Authors/Aristotle/metaphysics/l11

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Chapter 1

Greek Latin English
METHAPHISICE ARISTOTILIS LIBER UNDECIMUS Chapter 1. Aristotle Metaphysics Book 11 (K) 1 (See also B, chapters 2, 3). [59a 18]
[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: > Quod quidem sapientia circa principia scientia est, palam ex primis in quibus dubitatum est ad dicta ab aliis de principiis. THAT Wisdom is a science of first principles is evident from the introductory chapters, in which we have raised objections to the statements of others about the first principles;
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; Dubitabit autem utique quis utrum unam existimare esse oportet sapientiam scientiam aut multas. Si quidem enim unam, una autem est semper contrariorum, principia autem non contraria. Si autem non una, quales oportet ponere has? but one might ask the question whether Wisdom is to be conceived as one science or as several. If as one, it may be objected that one science always deals with contraries, but the first principles are not contrary. If it is not one, what sort of sciences are those with which it is to be identified?
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; Adhuc demonstrativa principia speculari unius aut plurium? si quidem enim unius, quid magis huius quam cuiuscumque? si autem plurium, quales oportet has ponere? Further, is it the business of one science, or of more than one, to examine the first principles of demonstration? If of one, why of this rather than of any other? If of more, what sort of sciences must these be said to be?
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. Adhuc utrum omnium substantiarum aut non? Si quidem enim non omnium, qualium difficile assignare. Si autem omnium una, non manifestum quomodo contingit plurium eandem scientiam esse. Further, does Wisdom investigate all substances or not? If not all, it is hard to say which; but if, being one, it investigates them all, it is doubtful how the same science can embrace several subject-matters.
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. Adhuc utrum circa substantias solum aut et circa accidentia demonstratio est? Si enim circa accidentia demonstratio est, circa substantias non est. Si autem altera, quae utraque et utra sapientia? Demonstrativa quidem enim sapientia quae circa accidentia, haec autem circa prima quae substantiarum. Further, does it deal with substances only or also with their attributes? If in the case of attributes demonstration is possible, in that of substances it is not. But if the two sciences are different, what is each of them and which is Wisdom? If we think of it as demonstrative, the science of the attributes is Wisdom, but if as dealing with what is primary, the science of substances claims the tide.
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): Sed neque > circa dictas in phisicis causas quesitam scientiam ponendum. neque enim circa quod cuius gratia, tale enim bonum; hoc autem in operabilibus existit et existentibus in motu, et hoc primum movet (tale enim finis), primum autem movens non est in immobilibus. But again the science we are looking for must not be supposed to deal with the causes which have been mentioned in the Physics. For (A) it does not deal with the final cause (for that is the nature of the good, and this is found in the field of action and movement; and it is the first mover-for that is the nature of the end-but in the case of things unmovable there is nothing that moved them first), and (B)
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 Totaliter autem dubitationem habet utrum quidem circa sensibiles substantias est quesita nunc scientia aut non, circa quas autem alteras. Si enim circa alias, aut circa species aut, si sint, circa mathematica. Species quidem enim quod non sunt, palam. in general it is hard to say whether perchance the science we are now looking for deals with perceptible substances or not with them, but with cer[59b]tain others. If with others, it must deal either with the Forms or with the objects of mathematics. Now (a) evidently the 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: At tamen dubitationem habet, et si esse quis ipsas ponat, propter quid quidem non quemadmodum in mathematicis sic habet et in aliis quorum sunt species. Dico autem quia mathematica quidem intermedia specierum ponunt et sensibilium velut tertia quaedam praeter species et quae hic, tertius autem homo non est neque equus praeter auton et singulares. (But it is hard to say, even if one suppose them to exist, why in the world the same is not true of the other things of which there are Forms, as of the objects of mathematics. I mean that these thinkers place the objects of mathematics between the Forms and perceptible things, as a kind of third set of things apart both from the Forms and from the things in this world; but there is not a third man or horse besides the ideal and the individuals.
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. Si autem iterum non est ut dicunt, circa qualia ponendum negotiari mathematicum? Non enim utique circa ea quae hic; horum enim nullum est quale mathematice quaerunt scientiarum. Neque etiam circa mathematica quesita nunc est scientia; separabile enim ipsorum nullum. Sed neque sensibilium substantiarum; corruptibiles enim. If on the other hand it is not as they say, with what sort of things must the mathematician be supposed to deal? Certainly not with the things in this world; for none of these is the sort of thing which the mathematical sciences demand.) Nor (b) does the science which we are now seeking treat of the objects of mathematics; for none of them can exist separately. But again it does not deal with perceptible substances; for they are perishable.
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. Totaliter autem dubitabit utique quis cuius est scientie dubitare de mathematicarum materia. Neque enim phisice, propter circa habentia in ipsis principium motus et quietis naturalis omne esse negotium. Neque etiam intendentis de demonstratione et scientia; circa hoc ipsum genus enim inquisitionem > facit. Relinquitur igitur propositam philosophiam de ipsis considerationem facere. In general one might raise the question, to what kind of science it belongs to discuss the difficulties about the matter of the objects of mathematics. Neither to physics (because the whole inquiry of the physicist is about the things that have in themselves a principle. of movement and rest), nor yet to the science which inquires into demonstration and science; for this is just the subject which it investigates. It remains then that it is the philosophy which we have set before ourselves that treats of those subjects.
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. Dubitabit autem utique quis si oportet quaerere quesitam scientiam circa principia vocata ab aliquibus elementa; haec autem omnes inexistentia compositis ponunt. Magis autem utiquae videbitur universalium oportere esse quesitam scientiam. Omnis enim ratio et omnis scientia universalium et non extremorum. Quare erit utique sic primorum generum, One might discuss the question whether the science we are seeking should be said to deal with the principles which are by some called elements; all men suppose these to be present in composite things. But it might be thought that the science we seek should treat rather of universals; for every definition and every science is of universals and not of infimae species, so that as far as this goes it would deal with the highest 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. haec autem fient utique ens et unum; haec enim maxime utique existimabuntur continere entia omnia et maxime principia videri quia sunt prima natura. Corruptis enim ipsis cointerimuntur reliqua; omnia enim ens et unum. Secundum quod autem differentias ipsis necesse participare, si ponat quis ipsa genera, differentia autem nulla genere participat, sic non utique videbitur oportere ipsa poni genera neque principia. These would turn out to be being and unity; for these might most of all be supposed to contain all things that are, and to be most like principles because they are by nature; for if they perish all other things are destroyed with them; for everything is and is one. But inasmuch as, if one is to suppose them to be genera, they must be predicable of their differentiae, and no genus is predicable of any of its differentiae, in this way it would seem that we should not make them genera nor 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. Adhuc autem si magis principium quod simplicius eo quod minus tale, ultima autem eorum quae ex genere simpliciora generibus (indivisibilia enim, genera autem in plura et differentia dividuntur), magis utique principium videbuntur esse species generibus. Qua autem cointerimuntur generibus species, genera principiis assimilantur magis; principium enim quod cointerimit. Quae quidem igitur dubitationem habent, haec et talia sunt altera. Further, if the simpler is more of a principle than the less simple, and the ultimate members of the genus are simpler than the genera (for they are indivisible, but the genera are divided into many and differing species), the species might seem to be the principles, rather than the genera. But inasmuch as the species are involved in the destruction of the genera, the genera are more like principles; for that which involves another in its destruction is a principle of [60a] it. These and others of the kind are the subjects that involve difficulties. (See also B, chapters 4-6).

