίας ἔστι τις ἑτέρα οὐσία, παρὰ ποίας τῶν αἰσθητῶν δεῖ τιθέναι ταύτην εἶναι; [15] τί γὰρ μᾶλλον παρὰ τοὺς ἀνθρώπους ἢ τοὺς ἵππους ἢ τῶν ἄλλων ζῴων θήσει τις αὐτὴν ἢ καὶ τῶν ἀψύχων ὅλως; τό γε μὴν ἴσας ταῖς αἰσθηταῖς καὶ φθαρταῖς οὐσίαις ἀϊδίους ἑτέρας κατασκευάζειν ἐκτὸς τῶν εὐλόγων δόξειεν ἂν πίπτειν.	914. Further, if there is another kind of substance apart from sensible substances, from what kind of sensible substances must it be assumed to be separate? For why should we suppose that it exists apart from men and from horses rather than from other animals or non-living things generally? Yet to devise various eternal substances equal in number to sensible and corruptible ones would seem to be unreasonable.
εἰ δὲ μὴ χωριστὴ τῶν σωμάτων ἡ ζητουμένη νῦν ἀρχή, [20] τίνα ἄν τις ἄλλην θείη μᾶλλον τῆς ὕλης; αὕτη γε μὴν ἐνεργείᾳ μὲν οὐκ ἔστι, δυνάμει δ᾽ ἔστιν. μᾶλλόν τ᾽ ἂν ἀρχὴ κυριωτέρα ταύτης δόξειεν εἶναι τὸ εἶδος καὶ ἡ μορφή: τοῦτο δὲ φθαρτόν, ὥσθ᾽ ὅλως οὐκ ἔστιν ἀΐδιος οὐσία χωριστὴ καὶ καθ᾽ αὑτήν. ἀλλ᾽ ἄτοπον: ἔοικε γὰρ καὶ ζητεῖται σχεδὸν [25] ὑπὸ τῶν χαριεστάτων ὡς οὖσά τις ἀρχὴ καὶ οὐσία τοιαύτη: πῶς γὰρ ἔσται τάξις μή τινος ὄντος ἀϊδίου καὶ χωριστοῦ καὶ μένοντος;	915. But if the principle we are now seeking is not separable from bodies, what could be more of a principle of things than matter? Yet matter does not exist actually but only potentially; and thus it would seem rather that the specifying principle or form is a more important principle than matter. But the form is corruptible [according to some]; and so in general there is no eternal substance which is separate and exists of itself. But this is absurd; for such a principle and substance seems to exist and is sought by almost all accomplished thinkers as something that exists. For how will there be order in the world if there is not a principle which is eternal, separable and permanent (235-246)?
ἔτι δ᾽ εἴπερ ἔστι τις οὐσία καὶ ἀρχὴ τοιαύτη τὴν φύσιν οἵαν νῦν ζητοῦμεν, καὶ αὕτη μία πάντων καὶ ἡ αὐτὴ τῶν ἀϊδίων τε καὶ φθαρτῶν, ἀπορίαν ἔχει διὰ τί ποτε τῆς [30] αὐτῆς ἀρχῆς οὔσης τὰ μέν ἐστιν ἀΐδια τῶν ὑπὸ τὴν ἀρχὴν τὰ δ᾽ οὐκ ἀΐδια (τοῦτο γὰρ ἄτοπον): εἰ δ᾽ ἄλλη μέν ἐστιν ἀρχὴ τῶν φθαρτῶν ἄλλη δὲ τῶν ἀϊδίων, εἰ μὲν ἀΐδιος καὶ ἡ τῶν φθαρτῶν, ὁμοίως ἀπορήσομεν (διὰ τί γὰρ οὐκ ἀϊδίου τῆς ἀρχῆς οὔσης καὶ τὰ ὑπὸ τὴν ἀρχὴν ἀΐδια;): φθαρτῆς δ᾽ [35] οὔσης ἄλλη τις ἀρχὴ γίγνεται ταύτης κἀκείνης ἑτέρα, καὶ τοῦτ᾽ εἰς ἄπειρον πρόεισιν.	916. Again, if there is some substance and principle of such a nature as that now being sought, and this one principle belongs to everything and is one and the same for both corruptible and eternal things, the question arises why it is, if this principle is the same for all, that some of the things which come under it should be eternal and some not; for this is absurd. But if all corruptible things have one principle, and eternal things another, we shall face the same problem if the principle of corruptible things is eternal; for if it is eternal, why are not the things which fall under this principle also eternal? But if it is corruptible, it in turn must have some other principle, and this again must have another, and so on to infinity (250-265).
εἰ δ᾽ αὖ τις τὰς δοκούσας μάλιστ᾽ ἀρχὰς ἀκινήτους εἶναι, τό τε ὂν καὶ τὸ ἕν, θήσει, πρῶτον μὲν εἰ μὴ τόδε τι καὶ οὐσίαν ἑκάτερον αὐτῶν σημαίνει, [1060β] [1] πῶς ἔσονται χωρισταὶ καὶ καθ᾽ αὑτάς; τοιαύτας δὲ ζητοῦμεν τὰς ἀϊδίους τε καὶ πρώτας ἀρχάς. εἴ γε μὴν τόδε τι καὶ οὐσίαν ἑκάτερον αὐτῶν δηλοῖ, πάντ᾽ ἐστὶν οὐσίαι τὰ ὄντα: κατὰ [5] πάντων γὰρ τὸ ὂν κατηγορεῖται (κατ᾽ ἐνίων δὲ καὶ τὸ ἕν): οὐσίαν δ᾽ εἶναι πάντα τὰ ὄντα ψεῦδος.	917. But on the other hand, if one were to posit those principles which are thought to be the most unchangeable, namely, being and unity, then, first, if each of these does not signify a particular thing or a substance, how will they be separable and exist of themselves? Yet the eternal and primary principles for which we are looking must be such. But if each of these does signify a particular thing or a substance, all beings will be substances; for being is predicated of all things, and unity is predicated of some. But it is false that all beings are substances.
ἔτι δὲ τοῖς τὴν πρώτην ἀρχὴν τὸ ἓν λέγουσι καὶ τοῦτ᾽ οὐσίαν, ἐκ δὲ τοῦ ἑνὸς καὶ τῆς ὕλης τὸν ἀριθμὸν γεννῶσι πρῶτον καὶ τοῦτον οὐσίαν φάσκουσιν εἶναι, πῶς ἐνδέχεται τὸ λεγόμενον ἀληθὲς εἶναι; [10] τὴν γὰρ δυάδα καὶ τῶν λοιπῶν ἕκαστον ἀριθμῶν τῶν συνθέτων πῶς ἓν δεῖ νοῆσαι; περὶ τούτου γὰρ οὔτε λέγουσιν οὐδὲν οὔτε ῥᾴδιον εἰπεῖν.	918. Again, how can the statement of those be true who say that unity is the first principle and a substance, and who generate number as the first thing produced from the unit and matter and say that it is substance? For how are we to understand that the number two and each of the other numbers composed of units is one? For they say nothing about this, nor is it easy to do so.
εἴ γε μὴν γραμμὰς ἢ τὰ τούτων ἐχόμενα (λέγω δὲ ἐπιφανείας τὰς πρώτας) θήσει τις ἀρχάς, ταῦτά γ᾽ οὐκ εἰσὶν οὐσίαι χωρισταί, τομαὶ δὲ καὶ διαιρέσεις αἱ μὲν [15] ἐπιφανειῶν αἱ δὲ σωμάτων (αἱ δὲ στιγμαὶ γραμμῶν), ἔτι δὲ πέρατα τῶν αὐτῶν τούτων: πάντα δὲ ταῦτα ἐν ἄλλοις ὑπάρχει καὶ χωριστὸν οὐδέν ἐστιν.	919. But if someone maintains that lines and what is derived from these (I mean surfaces) are the first principles of things, these are not separable substances but sections and divisions; the former of surfaces, and the latter of bodies (and points are the sections and divisions of lines); and further they are the limits of these same things. And all of these exist in other things, and none are separable.
ἔτι πῶς οὐσίαν ὑπολαβεῖν εἶναι δεῖ τοῦ ἑνὸς καὶ στιγμῆς; οὐσίας μὲν γὰρ πάσης γένεσις ἔστι, στιγμῆς δ᾽ οὐκ ἔστιν: διαίρεσις γὰρ ἡ στιγμή.	920. Again, how are we to understand that the unit and the point have substance. For every substance is generated but not the point; for the point amounts to a division (266-283).
παρέχει [20] δ᾽ ἀπορίαν καὶ τὸ πᾶσαν μὲν ἐπιστήμην εἶναι τῶν καθόλου καὶ τοῦ τοιουδί, τὴν δ᾽ οὐσίαν μὴ τῶν καθόλου εἶναι, μᾶλλον δὲ τόδε τι καὶ χωριστόν, ὥστ᾽ εἰ περὶ τὰς ἀρχάς ἐστιν ἐπιστήμη, πῶς δεῖ τὴν ἀρχὴν ὑπολαβεῖν οὐσίαν εἶναι;	921. There is also the problem that, while every science must be about universals and about such and such a universal, a substance is not a universal but is rather a particular and separable thing. Hence, if there is a science of principles, how are we to understand substance to be a principle (288-293) ?
ἔτι πότερον ἔστι τι παρὰ τὸ σύνολον ἢ οὔ (λέγω δὲ τὴν ὕλην καὶ [25] τὸ μετὰ ταύτης); εἰ μὲν γὰρ μή, τά γε ἐν ὕλῃ φθαρτὰ πάντα: εἰ δ᾽ ἔστι τι, τὸ εἶδος ἂν εἴη καὶ ἡ μορφή: τοῦτ᾽ οὖν ἐπὶ τίνων ἔστι καὶ ἐπὶ τίνων οὔ, χαλεπὸν ἀφορίσαι: ἐπ᾽ ἐνίων γὰρ δῆλον οὐκ ὂν χωριστὸν τὸ εἶδος, οἷον οἰκίας.	922. Again, the question arises whether or not there is any principle apart from the concrete whole? And by this I mean the matter and what is joined to it. For if not, then everything that is in matter is corruptible. But if there is some principle, it must be the specifying principle or form. Therefore it is difficult to determine in what cases this exists apart and in what not; for in some cases it is evident that the form is not separable, for example, in that of a house (235-247).
ἔτι πότερον αἱ ἀρχαὶ εἴδει ἢ ἀριθμῷ αἱ αὐταί; εἰ γὰρ ἀριθμῷ [30] ἕν, πάντ᾽ ἔσται ταὐτά.	923. Again, there is the question whether principles are the same specifically or numerically? For if they are the same numerically, all things will be the same (248-249).

ARISTOTLE’S TEXT Chapter 3: 1060b 31-1061b 17
ἐπεὶ δ᾽ ἐστὶν ἡ τοῦ φιλοσόφου ἐπιστήμη τοῦ ὄντος ᾗ ὂν καθόλου καὶ οὐ κατὰ μέρος, τὸ δ᾽ ὂν πολλαχῶς καὶ οὐ καθ᾽ ἕνα λέγεται τρόπον: εἰ μὲν οὖν ὁμωνύμως κατὰ δὲ κοινὸν μηδέν, οὐκ ἔστιν ὑπὸ μίαν ἐπιστήμην (οὐ γὰρ ἓν γένος [35] τῶν τοιούτων), εἰ δὲ κατά τι κοινόν, εἴη ἂν ὑπὸ μίαν ἐπιστήμην.	924. Since the science of the philosopher treats of being as being in general and not of some part of it, and the term being is used in many senses and not merely in one, it follows that, if being is used equivocally and not with a common meaning, being does not fall under one science (for such terms do not have a common class). But if the term is used according to one common meaning, being will fall under one science.
ἔοικε δὴ τὸν εἰρημένον λέγεσθαι τρόπον καθάπερ τό τε ἰατρικὸν καὶ ὑγιεινόν: καὶ γὰρ τούτων ἑκάτερον πολλαχῶς λέγομεν. [1061α] [1] λέγεται δὲ τοῦτον τὸν τρόπον ἕκαστον τῷ τὸ μὲν πρὸς τὴν ἰατρικὴν ἐπιστήμην ἀνάγεσθαί πως τὸ δὲ πρὸς ὑγίειαν τὸ δ᾽ ἄλλως, πρὸς ταὐτὸ δ᾽ ἕκαστον. ἰατρικὸς γὰρ λόγος καὶ μαχαίριον λέγεται τῷ τὸ μὲν ἀπὸ τῆς ἰατρικῆς [5] ἐπιστήμης εἶναι τὸ δὲ ταύτῃ χρήσιμον. ὁμοίως δὲ καὶ ὑγιεινόν: τὸ μὲν γὰρ ὅτι σημαντικὸν ὑγιείας τὸ δ᾽ ὅτι ποιητικόν. ὁ δ᾽ αὐτὸς τρόπος καὶ ἐπὶ τῶν λοιπῶν. τὸν αὐτὸν δὴ τρόπον καὶ τὸ ὂν ἅπαν λέγεται: τῷ γὰρ τοῦ ὄντος ᾗ ὂν πάθος ἢ ἕξις ἢ διάθεσις ἢ κίνησις ἢ τῶν ἄλλων τι τῶν τοιούτων [10] εἶναι λέγεται ἕκαστον αὐτῶν ὄν.	925. Therefore the term seems to be used in the way mentioned, like the terms medical and healthy; for each of these is used in many senses. Now the term is used in each of these ways because of some kind of reference. Thus the former is used in reference to the science of medicine; the latter, to health; and still another, to something else; yet in each case the term is referred to the same thing. For both a discussion and a knife are called medical: the one because it comes from the science of medicine, and the other because it is useful to it. The same is true of the term healthy; for one thing is called healthy because it is a sign of health, and another because it produces it. The same is true of other terms. Hence the same thing is true of every instance of being; for each thing is called a being because it is either a modification or a state or a disposition or a motion or something else of this kind which belongs to being as being.
ἐπεὶ δὲ παντὸς τοῦ ὄντος πρὸς ἕν τι καὶ κοινὸν ἡ ἀναγωγὴ γίγνεται, καὶ τῶν ἐναντιώσεων ἑκάστη πρὸς τὰς πρώτας διαφορὰς καὶ ἐναντιώσεις ἀναχθήσεται τοῦ ὄντος, εἴτε πλῆθος καὶ ἓν εἴθ᾽ ὁμοιότης καὶ ἀνομοιότης αἱ πρῶται τοῦ ὄντος εἰσὶ διαφοραί, εἴτ᾽ [15] ἄλλαι τινές: ἔστωσαν γὰρ αὗται τεθεωρημέναι.	926. And since every being is referred to something one and common, each of the contrarieties may also be referred to the primary differences and contrarieties of being, whether the primary differences are plurality and unity, likeness and unlikeness, or any others; for these have been considered (304).
διαφέρει δ᾽ οὐδὲν τὴν τοῦ ὄντος ἀναγωγὴν πρὸς τὸ ὂν ἢ πρὸς τὸ ἓν γίγνεσθαι. καὶ γὰρ εἰ μὴ ταὐτὸν ἄλλο δ᾽ ἐστίν, ἀντιστρέφει γε: τό τε γὰρ ἓν καὶ ὄν πως, τό τε ὂν ἕν.	927. And it makes no difference whether an existing thing is referred to being or to unity. For even if they are not the same but different, they are nevertheless interchangeable; for what is one is somehow a being, and what is a being is somehow one.
