Moraux (Budé, 1965) · Stocks (1922)
Stocks (1922)
Greek line numbers are exact. The translations carry no Bekker numbers of their own, so those beside the English are aligned to the Greek: upright = fixed (anchored to this point in the text), italic grey = approximate (interpolated estimate).
Book 1,Chapter 1 (268a1–268b10)
268a
1 Ἡ περὶ φύσεως ἐπιστήμη σχεδὸν ἡ πλείστη φαίνεται
περί τε σώματα καὶ μεγέθη καὶ τὰ τούτων οὖσα πάθη καὶ
τὰς κινήσεις, ἔτι δὲ περὶ τὰς ἀρχάς, ὅσαι τῆς τοιαύτης οὐσίας
εἰσίν· τῶν γὰρ φύσει συνεστώτων τὰ μέν ἐστι σώματα καὶ
5 μεγέθη, τὰ δ' ἔχει σῶμα καὶ μέγεθος, τὰ δ' ἀρχαὶ τῶν
ἐχόντων εἰσίν. Συνεχὲς μὲν οὖν ἐστι τὸ διαιρετὸν εἰς ἀεὶ διαιρετά,
σῶμα δὲ τὸ πάντῃ διαιρετόν. Μεγέθους δὲ τὸ μὲν ἐφ'
ἓν γραμμή, τὸ δ' ἐπὶ δύο ἐπίπεδον, τὸ δ' ἐπὶ τρία σῶμα·
καὶ παρὰ ταῦτα οὐκ ἔστιν ἄλλο μέγεθος διὰ τὸ τὰ τρία
10 πάντα εἶναι καὶ τὸ τρὶς πάντῃ. Καθάπερ γάρ φασι καὶ οἱ
Πυθαγόρειοι, τὸ πᾶν καὶ τὰ πάντα τοῖς τρισὶν ὥρισται· τελευτὴ
γὰρ καὶ μέσον καὶ ἀρχὴ τὸν ἀριθμὸν ἔχει τὸν τοῦ
παντός, ταῦτα δὲ τὸν τῆς τριάδος. Διὸ παρὰ τῆς φύσεως
εἰληφότες ὥσπερ νόμους ἐκείνης, καὶ πρὸς τὰς ἁγιστείας
15 χρώμεθα τῶν θεῶν τῷ ἀριθμῷ τούτῳ. Ἀποδίδομεν δὲ καὶ
τὰς προσηγορίας τὸν τρόπον τοῦτον· τὰ γὰρ δύο ἄμφω μὲν
λέγομεν καὶ τοὺς δύο ἀμφοτέρους, πάντας δ' οὐ λέγομεν,
ἀλλὰ κατὰ τῶν τριῶν ταύτην τὴν κατηγορίαν κατάφαμεν πρῶτον.
Ταῦτα δ', ὥσπερ εἴρηται, διὰ τὸ τὴν φύσιν αὐτὴν οὕτως
20 ἐπάγειν ἀκολουθοῦμεν. Ὥστ' ἐπεὶ τὰ πάντα καὶ τὸ πᾶν
καὶ τὸ τέλειον οὐ κατὰ τὴν ἰδέαν διαφέρουσιν ἀλλήλων,
ἀλλ' εἴπερ, ἐν τῇ ὕλῃ καὶ ἐφ' ὧν λέγονται, τὸ σῶμα
μόνον ἂν εἴη τῶν μεγεθῶν τέλειον· μόνον γὰρ ὥρισται τοῖς
τρισίν, τοῦτο δ' ἐστὶ πᾶν. Τριχῇ δὲ ὂν διαιρετὸν πάντῃ διαιρετόν
25 ἐστιν· τῶν δ' ἄλλων τὸ μὲν ἐφ' ἓν τὸ δ' ἐπὶ δύο· ὡς
γὰρ τοῦ ἀριθμοῦ τετυχήκασιν, οὕτω καὶ τῆς διαιρέσεως
καὶ τοῦ συνεχοῦς· τὸ μὲν γὰρ ἐφ' ἓν συνεχές, τὸ δ' ἐπὶ
δύο, τὸ δὲ πάντῃ τοιοῦτον. Ὅσα μὲν οὖν διαιρετὰ τῶν μεγεθῶν,
καὶ συνεχῆ ταῦτα· εἰ δὲ καὶ τὰ συνεχῆ πάντα διαιρετά,
30 οὔπω δῆλον ἐκ τῶν νῦν. Ἀλλ' ἐκεῖνο μὲν δῆλον, ὡς οὐκ
1The science which has to do with nature clearly concerns itself for the most part with bodies and magnitudes and their properties and movements, but also with the principles of this sort of substance, as many as they may be. For of things constituted by nature some are bodies and magnitudes, some 5possess body and magnitude, and some are principles of things which possess these. Now a continuum is that which is divisible into parts always capable of subdivision, and a body is that which is every way divisible. A magnitude if divisible one way is a line, if two ways a surface, and if three a body. Beyond these there is no other magnitude, because the three dimensions 10are all that there are, and that which is divisible in three directions is divisible in all. For, as the Pythagoreans say, the world and all that is in it is determined by the number three, since beginning and middle and end give the number of an 'all', and the