Chapter 2

Greek Latin English
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. Adhuc utrum oportet poni aliquid praeter singularia aut non, sed horum quesita scientia? Sed haec infinita. Quae vero praeter singularia genera aut species sunt, sed neutrius horum quesita nunc scientia; propter quod enim impossibile hoc, dic>tum est. Chapter 2. Further, must we suppose something apart from individual things, or is it these that the science we are seeking treats of? But these are infinite in number. Yet the things that are apart from the individuals are genera or species; but the science we now seek treats of neither of these. The reason why this is impossible has been stated.
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. Et enim totaliter dubitationem habet utrum oportet aliquam existimare substantiam separabilem praeter sensibiles substantias et eas quae hic aut non, sed haec esse entia et circa haec sapientiam existere. Quaerere quidem enim videmur aliam quandam, et propositum hoc est nobis, dico autem scire si quid separabile secundum se et nulli sensibilium existens. Indeed, it is in general hard to say whether one must assume that there is a separable substance besides the sensible substances (i.e. the substances in this world), or that these are the real things and Wisdom is concerned with them. For we seem to seek another kind of substance, and this is our problem, i.e. to see if there is something which can exist apart by 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. Adhuc autem si praeter sensibiles substantias est aliqua alia substantia, praeter quales sensibilium oportet ponere hanc esse? Quid enim magis praeter homines aut equos quam aliorum animalium ponet quis ipsam aut et inanimatorum totaliter? Equalesque sensibilibus et corruptibilibus substantiis perpetuas alteras construere extra rationabilia videbitur utique cadere. -Further, if there is another substance apart from and corresponding to sensible substances, which kinds of sensible substance must be supposed to have this corresponding to them? Why should one suppose men or horses to have it, more than either the other animals or even all lifeless things? On the other hand to set up other and eternal substances equal in number to the sensible and perishable substances would seem to fall beyond the bounds of probability.
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; Si autem non separabile a corporibus quesitum nunc principium est, quid utique aliud quis ponet magis materia? Haec tamen actu quidem non est, potentia autem est. Magisque utique principium principalius hac videbitur esse species et forma; hoc autem corruptibile. Quare totaliter non est perpetua substantia separabilis et secundum se. Sed inconveniens. Videtur enim et quaeritur fere a gratiosissimis tamquam existens quoddam principium et substantia talis; quomodo enim erit ordo non existente aliquo perpetuo et separabili et manente? But if the principle we now seek is not separable from corporeal things, what has a better claim to the name matter? This, however, does not exist in actuality, but exists in potency. And it would seem rather that the form or shape is a more important principle than this; but the form is perishable, so that there is no eternal substance at all which can exist apart and independent. But this is paradoxical; for such a principle and substance seems to exist and is sought by nearly all the most refined thinkers as something that exists; for how is there to be order unless there is something eternal and independent and permanent?
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. Adhuc autem siquidem est aliqua substantia et principium tale secundum naturam quale nunc quaerimus, et hoc unum omnium et idem perpetuorum et corruptibilium, dubitationem habet propter quid quidem eodem principio existente haec quidem sunt perpetua eorum quae sub principio, haec autem non perpetua; hoc enim inconveniens. Si autem aliud quidem principium est corruptibilium aliud autem perpetuorum, si quidem perpetuum et quod corruptibilium, similiter dubitabimus; prop>ter quid enim non, perpetuo principio existente, et quae sub principio perpetua? Corruptibili autem existente aliud aliquod principium fit huius, et illius alterum, et hoc in infinitum procedit. Further, if there is a substance or principle of such a nature as that which we are now seeking, and if this is one for all things, and the same for eternal and for perishable things, it is hard to say why in the world, if there is the same principle, some of the things that fall under the principle are eternal, and others are not eternal; this is paradoxical. But if there is one principle of perishable and another of eternal things, we shall be in a like difficulty if the principle of perishable things, as well as that of eternal, is eternal; for why, if the principle is eternal, are not the things that fall under the principle also eternal? But if it is perishable another principle is involved to account for it, and another to account for that, and this will go on to infinity.
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. Si autem rursum aliquis putata maxime principia immobilia esse, ens et unum, ponat, primo quidem si non hoc aliquid et substantiam utrumque ipsorum significat, quomodo erunt separabilia et per se? Talia autem quaerimus perpetuaque et prima principia. Si vero hoc aliquid et substantiam utrumque ipsorum significat, omnia erunt substantia entia; de omnibus enim ens predicatur, de quibusdam autem et unum. Substantiam autem esse omnia entia falsum. If on the other hand we are to set up what are thought to be the most unchangeable principles, being and unity, firstly, if each of these does not indicate a this or sub[60b]stance, how will they be separable and independent? Yet we expect the eternal and primary principles to be so. But if each of them does signify a this or substance, all things that are are substances; for being is predicated of all things (and unity also of some); but that all things that are are substance is false.
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. Adhuc autem primum principium quod unum dicentibus et hoc substantiam, ex uno autem et materia numerum generant primo et hunc substantiam dicunt esse, quomodo contingit quod dicitur verum esse? Dualitatem enim et reliquorum unumquemque numerum compositorum, quomodo unum oportet intelligere? De hoc enim neque dicunt nihil neque facile dicere. Further, how can they be right who say that the first principle is unity and this is substance, and generate number as the first product from unity and from matter, assert that number is substance? How are we to think of two , and each of the other numbers composed of units, as one? On this point neither do they say anything nor is it easy to say anything.
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. Si vero lineas aut hiis habita (dico autem superficies) prima ponat quis principia, haec autem non sunt substantiae separabiles, decisiones autem et divisiones hae quidem superficierum hae autem corporum, puncta autem linearum, adhuc autem termini eorundem horum; omnia autem haec in aliis existunt et separabile nullum est. But if we are to suppose lines or what comes after these (I mean the primary surfaces) to be principles, these at least are not separable substances, but sections and divisions-the former of surfaces, the latter of bodies (while points are sections and divisions of lines); and further they are limits of these same things; and all these are in other things and none is 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. Adhuc quomodo substantiam existimare esse oportet unius et puncti? Substantiae quidem enim omnis generatio est, puncti autem non est; divisio enim punctum. Further, how are we to suppose that there is a substance of unity and the point? Every substance comes into being by a gradual process, but a point does not; for the point is a division.
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; Exhibet autem dubitationem et omnem quidem scientiam esse universalium et talis, substantiam autem non universalium > esse, magis autem hoc aliquid et separabile. Quare si circa principia est scientia, quomodo oportet principium existimare substantiam esse? A further difficulty is raised by the fact that all knowledge is of universals and of the such , but substance is not a universal, but is rather a this -a separable thing, so that if there is knowledge about the first principles, the question arises, how are we to suppose the first principle to be substance?
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. Adhuc utrum est aliquid praeter synolon aut non? Dico autem materiam et quod cum hac. Si quidem enim non, quae quidem in materia corruptibilia omnia. Si autem est aliquid, species utique erit et forma. Hoc igitur in quibus est et in quibus non, difficile determinare; in quibusdam enim palam non existens separabilis species, puta domus. Further, is there anything apart from the concrete thing (by which I mean the matter and that which is joined with it), or not? If not, we are met by the objection that all things that are in matter are perishable. But if there is something, it must be the form or shape. Now it is hard to determine in which cases this exists apart and in which it does not; for in some cases the form is evidently not separable, e.g. in the case of a house.
ἔτι πότερον αἱ ἀρχαὶ εἴδει ἢ ἀριθμῷ αἱ αὐταί; εἰ γὰρ ἀριθμῷ [30] ἕν, πάντ᾽ ἔσται ταὐτά. Adhuc utrum principia specie aut numero eadem? Si enim numero, omnia erunt eadem. Further, are the principles the same in kind or in number? If they are one in number, all things will be the same. (See also G, chapters 1,2).

Chapter 3

Greek Latin English
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. Quoniam autem philosophi scientia entis in quantum ens universaliter et non secundum partem, ens autem multipliciter et non secundum unum dicitur modum: si quidem igitur equivoce secundum commune autem nihil, non est sub una scientia; non enim unum genus talium. Si autem secundum aliquid commune, erit utique sub una scientia. Chapter 3. Since the science of the philosopher treats of being qua being universally and not in respect of a part of it, and being has many senses and is not used in one only, it follows that if the word is used equivocally and in virtue of nothing common to its various uses, being does not fall under one science (for the meanings of an equivocal term do not form one genus); but if the word is used in virtue of something common, 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. Videtur itaque dicto modo dici quemadmodum medicativum et salubre; et enim horum unumquodque multipliciter. Dicitur autem secundum unumquemque modorum eo quod hoc quidem ad medicativam scientiam reducatur aliqualiter hoc autem ad sanitatem hoc autem aliter, ad idem autem unumquodque. Medicativus enim sermo et cultellus dicitur eo quod hic quidem a medicativa scientia sit hic autem huic utilis. Similiter autem et salubre; hoc quidem enim quia significativum sanitatis hoc autem quia factivum. Idem autem modus et in reliquis. Eodem itaque modo et ens omne dicitur; eo enim quod entis in quantum ens passio aut habitus aut dispositio aut motus aut aliorum aliquid talium > sit, dicitur unumquodque ipsorum ens. The term seems to be used in the way we have mentioned, like medical and healthy . For each of these also we use in [61a] many senses. Terms are used in this way by virtue of some kind of reference, in the one case to medical science, in the other to health, in others to something else, but in each case to one identical concept. For a discussion and a knife are called medical because the former proceeds from medical science, and the latter is useful to it. And a thing is called healthy in a similar way; one thing because it is indicative of health, another because it is productive of it. And the same is true in the other cases. Everything that is, then, is said to be in this same way; each thing that is is said to be because it is a modification of being qua being or a permanent or a transient state or a movement of it, or something else of the sort.
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. Quoniam autem omnis entis ad unum aliquid et commune reductio fit, et contrarietatum unaqueque ad primas differentias et contrarietates reducetur entis, sive pluralitas et unum sive similitudo et dissimilitudo prime entis sint differentiae, sive aliae alique; sint enim hae speculatae. And since everything that is may be referred to something single and common, each of the contrarieties also may be referred to the first differences and contrarieties of being, whether the first differences of being are plurality and unity, or likeness and unlikeness, or some other differences; let these be taken as already discussed.
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. Differt autem nihil entis reductionem ad ens aut ad unum fieri. Et enim si non idem sed est aliud, convertitur quidem; unum enim ens aliqualiter et ens unum. It makes no difference whether that which is be referred to being or to unity. For even if they are not the same but different, at least they are convertible; for that which is one is also somehow being, and that which is being is 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. Quoniam autem sunt contraria omnia eiusdem et unius scientiae speculari, dicitur autem unumquodque ipsorum secundum privationem, et utique quaedam dubitabit aliquis quomodo dicuntur secundum privationem quorum est intermedium aliquid, quemadmodum iniusti et iusti. Circa omnia itaque talia privationem oportet poni non totius rationis, sed ultime speciei; puta si est iustus secundum habitum quendam obediens legibus, non semper iniustus erit tota privatus ratione, circa persuaderi autem legibus deficiens in aliquo, et secundum hoc privatio inest ipsi. Eodem autem modo et in aliis. But since every pair of contraries falls to be examined by one and the same science, and in each pair one term is the privative of the other though one might regarding some contraries raise the question, how they can be privately related, viz. those which have an intermediate, e.g. unjust and just-in all such cases one must maintain that the privation is not of the whole definition, but of the infima species. if the just man is by virtue of some permanent disposition obedient to the laws , the unjust man will not in every case have the whole definition denied of him, but may be merely in some respect deficient in obedience to the laws , and in this respect the privation will attach to him; and similarly in all 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. Quemadmodum autem mathematicus circa ea quae ex ablatione theoriam facit, circumtollens enim omnia sensibilia speculatur, puta gravitatem et levitatem et duritiem et contrarium, adhuc autem caliditatem et frigiditatem et alias sensibiles contrarietates, solum autem derelinquit quantum et continuum, horum quidem ad unum horum autem ad duo horum vero ad tria, et passiones horum in quantum quanta sunt et continua et non secundum aliud aliquid speculatur, et horum quidem eas quae ad invicem positiones considerat et hiis existentia, > horum autem commensurationes et incommensurationes, horum vero rationes, sed tamen omnium unam et eandem ponimus scientiam geometricam: eodem modo habet et circa ens. As the mathematician investigates abstractions (for before beginning his investigation he strips off all the sensible qualities, e.g. weight and lightness, hardness and its contrary, and also heat and cold and the other sensible contrarieties, and leaves only the quantitative and continuous, sometimes in one, sometimes in two, sometimes in three dimensions, and the attributes of these qua quantitative and continuous, and does not consider them in any other respect, and examines the relative positions of some and the attributes of these, [61b] and the commensurabilities and incommensurabilities of others, and the ratios of others; but yet we posit one and the same science of all these things geometry) the same is true with regard to 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. Huic enim accidentia in quantum est ens et contrarietates ipsius in quantum ens non alterius scientie quam philosophiae speculari, naturali quidem enim non in quantum entia, magis autem in quantum motu participant, theoriam utique quis distribuet. Dialetica etiam et sophistica sunt accidentium quidem entibus, non autem in quantum entia neque circa ens ipsum in quantum ens est. Quare relinquitur philosophum, in quantum entis sunt, esse circa dicta speculativum. For the attributes of this in so far as it is being, and the contrarieties in it qua being, it is the business of no other science than philosophy to investigate; for to physics one would assign the study of things not qua being, but rather qua sharing in movement; while dialectic and sophistic deal with the attributes of things that are, but not of things qua being, and not with being itself in so far as it is being; therefore it remains that it is the philosopher who studies the things we have named, in so far as they are being.
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. Quoniam autem ens omne secundum unum aliquid et commune dicitur multipliciter dictum, et contraria eodem modo (ad primas enim contrarietates et differentias entis <reducuntur>), talia autem possunt sub una scientia esse, dissoluetur utique quae secundum principia dubitatio dicta. Dico autem in qua dubitatum est quomodo erit multorum et differentium genere una aliqua scientia. Since all that is is to be in virtue of something single and common, though the term has many meanings, and contraries are in the same case (for they are referred to the first contrarieties and differences of being), and things of this sort can fall under one science, the difficulty we stated at the beginning appears to be solved,-I mean the question how there can be a single science of things which are many and different in genus. (See also G, chapters 3,4).