ἐπεὶ δ᾽ ἐστὶ τὰ ἐναντία πάντα τῆς αὐτῆς καὶ μιᾶς ἐπιστήμης θεωρῆσαι, λέγεται [20] δ᾽ ἕκαστον αὐτῶν κατὰ στέρησιν—καίτοι γ᾽ ἔνια ἀπορήσειέ τις ἂν πῶς λέγεται κατὰ στέρησιν, ὧν ἔστιν ἀνὰ μέσον τι, καθάπερ ἀδίκου καὶ δικαίου—περὶ πάντα δὴ τὰ τοιαῦτα τὴν στέρησιν δεῖ τιθέναι μὴ τοῦ ὅλου λόγου, τοῦ τελευταίου δὲ εἴδους: οἷον εἰ ἔστιν ὁ δίκαιος καθ᾽ ἕξιν τινὰ [25] πειθαρχικὸς τοῖς νόμοις, οὐ πάντως ὁ ἄδικος ἔσται τοῦ ὅλου στερούμενος λόγου, περὶ δὲ τὸ πείθεσθαι τοῖς νόμοις ἐκλείπων πῃ, καὶ ταύτῃ ἡ στέρησις ὑπάρξει αὐτῷ: τὸν αὐτὸν δὲ τρόπον καὶ ἐπὶ τῶν ἄλλων.	928. Now since it is the office of one and the same science to study all contraries, and one of each pair involves privation (though one might be puzzled how some contraries are predicated privatively, i.e., those which have an intermediate, as just and unjust), in all such cases it is necessary to hold that the privation of the one is not the privation of the whole notion of the other, but only of the last species. For example, if a man is just because of some habitual tendency to obey the laws, the unjust man will not always be deprived of the perfection completely but will fail to obey the laws in some respect; and in this respect privation will belong to him. The same holds true in other cases.
καθάπερ δ᾽ ὁ μαθηματικὸς περὶ τὰ ἐξ ἀφαιρέσεως τὴν θεωρίαν ποιεῖται (περιελὼν γὰρ πάντα [30] τὰ αἰσθητὰ θεωρεῖ, οἷον βάρος καὶ κουφότητα καὶ σκληρότητα καὶ τοὐναντίον, ἔτι δὲ καὶ θερμότητα καὶ ψυχρότητα καὶ τὰς ἄλλας αἰσθητὰς ἐναντιώσεις, μόνον δὲ καταλείπει τὸ ποσὸν καὶ συνεχές, τῶν μὲν ἐφ᾽ ἓν τῶν δ᾽ ἐπὶ δύο τῶν δ᾽ ἐπὶ τρία, καὶ τὰ πάθη τὰ τούτων ᾗ ποσά ἐστι [35] καὶ συνεχῆ, καὶ οὐ καθ᾽ ἕτερόν τι θεωρεῖ, καὶ τῶν μὲν τὰς πρὸς ἄλληλα θέσεις σκοπεῖ καὶ τὰ ταύταις ὑπάρχοντα, [1061β] [1] τῶν δὲ τὰς συμμετρίας καὶ ἀσυμμετρίας, τῶν δὲ τοὺς λόγους, ἀλλ᾽ ὅμως μίαν πάντων καὶ τὴν αὐτὴν τίθεμεν ἐπιστήμην τὴν γεωμετρικήν), τὸν αὐτὸν δὴ τρόπον ἔχει καὶ περὶ τὸ ὄν.	929. Now the mathematician in a sense studies things which are gotten by taking something away; for he speculates by removing from things all sensible qualities, such as heaviness and lightness, hardness and its contrary, and also heat and cold and other sensible contrarieties, and leaves only the quantified and the continuous (some things being such in one, some in two, and some in three dimensions). And he studies the properties of the quantified and the continuous as such and not in any other respect. And of some he considers the relative positions and attributes, and of others the commensurability and incommensurability, and of others the ratios; yet we claim that there is only one science of all these things, namely, geometry. The same holds true of being.
τὰ γὰρ τούτῳ συμβεβηκότα καθ᾽ ὅσον ἐστὶν ὄν, καὶ [5] τὰς ἐναντιώσεις αὐτοῦ ᾗ ὄν, οὐκ ἄλλης ἐπιστήμης ἢ φιλοσοφίας θεωρῆσαι. τῇ φυσικῇ μὲν γὰρ οὐχ ᾗ ὄντα, μᾶλλον δ᾽ ᾗ κινήσεως μετέχει, τὴν θεωρίαν τις ἀπονείμειεν ἄν: ἥ γε μὴν διαλεκτικὴ καὶ ἡ σοφιστικὴ τῶν συμβεβηκότων μέν εἰσι τοῖς οὖσιν, οὐχ ᾗ δ᾽ ὄντα οὐδὲ περὶ τὸ ὂν αὐτὸ καθ᾽ ὅσον [10] ὄν ἐστιν: ὥστε λείπεται τὸν φιλοσόφον, καθ᾽ ὅσον ὄντ᾽ ἐστίν, εἶναι περὶ τὰ λεχθέντα θεωρητικόν.	930. For an investigation of the attributes of being as being, and of the contrarieties of being as being, belong to no other science than [first] philosophy; for one would not assign to the philosophy of nature the study of things insofar as they are beings but rather insofar as they participate in motion. For dialectics and sophistry are concerned with the accidents of existing things, but not as beings, nor do they deal with being as being. It follows, then, that it is the philosopher who speculates about the things which we have mentioned, insofar as they are beings.
ἐπεὶ δὲ τό τε ὂν ἅπαν καθ᾽ ἕν τι καὶ κοινὸν λέγεται πολλαχῶς λεγόμενον, καὶ τἀναντία τὸν αὐτὸν τρόπον (εἰς τὰς πρώτας γὰρ ἐναντιώσεις καὶ διαφορὰς τοῦ ὄντος ἀνάγεται), τὰ δὲ τοιαῦτα δυνατὸν [15] ὑπὸ μίαν ἐπιστήμην εἶναι, διαλύοιτ᾽ ἂν ἡ κατ᾽ ἀρχὰς ἀπορία λεχθεῖσα, λέγω δ᾽ ἐν ᾗ διηπορεῖτο πῶς ἔσται πολλῶν καὶ διαφόρων ὄντων τῷ γένει μία τις ἐπιστήμη.	931. And since every being is referred to some one common meaning, which is used in many senses, and the same applies to contraries (for they are referred to the primary differences and contrarieties of being), and such things can fall under one science, the difficulty which was stated at the beginning of this work (900-904) is solved in this way. I mean the question how there can be one science of things which are many and different in genus.

ARISTOTLE’S TEXT Chapter 4: 1061b 17-1061b 33
ἐπεὶ δὲ καὶ ὁ μαθηματικὸς χρῆται τοῖς κοινοῖς ἰδίως, καὶ τὰς τούτων ἀρχὰς ἂν εἴη θεωρῆσαι τῆς πρώτης φιλοσοφίας. ὅτι γὰρ [20] ἀπὸ τῶν ἴσων ἴσων ἀφαιρεθέντων ἴσα τὰ λειπόμενα, κοινὸν μέν ἐστιν ἐπὶ πάντων τῶν ποσῶν, ἡ μαθηματικὴ δ᾽ ἀπολαβοῦσα περί τι μέρος τῆς οἰκείας ὕλης ποιεῖται τὴν θεωρίαν, οἷον περὶ γραμμὰς ἢ γωνίας ἢ ἀριθμοὺς ἢ τῶν λοιπῶν τι ποσῶν, οὐχ ᾗ δ᾽ ὄντα ἀλλ᾽ ᾗ συνεχὲς αὐτῶν ἕκαστον ἐφ᾽ [25] ἓν ἢ δύο ἢ τρία: ἡ δὲ φιλοσοφία περὶ τῶν ἐν μέρει μέν, ᾗ τούτων ἑκάστῳ τι συμβέβηκεν, οὐ σκοπεῖ, περὶ τὸ ὂν δέ, ᾗ ὂν τῶν τοιούτων ἕκαστον, θεωρεῖ.	932. And since the mathematician uses the common axioms in a particular way, it must be the office of first philosophy to study principles of this kind. For the axiom or principle that “when equals are subtracted from equals the remainders are equal” is common to all quantities. But mathematics, assuming [principles of this kind], makes a study of some part of the quantified as its proper subject matter, for example, lines or angles or number or some of the other kinds of quantity. Yet it does not consider them inasmuch as they are beings but inasmuch as each is continuous in one, two or three dimensions. Philosophy, however, does not investigate those things which are in some part of matter insofar as each has some attribute, but it considers each of these particular things from the standpoint of being insofar as it is being.
τὸν αὐτὸν δ᾽ ἔχει τρόπον καὶ περὶ τὴν φυσικὴν ἐπιστήμην τῇ μαθηματικῇ: τὰ συμβεβηκότα γὰρ ἡ φυσικὴ καὶ τὰς ἀρχὰς θεωρεῖ τὰς τῶν ὄντων [30] ᾗ κινούμενα καὶ οὐχ ᾗ ὄντα (τὴν δὲ πρώτην εἰρήκαμεν ἐπιστήμην τούτων εἶναι καθ᾽ ὅσον ὄντα τὰ ὑποκείμενά ἐστιν, ἀλλ᾽ οὐχ ᾗ ἕτερόν τι): διὸ καὶ ταύτην καὶ τὴν μαθηματικὴν ἐπιστήμην μέρη τῆς σοφίας εἶναι θετέον.	933. Now what applies in the case of the science of mathematics is also true of the philosophy of nature; for the philosophy of nature studies the attributes and principles of beings inasmuch as they are moved, not inasmuch as they are beings. But, as we have said, the primary science considers these attributes and principles insofar as their subjects are beings, and not in any other respect. For this reason it is necessary to hold that this science and the science of mathematics are parts of wisdom (319-23; 900-01).

ARISTOTLE’S TEXT Chapters 5 & 6: 1061b 34-1062b 19
ἔστι δέ τις ἐν τοῖς οὖσιν ἀρχὴ περὶ ἣν οὐκ ἔστι διεψεῦσθαι, [35] τοὐναντίον δὲ ἀναγκαῖον ἀεὶ ποιεῖν, λέγω δὲ ἀληθεύειν, οἷον ὅτι οὐκ ἐνδέχεται τὸ αὐτὸ καθ᾽ ἕνα καὶ τὸν αὐτὸν χρόνον εἶναι καὶ μὴ εἶναι, [1062α] [1] καὶ τἆλλα τὰ τοῦτον αὑτοῖς ἀντικείμενα τὸν τρόπον.	934. There is a principle in existing things about which it is impossible to make a mistake, but of which one must always do the contrary, I mean acknowledge it as true, namely, that the same thing cannot both be and not be at one and the same time; and the same is also true of other things which are opposed in this way (326-328).
καὶ περὶ τῶν τοιούτων ἁπλῶς μὲν οὐκ ἔστιν ἀπόδειξις, πρὸς τόνδε δὲ ἔστιν: οὐ γὰρ ἔστιν ἐκ πιστοτέρας ἀρχῆς αὐτοῦ τούτου ποιήσασθαι συλλογισμόν, δεῖ δέ γ᾽ [5] εἴπερ ἔσται τὸ ἁπλῶς ἀποδεδεῖχθαι.	935. And while there is no demonstration in the strict sense of such principles, one may employ an argument ad hominem; for it is impossible to construct a syllogism from a more certain principle than this one. But this would be necessary if there were demonstration of it in the strict sense (329-330).
πρὸς δὲ τὸν λέγοντα τὰς ἀντικειμένας φάσεις τῷ δεικνύντι διότι ψεῦδος ληπτέον τι τοιοῦτον ὃ ταὐτὸ μὲν ἔσται τῷ μὴ ἐνδέχεσθαι ταὐτὸ εἶναι καὶ μὴ εἶναι καθ᾽ ἕνα καὶ τὸν αὐτὸν χρόνον, μὴ δόξει δ᾽ εἶναι ταὐτόν: οὕτω γὰρ μόνως ἂν ἀποδειχθείη πρὸς τὸν [10] φάσκοντα ἐνδέχεσθαι τὰς ἀντικειμένας φάσεις ἀληθεύεσθαι κατὰ τοῦ αὐτοῦ.	936. Now anyone who wants to prove to an opponent making statements opposite to one’s own that he is wrong must take some such principle which is the same as this one—that the same thing cannot both be and not be at the same time—but apparently is not the same. For this will be the only method of demonstration that can be used against one who says that opposite statements can be truly made about the same subject.
τοὺς δὴ μέλλοντας ἀλλήλοις λόγου κοινωνήσειν δεῖ τι συνιέναι αὑτῶν: μὴ γιγνομένου γὰρ τούτου πῶς ἔσται κοινωνία τούτοις πρὸς ἀλλήλους λόγου; δεῖ τοίνυν τῶν ὀνομάτων ἕκαστον εἶναι γνώριμον καὶ δηλοῦν τι, καὶ μὴ [15] πολλά, μόνον δὲ ἕν: ἂν δὲ πλείονα σημαίνῃ, φανερὸν ποιεῖν ἐφ᾽ ὃ φέρει τοὔνομα τούτων. ὁ δὴ λέγων εἶναι τοῦτο καὶ μὴ εἶναι, τοῦτο ὅ φησιν οὔ φησιν, ὥσθ᾽ ὃ σημαίνει τοὔνομα τοῦτ᾽ οὔ φησι σημαίνειν: τοῦτο δ᾽ ἀδύνατον. ὥστ᾽ εἴπερ σημαίνει τι τὸ εἶναι τόδε, τὴν ἀντίφασιν ἀδύνατον ἀληθεύειν.	937. Accordingly, those who are to join in some discussion must understand each other to some extent. And if this does not happen, how will they join in a common discussion? Therefore each of the terms used must be understood and must signify something, and not many things but only one. But if a term does signify many things, it must be made clear to which of these it refers. Hence, one who says that this is and is not, totally denies what he affirms, and thus denies that the term signifies what it signifies. But this is impossible. Hence, if to be this has some meaning, the contradictory cannot be said to be true of the same subject (332-340).
ἔτι δ᾽ εἴ [20] τι σημαίνει τοὔνομα καὶ τοῦτ᾽ ἀληθεύεται, δεῖ τοῦτ᾽ ἐξ ἀνάγκης εἶναι: τὸ δ᾽ ἐξ ἀνάγκης ὂν οὐκ ἐνδέχεταί ποτε μὴ εἶναι: τὰς ἀντικειμένας ἄρα οὐκ ἐνδέχεται φάσεις καὶ ἀποφάσεις ἀληθεύειν κατὰ τοῦ αὐτοῦ.	938. Again, if a term signifies something and this is affirmed truly, it must necessarily be so; and what is necessarily so cannot not be. Hence opposite affirmations and negations cannot be true of the same subject (337-338).
ἔτι δ᾽ εἰ μηθὲν μᾶλλον ἡ φάσις ἢ ἡ ἀπόφασις ἀληθεύεται, ὁ λέγων ἄνθρωπον ἢ [25] οὐκ ἄνθρωπον οὐθὲν μᾶλλον ἀληθεύσει: δόξειε δὲ κἂν οὐχ ἵππον εἶναι φάσκων τὸν ἄνθρωπον ἢ μᾶλλον ἢ οὐχ ἧττον ἀληθεύειν ἢ οὐκ ἄνθρωπον, ὥστε καὶ ἵππον φάσκων εἶναι τὸν αὐτὸν ἀληθεύσει (τὰς γὰρ ἀντικειμένας ὁμοίως ἦν ἀληθεύειν): συμβαίνει τοίνυν τὸν αὐτὸν ἄνθρωπον εἶναι καὶ ἵππον [30] ἢ τῶν ἄλλων τι ζῴων. ἀπόδειξις μὲν οὖν οὐδεμία τούτων ἐστὶν ἁπλῶς, πρὸς μέντοι τὸν ταῦτα τιθέμενον ἀπόδειξις.	939. Again, if the affirmation is in no way truer than the negation, it will not be truer to say that something is a man than to say that it is not a man. And it would also seem that it is either more or not less true to say that a man is not a horse than to say that he is not a man. Hence one will also be right in saying that the same thing is a horse; for it was assumed that opposite statements are equally true. Therefore it follows that the same thing is a man and a horse, or any other animal (343-345). Hence, while there is no demonstration in the strict sense of these principles, there is still a demonstration ad hominem against one who makes these assumptions.