number they give is the triad. And so, having taken these three from nature as (so to speak) laws of it, we make 15further use of the number three in the worship of the Gods. Further, we use the terms in practice in this way. Of two things, or men, we say 'both', but not 'all': three is the first number to which the term 'all' has been appropriated. And in this, as we have said, we do but follow the lead which nature gives. Therefore, since 'every' and 'all' and 'complete' do not differ 20from one another in respect of form, but only, if at all, in their matter and in that to which they are applied, body alone among magnitudes can be complete. For it alone is determined by the three dimensions, that is, is an 'all'. But if it is divisible in three dimensions it is every way divisible, while the other magnitudes are divisible in one dimension or in two 25alone: for the divisibility and continuity of magnitudes depend upon the number of the dimensions, one sort being continuous in one direction, another in two, another in all. All magnitudes, then, which are divisible are also continuous. Whether we can also say that whatever is continuous is divisible does not yet, on our present grounds, appear. One thing, however, is clear.
268b
1 ἔστιν εἰς ἄλλο γένος μετάβασις, ὥσπερ ἐκ μήκους εἰς
ἐπιφάνειαν, εἰς δὲ σῶμα ἐξ ἐπιφανείας· οὐ γὰρ ἂν ἔτι τὸ τοιοῦτον
τέλειον εἴη μέγεθος· ἀνάγκη γὰρ γίγνεσθαι τὴν ἔκβασιν
κατὰ τὴν ἔλλειψιν, οὐχ οἷόν τε δὲ τὸ τέλειον ἐλλείπειν·
5 πάντῃ γάρ ἐστιν. Τῶν μὲν οὖν ἐν μορίου εἴδει σωμάτων κατὰ
τὸν λόγον ἕκαστον τοιοῦτόν ἐστιν· πάσας γὰρ ἔχει τὰς διαστάσεις·
ἀλλ' ὥρισται πρὸς τὸ πλησίον ἁφῇ· διὸ τρόπον τινὰ
πολλὰ τῶν σωμάτων ἕκαστόν ἐστιν. Τὸ δὲ πᾶν οὗ ταῦτα μόρια,
τέλειον ἀναγκαῖον εἶναι καὶ καθάπερ τοὔνομα σημαίνει
10 πάντῃ, καὶ μὴ τῇ μὲν τῇ δὲ μή.
1We cannot pass beyond body to a further kind, as we passed from length to surface, and from surface to body. For if we could, it would cease to be true that body is complete magnitude. We could pass beyond it only in virtue of a defect in it; and that which is complete cannot be defective, since it has being in every respect. 5Now bodies which are classed as parts of the whole are each complete according to our formula, since each possesses every dimension. But each is determined relatively to that part which is next to it by contact, for which reason each of them is in a sense many bodies. But the whole of which they are parts must necessarily be complete, and thus, in accordance with the meaning of the word, have being, 10not in some respect only, but in every respect.
Book 1,Chapter 2 (268b11–269b17)
Περὶ μὲν οὖν τῆς τοῦ παντὸς φύσεως, εἴτ' ἄπειρός ἐστι
κατὰ τὸ μέγεθος εἴτε πεπέρανται τὸν σύνολον ὄγκον, ὕστερον
ἐπισκεπτέον· περὶ δὲ τῶν κατ' εἶδος αὐτοῦ μορίων νῦν λέγωμεν
ἀρχὴν ποιησάμενοι τήνδε. Πάντα γὰρ τὰ φυσικὰ σώματα
15 καὶ μεγέθη καθ' αὑτὰ κινητὰ λέγομεν εἶναι κατὰ
τόπον· τὴν γὰρ φύσιν κινήσεως ἀρχὴν εἶναί φαμεν αὐτοῖς.