Chapter 4

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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. Quoniam autem et mathematicus utitur communibus proprie, et horum principia erit utique speculari primae philosophiae. Quod enim ab equalibus equalibus ablatis quae relinquuntur equalia, commune quidem est in omnibus quantis. Mathematica autem absumens circa aliquam partem convenientis > materiae facit theoriam, puta circa lineas aut angulos aut numeros aut reliquorum aliquid quantorum, non in quantum autem entia sed in quantum continuum ipsorum unumquodque ad unum aut duo aut tria. Philosophia autem de hiis quae in parte quidem in quantum horum unicuique aliquid accidit non intendit, circa ens autem in quantum ens talium unumquodque speculatur. Chapter 4. Since even the mathematician uses the common axioms only in a special application, it must be the business of first philosophy to examine the principles of mathematics also. That when equals are taken from equals the remainders are equal, is common to all quantities, but mathematics studies a part of its proper matter which it has detached, e.g. lines or angles or numbers or some other kind of quantity-not, however, qua being but in so far as each of them is continuous in one or two or three dimensions; but philosophy does not inquire about particular subjects in so far as each of them has some attribute or other, but speculates about being, in so far as each particular thing is.
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. Eodem autem habet modo et circa naturalem scientiam mathematice. Naturalis enim accidentia et principia speculatur entium in quantum mota et non in quantum entia. Primam autem scientiam diximus horum esse secundum quod entia subiecta sunt, sed non alterum aliquid. Propter quod et hanc et mathematicam scientiam partes sapientie esse ponendum. -Physics is in the same position as mathematics; for physics studies the attributes and the principles of the things that are, qua moving and not qua being (whereas the primary science, we have said, deals with these, only in so far as the underlying subjects are existent, and not in virtue of any other character); and so both physics and mathematics must be classed as parts of Wisdom.

Chapter 5

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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. Est autem quoddam in entibus principium circa quod non est mentiri, contrarium autem necessarium semper facere, dico autem verum dicere: puta quod non contingit idem secundum unum et idem tempus esse et non esse, et alia ipsis opposita hoc modo. Chapter 5. There is a principle in things, about which we cannot be deceived, but must always, on the contrary recognize the truth,-viz. that the same thing cannot at one and the same [62a] time be and not be, or admit any other similar pair of opposites.
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. Et de talibus simpliciter quidem non est demonstratio, ad hunc autem est. Non enim est ex credibiliori principio hoc ipso facere sillogismum; oportet autem, siquidem erit simpliciter demonstrare. About such matters there is no proof in the full sense, though there is proof ad hominem. For it is not possible to infer this truth itself from a more certain principle, yet this is necessary if there is to be completed proof of it in the full sense.
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. Ad dicentem autem oppositas dictiones ostendenti quia falsum, sumendum aliquid tale quod idem quidem erit ei quod est non contingere idem esse et non esse secundum unum et idem tempus, non videbitur autem esse idem; sic enim solum utique demonstrabitur ad dicentem contingere oppositas dictiones verificari de eodem. But he who wants to prove to the asserter of opposites that he is wrong must get from him an admission which shall be identical with the principle that the same thing cannot be and not be at one and the same time, but shall not seem to be identical; for thus alone can his thesis be demonstrated to the man who asserts 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. Futuros itaque invicem ratione communicare oportet aliquid ipsorum intelligere; non facto autem hoc, quomodo est communicatio hiis ad invicem sermonis? Oportet igitur nominum unumquodque esse notum et significare aliquid et non multa, solum autem > unum; si autem plura significet, manifestum facere ad quod fert nomen horum. Dicens itaque esse hoc et non esse, hoc quod totaliter esse dicit non dicit, quare quod significat nomen, hoc non inquit significare; hoc autem impossibile. Quare siquidem significat aliquid esse hoc, contradictionem verificari impossibile de eodem. Those, then, who are to join in argument with one another must to some extent understand one another; for if this does not happen how are they to join in argument with one another? Therefore every word must be intelligible and indicate something, and not many things but only one; and if it signifies more than one thing, it must be made plain to which of these the word is being applied. He, then, who says this is and is not denies what he affirms, so that what the word signifies, he says it does not signify; and this is impossible. Therefore if this is signifies something, one cannot truly assert its contradictory.
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. Adhuc autem si quid significat nomen et hoc verificatur, oportet et hoc ex necessitate esse. Quod autem ex necessitate est non contingit tunc non esse; oppositas igitur non contingit dictiones et negationes verificari de eodem. Further, if the word signifies something and this is asserted truly, this connexion must be necessary; and it is not possible that that which necessarily is should ever not be; it is not possible therefore to make the opposed affirmations and negations truly of the same subject.
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. Adhuc autem si nihil magis dictio quam negatio verificatur, dicens hominem aut non hominem nihil magis verum dicet. Videbitur autem utique non equum esse dicens hominem et magis aut non minus verum dicere quam non hominem. Quare et equum dicens esse eundem verum dicet; oppositas enim similiter erat verum dicere. Accidit igitur eundem hominem esse et equum aut aliorum aliquod animalium. Demonstratio quidem igitur nulla horum est simpliciter, ad ponentem tamen haec demonstratio. Further, if the affirmation is no more true than the negation, he who says man will be no more right than he who says not-man . It would seem also that in saying the man is not a horse one would be either more or not less right than in saying he is not a man, so that one will also be right in saying that the same person is a horse; for it was assumed to be possible to make opposite statements equally truly. It follows then that the same person is a man and a horse, or any other animal. While, then, there is no proof of these things in the full sense, there is a proof which may suffice against one who will make these suppositions.
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. Cito autem utique quis et ipsum Eraclitum hoc interrogans modo cogeret confiteri numquam oppositas dictiones possibile esse de eisdem verificari. Nunc autem non intelligens se ipsum quid quidem dicit, hanc accepit opinionem. Totaliter autem si quod dicitur ab ipso est verum, neque utique ipsum hoc verum erit: dico autem contingere idem secundum unum et idem tempus esse et non esse. Quemadmodum enim et divisis ipsis nihil magis affirmatio quam negatio verificatur, eodem modo, et simul utriusque et simul complexi velut una quadam affirmatione existente, nihil magis negatio quam totum ut in affirmatione positum verum erit. And perhaps if one had questioned Heraclitus himself in this way one might have forced him to confess that opposite statements can never be true of the same subjects. But, as it is, he adopted this opinion without understanding what his statement involves. But in any case if what is said by him is true, not even this [62b] itself will be true-viz. that the same thing can at one and the same time both be and not be. For as, when the statements are separated, the affirmation is no more true than the negation, in the same way-the combined and complex statement being like a single affirmation-the whole taken as an affirmation will be no more true than the negation.
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. > Adhuc autem si nihil est vere affirmare, et utique hoc ipsum falsum erit: dicere nullam veram affirmationem existere. Si autem est aliquid, soluetur utique quod dicitur ab hiis qui talia instant et penitus auferentibus disputare. Further, if it is not possible to affirm anything truly, this itself will be false-the assertion that there is no true affirmation. But if a true affirmation exists, this appears to refute what is said by those who raise such objections and utterly destroy rational discourse. (See also G, chapters 5,8).