ταχέως δ᾽ ἄν τις καὶ αὐτὸν τὸν Ἡράκλειτον τοῦτον ἐρωτῶν τὸν τρόπον ἠνάγκασεν ὁμολογεῖν μηδέποτε τὰς ἀντικειμένας φάσεις δυνατὸν εἶναι κατὰ τῶν αὐτῶν ἀληθεύεσθαι: νῦν δ᾽ [35] οὐ συνιεὶς ἑαυτοῦ τί ποτε λέγει, ταύτην ἔλαβε τὴν δόξαν. ὅλως δ᾽ εἰ τὸ λεγόμενον ὑπ᾽ αὐτοῦ ἐστὶν ἀληθές, οὐδ᾽ ἂν αὐτὸ τοῦτο εἴη ἀληθές, [1062β] [1] λέγω δὲ τὸ ἐνδέχεσθαι τὸ αὐτὸ καθ᾽ ἕνα καὶ τὸν αὐτὸν χρόνον εἶναί τε καὶ μὴ εἶναι: καθάπερ γὰρ καὶ διῃρημένων αὐτῶν οὐδὲν μᾶλλον ἡ κατάφασις ἢ ἡ ἀπόφασις ἀληθεύεται, τὸν αὐτὸν τρόπον καὶ τοῦ συναμφοτέρου [5] καὶ τοῦ συμπεπλεγμένου καθάπερ μιᾶς τινὸς καταφάσεως οὔσης οὐθὲν μᾶλλον <�ἢ> ἡ ἀπόφασις [ἢ] τὸ ὅλον ὡς ἐν καταφάσει τιθέμενον ἀληθεύσεται.	940. And perhaps if one had questioned Heraclitus himself in this way, he would quickly have forced him to admit that opposite statements can never be true of the same subjects. But he adopted this view without understanding his own statement (328). And in general if what he said is true, not even this statement will be true—I mean that the same thing can both be and not be at one and the same time. For just as when they are separated the affirmation will not be truer than the negation (346), in a similar way when both are combined and taken together as though they were one affirmation, the negation will not be truer than the whole statement regarded as an affirmation.
ἔτι δ᾽ εἰ μηθὲν ἔστιν ἀληθῶς καταφῆσαι, κἂν αὐτὸ τοῦτο ψεῦδος εἴη τὸ φάναι μηδεμίαν ἀληθῆ κατάφασιν ὑπάρχειν. εἰ δ᾽ ἔστι τι, λύοιτ᾽ ἂν τὸ [10] λεγόμενον ὑπὸ τῶν τὰ τοιαῦτα ἐνισταμένων καὶ παντελῶς ἀναιρούντων τὸ διαλέγεσθαι.	941. Again, if it is possible to affirm nothing truly, even this statement-that no affirmation is true-will be false (396-397). But if there is a true affirmation, this will refute what is said by those who raise such objections and completely destroy discussion.
Chapter 6
παραπλήσιον δὲ τοῖς εἰρημένοις ἐστὶ καὶ τὸ λεχθὲν ὑπὸ τοῦ Πρωταγόρου: καὶ γὰρ ἐκεῖνος ἔφη πάντων εἶναι χρημάτων μέτρον ἄνθρωπον, οὐδὲν ἕτερον λέγων ἢ τὸ δοκοῦν ἑκάστῳ [15] τοῦτο καὶ εἶναι παγίως: τούτου δὲ γιγνομένου τὸ αὐτὸ συμβαίνει καὶ εἶναι καὶ μὴ εἶναι, καὶ κακὸν καὶ ἀγαθὸν εἶναι, καὶ τἆλλα τὰ κατὰ τὰς ἀντικειμένας λεγόμενα φάσεις, διὰ τὸ πολλάκις τοισδὶ μὲν φαίνεσθαι τόδε εἶναι καλὸν τοισδὶ δὲ τοὐναντίον, μέτρον δ᾽ εἶναι τὸ φαινόμενον ἑκάστῳ.	942. The statement made by Protagoras is similar to those mentioned; for he said that man is the measure of all things, meaning simply that whatever appears so to anyone is just as it appears to him. But if this is true, it follows that the same thing is and is not, and is good and evil, and that other statements involving opposites are true; because often a particular thing appears to be good to some and just the opposite to others, and that which appears to each man is the measure.

ARISTOTLE’S TEXT Chapter 6: 1062b 20-1063b 35
[20] λύοιτο δ᾽ ἂν αὕτη ἡ ἀπορία θεωρήσασι πόθεν ἐλήλυθεν ἡ ἀρχὴ [21] τῆς ὑπολήψεως ταύτης:	943. Now this difficulty may be solved by considering the origin of this view.
ἔοικε γὰρ ἐνίοις μὲν ἐκ τῆς τῶν φυσιολόγων δόξης γεγενῆσθαι, τοῖς δ᾽ ἐκ τοῦ μὴ ταὐτὰ περὶ τῶν αὐτῶν ἅπαντας γιγνώσκειν ἀλλὰ τοῖσδε μὲν ἡδὺ τόδε φαίνεσθαι τοῖσδε δὲ τοὐναντίον.	944. For it seems to have arisen in some cases from the opinion of the philosophers of nature, and in others from the fact that not all men apprehend the same thing in the same way, but something appears pleasant to some and the opposite to others (352).
τὸ γὰρ μηδὲν ἐκ μὴ ὄντος [25] γίγνεσθαι, πᾶν δ᾽ ἐξ ὄντος, σχεδὸν ἁπάντων ἐστὶ κοινὸν δόγμα τῶν περὶ φύσεως: ἐπεὶ οὖν οὐ λευκὸν γίγνεται λευκοῦ τελέως ὄντος καὶ οὐδαμῇ μὴ λευκοῦ [νῦν δὲ γεγενημένον μὴ λευκόν], γίγνοιτ᾽ ἂν ἐκ μὴ ὄντος λευκοῦ τὸ γιγνόμενον [μὴ] λευκόν: ὥστε ἐκ μὴ ὄντος γίγνοιτ᾽ ἂν κατ᾽ ἐκείνους, εἰ μὴ [30] ὑπῆρχε λευκὸν τὸ αὐτὸ καὶ μὴ λευκόν. οὐ χαλεπὸν δὲ διαλύειν τὴν ἀπορίαν ταύτην: εἴρηται γὰρ ἐν τοῖς φυσικοῖς πῶς ἐκ τοῦ μὴ ὄντος γίγνεται τὰ γιγνόμενα καὶ πῶς ἐξ ὄντος.	945. For the view that nothing comes from non-being but everything from being is a doctrine common to nearly all those who have dealt with nature. Thus, since the not-white comes from what is actually white, and not from the not-white, should the not-white have come to be, what becomes not-white will have come to be from what is not not-white. Hence whiteness must come from non being according to them, unless the white and the not-white are the same. But it is not hard to solve this difficulty; for we have stated in our physical treatises in what sense things which come to be come from non-being, and in what sense they come from being (355-356).
#964;ό γε μὴν ὁμοίως προσέχειν ταῖς δόξαις καὶ ταῖς φαντασίαις τῶν πρὸς αὑτοὺς διαμφισβητούντων εὔηθες: δῆλον [35] γὰρ ὅτι τοὺς ἑτέρους αὐτῶν ἀνάγκη διεψεῦσθαι. φανερὸν δὲ τοῦτ᾽ ἐκ τῶν γιγνομένων κατὰ τὴν αἴσθησιν: οὐδέποτε γὰρ τὸ αὐτὸ φαίνεται τοῖς μὲν γλυκὺ τοῖς δὲ τοὐναντίον, [1063α] [1] μὴ διεφθαρμένων καὶ λελωβημένων τῶν ἑτέρων τὸ αἰσθητήριον καὶ κριτήριον τῶν λεχθέντων χυμῶν. τούτου δ᾽ ὄντος τοιούτου τοὺς ἑτέρους μὲν ὑποληπτέον μέτρον εἶναι τοὺς δ᾽ ἄλλους οὐχ [5] ὑποληπτέον. ὁμοίως δὲ τοῦτο λέγω καὶ ἐπὶ ἀγαθοῦ καὶ κακοῦ, καὶ καλοῦ καὶ αἰσχροῦ, καὶ τῶν ἄλλων τῶν τοιούτων. οὐδὲν γὰρ διαφέρει τοῦτ᾽ ἀξιοῦν ἢ τὰ φαινόμενα τοῖς ὑπὸ τὴν ὄψιν ὑποβάλλουσι τὸν δάκτυλον καὶ ποιοῦσιν ἐκ τοῦ ἑνὸς φαίνεσθαι δύο, δύο δεῖν εἶναι διὰ τὸ φαίνεσθαι τοσαῦτα, καὶ πάλιν ἕν: [10] τοῖς γὰρ μὴ κινοῦσι τὴν ὄψιν ἓν φαίνεται τὸ ἕν.	946. But it is also foolish to occupy oneself equally with both opinions and with the fanciful statements of those who argue against themselves, because it is evident that one or the other of them must be wrong. This is clear from the facts of sensory perception; for the same thing never appears sweet to some and the opposite to others unless in some the organ of the sense which distinguish the above-mentioned savors has been impaired or injured. And such being the case, some must be taken as the measure and the others not. And I say that the same thing applies in the case of good and evil, of beautiful and ugly, and o other attributes of this kind. For to maintain this view is not different from maintaining that what appears to those who push their finger under their eye an make one object appear to be two must therefore be two because it appears to be so many, and yet that it must be one because to those who do not move their eye the one object appears to be one (369-375).
ὅλως δὲ ἄτοπον ἐκ τοῦ φαίνεσθαι τὰ δεῦρο μεταβάλλοντα καὶ μηδέποτε διαμένοντα ἐν τοῖς αὐτοῖς, ἐκ τούτου περὶ τῆς ἀληθείας τὴν κρίσιν ποιεῖσθαι: δεῖ γὰρ ἐκ τῶν ἀεὶ κατὰ ταὐτὰ ἐχόντων καὶ μηδεμίαν μεταβολὴν ποιουμένων τἀληθὲς θηρεύειν, [15] τοιαῦτα δ᾽ ἐστὶ τὰ κατὰ τὸν κόσμον: ταῦτα γὰρ οὐχ ὁτὲ μὲν τοιαδὶ πάλιν δ᾽ ἀλλοῖα φαίνεται, ταὐτὰ δ᾽ ἀεὶ καὶ μεταβολῆς οὐδεμιᾶς κοινωνοῦντα.	947. And in general seeing that things here are subject to change and never remain the same, it would be unfitting to base our judgment of the truth on this. For in pursuing the truth one must start with those things which are always the same and never undergo a single change. Such things are those which contain the world; for they do not appear at one time to be such and at another different but they are always the same and admit of no change (365).
ἔτι δ᾽ εἰ κίνησις ἔστι, καὶ κινούμενόν τι, κινεῖται δὲ πᾶν ἔκ τινος καὶ εἴς τι: δεῖ ἄρα τὸ κινούμενον εἶναι ἐν ἐκείνῳ ἐξ οὗ κινήσεται καὶ οὐκ [20] εἶναι ἐν αὐτῷ, καὶ εἰς τοδὶ κινεῖσθαι καὶ γίγνεσθαι ἐν τούτῳ, τὸ δὲ κατὰ τὴν ἀντίφασιν μὴ συναληθεύεσθαι κατ᾽ αὐτούς.	948. Further, if there is motion, there is also something that is moved; and everything is moved from something and to something. Therefore that which is moved must be in that from which it is moved, and yet not be in it; and it must be moved to this and come to be in it; but contradictories cannot be true at the same time, as they claim.
καὶ εἰ κατὰ τὸ ποσὸν συνεχῶς τὰ δεῦρο ῥεῖ καὶ κινεῖται, καί τις τοῦτο θείη καίπερ οὐκ ἀληθὲς ὄν, διὰ τί κατὰ τὸ ποιὸν οὐ μενεῖ; φαίνονται γὰρ οὐχ ἥκιστα τὰ κατὰ τὰς ἀντιφάσεις [25] ταὐτοῦ κατηγορεῖν ἐκ τοῦ τὸ ποσὸν ὑπειληφέναι μὴ μένειν ἐπὶ τῶν σωμάτων, διὸ καὶ εἶναι τετράπηχυ τὸ αὐτὸ καὶ οὐκ εἶναι. ἡ δ᾽ οὐσία κατὰ τὸ ποιόν, τοῦτο δὲ τῆς ὡρισμένης φύσεως, τὸ δὲ ποσὸν τῆς ἀορίστου.	949. And if things here are in a state of continuous change and motion as regards quantity, and one were to suppose this even though it is not true, why should they not be permanent as regards quality? For the view that contradictories may be predicated of the same subject seems to be based largely on the assumption that the quantity of bodies does not remain constant; and for this reason they say that the same thing is and is not four cubits long. But a thing’s substance involves quality, and this is of a determinate nature, whereas quantity is of an indeterminate nature (365).
ἔτι διὰ τί προστάττοντος τοῦ ἰατροῦ τοδὶ τὸ σιτίον προσενέγκασθαι προσφέρονται; [30] τί γὰρ μᾶλλον τοῦτο ἄρτος ἐστὶν ἢ οὐκ ἔστιν; ὥστ᾽ οὐθὲν ἂν διέχοι φαγεῖν ἢ μὴ φαγεῖν: νῦν δ᾽ ὡς ἀληθεύοντες περὶ αὐτὸ καὶ ὄντος τοῦ προσταχθέντος σιτίου τούτου προσφέρονται τοῦτο: καίτοι γ᾽ οὐκ ἔδει μὴ διαμενούσης παγίως μηδεμιᾶς φύσεως ἐν τοῖς αἰσθητοῖς ἀλλ᾽ ἀεὶ πασῶν κινουμένων [35] καὶ ῥεουσῶν.	950. Further, when a physician orders them to take some particular food, why do they take it? For why is this particular food bread rather than not bread? Hence it would make no difference whether they ate it or not. But they take the food prescribed as though they know the truth about it and that it is the food prescribed. Yet they should not do this if there is no nature which remains fixed in the sensible world, but everything is always in a state of motion and flux (349).
ἔτι δ᾽ εἰ μὲν ἀλλοιούμεθα ἀεὶ καὶ μηδέποτε διαμένομεν οἱ αὐτοί, τί καὶ θαυμαστὸν εἰ μηδέποθ᾽ ἡμῖν ταὐτὰ φαίνεται καθάπερ τοῖς κάμνουσιν [1063β] [1] (καὶ γὰρ τούτοις διὰ τὸ μὴ ὁμοίως διακεῖσθαι τὴν ἕξιν καὶ ὅθ᾽ ὑγίαινον, οὐχ ὅμοια φαίνεται τὰ κατὰ τὰς αἰσθήσεις, αὐτὰ μὲν οὐδεμιᾶς διά γε τοῦτο μεταβολῆς κοινωνοῦντα τὰ αἰσθητά, αἰσθήματα δ᾽ ἕτερα ποιοῦντα τοῖς κάμνουσι καὶ μὴ τὰ αὐτά: [5] τὸν αὐτὸν δὴ τρόπον ἔχειν καὶ τῆς εἰρημένης μεταβολῆς γιγνομένης ἴσως ἀναγκαῖόν ἐστιν); εἰ δὲ μὴ μεταβάλλομεν ἀλλ᾽ οἱ αὐτοὶ διατελοῦμεν ὄντες, εἴη ἄν τι μένον.	951. Again, if we are always undergoing change and never remain the same, what wonder is it if to us, as to those who are ill, things never appear the same? For to them also, since they are not in the same condition as when they were well, sensible qualities do not appear to be the same; yet sensible things themselves need not for this reason undergo any change, but they cause different, and not the same, impressions in those who are ill. And perhaps the same thing must happen to those who are well if the above-mentioned change takes place (950). However, if we do not change but always remain the same, there will be something permanent (357-359).