Πᾶσα δὲ κίνησις ὅση κατὰ τόπον, ἣν καλοῦμεν φοράν, ἢ
εὐθεῖα ἢ κύκλῳ ἢ ἐκ τούτων μικτή· ἁπλαῖ γὰρ αὗται δύο
μόναι. Αἴτιον δ' ὅτι καὶ τὰ μεγέθη ταῦτα ἁπλᾶ μόνον,
20 ἥ τ' εὐθεῖα καὶ ἡ περιφερής. Κύκλῳ μὲν οὖν ἐστιν ἡ περὶ τὸ
μέσον, εὐθεῖα δ' ἡ ἄνω καὶ κάτω. Λέγω δ' ἄνω μὲν τὴν
ἀπὸ τοῦ μέσου, κάτω δὲ τὴν ἐπὶ τὸ μέσον. Ὥστ' ἀνάγκη
πᾶσαν εἶναι τὴν ἁπλῆν φορὰν τὴν μὲν ἀπὸ τοῦ μέσου, τὴν
δ' ἐπὶ τὸ μέσον, τὴν δὲ περὶ τὸ μέσον. Καὶ ἔοικεν ἠκολουθηκέναι
25 κατὰ λόγον τοῦτο τοῖς ἐξ ἀρχῆς· τό τε γὰρ σῶμα
ἀπετελέσθη ἐν τρισὶ καὶ ἡ κίνησις αὐτοῦ. Ἐπεὶ δὲ τῶν σωμάτων
τὰ μέν ἐστιν ἁπλᾶ τὰ δὲ σύνθετα ἐκ τούτων (λέγω
δ' ἁπλᾶ μὲν ὅσα κινήσεως ἀρχὴν ἔχει κατὰ φύσιν, οἷον πῦρ
καὶ γῆν καὶ τὰ τούτων εἴδη καὶ τὰ συγγενῆ τούτοις), ἀνάγκη
30 καὶ τὰς κινήσεις εἶναι τὰς μὲν ἁπλᾶς τὰς δὲ μικτάς πως,
The question as to the nature of the whole, whether it is infinite in size or limited in its total mass, is a matter for subsequent inquiry. We will now speak of those parts of the whole which are specifically distinct. Let us take this as our starting-point. All natural bodies and magnitudes we hold to be, as such, capable of locomotion; for nature, we say, 15is their principle of movement. But all movement that is in place, all locomotion, as we term it, is either straight or circular or a combination of these two, which are the only simple movements. And the reason of this is that these two, the straight and the circular line, are the only simple magnitudes. Now revolution about the centre is circular motion, while the upward and downward movements are 20in a straight line, 'upward' meaning motion away from the centre, and 'downward' motion towards it. All simple motion, then, must be motion either away from or towards or about the centre. This seems to be in exact accord with what we said above: as body found its completion in three dimensions, so its movement completes itself in three forms.
Bodies are either simple or compounded of such; and by simple 25bodies I mean those which possess a principle of movement in their own nature, such as fire and earth with their kinds, and whatever is akin to them. Necessarily, then, movements also will be either simple or in some sort compound-simple in the case of the simple bodies, compound in that of the composite-and in the latter case the motion will be that of the simple body which prevails in the composition.
Bodies are either simple or compounded of such; and by simple 25bodies I mean those which possess a principle of movement in their own nature, such as fire and earth with their kinds, and whatever is akin to them. Necessarily, then, movements also will be either simple or in some sort compound-simple in the case of the simple bodies, compound in that of the composite-and in the latter case the motion will be that of the simple body which prevails in the composition.
269a
1 καὶ τῶν μὲν ἁπλῶν ἁπλᾶς, μικτὰς δὲ τῶν συνθέτων, κινεῖσθαι
δὲ κατὰ τὸ ἐπικρατοῦν. Εἴπερ οὖν ἐστιν ἁπλῆ κίνησις,
ἁπλῆ δ' ἡ κύκλῳ κίνησις, καὶ τοῦ τε ἁπλοῦ σώματος ἁπλῆ
ἡ κίνησις καὶ ἡ ἁπλῆ κίνησις ἁπλοῦ σώματος (καὶ γὰρ ἂν
5 συνθέτου ᾖ, κατὰ τὸ ἐπικρατοῦν ἔσται), ἀναγκαῖον εἶναί τι
σῶμα ἁπλοῦν ὃ πέφυκε φέρεσθαι τὴν κύκλῳ κίνησιν κατὰ
τὴν ἑαυτοῦ φύσιν· βίᾳ μὲν γὰρ ἐνδέχεται τὴν ἄλλου καὶ
ἑτέρου, κατὰ φύσιν δὲ ἀδύνατον, εἴπερ μία ἑκάστου κίνησις
ἡ κατὰ φύσιν τῶν ἁπλῶν. Ἔτι εἰ ἡ παρὰ φύσιν ἐναντία τῇ
10 κατὰ φύσιν καὶ ἓν ἑνὶ ἐναντίον, ἀνάγκη, ἐπεὶ ἁπλῆ ἡ κύκλῳ,
εἰ μὴ ἔσται κατὰ φύσιν τοῦ φερομένου σώματος,
παρὰ φύσιν αὐτοῦ εἶναι. Εἰ οὖν πῦρ ἢ ἄλλο τι τῶν τοιούτων
ἐστὶ τὸ κύκλῳ φερόμενον, ἐναντία ἡ κατὰ φύσιν αὐτοῦ φορὰ
ἔσται τῇ κύκλῳ. Ἀλλ' ἓν ἑνὶ ἐναντίον· ἡ δ' ἄνω καὶ κάτω
15 ἀλλήλαις ἐναντίαι. Εἰ δ' ἕτερόν τί ἐστι σῶμα τὸ φερόμενον