Chapter 6

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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. Simile autem dictis est et quod dictum est a Protagora. et enim ille dixit omnium esse rerum mensuram hominem, nihil aliud dicens quam quod videtur unicuique hoc et esse firmiter. Hoc autem facto idem accidit et esse et non esse, et malum et bonum esse, et alia secundum oppositas dictiones dicta, propter multotiens hiis quidem videri hoc esse bonum hiis autem contrarium, mensuram autem esse quod videtur unicuique. Chapter 6. The saying of Protagoras is like the views we have mentioned; he said that man is the measure of all things, meaning simply that that which seems to each man also assuredly is. If this is so, it follows that the same thing both is and is not, and is bad and good, and that the contents of all other opposite statements are true, because often a particular thing appears beautiful to some and the contrary of beautiful to others, and that which appears to each man is the measure.
[20] λύοιτο δ᾽ ἂν αὕτη ἡ ἀπορία θεωρήσασι πόθεν ἐλήλυθεν ἡ ἀρχὴ [21] τῆς ὑπολήψεως ταύτης: Solvetur autem utique haec dubitatio considerantibus unde venit principium existimationis huius. This difficulty may be solved by considering the source of this opinion.
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. Videtur enim quibusdam quidem ex phisiologorum opinione, aliis autem ex non eadem de eisdem omnes cognoscere, sed hiis quidem delectabile hoc videri hiis autem contrarium. It seems to have arisen in some cases from the doctrine of the natural philosophers, and in others from the fact that all men have not the same views about the same things, but a particular thing appears pleasant to some and the contrary of pleasant to others.
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. Nihil enim ex non ente fieri, omne autem ex ente, fere omnium est commune dogma eorum qui de natura. Quoniam igitur non album fit ex albo perfecte existente et nequaquam ex non albo, nunc autem factum non album, fiet utique ex non ente non albo quod fit non album; quare ex non ente fiet utique secundum illos, si non extitit non album idem et album. Non difficile autem dissoluere dubitationem hanc. Dictum est enim in phisicis quomodo ex non ente fiunt quae fiunt et quomodo ex ente. That nothing comes to be out of that which is not, but everything out of that which is, is a dogma common to nearly all the natural philosophers. Since, then, white cannot come to be if the perfectly white and in no respect not-white existed before, that which becomes white must come from that which is not white; so that it must come to be out of that which is not (so they argue), unless the same thing was at the beginning white and not-white. But it is not hard to solve this difficulty; for we have said in our works on physics in what sense things that come to be come to be from that which is not, and in what sense from that which is.
#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. Sed et similiter attendere > utrisque opinionibus et fantasiis ad ipsos dubitantium stultum; palam enim quod alteros ipsorum necesse mentiri. Palam autem hoc ex hiis quae fiunt secundum sensum. Numquam enim idem videtur hiis quidem dulce hiis autem contrarium, non corruptis et privatis alteris secundum organum sensus et iudicatorium dictorum saporum. Hoc autem existente tali, alteros quidem existimandum mensuram esse alteros autem non putandum, similiter autem hoc dico et in bono et malo et pulcro et turpi et aliis talibus. Nihil enim differt hoc dignificare quam quae apparent submittentibus sub visu digitum et facientibus ex uno videri duo oportere esse propter apparere tanta, et iterum unum; non moventibus enim visum unum apparet quod unum. But to attend equally to the opinions and the fancies of disputing parties is childish; for clearly one of them must be mistaken. And this is evident from what happens in respect of sensation; for the same thing never appears sweet to some [63a] and the contrary of sweet to others, unless in the one case the sense-organ which discriminates the aforesaid flavours has been perverted and injured. And if this is so the one party must be taken to be the measure, and the other must not. And say the same of good and bad, and beautiful and ugly, and all other such qualities. For to maintain the view we are opposing is just like maintaining that the things that appear to people who put their finger under their eye and make the object appear two instead of one must be two (because they appear to be of that number) and again one (for to those who do not interfere with their eye the one object appears one).
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. Totaliter autem inconveniens ex videri presentia permutantia et numquam permanentia in eisdem, ex hoc de veritate iudicium facere. Oportet enim ex semper secundum eadem habentibus et neque unam permutationem facientibus verum venari. Talia autem sunt quae secundum mundum; haec enim non quandoque quidem talia iterum autem alia videntur, eadem autem semper et permutatione nulla participant. In general, it is absurd to make the fact that the things of this earth are observed to change and never to remain in the same state, the basis of our judgement about the truth. For in pursuing the truth one must start from the things that are always in the same state and suffer no change. Such are the heavenly bodies; for these do not appear to be now of one nature and again of another, but are manifestly always the same and share in no change.
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. Adhuc autem si motus est, et motum aliquid, movetur autem omne ex aliquo et ad aliquid; oportet igitur quod movetur esse adhuc in illo ex quo movebit, et non esse in ipso, et ad hoc moveri et fieri in hoc, secundum contradictionem autem non verificari secundum ipsos. Further, if there is movement, there is also something moved, and everything is moved out of something and into something; it follows that that that which is moved must first be in that out of which it is to be moved, and then not be in it, and move into the other and come to be in it, and that the contradictory statements are not true at the same time, as these thinkers assert they are.
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. Et si secundum quantum continue presentia fluunt et moventur, et quis hoc ponat equidem non verum existens, propter quid secundum quale non manet? Videtur enim non minime quae secundum contradictiones eiusdem predicare ex existimare quantum non manere in corporibus, propter et esse quadricubitum idem et non esse. Substantia autem secundum quale; hoc quidem determinate nature, quantum autem indeterminate. And if the things of this earth continuously flow and move in respect of quantity-if one were to suppose this, although it is not true-why should they not endure in respect of quality? For the assertion of contradictory statements about the same thing seems to have arisen largely from the belief that the quantity of bodies does not endure, which, our opponents hold, justifies them in saying that the same thing both is and is not four cubits long. But essence depends on quality, and this is of determinate nature, though quantity is of indeterminate.
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. > Adhuc propter quid iubente medico hunc cibum offerre, offerunt? Quid enim magis panis est aut non est? Quare nihil utique aliquid habebit comedere aut non comedere. Nunc autem ut verum dicentes circa ipsum et existente iusso cibo hoc, offerunt hunc; quamvis non oportebat, non permanente firmiter nulla natura in sensibilibus sed semper omnibus motis et fluentibus. Further, when the doctor orders people to take some particular food, why do they take it? In what respect is this is bread truer than this is not bread ? And so it would make no difference whether one ate or not. But as a matter of fact they take the food which is ordered, assuming that they know the truth about it and that it is bread. Yet they should not, if there were no fixed constant nature in sensible things, but all natures moved and flowed for ever.
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. Adhuc si quidem alteramur semper et numquam permanemus iidem, quid mirabile si numquam nobis eadem videntur quemadmodum laborantibus? Et enim hiis propter non similiter disponi secundum habitum et quando sani erant, non similia videntur quae secundum sensus; ipsa tamen nulla propter hoc participantia permutatione sensibilia, impressiones autem alias facientia laborantibus et non eadem. Eodem itaque modo habere et dicta permutatione facta forte necessarium est. Si autem non permutamur sed iidem permanemus entes, erit utique aliquid manens. Again, if we are always changing and never remain the same, what wonder is it if to us, as to the sick, things never [63b] appear the same? (For to them also, because they are not in the same condition as when they were well, sensible qualities do not appear alike; yet, for all that, the sensible things themselves need not share in any change, though they produce different, and not identical, sensations in the sick. And the same must surely happen to the healthy if the afore-said change takes place.) But if we do not change but remain the same, there will be something that endures.
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. Ad habentes quidem igitur dictas dubitationes ex ratione, non facile dissoluere non ponentibus aliquid et horum non adhuc rationem exquirentibus; sic enim omnis ratio et omnis demonstratio fit; nihil enim ponentes interimunt disputare et totaliter rationem. Quare ad tales quidem non est sermo. Ad dubitantes autem ex datis defectibus, facile obuiare et dissoluere facientia dubitationem in ipsis. Palam autem ex dictis. As for those to whom the difficulties mentioned are suggested by reasoning, it is not easy to solve the difficulties to their satisfaction, unless they will posit something and no longer demand a reason for it; for it is only thus that all reasoning and all proof is accomplished; if they posit nothing, they destroy discussion and all reasoning. Therefore with such men there is no reasoning. But as for those who are perplexed by the traditional difficulties, it is easy to meet them and to dissipate the causes of their perplexity. This is evident from what has been said.
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. Quare manifestum ex hiis quod non contingit oppositas dictiones de eodem secundum unum tempus verificari, neque contraria, propter dici secundum privationem omnem contrarieta>tem. Palam autem hoc ad principium resoluentibus rationes contrariorum. Similiter autem neque intermediorum nullum possibile est predicari de uno et eodem. Albo enim existente subiecto dicentes ipsum esse neque album neque nigrum mentiemur; accidit enim esse album ipsum et non esse; alterum enim complexorum verificabitur de ipso, hoc autem est contradictio albi. It is manifest, therefore, from these arguments that contradictory statements cannot be truly made about the same subject at one time, nor can contrary statements, because every contrariety depends on privation. This is evident if we reduce the definitions of contraries to their principle. Similarly, no intermediate between contraries can be predicated of one and the same subject, of which one of the contraries is predicated. If the subject is white we shall be wrong in saying it is neither black nor white, for then it follows that it is and is not white; for the second of the two terms we have put together is true of it, and this is the contradictory of white.
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. Neque itaque secundum Eraclitum contingit dicentes verum dicere neque secundum Anaxagoram. Si autem non, accidet contraria de eodem predicari. Cum enim in omni dicat omnis esse partem, nihil magis esse dicit dulce quam amarum aut reliquarum quamcumque contrarietatum, siquidem in omni existit non potentia solum sed actu et segregatum. We could not be right, then, in accepting the views either of Heraclitus or of Anaxagoras. If we were, it would follow that contraries would be predicated of the same subject; for when Anaxagoras says that in everything there is a part of everything, he says nothing is sweet any more than it is bitter, and so with any other pair of contraries, since in everything everything is present not potentially only, 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] Similiter autem neque omnes falsas neque veras dictiones possibile esse, et propter alia multa collectarum utique difficultatum propter hanc positionem, et quia falsis quidem existentibus omnibus neque hoc ipsum quis dicens verum dicet, veris autem falsas esse omnes dicens non mentietur. And similarly all statements cannot be false nor all true, both because of many other difficulties which might be adduced as arising from this position, and because if all are false it will not be true to say even this, and if all are true it will not be false to say all are false. (See also E, chapter 1).

Chapter 7

Greek Latin English
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. Omnis autem scientia quaerit aliqua principia et causas circa unumquodque eorum quae sub ipsa scibilium, puta medicativa et exercitativa et reliquarum unaqueque factivarum et doctrinalium. Unaqueque enim harum circumscribens aliquod genus ipsi circa hoc negotiatur tamquam existens et ens, non in quantum autem ens; sed altera quaedam haec praeter has scientias est scientia. Chapter 7. Every science seeks certain principles and causes for each [64a] of its objects-e.g. medicine and gymnastics and each of the other sciences, whether productive or mathematical. For each of these marks off a certain class of things for itself and busies itself about this as about something existing and real,-not however qua real; the science that does this is another distinct from these.
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. Dictarum autem scientiarum unaqueque sumens aliqualiter quod quid est in unoquoque genere temptat ostendere reliqua debilius aut certius. Sumunt autem quod quid est hae quidem per sensum hae autem supponentes; propter quod et palam ex tali inductione quod substantiae et eius quod quid est non est demonstratio. Of the sciences mentioned each gets somehow the what in some class of things and tries to prove the other truths, with more or less precision. Some get the what through perception, others by hypothesis; so that it is clear from an induction of this sort that there is no demonstration. of the substance or what .
[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): Quoniam autem est quaedam de natura scientia, palam quia et a practica altera et a factiva erit. Factive quidem enim in faciente et non in facto motus principium, et hoc est sive ars > aliqua sive aliqua alia potentia. Similiter autem et practice non in agibili, magis autem in agentibus motus. Quae autem phisici circa habentia in ipsis motus principium est. Quod quidem igitur neque activam neque factivam sed speculativam necessarium esse naturalem scientiam, palam ex hiis. In unum enim aliquod horum generum necesse cadere ipsam. There is a science of nature, and evidently it must be different both from practical and from productive science. For in the case of productive science the principle of movement is in the producer and not in the product, and is either an art or some other faculty. And similarly in practical science the movement is not in the thing done, but rather in the doers. But the science of the natural philosopher deals with the things that have in themselves a principle of movement. It is clear from these facts, then, that natural science must be neither practical nor productive, but theoretical (for it must fall into some 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. Quoniam autem quod quid est necessarium unicuique aliqualiter scientiarum scire et hoc uti principio, oportet non latere qualiter diffiniendum naturali et qualiter substantiae ratio sumenda, utrum ut simum aut magis ut concauum. Horum enim simi quidem ratio cum materia dicitur ea quae rei, quae autem concavi sine materia. simitas enim in naso fit, propter quod et ratio ipsius cum hoc dicta est; simum enim est nasus concavus. Manifestum igitur quod et carnis et oculi et reliquarum partium cum materia semper rationem reddendum. And since each of the sciences must somehow know the what and use this as a principle, we must not fall to observe how the natural philosopher should define things and how he should state the definition of the essence-whether as akin to snub or rather to concave . For of these the definition of snub includes the matter of the thing, but that of concave is independent of the matter; for snubness is found in a nose, so that we look for its definition without eliminating the nose, for what is snub is a concave nose. Evidently then the definition of flesh also and of the eye and of the other parts must always be stated without eliminating the 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. Quoniam autem est quaedam scientia entis in quantum ens et separabile, considerandum utrum quidem naturali eandem ponendum esse hanc aut magis alteram. Naturalis quidem igitur circa habentia motus principium in ipsis est; mathematica autem speculativa quidem et circa manentia quaedam haec, sed non separabilia. Circa separabile igitur ens et immobile altera ab hiis ambabus scientiis est aliqua, siquidem existit aliqua substantia talis, dico autem separabilis et immobilis, quod quidem temptabimus ostendere. Et siquidem est aliqua talis natura in entibus, hic utique erit alicubi et quod divinum, et haec utique erit primum et principalissimum principium. Palam igitur quod tria genera speculativarum scientiarum sunt: naturalis, mathematica, theologica. Since there is a science of being qua being and capable of existing apart, we must consider whether this is to be regarded as the same as physics or rather as different. Physics deals with the things that have a principle of movement in themselves; mathematics is theoretical, and is a science that deals with things that are at rest, but its subjects cannot exist apart. Therefore about that which can exist apart and is unmovable there is a science different from both of these, if there is a substance of this nature (I mean separable and unmovable), as we shall try to prove there is. And if there is such a kind of thing in the world, here must surely be the divine, and this must be the first [64b] and most dominant principle. Evidently, then, there are three kinds of theoretical sciences-physics, mathematics, 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. Optimum quidem igitur speculativarum genus, harum autem ipsarum ultima dicta; circa honorabilissimum enim est entium. Melior autem et dete>rior unaqueque dicitur secundum proprium scibile. The class of theoretical sciences is the best, and of these themselves the last named is best; for it deals with the highest of existing things, and each science is called better or worse in virtue 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] Dubitabit autem utique quis utrum entis in quantum ens scientiam universalem oportet poni aut non. Mathematicarum quidem enim unaqueque circa unum aliquod genus determinatum est, quae autem universalis communiter de omnibus. Si quidem igitur naturales substantiae prime entium sunt, et naturalis utique prima scientiarum erit. Si autem est altera natura et substantia separabilis et immobilis, alteram necesse et scientiam ipsius esse et priorem naturali et universalem eo quod priorem. One might raise the question whether the science of being qua being is to be regarded as universal or not. Each of the mathematical sciences deals with some one determinate class of things, but universal mathematics applies alike to all. Now if natural substances are the first of existing things, physics must be the first of sciences; but if there is another entity and substance, separable and unmovable, the knowledge of it must be different and prior to physics and universal because it is prior.