πρὸς μὲν οὖν τοὺς ἐκ λόγου τὰς εἰρημένας ἀπορίας ἔχοντας οὐ ῥᾴδιον διαλῦσαι μὴ τιθέντων τι καὶ τούτου μηκέτι λόγον ἀπαιτούντων: [10] οὕτω γὰρ πᾶς λόγος καὶ πᾶσα ἀπόδειξις γίγνεται: μηθὲν γὰρ τιθέντες ἀναιροῦσι τὸ διαλέγεσθαι καὶ ὅλως λόγον, ὥστε πρὸς μὲν τοὺς τοιούτους οὐκ ἔστι λόγος, πρὸς δὲ τοὺς διαποροῦντας ἐκ τῶν παραδεδομένων ἀποριῶν ῥᾴδιον ἀπαντᾶν καὶ διαλύειν τὰ ποιοῦντα τὴν ἀπορίαν ἐν αὐτοῖς: δῆλον δ᾽ ἐκ τῶν [15] εἰρημένων. ὥστε φανερὸν ἐκ τούτων.	952. Hence, in the case of those who raise the foregoing difficulties as a result of reasoning, it is not easy to meet their arguments unless they assume something and do not demand a reason for it; for every argument and demonstration comes about in this way. For those who admit nothing destroy discussion and reasoning in general, and thus there is no reasoning with such men. But in the case of those who are puzzled by the usual problems, it is easy to meet them and to reject the arguments which cause their difficulty. This becomes clear from what has been said above (943-951).
ὅτι οὐκ ἐνδέχεται τὰς ἀντικειμένας φάσεις περὶ τοῦ αὐτοῦ καθ᾽ ἕνα χρόνον ἀληθεύειν, οὐδὲ τὰ ἐναντία, διὰ τὸ λέγεσθαι κατὰ στέρησιν πᾶσαν ἐναντιότητα: δῆλον δὲ τοῦτ᾽ ἐπ᾽ ἀρχὴν τοὺς λόγους ἀναλύουσι τοὺς τῶν ἐναντίων. ὁμοίως δ᾽ οὐδὲ τῶν ἀνὰ μέσον οὐδὲν οἷόν τε [20] κατηγορεῖσθαι καθ᾽ ἑνὸς καὶ τοῦ αὐτοῦ: λευκοῦ γὰρ ὄντος τοῦ ὑποκειμένου λέγοντες αὐτὸ εἶναι οὔτε μέλαν οὔτε λευκὸν ψευσόμεθα: συμβαίνει γὰρ εἶναι λευκὸν αὐτὸ καὶ μὴ εἶναι: θάτερον γὰρ τῶν συμπεπλεγμένων ἀληθεύσεται κατ᾽ αὐτοῦ, τοῦτο δ᾽ ἐστὶν ἀντίφασις τοῦ λευκοῦ.	953. It is evident from these considerations, then, that opposite statements cannot be verified of the same subject at one time (353; 376-377), nor can contrary ones, because every contrariety involves privation. This becomes clear if we reduce the definitions of all contraries to their principle (382). Similarly no intermediate can be predicated of one and the same subject. For if the subject is white, those who say that it is neither white nor black are wrong, for it then follows that it is white and is not white; for the second of the two terms which we have combined is true of it, and this is the contradictory of white (383-391).
οὔτε δὴ καθ᾽ Ἡράκλειτον [25] ἐνδέχεται λέγοντας ἀληθεύειν, οὔτε κατ᾽ Ἀναξαγόραν: εἰ δὲ μή, συμβήσεται τἀναντία τοῦ αὐτοῦ κατηγορεῖν: ὅταν γὰρ ἐν παντὶ φῇ παντὸς εἶναι μοῖραν, οὐδὲν μᾶλλον εἶναί φησι γλυκὺ ἢ πικρὸν ἢ τῶν λοιπῶν ὁποιανοῦν ἐναντιώσεων, εἴπερ ἐν ἅπαντι πᾶν ὑπάρχει μὴ δυνάμει μόνον ἀλλ᾽ ἐνεργεία [30] ι καὶ ἀποκεκριμένον.	954. One cannot be right, then, in holding the views either of Heraclitus (940) or of Anaxagoras; and if this were not so it would follow that contraries would be predicated of the same subject. For when Anaxagoras says that there is a part of everything in everything else, he says that nothing is sweet any more than it is bitter, and so on with any of the other pairs of contraries, since everything is present in everything else, not potentially, but actually and separately.
ὁμοίως δὲ οὐδὲ πάσας ψευδεῖς οὐδ᾽ ἀληθεῖς τὰς φάσεις δυνατὸν εἶναι, δι᾽ ἄλλα τε πολλὰ τῶν συναχθέντων ἂν δυσχερῶν διὰ ταύτην τὴν θέσιν, καὶ διότι ψευδῶν μὲν οὐσῶν πασῶν οὐδ᾽ αὐτὸ τοῦτό τις φάσκων ἀληθεύσει, ἀληθῶν δὲ ψευδεῖς εἶναι πάσας λέγων οὐ ψεύσεται. [35]	955. And similarly all statements cannot be true or all false, both because of many other difficulties which might be brought forward on the basis of this position, and because, if all statements are false, anyone who says this will not speak the truth; and if all are true, it will not be false to say that all are false (392).

ARISTOTLE’S TEXT Chapter 7: 1063b 36-1064b 14
πᾶσα δ᾽ ἐπιστήμη ζητεῖ τινὰς ἀρχὰς καὶ αἰτίας περὶ ἕκαστον τῶν ὑφ᾽ αὑτὴν ἐπιστητῶν, [1064α] [1] οἷον ἰατρικὴ καὶ γυμναστικὴ καὶ τῶν λοιπῶν ἑκάστη τῶν ποιητικῶν καὶ μαθηματικῶν. ἑκάστη γὰρ τούτων περιγραψαμένη τι γένος αὑτῇ περὶ τοῦτο πραγματεύεται ὡς ὑπάρχον καὶ ὄν, οὐχ ᾗ δὲ ὄν, ἀλλ᾽ ἑτέρα τις αὕτη παρὰ ταύτας τὰς ἐπιστήμας ἐστὶν ἐπιστήμη.	956. Every science seeks certain principles and causes of each of the knowable objects which comes within its scope; for example, medicine and gymnastics do this, and so does each of the other sciences, productive as well as doctrinal. For each of these marks off for itself some class of things and occupies itself with this as with something that is real and a being, though not as being; but there is a certain other science distinct from these which does this.
τῶν δὲ [5] λεχθεισῶν ἐπιστημῶν ἑκάστη λαβοῦσά πως τὸ τί ἐστιν ἐν ἑκάστῳ γένει πειρᾶται δεικνύναι τὰ λοιπὰ μαλακώτερον ἢ ἀκριβέστερον. λαμβάνουσι δὲ τὸ τί ἐστιν αἱ μὲν δι᾽ αἰσθήσεως αἱ δ᾽ ὑποτιθέμεναι: διὸ καὶ δῆλον ἐκ τῆς τοιαύτης ἐπαγωγῆς ὅτι τῆς οὐσίας καὶ τοῦ τί ἐστιν οὐκ ἔστιν ἀπόδειξις.	957. And each of the sciences mentioned somehow assumes the quiddity in some class of things and tries to prove the rest, with greater or lesser certainty. Some derive the quiddity from sensory perception, and some by assuming it from some other science. Hence from such a process of induction it becomes evident that there is no demonstration of the substance and of its quiddity.
[10] ἐπεὶ δ᾽ ἔστι τις ἡ περὶ φύσεως ἐπιστήμη, δῆλον ὅτι καὶ πρακτικῆς ἑτέρα καὶ ποιητικῆς ἔσται. ποιητικῆς μὲν γὰρ ἐν τῷ ποιοῦντι καὶ οὐ τῷ ποιουμένῳ τῆς κινήσεως ἡ ἀρχή, καὶ τοῦτ᾽ ἔστιν εἴτε τέχνη τις εἴτ᾽ ἄλλη τις δύναμις: ὁμοίως δὲ καὶ τῆς πρακτικῆς οὐκ ἐν τῷ πρακτῷ μᾶλλον δ᾽ ἐν τοῖς [15] πράττουσιν ἡ κίνησις. ἡ δὲ τοῦ φυσικοῦ περὶ τὰ ἔχοντ᾽ ἐν ἑαυτοῖς κινήσεως ἀρχήν ἐστιν. ὅτι μὲν τοίνυν οὔτε πρακτικὴν οὔτε ποιητικὴν ἀλλὰ θεωρητικὴν ἀναγκαῖον εἶναι τὴν φυσικὴν ἐπιστήμην, δῆλον ἐκ τούτων (εἰς ἓν γάρ τι τούτων τῶν γενῶν ἀνάγκη πίπτειν):	958. Now since there is a science of nature, it is evident that it must differ from both the practical and the productive sciences. For in the case of a productive science the source of motion is in the maker and not in the thing made, and it is either the art or some kind of potency. And similarly in the case of a practical science the motion is not in the thing done but rather in the agents. But the science of the philosopher of nature is concerned with things which have a source of motion in themselves. It is evident from these considerations, then, that the philosophy of nature must be neither practical nor productive but speculative; for it must fall in one of these classes.
ἐπεὶ δὲ τὸ τί ἐστιν ἀναγκαῖον [20] ἑκάστῃ πως τῶν ἐπιστημῶν εἰδέναι καὶ τούτῳ χρῆσθαι ἀρχῇ, δεῖ μὴ λανθάνειν πῶς ὁριστέον τῷ φυσικῷ καὶ πῶς ὁ τῆς οὐσίας λόγος ληπτέος, πότερον ὡς τὸ σιμὸν ἢ μᾶλλον ὡς τὸ κοῖλον. τούτων γὰρ ὁ μὲν τοῦ σιμοῦ λόγος μετὰ τῆς ὕλης λέγεται τῆς τοῦ πράγματος, ὁ δὲ τοῦ κοίλου χωρὶς τῆς ὕλης: [25] ἡ γὰρ σιμότης ἐν ῥινὶ γίγνεται, διὸ καὶ ὁ λόγος αὐτῆς μετὰ ταύτης θεωρεῖται: τὸ σιμὸν γάρ ἐστι ῥὶς κοίλη. φανερὸν οὖν ὅτι καὶ σαρκὸς καὶ ὀφθαλμοῦ καὶ τῶν λοιπῶν μορίων μετὰ τῆς ὕλης ἀεὶ τὸν λόγον ἀποδοτέον.	959. And since it is necessary that each one of the sciences have some knowledge of the quiddity and must use it as a starting point, we must not fail to consider how the philosophy of nature should define things, and how it should consider the intelligible structure of the substance: whether in the same way as the term snub or rather as the term concave. For of these the notion of snub includes the matter of the object, but that of concave is expressed without matter. For snubness comes into being in a nose, and for this reason its intelligible structure includes matter; for snub is a concave nose. It is evident, then, that the intelligible structure of flesh and of eye and of the other parts of the body must always be given along with matter.
ἐπεὶ δ᾽ ἔστι τις ἐπιστήμη τοῦ ὄντος ᾗ ὂν καὶ χωριστόν, σκεπτέον πότερόν ποτε τῇ φυσικῆ [30] ι τὴν αὐτὴν θετέον εἶναι ταύτην ἢ μᾶλλον ἑτέραν. ἡ μὲν οὖν φυσικὴ περὶ τὰ κινήσεως ἔχοντ᾽ ἀρχὴν ἐν αὑτοῖς ἐστίν, ἡ δὲ μαθηματικὴ θεωρητικὴ μὲν καὶ περὶ μένοντά τις αὕτη, ἀλλ᾽ οὐ χωριστά. περὶ τὸ χωριστὸν ἄρα ὂν καὶ ἀκίνητον ἑτέρα τούτων ἀμφοτέρων τῶν ἐπιστημῶν ἔστι τις, εἴπερ [35] ὑπάρχει τις οὐσία τοιαύτη, λέγω δὲ χωριστὴ καὶ ἀκίνητος, ὅπερ πειρασόμεθα δεικνύναι. καὶ εἴπερ ἔστι τις τοιαύτη φύσις ἐν τοῖς οὖσιν, ἐνταῦθ᾽ ἂν εἴη που καὶ τὸ θεῖον, καὶ αὕτη ἂν εἴη πρώτη καὶ κυριωτάτη ἀρχή. [1064β] [1] δῆλον τοίνυν ὅτι τρία γένη τῶν θεωρητικῶν ἐπιστημῶν ἔστι, φυσική, μαθηματική, θεολογική.	960. And since there is a science of being as being and as separable, one must consider whether this science should be held to be the same as the philosophy of nature or rather a science distinct from it. The philosophy of nature deals with things which have a principle of motion in themselves, and mathematics is speculative and is concerned with things which are permanent but are not separable. Therefore there is a science distinct from both of these, which treats of what is separable and immovable; that is to say, if there is some such substance, and I mean one which is separable and immovable, as we shall attempt to prove (1055-76). And if there is some such nature among existing things, this will exist somewhere and will be divine, and it will be the primary and highest principle. It is evident, then, that there are three classes of speculative science: the philosophy of nature, mathematics and theology.
βέλτιστον μὲν οὖν τὸ τῶν θεωρητικῶν γένος, τούτων δ᾽ αὐτῶν ἡ τελευταία λεχθεῖσα: περὶ τὸ τιμιώτατον [5] γάρ ἐστι τῶν ὄντων, βελτίων δὲ καὶ χείρων ἑκάστη λέγεται κατὰ τὸ οἰκεῖον ἐπιστητόν.	961. The class of speculative sciences, then, is the highest, and of these the last mentioned is highest of all. For it is concerned with the noblest of beings, and each science is said to be higher or lower by reason of its proper object.
ἀπορήσειε δ᾽ ἄν τις πότερόν ποτε τὴν τοῦ ὄντος ᾗ ὂν ἐπιστήμην καθόλου δεῖ θεῖναι ἢ οὔ. τῶν μὲν γὰρ μαθηματικῶν ἑκάστη περὶ ἕν τι γένος ἀφωρισμένον ἐστίν, ἡ δὲ καθόλου κοινὴ περὶ πάντων. εἰ μὲν οὖν [10] αἱ φυσικαὶ οὐσίαι πρῶται τῶν ὄντων εἰσί, κἂν ἡ φυσικὴ πρώτη τῶν ἐπιστημῶν εἴη: εἰ δ᾽ ἔστιν ἑτέρα φύσις καὶ οὐσία χωριστὴ καὶ ἀκίνητος, ἑτέραν ἀνάγκη καὶ τὴν ἐπιστήμην αὐτῆς εἶναι καὶ προτέραν τῆς φυσικῆς καὶ καθόλου τῷ προτέραν. [15]	962. However, one might raise the question whether the science of being as being is universal or not. For each of the mathematical sciences deals with some one determinate class of things, but a universal science is common to all. If, then, natural substances are the primary beings, the philosophy of nature must be the primary science. But if there is another nature and substance which is separable and immovable, the science which treats of this must be different from and prior to the philosophy of nature, and must be universal because it is prior (902).

ARISTOTLE’S TEXT Chapter 8: 1064b 15-1065b 4
ἐπεὶ δὲ τὸ ἁπλῶς ὂν κατὰ πλείους λέγεται τρόπους, ὧν εἷς ἐστὶν ὁ κατὰ συμβεβηκὸς εἶναι λεγόμενος, σκεπτέον πρῶτον περὶ τοῦ οὕτως ὄντος.	963. Since the term being in its unqualified sense has many meanings, and one of these is the accidental, it is first necessary to consider this sense of being.