κύκλῳ παρὰ φύσιν, ἔσται τις αὐτοῦ ἄλλη κίνησις κατὰ
φύσιν. Ἀλλὰ τοῦτ' ἀδύνατον· εἰ μὲν γὰρ ἡ ἄνω, πῦρ ἔσται ἢ
ἀήρ, εἰ δ' ἡ κάτω, ὕδωρ ἢ γῆ. Ἀλλὰ μὴν καὶ πρώτην γε
ἀναγκαῖον εἶναι τὴν τοιαύτην φοράν. Τὸ γὰρ τέλειον πρότερον
20 τῇ φύσει τοῦ ἀτελοῦς, ὁ δὲ κύκλος τῶν τελείων, εὐθεῖα
δὲ γραμμὴ οὐδεμία· οὔτε γὰρ ἡ ἄπειρος (ἔχοι γὰρ ἂν πέρας
καὶ τέλος) οὔτε τῶν πεπερασμένων οὐδεμία (πασῶν γάρ
ἐστί τι ἐκτός· αὐξῆσαι γὰρ ἐνδέχεται ὁποιανοῦν). Ὥστ' εἴπερ
ἡ μὲν προτέρα κίνησις προτέρου τῇ φύσει σώματος, ἡ δὲ
25 κύκλῳ προτέρα τῆς εὐθείας, ἡ δ' ἐπ' εὐθείας τῶν ἁπλῶν
σωμάτων ἐστί (τό τε γὰρ πῦρ ἐπ' εὐθείας ἄνω φέρεται καὶ
τὰ γεηρὰ κάτω πρὸς τὸ μέσον), ἀνάγκη καὶ τὴν κύκλῳ
κίνησιν τῶν ἁπλῶν τινος εἶναι σωμάτων· τῶν γὰρ μικτῶν
τὴν φορὰν ἔφαμεν εἶναι κατὰ τὸ ἐπικρατοῦν ἐν τῇ μίξει
30 τῶν ἁπλῶν. Ἔκ τε δὴ τούτων φανερὸν ὅτι πέφυκέ τις οὐσία
σώματος ἄλλη παρὰ τὰς ἐνταῦθα συστάσεις, θειοτέρα καὶ
προτέρα τούτων ἁπάντων, κἂν εἴ τις ἔτι λάβοι πᾶσαν εἶναι
κίνησιν ἢ κατὰ φύσιν ἢ παρὰ φύσιν, καὶ τὴν ἄλλῳ παρὰ
φύσιν ἑτέρῳ κατὰ φύσιν, οἷον ἡ ἄνω καὶ ἡ κάτω πέπονθεν·
35 ἡ μὲν γὰρ τῷ πυρί, ἡ δὲ τῇ γῇ παρὰ φύσιν καὶ κατὰ φύσιν·
1Supposing, then, that there is such a thing as simple movement, and that circular movement is an instance of it, and that both movement of a simple body is simple and simple movement is of a simple body (for if it is movement of a compound it will be in virtue of a prevailing simple element), 5then there must necessarily be some simple body which revolves naturally and in virtue of its own nature with a circular movement. By constraint, of course, it may be brought to move with the motion of something else different from itself, but it cannot so move naturally, since there is one sort of movement natural to each of the simple bodies. Again, if the unnatural 10movement is the contrary of the natural and a thing can have no more than one contrary, it will follow that circular movement, being a simple motion, must be unnatural, if it is not natural, to the body moved. If then (1) the body, whose movement is circular, is fire or some other element, its natural motion must be the contrary of the circular motion. But a single 15thing has a single contrary; and upward and downward motion are the contraries of one another. If, on the other hand, (2) the body moving with this circular motion which is unnatural to it is something different from the elements, there will be some other motion which is natural to it. But this cannot be. For if the natural motion is upward, it will be fire or 20air, and if downward, water or earth. Further, this circular motion is necessarily primary. For the perfect is naturally prior to the imperfect, and the circle is a perfect thing. This cannot be said of any straight line:-not of an infinite line; for, if it were perfect, it would have a limit and an end: nor of any finite line; for in every case there is something 25beyond it, since any finite line can be extended. And so, since the prior movement belongs to the body which naturally prior, and circular movement is prior to straight, and movement in a straight line belongs to simple bodies-fire moving straight upward and earthy bodies straight downward towards the centre-since this is so, it follows that circular movement also must 30be the movement of some simple body. For the movement of composite bodies is, as we said, determined by that simple body which preponderates in the composition. These premises clearly give the conclusion that there is in nature some bodily substance other than the formations we know, prior to them all and more divine than they. But it may also be proved as follows.