Chapter 8

Greek Latin English
ἐπεὶ δὲ τὸ ἁπλῶς ὂν κατὰ πλείους λέγεται τρόπους, ὧν εἷς ἐστὶν ὁ κατὰ συμβεβηκὸς εἶναι λεγόμενος, σκεπτέον πρῶτον περὶ τοῦ οὕτως ὄντος. Quoniam autem simpliciter ens secundum plures dicitur modos, quorum unus est qui secundum accidens dicitur, considerandum primo de sic ente. Chapter 8. Since being in general has several senses, of which one is being by accident , we must consider first that which is in this sense.
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: Quod quidem igitur nulla traditarum scientiarum negotiatur circa accidens, palam; neque enim edificativa considerat quod accidet utentibus domo, puta si triste aut contrarie habitabunt, neque textiva neque coriativa neque coquinaria. Quod autem secundum ipsam proprium unaqueque harum considerat scientiarum solum, hoc autem est proprius finis. Evidently none of the traditional sciences busies itself about the accidental. For neither does architecture consider what will happen to those who are to use the house (e.g. whether they have a painful life in it or not), nor does weaving, or shoemaking, or the confectioner's art, do the like; but each of these sciences considers only what is peculiar to it, i.e. its proper 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): Neque in quantum musicum et gramaticum, neque existentem musicum quia factus gramaticus simul erit ambo prius non ens, quod autem non semper ens est factum est hoc, quare simul musicus factus est et gramaticus: hoc autem nulla quaerit confesse existentium scientiarum nisi sophistica; circa accidens enim haec sola negotiatur, propter quod Plato non male dixit dicens sophistam circa non ens versari. And as for the argument that when he who is musical becomes lettered he will be both at once, not having been both before; and that which is, not always having been, must have come to be; therefore he must have at once become musical and lettered _ ,-this none of the recognized sciences considers, but only sophistic; for this alone busies itself about the accidental, so that Plato is not far wrong when he says that the sophist spends his time on 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. Quod autem neque contingens est esse accidentis scientiam, manifestum erit temptantibus scire quid est accidens. Omne itaque dicimus esse hoc quidem semper et ex necessitate (necessitate autem non secundum violentiam dicta sed secundum quod utimur in hiis quae secundum demonstrationes), hoc autem ut in plus, hoc vero neque ut in plus neque semper et ex necessitate > sed ut contingit, puta sub cane fiet utique frigus, sed hoc neque ut semper et ex necessitate neque in plus fit, accidet tamen aliquando utique. Est itaque accidens quod fit quidem, non semper autem neque ex necessitate neque ut in plus. Quid quidem igitur est accidens, dictum est. Quia autem non est scientia talis, palam. Scientia quidem enim omnis semper entis aut ut in plus, accidens autem in neutro horum est. That a science of the accidental is not even possible will be evident if we try to see what the accidental really is. We say that everything either is always and of necessity (necessity not in the sense of violence, but that which we appeal to in demonstrations), or is for the most part, or is neither for the most part, nor always and of necessity, but merely as it chances; e.g. there might be cold in the dogdays, but this occurs neither always and of necessity, nor for the most part [65a], though it might happen sometimes. The accidental, then, is what occurs, but not always nor of necessity, nor for the most part. Now we have said what the accidental is, and it is obvious why there is no science of such a thing; for all science is of that which is always or for the most part, but the accidental is in neither of these classes.
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. Quod autem secundum accidens entis non sunt causae et principia talia qualia quidem secundum se entis, palam; erunt enim omnia ex necessitate. Si enim hoc quidem est huius entis hoc autem huius, hoc autem non ut contingit sed ex necessitate, ex necessitate erit et cuius hoc erat causa usque ad ultimum dictum causatum; hoc autem erat secundum accidens. Quare ex necessitate omnia erunt; et quod utcumque contingit et accidere et fieri et non: omnino ex generatis aufertur. Et si non existens sed quae fit causa supponatur, eadem accident; omne enim ex necessitate fiet. Si enim cras eclipsis fiet si hoc fuerit, hoc autem si alterum aliquid, et hoc si aliud; et hoc itaque modo a finito tempore eo quod a nunc usque cras ablato tempore veniet quandoque ad existens. Quare siquidem hoc est, omnia ex necessitate quae post hoc fient, ut omnia ex necessitate fiant. Evidently there are not causes and principles of the accidental, of the same kind as there are of the essential; for if there were, everything would be of necessity. If A is when B is, and B is when C is, and if C exists not by chance but of necessity, that also of which C was cause will exist of necessity, down to the last causatum as it is called (but this was supposed to be accidental). Therefore all things will be of necessity, and chance and the possibility of a thing's either occurring or not occurring are removed entirely from the range of events. And if the cause be supposed not to exist but to be coming to be, the same results will follow; everything will occur of necessity. For to-morrow's eclipse will occur if A occurs, and A if B occurs, and B if C occurs; and in this way if we subtract time from the limited time between now and to-morrow we shall come sometime to the already existing condition. Therefore since this exists, everything after this will occur of necessity, so that all things 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. Quod autem ut vere ens et secundum accidens: hoc quidem est in complexione mentis et passio in hac, propter quod circa sic quidem ens non quaeruntur principia, circa autem quod extra ens et separabile; hoc autem non necessarium sed infinitum, dico autem quod secundum accidens, talis autem inordinatae et infinitae causae. As to that which is in the sense of being true or of being by accident, the former depends on a combination in thought and is an affection of thought (which is the reason why it is the principles, not of that which is in this sense, but of that which is outside and can exist apart, that are sought); and the latter is not necessary but indeterminate (I mean the accidental); and of such a thing the causes are unordered and indefinite.
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, Quod autem gratia huius in hiis quae a natura fiunt et a > mente est. Fortuna autem est quando aliquid horum fuerit secundum accidens. Sicut enim et ens est hoc quidem secundum se hoc autem secundum accidens, sic et causa. Fortuna autem causa secundum accidens in factis secundum electionem eorum quae gratia huius. Adaptation to an end is found in events that happen by nature or as the result of thought. It is luck when one of these events happens by accident. For as a thing may exist, so it may be a cause, either by its own nature or by accident. Luck is an accidental cause at work in such events adapted to an end as are usually effected in accordance with purpose.
διὸ περὶ ταὐτὰ τύχη καὶ διάνοια: προαίρεσις γὰρ οὐ χωρὶς διανοίας. Propter quod circa eadem fortuna et mens; electio enim non sine mente. And so luck and thought are concerned with the same sphere; for purpose cannot exist without thought.
τὰ δ᾽ αἴτια ἀόριστα ἀφ᾽ ὧν ἂν γένοιτο τὰ ἀπὸ τύχης, διὸ ἄδηλος ἀνθρωπίνῳ λογισμῷ καὶ αἴτιον κατὰ συμβεβηκός, ἁπλῶς δ᾽ [35] οὐδενός. Causae autem infinitae a quibus utique fiet quod a fortuna; propter quod incerta humane cogitationi et causa secundum accidens, simpliciter autem nullius. The causes from which lucky results might happen are indeterminate; and so luck is obscure to human calculation and is a cause by accident, but in the unqualified sense a cause of nothing.
ἀγαθὴ δὲ τύχη καὶ κακὴ ὅταν ἀγαθὸν ἢ φαῦλον ἀποβῇ: εὐτυχία δὲ καὶ δυστυχία περὶ μέγεθος τούτων. bona autem fortuna et mala cum bonum aut maium euenerit; eutichia autem et infortunium circa magnitudinem horum. It is good or bad luck when [65b] the result is good or evil; and prosperity or misfortune when the scale of the results is large.
[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] Quoniam autem nullum secundum accidens prius hiis quae secundum se, neque igitur causa. Si igitur fortuna aut casus causa celi, prius intellectus causa et natura. Since nothing accidental is prior to the essential, neither are accidental causes prior. If, then, luck or spontaneity is a cause of the material universe, reason and nature are causes before it.