ὅτι μὲν οὖν οὐδεμία τῶν παραδεδομένων ἐπιστημῶν πραγματεύεται περὶ τὸ συμβεβηκός, δῆλον (οὔτε γὰρ οἰκοδομικὴ σκοπεῖ τὸ συμβησόμενον τοῖς τῇ [20] οἰκίᾳ χρησομένοις, οἷον εἰ λυπηρῶς ἢ τοὐναντίον οἰκήσουσιν, οὔθ᾽ ὑφαντικὴ οὔτε σκυτοτομικὴ οὔτε ὀψοποιική, τὸ δὲ καθ᾽ αὑτὴν ἴδιον ἑκάστη τούτων σκοπεῖ τῶν ἐπιστημῶν μόνον, τοῦτο δ᾽ ἐστὶ τὸ οἰκεῖον τέλος:	964. Now it is evident that none of the traditional sciences are concerned with the accidental. The science of building does not consider what will happen to the occupants of a house, for example, whether they will dwell there unhappily or in the opposite way; nor is the art of weaving or of shoemaking or of cooking concerned with it. But each of these sciences considers only what is proper to itself, and this is its particular end.
[οὐδὲ μουσικὸν καὶ γραμματικόν,] οὐδὲ τὸν ὄντα μουσικὸν ὅτι γενόμενος γραμματικὸς ἅμα ἔσται τὰ [25] ἀμφότερα, πρότερον οὐκ ὤν, ὃ δὲ μὴ ἀεὶ ὂν ἔστιν, ἐγένετο τοῦτο, ὥσθ᾽ ἅμα μουσικὸς ἐγένετο καὶ γραμματικός, τοῦτο δὲ οὐδεμία ζητεῖ τῶν ὁμολογουμένως οὐσῶν ἐπιστημῶν πλὴν ἡ σοφιστική: περὶ τὸ συμβεβηκὸς γὰρ αὕτη μόνη πραγματεύεται, διὸ Πλάτων οὐ κακῶς εἴρηκε φήσας τὸν σοφιστὴν [30] περὶ τὸ μὴ ὂν διατρίβειν):	965. Further, no science considers a man insofar as he is a musician or also a grammarian; nor does any science consider the quibble that “when one who is a musician has become a grammarian he will be both at the same time, although he was not so before; but that which is and has not always been, must have come to be; and therefore he must have at the same time become both a musician and a grammarian.” None of the known sciences are concerned with this except sophistry, and thus Plato was not wrong in saying that sophistry is concerned with non-being.
ὅτι δ᾽ οὐδ᾽ ἐνδεχόμενόν ἐστιν εἶναι τοῦ συμβεβηκότος ἐπιστήμην, φανερὸν ἔσται πειραθεῖσιν ἰδεῖν τί ποτ᾽ ἐστὶ τὸ συμβεβηκός. πᾶν δή φαμεν εἶναι τὸ μὲν ἀεὶ καὶ ἐξ ἀνάγκης (ἀνάγκης δ᾽ οὐ τῆς κατὰ τὸ βίαιον λεγομένης ἀλλ᾽ ᾗ χρώμεθα ἐν τοῖς κατὰ τὰς ἀποδείξεις), [35] τὸ δ᾽ ὡς ἐπὶ τὸ πολύ, τὸ δ᾽ οὔθ᾽ ὡς ἐπὶ τὸ πολὺ οὔτ᾽ ἀεὶ καὶ ἐξ ἀνάγκης ἀλλ᾽ ὅπως ἔτυχεν: οἷον ἐπὶ κυνὶ γένοιτ᾽ ἂν ψῦχος, ἀλλὰ τοῦτ᾽ οὔτ᾽ [ὡς] ἀεὶ καὶ ἐξ ἀνάγκης οὔθ᾽ ὡς ἐπὶ τὸ πολὺ γίγνεται, συμβαίη δέ ποτ᾽ ἄν. [1065α] [1] ἔστι δὴ τὸ συμβεβηκὸς ὃ γίγνεται μέν, οὐκ ἀεὶ δ᾽ οὐδ᾽ ἐξ ἀνάγκης οὐδ᾽ ὡς ἐπὶ τὸ πολύ. τί μὲν οὖν ἐστὶ τὸ συμβεβηκός, εἴρηται, διότι δ᾽ οὐκ ἔστιν ἐπιστήμη τοῦ τοιούτου, δῆλον: ἐπιστήμη μὲν γὰρ πᾶσα τοῦ [5] ἀεὶ ὄντος ἢ ὡς ἐπὶ τὸ πολύ, τὸ δὲ συμβεβηκὸς ἐν οὐδετέρῳ τούτων ἐστίν.	966. That it is impossible to have a science of the accidental will be evident to those who are trying to learn what the accidental is. Accordingly, we say of all things that some are always and of necessity (not necessity in the sense of what is done by force but with the meaning used in matters of demonstration); others are for the most part; and others are neither for the most part nor always and of necessity, but are such as occur by chance. For example, there might be cold weather during the dog days, but this occurs neither always and of necessity nor for the most part, though it might happen sometimes. Hence the accidental is what occurs, but neither always and of necessity nor for the most part. What the accidental is, then, has been stated; and it is evident that there is no science of it. For every science deals with what is always or for the most part, but the accidental belongs to neither of these.
ὅτι δὲ τοῦ κατὰ συμβεβηκὸς ὄντος οὐκ εἰσὶν αἰτίαι καὶ ἀρχαὶ τοιαῦται οἷαίπερ τοῦ καθ᾽ αὑτὸ ὄντος, δῆλον: ἔσται γὰρ ἅπαντ᾽ ἐξ ἀνάγκης. εἰ γὰρ τόδε μὲν ἔστι τοῦδε ὄντος τόδε δὲ τοῦδε, τοῦτο δὲ μὴ ὅπως ἔτυχεν ἀλλ᾽ ἐξ [10] ἀνάγκης, ἐξ ἀνάγκης ἔσται καὶ οὗ τοῦτ᾽ ἦν αἴτιον ἕως τοῦ τελευταίου λεγομένου αἰτιατοῦ (τοῦτο δ᾽ ἦν κατὰ συμβεβηκός), ὥστ᾽ ἐξ ἀνάγκης ἅπαντ᾽ ἔσται, καὶ τὸ ὁποτέρως ἔτυχε καὶ τὸ ἐνδέχεσθαι καὶ γενέσθαι καὶ μὴ παντελῶς ἐκ τῶν γιγνομένων ἀναιρεῖται. κἂν μὴ ὂν δὲ ἀλλὰ γιγνόμενον τὸ [15] αἴτιον ὑποτεθῇ, ταὐτὰ συμβήσεται: πᾶν γὰρ ἐξ ἀνάγκης γενήσεται. ἡ γὰρ αὔριον ἔκλειψις γενήσεται ἂν τόδε γένηται, τοῦτο δ᾽ ἐὰν ἕτερόν τι, καὶ τοῦτ᾽ ἂν ἄλλο: καὶ τοῦτον δὴ τὸν τρόπον ἀπὸ πεπερασμένου χρόνου τοῦ ἀπὸ τοῦ νῦν μέχρι αὔριον ἀφαιρουμένου χρόνου ἥξει ποτὲ εἰς τὸ ὑπάρχον, ὥστ᾽ [20] ἐπεὶ τοῦτ᾽ ἔστιν, ἅπαντ᾽ ἐξ ἀνάγκης τὰ μετὰ τοῦτο γενήσεται, ὥστε πάντα ἐξ ἀνάγκης γίγνεσθαι.	967. It is also evident that there are no causes and principles of accidental being such as there are of essential being; for if there were, everything would be of necessity. For if one thing exists when another does, and this again when something else does, and if this last thing is not a matter of chance but exists of necessity, then that of which it was the cause will also exist of necessity, and so on right down to the last thing said to be caused. But this was assumed to be accidental. Hence everything will be of necessity, and the possibility of anything happening by chance or being contingent and of coming to be or not coming to be will be entirely removed from the sphere of things which are generated. And if the cause is assumed not to exist but to be something which is coming to be, the same results will follow; for everything will come to be of necessity. For tomorrow’s eclipse will occur if something else does, and this again if some other thing occurs, and the latter if still another thing occurs. And if time is subtracted in this way from the limited time between the present and tomorrow, we shall at some point reach something which exists now. Therefore, since this exists, everything which comes after it will occur of necessity, so that everything will occur of necessity.
τὸ δ᾽ ὡς ἀληθὲς ὂν καὶ κατὰ συμβεβηκὸς τὸ μέν ἐστιν ἐν συμπλοκῇ διανοίας καὶ πάθος ἐν ταύτῃ (διὸ περὶ μὲν τὸ οὕτως ὂν οὐ ζητοῦνται αἱ ἀρχαί, περὶ δὲ τὸ ἔξω ὂν καὶ χωριστόν): τὸ δ᾽ οὐκ [25] ἀναγκαῖον ἀλλ᾽ ἀόριστον, λέγω δὲ τὸ κατὰ συμβεβηκός: τοῦ τοιούτου δ᾽ ἄτακτα καὶ ἄπειρα τὰ αἴτια.	968. Regarding being in the sense of what is true and accidental being, the former depends upon the combination which the mind makes and is a modification of it. It is for this reason that it is not the principles of this kind of being that are sought but of that which exists outside the mind and is separable; and the latter kind of being is not necessary but indeterminate (and by this I mean the accidental); and the causes. of this kind of being are indeterminate and unordered (543-59).
τὸ δὲ ἕνεκά του ἐν τοῖς φύσει γιγνομένοις ἢ ἀπὸ διανοίας ἐστίν, τύχη δέ ἐστιν ὅταν τι τούτων γένηται κατὰ συμβεβηκός: ὥσπερ γὰρ καὶ ὄν ἐστι τὸ μὲν καθ᾽ αὑτὸ τὸ δὲ κατὰ συμβεβηκός, οὕτω [30] καὶ αἴτιον. ἡ τύχη δ᾽ αἰτία κατὰ συμβεβηκὸς ἐν τοῖς κατὰ προαίρεσιν τῶν ἕνεκά του γιγνομένοις,	969. And that for the sake of which something exists is found both in things which come to be by nature and in those which are a result of mind. It is luck when one of these comes about accidentally; for just as a being is either essential or accidental, so also is a cause. And luck is an accidental cause of those things which come to be for some end as a result of choice.
διὸ περὶ ταὐτὰ τύχη καὶ διάνοια: προαίρεσις γὰρ οὐ χωρὶς διανοίας.	970. And for this reason both luck and mind are concerned with the same thing; for there is no choice without mind.
τὰ δ᾽ αἴτια ἀόριστα ἀφ᾽ ὧν ἂν γένοιτο τὰ ἀπὸ τύχης, διὸ ἄδηλος ἀνθρωπίνῳ λογισμῷ καὶ αἴτιον κατὰ συμβεβηκός, ἁπλῶς δ᾽ [35] οὐδενός.	971. However, the causes from which some lucky result comes to be are indeterminate; and for this reason luck is uncertain for human knowledge and is an accidental cause, although in an absolute sense it is a cause of nothing.
ἀγαθὴ δὲ τύχη καὶ κακὴ ὅταν ἀγαθὸν ἢ φαῦλον ἀποβῇ: εὐτυχία δὲ καὶ δυστυχία περὶ μέγεθος τούτων.	972. There is good or bad luck when the result is good or bad, and prosperity or misfortune when this occurs on a large scale.
[1065β] [1] ἐπεὶ δ᾽ οὐθὲν κατὰ συμβεβηκὸς πρότερον τῶν καθ᾽ αὑτό, οὐδ᾽ ἄρ᾽ αἴτια: εἰ ἄρα τύχη ἢ τὸ αὐτόματον αἴτιον τοῦ οὐρανοῦ, πρότερον νοῦς αἴτιος καὶ φύσις. [5]	973. And since nothing accidental is prior to things which are essential, neither are accidental causes prior. Therefore, if luck or chance is the cause of the heavens, mind and nature are prior causes.

ARISTOTLE’S TEXT Chapter 9: 1065b 5-1066a 34 1
ἔστι δὲ τὸ μὲν ἐνεργείᾳ μόνον τὸ δὲ δυνάμει τὸ δὲ δυνάμει καὶ ἐνεργείᾳ, τὸ μὲν ὂν τὸ δὲ ποσὸν τὸ δὲ τῶν λοιπῶν. οὐκ ἔστι δέ τις κίνησις παρὰ τὰ πράγματα: μεταβάλλει γὰρ ἀεὶ κατὰ τὰς τοῦ ὄντος κατηγορίας, κοινὸν δ᾽ ἐπὶ τούτων οὐδέν ἐστιν ὃ οὐδ᾽ ἐν μιᾷ κατηγορίᾳ. ἕκαστον δὲ διχῶς [10] ὑπάρχει πᾶσιν (οἷον τὸ τόδε—τὸ μὲν γὰρ μορφὴ αὐτοῦ τὸ δὲ στέρησις—καὶ κατὰ τὸ ποιὸν τὸ μὲν λευκὸν τὸ δὲ μέλαν, καὶ κατὰ τὸ ποσὸν τὸ μὲν τέλειον τὸ δὲ ἀτελές, καὶ κατὰ φορὰν τὸ μὲν ἄνω τὸ δὲ κάτω, ἢ κοῦφον καὶ βαρύ): ὥστε κινήσεως καὶ μεταβολῆς τοσαῦτ᾽ εἴδη ὅσα τοῦ ὄντος.	974. One thing is actual only, another potential, and others both actual and potential; and of these one is a being, another a quantity, and another one of the other categories. Motion is not something apart from things themselves; for a thing is always changed according to the categories of being, and there is nothing that is common to these and in no one category. And each belongs to all its members in a twofold way, for example, this particular thing; for sometimes this is the form of a thing and sometimes its privation. And with regard to quality, one thing is white and another black; and with regard to quantity, one is perfect and another imperfect; and with regard to motion in space, one thing tends upwards and another downwards, or one is light and another heavy. Hence there are as many kinds of motion and change as there are of being.
διῃρημένου [15] δὲ καθ᾽ ἕκαστον γένος τοῦ μὲν δυνάμει τοῦ δ᾽ ἐντελεχείᾳ, τὴν τοῦ δυνάμει ᾗ τοιοῦτόν ἐστιν ἐνέργειαν λέγω κίνησιν.	975. Now since each class of things is divided by potentiality and actuality, I call motion the actualization of what is potential as such.
ὅτι δ᾽ ἀληθῆ λέγομεν, ἐνθένδε δῆλον: ὅταν γὰρ τὸ οἰκοδομητόν, ᾗ τοιοῦτον αὐτὸ λέγομεν εἶναι, ἐνεργείᾳ ᾖ, οἰκοδομεῖται, καὶ ἔστι τοῦτο οἰκοδόμησις: ὁμοίως μάθησις, ἰάτρευσις, βάδισις, [20] ἅλσις, γήρανσις, ἅδρυνσις. συμβαίνει δὲ κινεῖσθαι ὅταν ἡ ἐντελέχεια ᾖ αὐτή, καὶ οὔτε πρότερον οὔθ᾽ ὕστερον. ἡ δὴ τοῦ δυνάμει ὄντος, ὅταν ἐντελεχείᾳ ὂν ἐνεργῇ, οὐχ ᾗ αὐτὸ ἀλλ᾽ ᾗ κινητόν, κίνησίς ἐστιν.	976. That our account is true becomes evident as follows: when the buildable in the sense in which we call it such actually exists, it is being built; and this is the process of building. The same is true of learning, walking, healing, dancing and bereaving. And motion occurs when something is in this very act, and neither before nor after. Motion, then, belongs to what is potential when it is actual and is engaged in activity, not inasmuch as it is itself, but inasmuch as it is movable.