Chapter 9

Greek Latin English
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. Est autem hoc quidem actu solum hoc autem potentia hoc autem potentia et actu, hoc quidem ens hoc autem quantum hoc autem reliquorum. Non est autem aliquid motus praeter res; permutatur enim semper secundum entis cathegorias, commune autem in hiis nullum est quod neque in una cathegoria. Unumquodque autem dupliciter existit omnibus, ut puta quod hoc: istud quidem forma ipsius hoc autem privatio; et secundum quale hoc quidem album hoc autem nigrum, et secundum quantum hoc quidem perfectum hoc autem imperfectum, et secundum lationem hoc quidem sursum hoc autem deorsum, aut leue hoc autem grave. Quare motus et permutationis tot species quot entis. Chapter 9. Some things are only actually, some potentially, some potentially and actually, what they are, viz. in one case a particular reality, in another, characterized by a particular quantity, or the like. There is no movement apart from things; for change is always according to the categories of being, and there is nothing common to these and in no one category. But each of the categories belongs to all its subjects in either of two ways (e.g. this-ness -for one kind of it is positive form , and the other is privation ; and as regards quality one kind is white and the other black , and as regards quantity one kind is complete and the other incomplete , and as regards spatial movement one is upwards and the other downwards , or one thing is light and another heavy ); so that there are as many kinds of movement and change as of being.
διῃρημένου [15] δὲ καθ᾽ ἕκαστον γένος τοῦ μὲν δυνάμει τοῦ δ᾽ ἐντελεχείᾳ, τὴν τοῦ δυνάμει ᾗ τοιοῦτόν ἐστιν ἐνέργειαν λέγω κίνησιν. Diviso autem secundum unumquodque genus hoc quidem potentia hoc autem actu, eius quod potentia in quantum tale > est actum dico motum. There being a distinction in each class of things between the potential and the completely real, I call the actuality of the potential as such, movement.
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. Quod autem vera dicimus, hinc palam. cum enim edificabile in quantum tale ipsum dicimus esse actu in quantum edificatur, et est hoc edificatio. Similiter doctrinatio, curatio, ambulatio, saltatio, orbatio, ingrossatio. Accidit autem moveri cum fuerit actu eadem, et neque prius neque posterius; iam potentia entis, cum actu ens operetur, non in quantum ipsum sed in quantum mobile, motus est. Dico autem ‘in quantum’ sic: est enim es potentia statua; sed tamen non eris actus in quantum es motus est. That what we say is true, is plain from the following facts. When the buildable , in so far as it is what we mean by buildable , exists actually, it is being built, and this is the process of building. Similarly with learning, healing, walking, leaping, ageing, ripening. Movement takes when the complete reality itself exists, and neither earlier nor later. The complete reality, then, of that which exists potentially, when it is completely real and actual, not qua itself, but qua movable, is movement.
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. Non enim idem eri esse et potentie alicui. Quoniam si idem erat simpliciter secundum rationem, erat utique eris actus motus quidam. Non est autem idem. Palam autem in contrariis; posse quidem enim sanari et posse laborare non idem (et enim si, sanari et laborare idem esset), subiectum autem et sanum et languens, sive humiditas sive sanguis, idem et unum. Quoniam autem non idem, quemadmodum neque color idem et visibile, possibilis in quantum possibile actus motus est. By qua I mean this: bronze is potentially a statue; but yet it is not the complete reality of bronze qua bronze that is movement. For it is not the same thing to be bronze and to be a certain potency. If it were absolutely the same in its definition, the complete reality of bronze would have been a movement. But it is not the same. (This is evident in the case of contraries; for to be capable of being well and to be capable of being ill are not the same-for if they were, being well and being ill would have been the same-it is that which underlies and is healthy or diseased, whether it is moisture or blood, that is one and the same.) And since it is not. the same, as colour and the visible are not the same, it is the complete reality of the potential, and as potential, that is movement.
[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): Quod quidem enim est hic, et quod accidit tunc moveri quando fuerit actu hic, et neque prius neque posterius, palam. Contingit enim unumquodque aliquando quidem actu esse aliquando autem non, puta edificabile in quantum edificabile; et edificabilis actus in quantum edificabile edificatio est. Aut enim hoc domus est, aut edificatio actus. Sed cum domus fuerit, non adhuc edificabile erit, edificatur autem edificabile. Necesse igitur edificationem actum esse, edificatio autem motus quidam. Eadem autem ratio et in aliis motibus. That it is this, and that movement takes place when the complete reality itself exists, and [66a] neither earlier nor later, is evident. For each thing is capable of being sometimes actual, sometimes not, e.g. the buildable qua buildable; and the actuality of the buildable qua buildable is building. For the actuality is either this-the act of building-or the house. But when the house exists, it is no longer buildable; the buildable is what is being built. The actuality, then, must be the act of building, and this is a movement. And the same account applies to all other movements.
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: > Quod autem bene dictum est, palam ex quibus alii dicunt de ipso, et ex eo quod non facile est diffinire aliter ipsum. Neque enim in alio aliquis genere poterit utique ponere ipsum. That what we have said is right is evident from what all others say about movement, and from the fact that it is not easy to define it otherwise. For firstly one cannot put it in any class.
δῆλον δ᾽ ἐξ ὧν λέγουσιν: οἱ μὲν γὰρ ἑτερότητα καὶ ἀνισότητα καὶ τὸ μὴ ὄν, Palam autem ex quibus dicunt. Hii quidem alteritatem et inequalitatem et non ens, This is evident from what people say. Some call it otherness and inequality and the unreal;
ὧν οὐδὲν ἀνάγκη κινεῖσθαι, ἀλλ᾽ οὐδ᾽ ἡ μεταβολὴ οὔτ᾽ εἰς ταῦτα οὔτ᾽ ἐκ τούτων μᾶλλον ἢ τῶν ἀντικειμένων. quorum nullum necesse moveri; sed neque permutatio neque in haec neque ex hiis magis quam ex oppositis. none of these, however, is necessarily moved, and further, change is not either to these or from these any more than 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. Causa autem in haec ponendi quia infinitum aliquid videtur esse motus, alterius autem coelementationis principia quia privativa sunt indeterminata; neque enim hoc neque tale nullum ipsorum neque reliquorum predicamentorum. The reason why people put movement in these classes is that it is thought to be something indefinite, and the principles in one of the two columns of contraries are indefinite because they are privative, for none of them is either a this or a such or in 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. Cur autem videatur indeterminatus esse motus, causa quia neque in potentiam entium neque in actum est ponere ipsum. Neque enim possibile quantum esse movetur ex necessitate, neque quod actu quantum; motusque actus quidem esse videtur aliquis, imperfectus autem. Causa autem quia imperfectum quod possibile cuius est actus. Et propter hoc difficile ipsum sumere quid est; aut enim in privationem necesse poni aut in potentiam aut in actum simplicem, horum autem nullum videtur contingens. Quare relinquitur quod dictum est esse, et actum et non actum dictum, videre quidem difficilem contingentem autem esse. And the reason why movement is thought to be indefinite is that it cannot be classed either with the potency of things or with their actuality; for neither that which is capable of being of a certain quantity, nor that which is actually of a certain quantity, is of necessity moved, and movement is thought to be an actuality, but incomplete; the reason is that the potential, whose actuality it is, is incomplete. And therefore it is hard to grasp what movement is; for it must be classed either under privation or under potency or under absolute actuality, but evidently none of these is possible. Therefore what remains is that it must be what we said-both actuality and the actuality we have described-which is hard to detect but capable of existing.
καὶ ὅτι ἐστὶν ἡ κίνησις ἐν τῷ κινητῷ, δῆλον: ἐντελέχεια γάρ ἐστι τούτου ὑπὸ τοῦ κινητικοῦ. Et quod est motus in mobili, palam; actus enim est huius a motivo, et motivi actus non alius est. And evidently movement is in the movable; for it is the complete realization of this by that which is capable of causing movement.
καὶ ἡ τοῦ κινητικοῦ ἐνέργεια οὐκ ἄλλη ἐστίν. δεῖ μὲν γὰρ εἶναι ἐντελέχειαν ἀμφοῖν: Oportet quidem enim esse actum amborum. And the actuality of that which is capable of causing movement is no other than that of the movable. For it must be the complete reality of both.
κινητικὸν [30] μὲν γάρ ἐστι τῷ δύνασθαι, κινοῦν δὲ τῷ ἐνεργεῖν, Motivum quidem enim est in posse, For while a thing is capable of causing movement because it can do this, it is a mover because it is active;
ἀλλ᾽ ἔστιν ἐνεργητικὸν τοῦ κινητοῦ, ὥσθ᾽ ὁμοίως μία ἡ ἀμφοῖν ἐνέργεια sed est activum mobilis. Quare similiter unus amborum actus, movens autem in operari; but it is on the movable that it is capable of acting, so that the actuality of both 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] quemadmodum eadem > distantia unum ad duo et duo ad unum, et ascendentes et descendentes; sed esse non unum. Similiter autem et in movente et moto. just as there is the same interval from one to two as from two to one, and as the steep ascent and the steep descent are one, but the being of them is not one; the case of the mover and the moved is similar.