λέγω δὲ τὸ ᾗ ὧδε. ἔστι γὰρ ὁ χαλκὸς δυνάμει ἀνδριάς: ἀλλ᾽ ὅμως οὐχ ἡ τοῦ [25] χαλκοῦ ἐντελέχεια, ᾗ χαλκός, κίνησίς ἐστιν. οὐ γὰρ ταὐτὸν χαλκῷ εἶναι καὶ δυνάμει τινί, ἐπεὶ εἰ ταὐτὸν ἦν ἁπλῶς κατὰ τὸν λόγον, ἦν ἂν ἡ τοῦ χαλκοῦ ἐντελέχεια κίνησίς τις. οὐκ ἔστι δὲ ταὐτό (δῆλον δ᾽ ἐπὶ τῶν ἐναντίων: τὸ μὲν γὰρ δύνασθαι ὑγιαίνειν καὶ δύνασθαι κάμνειν οὐ ταὐτόν—καὶ γὰρ [30] ἂν τὸ ὑγιαίνειν καὶ τὸ κάμνειν ταὐτὸν ἦν—τὸ δ᾽ ὑποκείμενον καὶ ὑγιαῖνον καὶ νοσοῦν, εἴθ᾽ ὑγρότης εἴθ᾽ αἷμα, ταὐτὸ καὶ ἕν). ἐπεὶ δὲ οὐ τὸ αὐτό, ὥσπερ οὐδὲ χρῶμα ταὐτὸν καὶ ὁρατόν, ἡ τοῦ δυνατοῦ καὶ ᾗ δυνατὸν ἐντελέχεια κίνησίς ἐστιν.	977. And by the phrase inasmuch as I mean this: bronze is potentially a statue, but the actuality of bronze inasmuch as it is bronze is not motion; for to be bronze and to be some potentiality are not the same. If they were absolutely the same in meaning, the actuality of bronze would be a kind of motion; but they are not the same. This is evident in the case of contraries; for the potentiality of being healed and that of being ill are not the same, because being). healed would then be the same as being ill. But it is the subject which is both healed and ill, whether it be moisture or blood, that is one and the same. And since they are not the same, just as color and the visible object are not the same, it is the actualization of what is potential insofar as it is potential that is motion.
[34] ὅτι μὲν οὖν ἐστιν αὕτη, καὶ ὅτι συμβαίνει τότε κινεῖσθαι ὅταν [35] ἡ ἐντελέχεια ᾖ αὐτή, καὶ οὔτε πρότερον οὔθ᾽ ὕστερον, δῆλον (ἐνδέχεται γὰρ ἕκαστον ὁτὲ μὲν ἐνεργεῖν ὁτὲ δὲ μή, [1066α] [1] οἷον τὸ οἰκοδομητὸν ᾗ οἰκοδομητόν, καὶ ἡ τοῦ οἰκοδομητοῦ ἐνέργεια ᾗ οἰκοδομητὸν οἰκοδόμησίς ἐστιν: ἢ γὰρ τοῦτό ἐστιν, ἡ οἰκοδόμησις, ἡ ἐνέργεια, ἢ οἰκία: ἀλλ᾽ ὅταν οἰκία ᾖ, οὐκέτι οἰκοδομητόν, [5] οἰκοδομεῖται δὲ τὸ οἰκοδομητόν: ἀνάγκη ἄρα οἰκοδόμησιν τὴν ἐνέργειαν εἶναι, ἡ δ᾽ οἰκοδόμησις κίνησίς τις, ὁ δ᾽ αὐτὸς λόγος καὶ ἐπὶ τῶν ἄλλων κινήσεων):	978. That motion is this, and that a thing is being moved when it is actual in this way, and neither before nor after, is evident. For each thing is capable of being at one time actual and at another not, for example, the buildable as buildable; and the actualization of the buildable as buildable is the process of building. For the actuality is either the process of building or this particular house. But when the house exists, it will no longer be buildable; but what is being built is what is buildable. Therefore the process of building must be its actualization; and the process of building is a kind of motion. The same reasoning also applies to other motions.
ὅτι δὲ καλῶς εἴρηται, δῆλον ἐξ ὧν οἱ ἄλλοι λέγουσι περὶ αὐτῆς, καὶ ἐκ τοῦ μὴ ῥᾴδιον εἶναι διορίσαι ἄλλως αὐτήν. οὔτε γὰρ ἐν ἄλλῳ [10] τις γένει δύναιτ᾽ ἂν θεῖναι αὐτήν:	979. That this account is true is evident from what others say about motion, and because it is not easy to define it otherwise. For one cannot place it in another class.
δῆλον δ᾽ ἐξ ὧν λέγουσιν: οἱ μὲν γὰρ ἑτερότητα καὶ ἀνισότητα καὶ τὸ μὴ ὄν,	980. This is evident from what some say; for they call it otherness and inequality and non-being.
ὧν οὐδὲν ἀνάγκη κινεῖσθαι, ἀλλ᾽ οὐδ᾽ ἡ μεταβολὴ οὔτ᾽ εἰς ταῦτα οὔτ᾽ ἐκ τούτων μᾶλλον ἢ τῶν ἀντικειμένων.	981. However, no one of these is necessarily moved, and change is not to these or from these anymore than to or from their opposites.
αἴτιον δὲ τοῦ εἰς ταῦτα τιθέναι ὅτι ἀόριστόν τι δοκεῖ εἶναι ἡ κίνησις, τῆς [15] δ᾽ ἑτέρας συστοιχίας αἱ ἀρχαὶ διὰ τὸ στερητικαὶ εἶναι ἀόριστοι: οὔτε γὰρ τόδε οὔτε τοιόνδε οὐδεμία αὐτῶν οὔτε τῶν λοιπῶν κατηγοριῶν.	982. The reason for putting motion in this class is that it seems to be something indefinite; and the principles in one of the columns of opposites (60) are indefinite because they are privative, for no one of them is either a this or such or any of the other categories.
τοῦ δὲ δοκεῖν ἀόριστον εἶναι τὴν κίνησιν αἴτιον ὅτι οὔτ᾽ εἰς δύναμιν τῶν ὄντων οὔτ᾽ εἰς ἐνέργειαν ἔστι θεῖναι αὐτήν: οὔτε γὰρ τὸ δυνατὸν ποσὸν εἶναι κινεῖται ἐξ [20] ἀνάγκης, οὔτε τὸ ἐνεργείᾳ ποσόν, ἥ τε κίνησις ἐνέργεια μὲν εἶναι δοκεῖ τις, ἀτελὴς δέ: αἴτιον δ᾽ ὅτι ἀτελὲς τὸ δυνατὸν οὗ ἐστὶν ἐνέργεια. καὶ διὰ τοῦτο χαλεπὸν αὐτὴν λαβεῖν τί ἐστιν: ἢ γὰρ εἰς στέρησιν ἀνάγκη θεῖναι ἢ εἰς δύναμιν ἢ εἰς ἐνέργειαν ἁπλῆν, τούτων δ᾽ οὐδὲν φαίνεται ἐνδεχόμενον, ὥστε [25] λείπεται τὸ λεχθὲν εἶναι, καὶ ἐνέργειαν καὶ [μὴ] ἐνέργειαν τὴν εἰρημένην, ἰδεῖν μὲν χαλεπὴν ἐνδεχομένην δ᾽ εἶναι.	983. The reason why motion seems to be indefinite is that it cannot be identified either with the potentiality or with the actuality of existing things; for neither what is capable of having a certain quantity nor what actually has it is necessarily being moved. And motion seems to be an actuality, but an incomplete one; and the reason for this is that the potentiality of which it is the actuality is incomplete. Hence it is difficult to grasp what motion is; for it must be put under privation or under potentiality or under simple actuality; but none of these appear to be possible. It remains, then, that it must be as we have said, i.e., both an actuality and a non-actuality as explained, which is difficult to see but capable of existing.’
καὶ ὅτι ἐστὶν ἡ κίνησις ἐν τῷ κινητῷ, δῆλον: ἐντελέχεια γάρ ἐστι τούτου ὑπὸ τοῦ κινητικοῦ.	984. That motion belongs to the thing moved is evident; for it is the actualization of the thing moved by what is capable of causing motion.
καὶ ἡ τοῦ κινητικοῦ ἐνέργεια οὐκ ἄλλη ἐστίν. δεῖ μὲν γὰρ εἶναι ἐντελέχειαν ἀμφοῖν:	985. And the actuality of what is capable of causing motion is no other than this; for it must be the actuality of both.
κινητικὸν [30] μὲν γάρ ἐστι τῷ δύνασθαι, κινοῦν δὲ τῷ ἐνεργεῖν,	986. And a thing is capable of causing motion because of its power, but it is a mover because of its activity.
ἀλλ᾽ ἔστιν ἐνεργητικὸν τοῦ κινητοῦ, ὥσθ᾽ ὁμοίως μία ἡ ἀμφοῖν ἐνέργεια	987. But it is on the thing moved that it is capable of acting. Thus the actuality of both alike is one.
ὥσπερ τὸ αὐτὸ διάστημα ἓν πρὸς δύο καὶ δύο πρὸς ἕν, καὶ τὸ ἄναντες καὶ τὸ κάταντες, ἀλλὰ τὸ εἶναι οὐχ ἕν: ὁμοίως δὲ καὶ ἐπὶ τοῦ κινοῦντος καὶ κινουμένου. [35]	988. And it is one just as the distance from one to two and that from two to one are the same, and just as what goes up and what comes down are the same, although their being is not one. The same applies in the case of the mover and the thing moved.

ARISTOTLE’S TEXT Chapter 10: 1066a 35-1067a 371
τὸ δ᾽ ἄπειρον ἢ τὸ ἀδύνατον διελθεῖν τῷ μὴ πεφυκέναι διιέναι, καθάπερ ἡ φωνὴ ἀόρατος, ἢ τὸ διέξοδον ἔχον ἀτελεύτητον, ἢ ὃ μόλις, ἢ ὃ πεφυκὸς ἔχειν μὴ ἔχει διέξοδον ἢ πέρας:	989. The infinite is either what cannot be spanned because it is not naturally fitted to be spanned (just as the spoken word is invisible); or what is imperfectly spanned; or what is spanned with difficulty; or what is not actually spanned, although it admits of being spanned or of having a terminus.
ἔτι προσθέσει ἢ ἀφαιρέσει ἢ ἄμφω.	990. Further, a thing may be infinite either by addition or by subtraction or by both.
[1066β] [1] χωριστὸν μὲν δὴ αὐτό τι ὂν οὐχ οἷόν τ᾽ εἶναι: εἰ γὰρ μήτε μέγεθος μήτε πλῆθος, οὐσία δ᾽ αὐτὸ τὸ ἄπειρον καὶ μὴ συμβεβηκός, ἀδιαίρετον ἔσται (τὸ γὰρ διαιρετὸν ἢ μέγεθος ἢ πλῆθος), εἰ [5] δὲ ἀδιαίρετον, οὐκ ἄπειρον, εἰ μὴ καθάπερ ἡ φωνὴ ἀόρατος: ἀλλ᾽ οὐχ οὕτω λέγουσιν οὐδ᾽ ἡμεῖς ζητοῦμεν, ἀλλ᾽ ὡς ἀδιέξοδον.	991. That the infinite should be a separate entity and be perceptible is impossible. For if it is neither a continuous quantity nor a plurality, and is a substance and not an accident, it will be indivisible; for what is divisible is either a continuous quantity or a plurality. But if it is indivisible, it is not infinite, except in the sense in which the spoken word is invisible. But people do not use the term in this sense, nor is this the sense of the infinite which we are investigating, but the infinite in the sense of what cannot be spanned.
ἔτι πῶς ἐνδέχεται καθ᾽ αὑτὸ εἶναι ἄπειρον, εἰ μὴ καὶ ἀριθμὸς καὶ μέγεθος, ὧν πάθος τὸ ἄπειρον;	992. Further, how can the infinite exist of itself if number and continuous quantity, of which the infinite is an attribute, do not exist of themselves?
ἔτι εἰ κατὰ συμβεβηκός, οὐκ ἂν εἴη στοιχεῖον τῶν ὄντων [10] ᾗ ἄπειρον, ὥσπερ οὐδὲ τὸ ἀόρατον τῆς διαλέκτου, καίτοι ἡ φωνὴ ἀόρατος. καὶ ὅτι οὐκ ἔστιν ἐνεργείᾳ εἶναι τὸ ἄπειρον, δῆλον. ἔσται γὰρ ὁτιοῦν αὐτοῦ ἄπειρον μέρος τὸ λαμβανόμενον (τὸ γὰρ ἀπείρῳ εἶναι καὶ ἄπειρον τὸ αὐτό, εἴπερ οὐσία τὸ ἄπειρον καὶ μὴ καθ᾽ ὑποκειμένου), ὥστε ἢ ἀδιαίρετον, ἢ εἰς [15] ἄπειρα διαιρετόν, εἰ μεριστόν: πολλὰ δ᾽ εἶναι τὸ αὐτὸ ἀδύνατον ἄπειρα (ὥσπερ γὰρ ἀέρος ἀὴρ μέρος, οὕτως ἄπειρον ἀπείρου, εἰ ἔστιν οὐσία καὶ ἀρχή): ἀμέριστον ἄρα καὶ ἀδιαίρετον. ἀλλὰ ἀδύνατον τὸ ἐντελεχείᾳ ὂν ἄπειρον (ποσὸν γὰρ εἶναι ἀνάγκη): κατὰ συμβεβηκὸς ἄρα ὑπάρχει. ἀλλ᾽ εἰ [20] οὕτως, εἴρηται ὅτι οὐκ ἐνδέχεται εἶναι ἀρχήν, ἀλλ᾽ ἐκεῖνο ᾧ συμβέβηκε, τὸν ἀέρα ἢ τὸ ἄρτιον. αὕτη μὲν οὖν ἡ ζήτησις καθόλου,	993. Again, if the infinite is an accident, it cannot, inasmuch as it is infinite, be an element of existing things, just as the invisible is not an element of speech although the spoken word is invisible.’ It is also evident that the infinite cannot be actual; for any part of it which might be taken would be infinite, since infinity and the infinite are the same if the infinite is a substance and is not predicated of a subject. Hence it is either indivisible, or if it is divisible, the parts into which it is divided are infinite in number. But it is impossible that the same thing should be many infinites; for, just as a part of air is air, so too a part of the infinite must be infinite if the infinite is a substance and principle. Therefore it cannot be divided into parts, and so is indivisible. But this cannot apply to the actually infinite, for it must be a quantity. Hence it is an accidental attribute. But if this is so, then, as we have said, it cannot be it that is a principle, but that of which it is an accident, for example, air or the even This investigation, then, is universal.
ὅτι δ᾽ ἐν τοῖς αἰσθητοῖς οὐκ ἔστιν, ἐνθένδε δῆλον: εἰ γὰρ σώματος λόγος τὸ ἐπιπέδοις ὡρισμένον, οὐκ εἴη ἂν ἄπειρον σῶμα οὔτ᾽ αἰσθητὸν οὔτε νοητόν,	994. That the infinite does not exist in sensible things is made clear as follows: if it is the nature of a body to be bounded by surfaces, then no body, whether it is perceptible or intelligible, can be infinite.
οὐδ᾽ ἀριθμὸς ὡς [25] κεχωρισμένος καὶ ἄπειρος: ἀριθμητὸν γὰρ ὁ ἀριθμὸς ἢ τὸ ἔχον ἀριθμόν.	995. Nor can there be any separate and infinite number; for a number or that which has a number is numerable.
φυσικῶς δὲ ἐκ τῶνδε δῆλον: οὔτε γὰρ σύνθετον οἷόν τ᾽ εἶναι οὔθ᾽ ἁπλοῦν. σύνθετον μὲν γὰρ οὐκ ἔσται σῶμα, εἰ πεπέρανται τῷ πλήθει τὰ στοιχεῖα (δεῖ γὰρ ἰσάζειν τὰ ἐναντία καὶ μὴ εἶναι ἓν αὐτῶν ἄπειρον: εἰ γὰρ ὁτῳοῦν [30] λείπεται ἡ θατέρου σώματος δύναμις, φθαρήσεται ὑπὸ τοῦ ἀπείρου τὸ πεπερασμένον: ἕκαστον δ᾽ ἄπειρον εἶναι ἀδύνατον, σῶμα γάρ ἐστι τὸ πάντῃ ἔχον διάστασιν, ἄπειρον δὲ τὸ ἀπεράντως διεστηκός, ὥστ᾽ εἰ τὸ ἄπειρον σῶμα, πάντῃ ἔσται ἄπειρον):	996. This is evident from the following argument drawn from nature: the infinite can be neither composite nor simple. It cannot be a composite body if the elements are limited in number; for the contraries must be equal, and no one of them must be infinite; for if the active power of one of two elemental bodies is inferior to that of the other, the finite body will be destroyed by the infinite body. And that each should be infinite is impossible, because a body is what is extended in all directions, and the infinite is what is extended without limit; so if the infinite is a body, it must be infinite in all directions.