Chapter 10

Greek Latin English
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: Infinitum autem aut quod impossibije pertransire eo quod non sit natum pertransiri, quemadmodum vox invisibilis, aut pertransitionem habens imperfectam aut quod vix, aut quod natum est habere non habet pertransitionem aut terminum; Chapter 10. The infinite is either that which is incapable of being traversed because it is not its nature to be traversed (this corresponds to the sense in which the voice is invisible ), or that which admits only of incomplete traverse or scarcely admits of traverse, or that which, though it naturally admits of traverse, is not traversed or limited;
ἔτι προσθέσει ἢ ἀφαιρέσει ἢ ἄμφω. adhuc appositione aut ablatione aut ambo. further, a thing may be infinite in respect of addition or of subtrac[66b]tion, or 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. Separabile quidem itaque ipsum aliquid ens non possibile esse. Si enim neque magnitudo est neque multitudo, substantia autem ipsum infinitum et non accidens, indivisibile erit; quod enim divisibile aut magnitudo aut multitudo. Si autem indivisibile, non infinitum, nisi sicut vox inuisibilis; sed non sic dicunt neque nos quaerimus, sed tamquam impertransibile. The infinite cannot be a separate, independent thing. For if it is neither a spatial magnitude nor a plurality, but infinity itself is its substance and not an accident of it, it will be indivisible; for the divisible is either magnitude or plurality. But if indivisible, it is not infinite, except as the voice is invisible; but people do not mean this, nor are we examining this sort of infinite, but the infinite as untraversable.
ἔτι πῶς ἐνδέχεται καθ᾽ αὑτὸ εἶναι ἄπειρον, εἰ μὴ καὶ ἀριθμὸς καὶ μέγεθος, ὧν πάθος τὸ ἄπειρον; Adhuc quomodo contingit per se esse infinitum, si non et numerus et magnitudo, quorum passio infinitum? Further, how can an infinite exist by itself, unless number and magnitude also exist by themselvess-since infinity is an attribute of these?
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, Adhuc si secundum accidens, non utique erit elementum entium in quantum infinitum, quemadmodum neque inuisibile loquele, quamvis vox inuisibilis. Et quod non est actu esse infinitum, palam; erit enim quaecumque ipsius infinita pars accepta. Infinito enim esse et infinitum idem, siquidem substantia infinitum et non de subiecto. quare aut indivisibile, aut in infinita divisibile, si partibile. Multa autem esse idem impossibile infinita; quemadmodum enim pars aer aeris, sic infinitum infiniti, si est substantia et principium. Impartibile igitur et indivisibile. Sed impossibile actu ens infinitum; quantum enim esse necesse. Secundum accidens igitur existit. Sed si sic, dictum est quod non contingit > esse principium, sed illud cui accidit, aerem aut parem. Haec quidem igitur inquisitio universalis. Further, if the infinite is an accident of something else, it cannot be qua infinite an element in things, as the invisible is not an element in speech, though the voice is invisible. And evidently the infinite cannot exist actually. For then any part of it that might be taken would be infinite (for to be infinite and the infinite are the same, if the infinite is substance and not predicated of a subject). Therefore it is either indivisible, or if it is partible, it is divisible into infinites; but the same thing cannot be many infinites (as a part of air is air, so a part of the infinite would be infinite, if the infinite is substance and a principle). Therefore it must be impartible and indivisible. But the actually infinite cannot be indivisible; for it must be of a certain quantity. Therefore infinity belongs to its subject incidentally. But if so, then (as we have said) it cannot be it that is a principle, but that of which it is an accident-the air or the even number. This inquiry 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, Quod autem in sensibilibus non est, hinc palam. Si enim corporis ratio ‘superficiebus determinatum\ non erit utique infinitum corpus neque sensibile neque intellectuale, but that the infinite is not among sensible things, is evident from the following argument. If the definition of a body is that which is bounded by planes , there cannot be an infinite body either sensible or intelligible;
οὐδ᾽ ἀριθμὸς ὡς [25] κεχωρισμένος καὶ ἄπειρος: ἀριθμητὸν γὰρ ὁ ἀριθμὸς ἢ τὸ ἔχον ἀριθμόν. neque numerus ut separatus et infinitus, numerabile enim numerus aut habens numerum. nor a separate and infinite number, for 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): Naturaliter autem ex hiis palam. Neque enim compositum possibile esse neque simplex. Compositum quidem enim non erit corpus, si finita sunt multitudine elementa. Oportet enim equari contraria et non esse unum ipsorum infinitum; si enim cuicumque deficit alterius corporis virtus, corrumpetur ab infinito finitum. Unumquodque autem infinitum esse impossibile. Corpus enim quod omnino habet distentionem, infinitum autem quod infinite distat; quare infinitum corpus omnino erit infinitum. Concretely, the truth is evident from the following argument. The infinite can neither be composite nor simple. For (a) it cannot be a composite body, since the elements are limited in multitude. For the contraries must be equal and no one of them must be infinite; for if one of the two bodies falls at all short of the other in potency, the finite will be destroyed by the infinite. And that each should be infinite is impossible. For body is that which has extension in all directions, and the infinite is the boundlessly extended, so that if the infinite is a body it will be infinite in every direction.
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. Neque unum autem simplex contingit infinitum esse corpus, neque ut dicunt quidam praeter elementa ex quo generant haec (non enim est tale corpus praeter elementa; omne enim ex quo est et dissolvitur in hoc, non videtur autem hoc circa simplicia corpora), neque ignis neque aliud aliquod elementorum nullum. Sine enim eo quod est infinitum esse aliquid ipsorum, impossibile omne, et si sit finitum, aut esse aut fieri unum aliquod ipsorum, quemadmodum Eraclitus ait omnia fieri aliquando ignem. Eadem autem ratio et in uno quod faciunt praeter elementa phisici; omne enim permutat ex contrario, puta ex calido in frigidum. Nor (b) can the infinite body be one and simple-neither, as some say, something apart from the elements, from which they generate these (for there is no such body apart from the elements; for everything can be resolved into that of which it consists, but no such product of [67a] analysis is observed except the simple bodies), nor fire nor any other of the elements. For apart from the question how any of them could be infinite, the All, even if it is finite, cannot either be or become any one of them, as Heraclitus says all things sometime become fire. The same argument applies to this as to the One which the natural philosophers posit besides the elements. For everything changes from contrary to contrary, e.g. from hot to cold.
ἔτι τὸ αἰσθητὸν σῶμα πού, καὶ ὁ αὐτὸς τόπος ὅλου καὶ μορίου, οἷον τῆς γῆς, >Adhuc sensibile corpus alicubi, et idem locus totius et partis, puta terre. Further, a sensible body is somewhere, and whole and part have the same proper place, e.g. the whole earth and part of the earth.
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): Quare si quidem eiusdem speciei, immobile erit aut semper feretur; hoc autem impossibile. Quid enim magis deorsum quam sursum aut ubicumque? Puta si bolus fuerit, ubi hic movebitur aut manebit? Locus enim ipsius connaturalis corporis infinitus. Optinebit igitur totum locum. Et quomodo? Quae igitur mansio et motus? Aut ubique manet, non movebitur igitur, aut ubique, non igitur stabit. Therefore if (a) the infinite body is homogeneous, it will be unmovable or it will be always moving. But this is impossible; for why should it rather rest, or move, down, up, or anywhere, rather than anywhere else? E.g. if there were a clod which were part of an infinite body, where will this move or rest? The proper place of the body which is homogeneous with it is infinite. Will the clod occupy the whole place, then? And how? (This is impossible.) What then is its rest or its movement? It will either rest everywhere, and then it cannot move; or it will move everywhere, and then it cannot be still.
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. Si autem dissimile totum, dissimilia et loca, et primo quidem non unum corpus omnis nisi tactu. Deinde aut finita haec erunt aut infinita specie. Finita quidem igitur non possibile; erunt enim haec quidem infinita haec autem non, si omne infinitum, puta ignis aut aqua; corruptio autem quod tale contrariis. Si autem infinita et simplicia, et loca infinita et erunt infinita elementa. Si autem hoc impossibile et loca finita, et omne necesse finitum esse. But (b) if the All has unlike parts, the proper places of the parts are unlike also, and, firstly, the body of the All is not one except by contact, and, secondly, the parts will be either finite or infinite in variety of kind. Finite they cannot be; for then those of one kind will be infinite in quantity and those of another will not (if the All is infinite), e.g. fire or water would be infinite, but such an infinite element would be destruction to the contrary elements. But if the parts are infinite and simple, their places also are infinite and there will be an infinite number of elements; and if this is impossible, and the places are finite, the All also must be limited.
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; Totaliter autem impossibile infinitum esse corpus et locum corporibus, si omne corpus sensibile aut gravitatem aut levitatem habet; aut enim ad medium aut sursum feretur. Impossibile autem infinitum, aut omne aut dimidium, quodcumque passum esse. Quomodo enim divides, aut qualiter infiniti erit hoc quidem deorsum hoc autem sursum, aut extremum et medium? In general, there cannot be an infinite body and also a proper place for bodies, if every sensible body has either weight or lightness. For it must move either towards the middle or upwards, and the infinite either the whole or the half of it-cannot do either; for how will you divide it? Or how will part of the infinite be down and part up, or part extreme and part middle?
ἔτι πᾶν σῶμα αἰσθητὸν ἐν τόπῳ, τόπου δὲ εἴδη ἕξ, ἀδύνατον δ᾽ ἐν τῷ [30] ἀπείρῳ σώματι ταῦτ᾽ εἶναι. Adhuc omne sensibile corpus in loco, loci autem species sex, impossibile autem in infinito corpore haec esse. Further, every sensible body is in a place, and there are six kinds of place, but these cannot exist in 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. Totaliter autem si impossibile locum infinitum esse, et corpus impossibile. Quod > enim in loco alicubi, hoc autem significat aut sursum aut deorsum aut reliquorum aliquod, horum autem unumquodque terminus aliquis. In general, if there cannot be an infinite place, there cannot be an infinite body; (and there cannot be an infinite place,) for that which is in a place is somewhere, and this means either up or down or in one of the other directions, 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] Infinitum autem non idem in magnitudine et motu et tempore, ut una quaedam natura, sed quod posterius dicitur secundum prius, puta motus secundum magnitudinem in qua movetur aut alteratur aut augetur, tempus autem propter motum. The infinite is not the same in the sense that it is a single thing whether exhibited in distance or in movement or in time, but the posterior among these is called infinite in virtue of its relation to the prior; i.e. a movement is called infinite in virtue of the distance covered by the spatial movement or alteration or growth, and a time is called infinite because of the movement which occupies it.

Chapter 11

Greek Latin English
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. Permutatur autem quod permutatur hoc quidem secundum accidens, ut musicum ambulare, hoc autem eo quod huius aliquid permutatur simpliciter dicitur permutari, puta quaecumque secundum partes; sanatur enim corpus, quia oculus. Est autem aliquid et quod ipsum primum movetur, et hoc est per se mobile. Chapter 11. Of things which change, some change in an accidental sense, like that in which the musical may be said to walk, and others are said, without qualification, to change, because something in them changes, i.e. the things that change in parts; the body becomes healthy, because the eye does. But there is something which is by its own nature moved directly, and this is the essentially movable.
ἔστι δέ [τι] καὶ ἐπὶ τοῦ κινοῦντος ὡσαύτως: κινεῖ γὰρ κατὰ συμβεβηκὸς τὸ δὲ κατὰ μέρος τὸ δὲ καθ᾽ αὑτό: Est autem aliquid et in movente eodem modo; movet enim secundum accidens, hoc quidem secundum partem, hoc autem per se. The same distinction is found in the case of the mover; for it causes movement either in an accidental sense or in respect of a 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. Est autem aliquid movens primum; est autem aliquid quod movetur. Adhuc in quo tempore et ex quo et in quod. Species autem et passiones et locus, in quae moventur mota quae mobilia sunt, puta scientia et caliditas; est autem non caliditas motus sed calefactio. There is something that directly causes movement; and there is something that is moved, also the time in which it is moved, and that from which and that into which it is moved. But the forms and the affections and the place, which are the terminals of the movement of moving things, are unmovable, e.g. knowledge or heat; it is not heat that is a movement, but heating.
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. Quae autem non secundum accidens permutatio non in omnibus existit, sed in contrariis et intermediis et in contradictione; huius autem fides ex inductione. Permutatur autem quod permutatur aut ex subiecto in subiectum, aut ex non subiecto in non subiectum, aut ex subiecto in non subiectum, aut ex non subiecto in subiectum. Dico autem subiectum quod affirmatione monstramus. Quare necesse tres esse permutationes; quae enim ex non subiecto in non subiectum non est permutatio; neque > enim contraria neque contradictio est, quia non oppositio. Change which is not accidental is found not in all things, but between contraries, and their intermediates, and between contradictories. We may convince ourselves of this by induction. That which changes changes either from positive into positive, or from negative into negative, or from positive into negative, or from negative into positive. (By positive I mean that which is expressed by an affirmative term.) Therefore there must be three changes; that from negative into negative is not change, because (since the terms are neither contraries nor contradictories) there is no opposition.
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. Quae quidem igitur ex non subiecto in subiectum secundum contradictionem generatio est, quae quidem simpliciter simplex, quae autem quaedam alicuius. Quae autem ex subiecto in non subiectum corruptio, quae quidem simpliciter simplex, quae autem alicuius quaedam. The change from the negative into the positive which is its contradictory is generation-absolute change absolute generation, and partial change partial generation; and the change from positive to negative is destruction-absolute change absolute destruction, and partial change partial 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. Si itaque non ens dicitur multipliciter, et neque quod secundum compositionem aut divisionem contingit moveri neque quod secundum potentiam, quod simpliciter enti oppositum (quod enim non album aut non bonum tamen contingit moveri secundum accidens; erit enim utique homo quod non album; quod autem simpliciter non hoc nequaquam): impossibile non ens moveri. Si autem hoc, et generationem motum esse; generatur enim non ens. Si enim et quam maxime secundum accidens generatur, sed tamen verum dicere quod existit non ens de generato simpliciter. Similiter autem et quiescere. Haec itaque accidunt difficilia. Et si omne quod movetur in loco, non ens autem non est in loco; erit enim utique alicubi. Neque itaque corruptio motus; contrarium enim motui motus aut quies, corruptio autem generationi. If, then, that which is not has several senses, and movement can attach neither to that which implies putting together or separating, nor to that which implies potency and is opposed to that which is in the full sense (true, the not-white or not-good can be moved incidentally, for the not-white might be a man; but that which is not a particular thing at all can in no wise be moved), that which is not cannot be moved (and if this is so, generation cannot be movement; for that which is not is generated; for even if we admit to the full that its generation is accidental, yet it is true to say that not-being is predicable of that which is generated absolutely). Similarly rest cannot be long to that which is not. These consequences, then, turn out to be awkward, and also this, that everything that is moved is in a place, but that which is not is not in a place; for then it would be somewhere. Nor is destruction movement; for the contrary of movement is rest, but the contrary of destruction [68a] 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. Quoniam autem omnis motus permutatio quaedam, permutationes autem tres dicte, harum autem quae secundum generationem et corruptionem non motus, hae autem sunt quae secundum contradictionem, necesse eam quae ex subiecto in subiectum motum esse solam. Subiecta autem aut contraria aut intermedia; et enim privatio ponatur contrarium, et monstratur affirmatione, puta nudum et edentulum et nigrum. Since every movement is a change, and the kinds of change are the three named above, and of these those in the way of generation and destruction are not movements, and these are the changes from a thing to its contradictory, it follows that only the change from positive into positive is movement. And the positives are either contrary or intermediate (for even privation must be regarded as contrary), and are expressed by an affirmative term, e.g. naked or toothless or black .

Chapter 12

Greek Latin English
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: > Si igitur predicamenta divisa sunt substantia, qualitate, ioco, facere aut pati, ad aliquid, quanto, necesse tres esse motus: qualis, quanti, loci. Chapter 12. If the categories are classified as substance, quality, place, acting or being acted on, relation, quantity, there must be three kinds of movement-of quality, of quantity, of place.
κατ᾽ οὐσίαν δ᾽ οὔ, διὰ τὸ μηθὲν εἶναι οὐσίᾳ ἐναντίον, Secundum substantiam autem non, propter nullum esse substantiae contrarium. There is no movement in respect of substance (because there is nothing contrary to substance),
οὐδὲ τοῦ πρός τι (ἔστι γὰρ θατέρου μεταβάλλοντος μὴ ἀληθεύεσθαι θάτερον μηδὲν μεταβάλλον, ὥστε κατὰ συμβεβηκὸς ἡ κίνησις αὐτῶν), Neque ad aliquid; est enim altero nihil permutato verificari alterum nihil permutatum. Quare secundum accidens motus ipsorum. nor of relation (for it is possible that if one of two things in relation changes, the relative term which was true of the other thing ceases to be true, though this other does not change at all,-so that their movement is 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. Neque facientis et patientis aut moventis et moti, quia non est motus motus neque generationis generatio, neque totaliter permutatio permutationis. Dupliciter enim contingit motus esse motum. Aut ut subiecti, velut homo movetur quia ex albo in nigrum permutatur, quare sic et motus aut calefit aut infrigidatur aut locum permutat aut augetur. Hoc autem impossibile; non enim subiectorum aliquid permutatio. Aut eo quod alterum aliquod subiectum ex permutatione permutetur in aliam speciem, velut homo ex langore in sanitatem. Sed neque hoc possibile nisi secundum accidens. Omnis enim motus ex alio in aliud est permutatio; et generatio et corruptio eodem modo, verumptamen quae quidem ex oppositis sic aut sic non motus. Simul igitur permutat ex sanitate in egritudinem, et ex hac ipsa permutatione in aliam. Palam autem quia si languerit permutatus erit in qualiacumque; contingit enim quiescere. Et adhuc in non contingentem semper, et illa ex aliquo in aliquid aliud erit. quare opposita, sanatio. Sed per accidere, velut ex reminiscentia in oblivionem permutatur quia cui existit illud permutatur, quandoque quidem in scientiam, quandoque autem in sanitatem. nor of agent and patient, or mover and moved, because there is no movement of movement nor generation of generation, nor, in general, change of change. For there might be movement of movement in two senses; (1) movement might be the subject moved, as a man is moved because he changes from pale to dark,-so that on this showing movement, too, may be either heated or cooled or change its place or increase. But this is impossible; for change is not a subject. Or (2) some other subject might change from change into some other form of existence (e.g. a man from disease into health). But this also is not possible except incidentally. For every movement is change from something into something. (And so are generation and destruction; only, these are changes into things opposed in certain ways while the other, movement, is into things opposed in another way.) A thing changes, then, at the same time from health into illness, and from this change itself into another. Clearly, then, if it has become ill, it will have changed into whatever may be the other change concerned (though it may be at rest), and, further, into a determinate change each time; and that new change will be from something definite into some other definite thing; therefore it will be the opposite change, that of growing well. We answer that this happens only incidentally; e.g. there is a change from the process of recollection to that of forgetting, only because that to which the process attaches is changing, now into a state of knowledge, now into 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. >Adhuc in infinitum ibit, si erit permutationis permutatio et generationis generatio. Necesse igitur et priorem, si posterior; puta si simplex generatio fiebat aliquando, et quod fit fiebat; quare nondum erat quod fiebat simpliciter, sed aliquid fiens simpliciter aut factum. Si itaque et hoc fiebat aliquando, quare nondum erat tunc genitum. Quoniam autem infinitorum non est primum, non erit primum, quare neque habitum. Neque fieri igitur neque moveri possibile est neque permutari nullum. Further, the process will go on to infinity, if there is to be change of change and coming to be of coming to be. What is true of the later, then, must be true of the earlier; e.g. if the simple coming to be was once coming to be, that which [68b] comes to be something was also once coming to be; therefore that which simply comes to be something was not yet in existence, but something which was coming to be coming to be something was already in existence. And this was once coming to be, so that at that time it was not yet coming to be something else. Now since of an infinite number of terms there is not a first, the first in this series will not exist, and therefore no following term exist. Nothing, then, can either come term wi to be or move or change.
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. Adhuc eiusdem motus contrarius et quies et generatio et corruptio. Quare quod fit, cum fiat fiens, tunc corrumpitur; neque enim confestim factum neque posterius; esse enim oportet quod corrumpitur. Further, that which is capable of a movement is also capable of the contrary movement and rest, and that which comes to be also ceases to be. Therefore that which is coming to be is ceasing to be when it has come to be coming to be; for it cannot cease to be as soon as it is coming to be coming to be, nor after it has come to be; for that which is ceasing to be 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. Adhuc oportet materiam subesse ei quod fit et permutato. Quae igitur erit? Quemadmodum alterabile corpus aut anima aliquid, sic aliquid quod fit motus et generatio, et aliquid in quod moventur. Oportet enim esse aliquid eum qui huius ex hoc in hoc motum, non motum. Qualiter igitur? neque enim erit disciplina disciplinationis, quare neque generatio generationis. Further, there must be a matter underlying that which comes to be and changes. What will this be, then,-what is it that becomes movement or becoming, as body or soul is that which suffers alteration? And; again, what is it that they move into? For it must be the movement or becoming of something from something into something. How, then, can this condition be fulfilled? There can be no learning of learning, and therefore no becoming of becoming.
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. Quoniam autem neque substantiae neque eius quod ad aliquid neque eius quod facere et pati, relinquitur secundum quale et quantum et ubi motum esse; horum enim unicuique contrarietas est. Dico autem quale non quod in substantia (et enim differentia quale), sed quod passivum, secundum quod dicitur pati aut impassibile esse. Since there is not movement either of substance or of relation or of activity and passivity, it remains that movement is in respect of quality and quantity and place; for each of these admits of contrariety. By quality I mean not that which is in the substance (for even the differentia is a quality), but the passive quality, in virtue of which a thing is said to be acted on or to be incapable of being acted on.
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. Immobile autem et quod totaliter impossibile moveri, et quod vix in tempore multo tarde incipiens, et quod natum quidem moveri non potens autem quando natum est et ubi et ut; quod voco quiescere immobilium solum. Contrarium enim quies motui; quare privatio utique erit susceptivi. > The immobile is either that which is wholly incapable of being moved, or that which is moved with difficulty in a long time or begins slowly, or that which is of a nature to be moved and can be moved but is not moved when and where and as it would naturally be moved. This alone among immobiles I describe as being at rest; for rest is contrary to movement, so that it must be a privation in that which is receptive of movement.
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, Simul secundum locum quaecumque in uno loco primo, et seorsum quaecumque in alio. Tangi autem quorum ultima simul. Intermedium autem in quod natum est prius pervenire quod permutatur quam in quod ultimum permutatur secundum naturam continve permutans. Contrarium secundum locum quod secundum rectam plurimum distans. Consequenter autem quo post principium ente, positione aut specie aut aliter qualiter determinato, nihil intermedium est eorum quae in eodem genere et cuius consequenter est, ut lineae lineae aut unitates unitatis aut domus domus; aliud autem nihil prohibet intermedium esse. Quod enim consequenter alicuius consequenter et posterius aliquid; non enim unum consequenter duorum neque noua luna secunde. Habitum autem quodcumque consequenter ens tangit. Quoniam autem omnis permutatio in oppositis, haec autem contraria et contradictio, contradictionis autem nullum intermedium, palam quod in contrariis intermedium. Continuum autem quod quidem habitum aliquid. Dico autem continuum cum idem fuerit et unum utriusque terminus quibus tangunt et continentur. Things which are in one proximate place are together in place, and things which are in different places are apart: things whose extremes are together touch: that at which a changing thing, if it changes continuously according to its nature, naturally arrives before it arrives at the extreme into which it is changing, is between. That which is most distant in a straight line is contrary in place. That is successive which is after the beginning (the order being determined by position or form or in some other way) and has nothing of the same class between it and that which it succeeds, e.g. lines in the case of a line, units in that of a unit, or a house in that of a house. (There is nothing to prevent a thing of some other class from being between.) For the successive succeeds something and is something later; one does not succeed two , nor the first day of [69a] the month the second. That which, being successive, touches, is contiguous. (Since all change is between opposites, and these are either contraries or contradictories, and there is no middle term for contradictories, clearly that which is between is between contraries.) The continuous is a species of the contiguous. I call two things continuous when the limits of each, with which they touch and by which they are kept together, become one and the same,
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. Quare palam quod continuum in hiis ex quibus unum aliquid natum est fieri secundum contactum. Et quia primum quod consequenter, palam. Quod enim consequenter non tangit, hoc autem consequenter; et si continuum, tangit, si autem tangit, nondum continuum; in quibus autem non est tactus, non est connascentia in hiis. Quare non est punctum unitati idem; hiis quidem enim inest tangi, hiis autem non, sed ad consequenter; et horum quidem intermedium aliquid, horum autem non. so that plainly the continuous is found in the things out of which a unity naturally arises in virtue of their contact. And plainly the successive is the first of these concepts (for the successive does not necessarily touch, but that which touches is successive; and if a thing is continuous, it touches, but if it touches, it is not necessarily continuous; and in things in which there is no touching, there is no organic unity); therefore a point is not the same as a unit; for contact belongs to points, but not to units, which have only succession; and there is something between two of the former, but not between two of the latter.


Notes


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