οὐδὲ ἓν δὲ καὶ ἁπλοῦν ἐνδέχεται τὸ ἄπειρον εἶναι [35] σῶμα, οὔθ᾽ ὡς λέγουσί τινες, παρὰ τὰ στοιχεῖα ἐξ οὗ γεννῶσι ταῦτα (οὐκ ἔστι γὰρ τοιοῦτο σῶμα παρὰ τὰ στοιχεῖα: ἅπαν γάρ, ἐξ οὗ ἐστί, καὶ διαλύεται εἰς τοῦτο, οὐ φαίνεται δὲ τοῦτο παρὰ τὰ ἁπλᾶ σώματα), [1067α] [1] οὐδὲ πῦρ οὐδ᾽ ἄλλο τῶν στοιχείων οὐθέν: χωρὶς γὰρ τοῦ ἄπειρον εἶναί τι αὐτῶν, ἀδύνατον τὸ ἅπαν, κἂν ᾖ πεπερασμένον, ἢ εἶναι ἢ γίγνεσθαι ἕν τι αὐτῶν, ὥσπερ Ἡράκλειτός φησιν ἅπαντα γίγνεσθαί ποτε [5] πῦρ. ὁ δ᾽ αὐτὸς λόγος καὶ ἐπὶ τοῦ ἑνὸς ὃ ποιοῦσι παρὰ τὰ στοιχεῖα οἱ φυσικοί: πᾶν γὰρ μεταβάλλει ἐξ ἐναντίου, οἷον ἐκ θερμοῦ εἰς ψυχρόν.	997. Nor can the infinite be a single simple body: neither, as some say, something apart from the elements, from which they generate these (for there is no such body apart from the elements, because everything can be dissolved into that of which it is composed; but there does not appear to be anything apart from the simple bodies), nor fire, nor any of the other elements. For unless some of them are infinite, the whole, even though it is finite, could not be or become any one of them, as Heraclitus says that all things at one time become fire. The same reasoning also applies to “the one,” which the philosophers of nature posited as an entity over and above the elements (997). For everything is changed from a contrary, for example, from hot to cold.
ἔτι τὸ αἰσθητὸν σῶμα πού, καὶ ὁ αὐτὸς τόπος ὅλου καὶ μορίου, οἷον τῆς γῆς,	998. Again, a sensible body is somewhere, and the place of the whole and that of a part (of the earth, for example) is the same.
ὥστ᾽ εἰ μὲν ὁμοειδές, ἀκίνητον ἔσται ἢ ἀεὶ οἰσθήσεται, τοῦτο δὲ [10] ἀδύνατον (τί γὰρ μᾶλλον κάτω ἢ ἄνω ἢ ὁπουοῦν; οἷον εἰ βῶλος εἴη, ποῦ αὕτη κινήσεται ἢ μενεῖ; ὁ γὰρ τόπος τοῦ συγγενοῦς αὐτῇ σώματος ἄπειρος: καθέξει οὖν τὸν ὅλον τόπον; καὶ πῶς; τίς οὖν ἡ μονὴ καὶ ἡ κίνησις; ἢ πανταχοῦ μενεῖ—οὐ κινηθήσεται ἄρα, ἢ πανταχοῦ κινηθήσεται [15] —οὐκ ἄρα στήσεται):	999. Hence, if the infinite is composed of like parts, it will be immovable or will always be undergoing motion. But this is impossible. For why should it be moved upwards rather than downwards or in some other direction? For example, if it were a clod of earth, where would it move to or where remain at rest? For the place of the body naturally fitted to this will be infinite. Will it then occupy the whole place? And how will it do this? And what then will be its place of rest and of motion? For if it rests everywhere, it will not be in motion. And if it is moved everywhere, it will not be at rest.
εἰ δ᾽ ἀνόμοιον τὸ πᾶν, ἀνόμοιοι καὶ οἱ τόποι, καὶ πρῶτον μὲν οὐχ ἓν τὸ σῶμα τοῦ παντὸς ἀλλ᾽ ἢ τῷ ἅπτεσθαι, εἶτα ἢ πεπερασμένα ταῦτ᾽ ἔσται ἢ ἄπειρα εἴδει. πεπερασμένα μὲν οὖν οὐχ οἷόν τε (ἔσται γὰρ τὰ μὲν ἄπειρα τὰ δ᾽ οὔ, εἰ τὸ πᾶν ἄπειρον, οἷον πῦρ ἢ ὕδωρ: [20] φθορὰ δὲ τὸ τοιοῦτον τοῖς ἐναντίοις): εἰ δ᾽ ἄπειρα καὶ ἁπλᾶ, καὶ οἱ τόποι ἄπειροι καὶ ἔσται ἄπειρα στοιχεῖα: εἰ δὲ τοῦτ᾽ ἀδύνατον καὶ οἱ τόποι πεπερασμένοι, καὶ τὸ πᾶν ἀνάγκη πεπεράνθαι.	1000. And if the whole is composed throughout of unlike parts, their places will also be unlike. And, first, the body of the whole will be one only by contact; and, second, the parts will be either finite or infinite in species. But they cannot be finite, for some would then be infinite and some not (if the whole is infinite), for example, fire or water. But such an infinite element would necessitate the destruction of contrary elements (996). But if the parts are infinite and simple, their places will be infinite, and the elements will be infinite in number. And since this is impossible, their places will be finite and the whole finite.
ὅλως δ᾽ ἀδύνατον ἄπειρον εἶναι σῶμα καὶ τόπον τοῖς σώμασιν, εἰ πᾶν σῶμα αἰσθητὸν ἢ βάρος ἔχει [25] ἢ κουφότητα: ἢ γὰρ ἐπὶ τὸ μέσον ἢ ἄνω οἰσθήσεται, ἀδύνατον δὲ τὸ ἄπειρον ἢ πᾶν ἢ τὸ ἥμισυ ὁποτερονοῦν πεπονθέναι: πῶς γὰρ διελεῖς; ἢ πῶς τοῦ ἀπείρου ἔσται τὸ μὲν κάτω τὸ δ᾽ ἄνω, ἢ ἔσχατον καὶ μέσον;	1001. And in general there cannot be an infinite body and a place for bodies if every sensible body has either heaviness or lightness; for it will tend either to the center or upwards. But the infinite-either the whole or a half of it-is incapable of any of these motions. For how can you divide it? Or how can one part tend upwards and another downwards, or one part tend to the extreme and another to the center?
ἔτι πᾶν σῶμα αἰσθητὸν ἐν τόπῳ, τόπου δὲ εἴδη ἕξ, ἀδύνατον δ᾽ ἐν τῷ [30] ἀπείρῳ σώματι ταῦτ᾽ εἶναι.	1002. Further, every sensible body is in a place, and there are six kinds of place, but these cannot pertain to an infinite body.
ὅλως δ᾽ εἰ ἀδύνατον τόπον ἄπειρον εἶναι, καὶ σῶμα ἀδύνατον: τὸ γὰρ ἐν τόπῳ πού, τοῦτο δὲ σημαίνει ἢ ἄνω ἢ κάτω ἢ τῶν λοιπῶν τι, τούτων δ᾽ ἕκαστον πέρας τι.	1003. And in general if a place cannot be infinite, neither can a body be infinite; for to be in a place is to be somewhere, and this means to be either down or up or in some one of the other places, and each of these is a limit.
τὸ δ᾽ ἄπειρον οὐ ταὐτὸν ἐν μεγέθει καὶ κινήσει καὶ χρόνῳ ὡς μία τις φύσις, ἀλλὰ τὸ ὕστερον [35] λέγεται κατὰ τὸ πρότερον, οἷον κίνησις κατὰ τὸ μέγεθος ἐφ᾽ οὗ κινεῖται ἢ ἀλλοιοῦται ἢ αὔξεται, χρόνος δὲ διὰ τὴν κίνησιν. [1067β] [1]	1004. And the infinite is not the same in the case of continuous quantity, of motion, and of time, as though it were a single reality; but the secondary member is said to be infinite inasmuch as the primary one is; for example, motion is said to be infinite in reference to the continuous quantity in which it is moved or altered or increased, and time is said to be such in reference to motion.

ARISTOTLE’S TEXT Chapter it: 1067b 1-1068a 7
μεταβάλλει δὲ τὸ μεταβάλλον τὸ μὲν κατὰ συμβεβηκός, [2] ὡς τὸ μουσικὸν βαδίζει, τὸ δὲ τῷ τούτου τι μεταβάλλειν ἁπλῶς λέγεται μεταβάλλειν, οἷον ὅσα κατὰ μέρη (ὑγιάζεται γὰρ τὸ σῶμα, ὅτι ὁ ὀφθαλμός), ἔστι δέ [5] τι ὃ καθ᾽ αὑτὸ πρῶτον κινεῖται, καὶ τοῦτ᾽ ἔστι τὸ καθ᾽ αὑτὸ κινητόν.	1005. Everything which is changed is changed either accidentally, as when we say that a musician walks; or it is changed without qualification because something belonging to it is changed, as what is changed in some of its parts; for example, the body is said to be healed because the eye is. And there is some primary thing which is moved of itself, and this is what is essentially movable.
ἔστι δέ [τι] καὶ ἐπὶ τοῦ κινοῦντος ὡσαύτως: κινεῖ γὰρ κατὰ συμβεβηκὸς τὸ δὲ κατὰ μέρος τὸ δὲ καθ᾽ αὑτό:	1006. The same division applies to a mover, for it causes motion either accidentally or in some part of itself or essentially.
ἔστι δέ τι τὸ κινοῦν πρῶτον: ἔστι δέ τι τὸ κινούμενον, ἔτι ἐν ᾧ χρόνῳ καὶ ἐξ οὗ καὶ εἰς ὅ. τὰ δ᾽ εἴδη καὶ τὰ πάθη καὶ [10] ὁ τόπος, εἰς ἃ κινοῦνται τὰ κινούμενα, ἀκίνητά ἐστιν, οἷον ἐπιστήμη καὶ θερμότης: ἔστι δ᾽ οὐχ ἡ θερμότης κίνησις ἀλλ᾽ ἡ θέρμανσις.	1007. And there is a primary mover and something which is moved. And there is also a time in which it is moved, and something from which it is moved, and something to which it is moved. But the forms and modifications and place to which things in motion are moved are immovable, as science and heat. Heat is not motion, but heating is.
ἡ δὲ μὴ κατὰ συμβεβηκὸς μεταβολὴ οὐκ ἐν ἅπασιν ὑπάρχει ἀλλ᾽ ἐν τοῖς ἐναντίοις καὶ μεταξὺ καὶ ἐν ἀντιφάσει: τούτου δὲ πίστις ἐκ τῆς ἐπαγωγῆς. μεταβάλλει [15] δὲ τὸ μεταβάλλον ἢ ἐξ ὑποκειμένου εἰς ὑποκείμενον, ἢ οὐκ ἐξ ὑποκειμένου εἰς οὐχ ὑποκείμενον, ἢ ἐξ ὑποκειμένου εἰς οὐχ ὑποκείμενον, ἢ οὐκ ἐξ ὑποκειμένου εἰς ὑποκείμενον (λέγω δὲ ὑποκείμενον τὸ καταφάσει δηλούμενον), ὥστ᾽ ἀνάγκη τρεῖς εἶναι μεταβολάς: ἡ γὰρ ἐξ οὐχ ὑποκειμένου [20] εἰς μὴ ὑποκείμενον οὐκ ἔστι μεταβολή: οὔτε γὰρ ἐναντία οὔτε ἀντίφασίς ἐστιν, ὅτι οὐκ ἀντίθεσις.	1008. Now change which is not accidental is not found in all things, but between contraries and between their intermediates and between contradictories. We may be convinced of this by induction. Whatever is changed is changed either from a subject to a subject, or from a non-subject to a non-subject, or from a subject to a non-subject, or from a non-subject to a subject. And by subject I mean what is expressed by an affirmative term. Hence there must be three changes; for to go from a non-subject to a non-subject is not change, because, since the limits are neither contraries nor contradictories, there is no opposition (1008).
ἡ μὲν οὖν οὐκ ἐξ ὑποκειμένου εἰς ὑποκείμενον κατ᾽ ἀντίφασιν γένεσίς ἐστιν, ἡ μὲν ἁπλῶς ἁπλῆ, ἡ δὲ τινὸς τίς: ἡ δ᾽ ἐξ ὑποκειμένου εἰς μὴ ὑποκείμενον φθορά, ἡ μὲν ἁπλῶς ἁπλῆ, ἡ δὲ τινὸς [25] τίς.	1009. The change from a non-subject to a subject which is its contradictory is generation; and if it is unqualified, it is generation in an unqualified sense, and if in a part, partial generation; and the change from a subject to a non-subject is destruction.
εἰ δὴ τὸ μὴ ὂν λέγεται πλεοναχῶς, καὶ μήτε τὸ κατὰ σύνθεσιν ἢ διαίρεσιν ἐνδέχεται κινεῖσθαι μήτε τὸ κατὰ δύναμιν τὸ τῷ ἁπλῶς ὄντι ἀντικείμενον (τὸ γὰρ μὴ λευκὸν ἢ μὴ ἀγαθὸν ὅμως ἐνδέχεται κινεῖσθαι κατὰ συμβεβηκός, εἴη γὰρ ἂν ἄνθρωπος τὸ μὴ λευκόν: τὸ δ᾽ ἁπλῶς [30] μὴ τόδε οὐδαμῶς), ἀδύνατον τὸ μὴ ὂν κινεῖσθαι (εἰ δὲ τοῦτο, καὶ τὴν γένεσιν κίνησιν εἶναι: γίγνεται γὰρ τὸ μὴ ὄν: εἰ γὰρ καὶ ὅτι μάλιστα κατὰ συμβεβηκὸς γίγνεται, ἀλλ᾽ ὅμως ἀληθὲς εἰπεῖν ὅτι ὑπάρχει τὸ μὴ ὂν κατὰ τοῦ γιγνομένου ἁπλῶς): ὁμοίως δὲ καὶ τὸ ἠρεμεῖν. ταῦτά [35] τε δὴ συμβαίνει δυσχερῆ, καὶ εἰ πᾶν τὸ κινούμενον ἐν τόπῳ, τὸ δὲ μὴ ὂν οὐκ ἔστιν ἐν τόπῳ: εἴη γὰρ ἂν πού. οὐδὲ δὴ ἡ φθορὰ κίνησις: ἐναντίον γὰρ κινήσει κίνησις ἢ ἠρεμία, φθορὰ δὲ γενέσει.	1010. If non-being has several different meanings, then neither that which involves a combination or separation of terms, nor that which refers to potentiality and is opposed to being in an unqualified sense, is capable of being moved (for what is not-white or not-good can be moved only accidentally, since what is not-white may be a man). But non-being in an unqualified sense cannot be moved in any way, because it is impossible for non-being to be moved. And if this is so, generation cannot be motion, because non-being is generated. For even if it is most certainly generated accidentally, it will still be true to say that what is generated in an unqualified sense is non-being. The same argument applies to rest. These are the difficulties, then, which result from this view. And if everything moved is in a place, though non-being is not in a place, it would have to be somewhere. Nor is destruction motion; for the contrary of motion is motion or rest, but the contrary of destruction is generation.
[1068α] [1] ἐπεὶ δὲ πᾶσα κίνησις μεταβολή τις, μεταβολαὶ δὲ τρεῖς αἱ εἰρημέναι, τούτων δ᾽ αἱ κατὰ γένεσιν καὶ φθορὰν οὐ κινήσεις, αὗται δ᾽ εἰσὶν αἱ κατ᾽ ἀντίφασιν, ἀνάγκη τὴν ἐξ ὑποκειμένου εἰς ὑποκείμενον κίνησιν εἶναι [5] μόνην. τὰ δ᾽ ὑποκείμενα ἢ ἐναντία ἢ μεταξύ (καὶ γὰρ ἡ στέρησις κείσθω ἐναντίον), καὶ δηλοῦται καταφάσει, οἷον τὸ γυμνὸν καὶ νωδὸν καὶ μέλαν.	1011. And since every motion is a kind of change, and the three changes are those described (1008), and of these those which refer to generation and destruction are not motions, and these are changes between contradictories, only change from a subject to a subject must be motion. And the subjects are either contraries or their intermediates—for privation is given as a contrary—and they are expressed by an affirmative term, for example, naked or toothless or black.

ARISTOTLE’S TEXT Chapter 12: 1068a 8-1068b 25
εἰ οὖν αἱ κατηγορίαι διῄρηνται οὐσίᾳ, ποιότητι, τόπῳ, τῷ ποιεῖν ἢ πάσχειν, τῷ πρός τι, τῷ ποσῷ, ἀνάγκη τρεῖς [10] εἶναι κινήσεις, ποιοῦ ποσοῦ τόπου:	1012. If the categories are divided into substance, quality, place, action, passion, relation and quantity, there must be three kinds of motion, namely, of quality, of quantity and of place.
κατ᾽ οὐσίαν δ᾽ οὔ, διὰ τὸ μηθὲν εἶναι οὐσίᾳ ἐναντίον,	1013. There is no motion of substance, because substance has no contrary.
οὐδὲ τοῦ πρός τι (ἔστι γὰρ θατέρου μεταβάλλοντος μὴ ἀληθεύεσθαι θάτερον μηδὲν μεταβάλλον, ὥστε κατὰ συμβεβηκὸς ἡ κίνησις αὐτῶν),	1014. Nor is there motion of relation; for it is possible that, when one of two relative things has undergone a change, the other may be truly referred to under a new term even though it has not been changed in any way. Hence the motion of these relative things will be accidental.
οὐδὲ ποιοῦντος καὶ πάσχοντος, ἢ κινοῦντος καὶ κινουμένου, ὅτι οὐκ ἔστι [15] κινήσεως κίνησις οὐδὲ γενέσεως γένεσις, οὐδ᾽ ὅλως μεταβολῆς μεταβολή. διχῶς γὰρ ἐνδέχεται κινήσεως εἶναι κίνησιν, ἢ ὡς ὑποκειμένου (οἷον ὁ ἄνθρωπος κινεῖται ὅτι ἐκ λευκοῦ εἰς μέλαν μεταβάλλει, ὥστε οὕτω καὶ ἡ κίνησις ἢ θερμαίνεται ἢ ψύχεται ἢ τόπον ἀλλάττει ἢ αὔξεται: τοῦτο [20] δὲ ἀδύνατον: οὐ γὰρ τῶν ὑποκειμένων τι ἡ μεταβολή), ἢ τῷ ἕτερόν τι ὑποκείμενον ἐκ μεταβολῆς μεταβάλλειν εἰς ἄλλο εἶδος, οἷον ἄνθρωπον ἐκ νόσου εἰς ὑγίειαν. ἀλλ᾽ οὐδὲ τοῦτο δυνατὸν πλὴν κατὰ συμβεβηκός. πᾶσα γὰρ κίνησις ἐξ ἄλλου εἰς ἄλλο ἐστὶ μεταβολή, καὶ γένεσις καὶ φθορὰ [25] ὡσαύτως: πλὴν αἱ μὲν εἰς ἀντικείμενα ὡδί, ἡ δ᾽ ὡδί, ἡ κίνησις. ἅμα οὖν μεταβάλλει ἐξ ὑγιείας εἰς νόσον, καὶ ἐξ αὐτῆς ταύτης τῆς μεταβολῆς εἰς ἄλλην. δῆλον δὴ ὅτι ἂν νοσήσῃ, μεταβεβληκὸς ἔσται εἰς ὁποιανοῦν (ἐνδέχεται γὰρ ἠρεμεῖν) καὶ ἔτι εἰς μὴ τὴν τυχοῦσαν ἀεί: κἀκείνη ἔκ τινος εἴς [30] τι ἄλλο ἔσται: ὥσθ᾽ ἡ ἀντικειμένη ἔσται, ὑγίανσις, ἀλλὰ τῷ συμβεβηκέναι, οἷον ἐξ ἀναμνήσεως εἰς λήθην μεταβάλλει ὅτι ᾧ ὑπάρχει ἐκεῖνο μεταβάλλει, ὁτὲ μὲν εἰς ἐπιστήμην ὁτὲ δὲ εἰς ἄγνοιαν.	1015. Nor is there motion of agent or of patient as of mover and thing moved, because there is no motion of motion or generation of generation. There are two ways in which there might be motion of motion. First, motion might be of the subject moved, as a man is moved because he is changed from white to black. Thus motion might be heated or cooled or might change its place or might increase. But this is impossible, for change is not a subject. Or, second, some other subject might be changed from change to some other form of being, as a man might be changed from sickness to health. But this is possible only accidentally; for every motion is a change from one thing to something else. The same applies to generation and destruction; although the opposites involved in these changes are different from those of motion. Therefore a man changes at the same time from health to sickness, and from this change itself to another. And it is evident that, if a man has become ill, he will be changed into something else whatever it may be (for he can come to rest); and further this will always be to some opposite which is not contingent; and that change will be from something to something else. Hence, its opposite will be becoming healthy; but this will happen accidentally; for example, there is a change from recollection to forgetting, because the subject to which forgetting belongs is changed, sometimes to a state of knowledge and sometimes to one of ignorance.
ἔτι εἰς ἄπειρον βαδιεῖται, εἰ ἔσται μεταβολῆς μεταβολὴ καὶ γενέσεως γένεσις. ἀνάγκη [35] δὴ καὶ τὴν προτέραν, εἰ ἡ ὑστέρα: οἷον εἰ ἡ ἁπλῆ γένεσις ἐγίγνετό ποτε, καὶ τὸ γιγνόμενον ἐγίγνετο: [1068β] [1] ὥστε οὔπω ἦν τὸ γιγνόμενον ἁπλῶς, ἀλλά τι γιγνόμενον [ἢ] γιγνόμενον ἤδη. καὶ τοῦτ᾽ ἐγίγνετό ποτε, ὥστ᾽ οὐκ ἦν πω τότε γιγνόμενον. ἐπεὶ δὲ τῶν ἀπείρων οὐκ ἔστι τι πρῶτον, οὐκ [5] ἔσται τὸ πρῶτον, ὥστ᾽ οὐδὲ τὸ ἐχόμενον. οὔτε γίγνεσθαι οὖν οὔτε κινεῖσθαι οἷόν τε οὔτε μεταβάλλειν οὐδέν.	1016. Further, the process will go on to infinity if there is change of change and generation of generation. Therefore, if the latter comes to be, the former must also; for example, if generation in an unqualified sense at one time was coming to be, that which is coming to be something was also coming to be. Hence that which was coming to be in an unqualified sense did not yet exist, but there was something which was coming to be, or which has already come to be. Therefore, if this also at one time was coming to be, then at that time it was not coming to be something. However, since there is no first term in infinite things, neither will there be a subsequent one. Hence it is impossible for anything to come to be or be moved or be changed in any way.
ἔτι τοῦ αὐτοῦ κίνησις ἡ ἐναντία καὶ ἠρέμησις, καὶ γένεσις καὶ φθορά, ὥστε τὸ γιγνόμενον, ὅταν γένηται γιγνόμενον, τότε φθείρεται: οὔτε γὰρ εὐθὺς γιγνόμενον οὔθ᾽ ὕστερον: εἶναι γὰρ δεῖ [10] τὸ φθειρόμενον.	1017. Further, of the same thing of which there is contrary motion and rest there is also generation and destruction. Hence when that which is coming to be becomes that which is coming to be, it is then being destroyed; for it is not destroyed as soon as it is generated or afterwards; for that which is being destroyed must be.
ἔτι δεῖ ὕλην ὑπεῖναι τῷ γιγνομένῳ καὶ μεταβάλλοντι. τίς οὖν ἔσται ὥσπερ τὸ ἀλλοιωτὸν σῶμα ἢ ψυχή—οὕτω τί τὸ γιγνόμενον κίνησις ἢ γένεσις; καὶ ἔτι τί εἰς ὃ κινοῦνται; δεῖ γὰρ εἶναι τὴν τοῦδε ἐκ τοῦδε εἰς τόδε κίνησιν ἢ γένεσιν. πῶς οὖν; οὐ γὰρ ἔσται μάθησις τῆς [15] μαθήσεως, ὥστ᾽ οὐδὲ γένεσις γενέσεως.	1018. Further, there must be some matter underlying the thing which is coming to be or being changed. What then will it be that becomes motion or generation in the same way that a body or a soul or something else of this kind is alterable? Further, what is the thing to which motion proceeds; for motion must be of this particular thing from this to that, and yet the latter should not be a motion at all. In what way then is this to take place? For there can be no learning of learning, and therefore no generation of generation (1008-9).
ἐπεὶ δ᾽ οὔτ᾽ οὐσίας οὔτε τοῦ πρός τι οὔτε τοῦ ποιεῖν καὶ πάσχειν, λείπεται κατὰ τὸ ποιὸν καὶ ποσὸν καὶ τόπον κίνησιν εἶναι (τούτων γὰρ ἑκάστῳ ἐναντίωσις ἔστιν), λέγω δὲ τὸ ποιὸν οὐ τὸ ἐν τῇ οὐσίᾳ (καὶ γὰρ ἡ διαφορὰ ποιόν) ἀλλὰ τὸ παθητικόν, καθ᾽ ὃ [20] λέγεται πάσχειν ἢ ἀπαθὲς εἶναι.	1019. And since there is no motion of substance or of relation or of action or of passion, it follows that there is motion of quality, of quantity and of location; for each of these admits of contrariety. By quality I mean, not that which comes under the category of substance (for even difference is quality), but the passive power in virtue of which a thing is said to be acted upon or to be incapable of being acted upon.
τὸ δὲ ἀκίνητον τό τε ὅλως ἀδύνατον κινηθῆναι καὶ τὸ μόλις ἐν χρόνῳ πολλῷ ἢ βραδέως ἀρχόμενον, καὶ τὸ πεφυκὸς μὲν κινεῖσθαι καὶ δυνάμενον <�μὴ κινούμενον> δὲ ὅτε πέφυκε καὶ οὗ καὶ ὥς: ὃ καλῶ ἠρεμεῖν τῶν ἀκινήτων μόνον: ἐναντίον γὰρ ἠρεμία [25] κινήσει, ὥστε στέρησις ἂν εἴη τοῦ δεκτικοῦ.	1020. The immovable is what is totally incapable of being moved, or what is moved with difficulty over a long period of time or begins to be moved slowly, or what is naturally fit to be moved but is not capable of being moved when it is so fit, and where, and in the way in which it would naturally be moved. And this is the only kind of immobility which I call rest; for rest is contrary to motion. Hence it will be the privation of what is receptive of motion.

ARISTOTLE’S TEXT Chapter 12: 1068b 26-1069a 14
ἅμα κατὰ τόπον ὅσα ἐν ἑνὶ τόπῳ πρώτῳ, καὶ χωρὶς ὅσα ἐν ἄλλῳ: ἅπτεσθαι δὲ ὧν τὰ ἄκρα ἅμα: μεταξὺ δ᾽ εἰς ὃ πέφυκε πρότερον ἀφικνεῖσθαι τὸ μεταβάλλον ἢ εἰς ὃ ἔσχατον μεταβάλλει κατὰ φύσιν τὸ συνεχῶς μεταβάλλον. [30] ἐναντίον κατὰ τόπον τὸ κατ᾽ εὐθεῖαν ἀπέχον πλεῖστον: ἑξῆς δὲ οὗ μετὰ τὴν ἀρχὴν ὄντος, θέσει ἢ εἴδει ἢ ἄλλως πως ἀφορισθέντος, μηθὲν μεταξύ ἐστι τῶν ἐν ταὐτῷ γένει καὶ οὗ ἐφεξῆς ἐστίν, οἷον γραμμαὶ γραμμῆς ἢ μονάδες μονάδος ἢ οἰκίας οἰκία (ἄλλο δ᾽ οὐθὲν κωλύει μεταξὺ [35] εἶναι). τὸ γὰρ ἑξῆς τινὸς ἐφεξῆς καὶ ὕστερόν τι: οὐ γὰρ τὸ ἓν ἑξῆς τῶν δύο οὐδ᾽ ἡ νουμηνία τῆς δευτέρας. [1069α] [1] ἐχόμενον δὲ ὃ ἂν ἑξῆς ὂν ἅπτηται. ἐπεὶ δὲ πᾶσα μεταβολὴ ἐν τοῖς ἀντικειμένοις, ταῦτα δὲ τὰ ἐναντία καὶ ἀντίφασις, ἀντιφάσεως δ᾽ οὐδὲν ἀνὰ μέσον, δῆλον ὡς ἐν τοῖς ἐναντίοις τὸ [5] μεταξύ. τὸ δὲ συνεχὲς ὅπερ ἐχόμενόν τι. λέγω δὲ συνεχὲς ὅταν ταὐτὸ γένηται καὶ ἓν τὸ ἑκατέρου πέρας οἷς ἅπτονται καὶ συνέχονται,	1021. Things which are in one primary place are together in place, and those which are in different places are separate, and those whose extremities are together are in contact. And an intermediate is that at which something continuously changing according to its nature naturally arrives before it reaches the limit to which it is changing. That is contrary in place which is most distant in a straight line. That is subsequent which comes after a starting point (the order being determined by position or form or in some other way) and has nothing in the same genus between itself and that which it follows; for example, lines in the case of a line, and units in the case of a unit, or a house in the case of a house. But there is nothing to prevent something else from coming between. For that which follows something is subsequent and comes after something else; for one does not follow two, nor does [the first day of] the new moon follow the second. Again, what is subsequent and in contact is contiguous. And since every change is between opposites, and these are contraries and contradictories, and since there is no intermediate between contradictories, it is evident that an intermediate is between contraries. The continuous has something of the nature of the contiguous; and I call two things continuous when both have the same extremity in which they are in contact and are uninterrupted.
ὥστε δῆλον ὅτι τὸ συνεχὲς ἐν τούτοις ἐξ ὧν ἕν τι πέφυκε γίγνεσθαι κατὰ τὴν σύναψιν. καὶ ὅτι πρῶτον τὸ ἐφεξῆς, δῆλον (τὸ γὰρ ἐφεξῆς οὐχ ἅπτεται, [10] τοῦτο δ᾽ ἐφεξῆς: καὶ εἰ συνεχές, ἅπτεται, εἰ δ᾽ ἅπτεται, οὔπω συνεχές: ἐν οἷς δὲ μὴ ἔστιν ἁφή, οὐκ ἔστι σύμφυσις ἐν τούτοις): ὥστ᾽ οὐκ ἔστι στιγμὴ μονάδι ταὐτόν: ταῖς μὲν γὰρ ὑπάρχει τὸ ἅπτεσθαι, ταῖς δ᾽ οὔ, ἀλλὰ τὸ ἐφεξῆς: καὶ τῶν μὲν μεταξύ τι τῶν δ᾽ οὔ.	1022. It is evident, then, that the continuous belongs to those things from which one thing results in virtue of their contact. And it is evident that the subsequent is the first of these; for things which are subsequent are not necessarily in contact, but what is in contact is subsequent. But if it is in contact it is not necessarily continuous. And in things in which there is no contact there is no natural coherence. The point, then, is not the same as the unit; for contact belongs to the former but not to the latter, but only successiveness, and there is an intermediate between the former but not between the latter.