269b
1 ὥστ' ἀναγκαῖον καὶ τὴν κύκλῳ κίνησιν, ἐπειδὴ τούτοις
παρὰ φύσιν, ἑτέρου τινὸς εἶναι κατὰ φύσιν. Πρὸς δὲ τούτοις
εἰ μέν ἐστιν ἡ κύκλῳ τινὶ φορὰ κατὰ φύσιν, δῆλον ὡς εἴη
ἄν τι σῶμα τῶν ἁπλῶν καὶ πρώτων, ὃ πέφυκεν, ὥσπερ
5 τὸ πῦρ ἄνω καὶ ἡ γῆ κάτω, ἐκεῖνο κύκλῳ φέρεσθαι κατὰ
φύσιν. Εἰ δὲ παρὰ φύσιν φέρεται τὰ φερόμενα κύκλῳ τὴν
πέριξ φοράν, θαυμαστὸν καὶ παντελῶς ἄλογον τὸ μόνην
εἶναι συνεχῆ ταύτην τὴν κίνησιν καὶ ἀΐδιον, οὖσαν παρὰ
φύσιν· φαίνεται γὰρ ἔν γε τοῖς ἄλλοις τάχιστα φθειρόμενα
10 τὰ παρὰ φύσιν. Ὥστ' εἴπερ ἐστὶ πῦρ τὸ φερόμενον,
καθάπερ φασί τινες, οὐδὲν ἧττον αὐτῷ παρὰ φύσιν ἡ κίνησίς
ἐστιν αὕτη ἢ ἡ κάτω· πυρὸς γὰρ κίνησιν ὁρῶμεν τὴν ἀπὸ
τοῦ μέσου κατ' εὐθεῖαν. Διόπερ ἐξ ἁπάντων ἄν τις τούτων
συλλογιζόμενος πιστεύσειεν ὡς ἔστι τι παρὰ τὰ σώματα
15 τὰ δεῦρο καὶ περὶ ἡμᾶς ἕτερον κεχωρισμένον, τοσούτῳ
τιμιωτέραν ἔχον τὴν φύσιν ὅσῳπερ ἀφέστηκε τῶν ἐνταῦθα
πλεῖον.
1We may take it that all movement is either natural or unnatural, and that the movement which is unnatural to one body is natural to another-as, for instance, is the case with the upward and downward movements, which are natural and unnatural to fire and earth respectively. It necessarily follows that circular 5movement, being unnatural to these bodies, is the natural movement of some other. Further, if, on the one hand, circular movement is natural to something, it must surely be some simple and primary body which is ordained to move with a natural circular motion, as fire is ordained to fly up and earth down. If, on the other hand, the movement of the rotating bodies about the centre is 10unnatural, it would be remarkable and indeed quite inconceivable that this movement alone should be continuous and eternal, being nevertheless contrary to nature. At any rate the evidence of all other cases goes to show that it is the unnatural which quickest passes away. And so, if, as some say, the body so moved is fire, this movement is just as unnatural to it as downward movement; 15for any one can see that fire moves in a straight line away from the centre. On all these grounds, therefore, we may infer with confidence that there is something beyond the bodies that are about us on this earth, different and separate from them; and that the superior glory of its nature is proportionate to its distance from this world of ours.
Book 1,Chapter 3 (269b18–270b31)
Ἐπεὶ δὲ τὰ μὲν ὑπόκειται τὰ δ' ἀποδέδεικται τῶν
εἰρημένων, φανερὸν ὅτι οὔτε κουφότητα οὔτε βάρος ἔχει
20 σῶμα ἅπαν, δεῖ δὲ ὑποθέσθαι τί λέγομεν τὸ βαρὺ καὶ τὸ
κοῦφον, νῦν μὲν ἱκανῶς ὡς πρὸς τὴν παροῦσαν χρείαν, ἀκριβέστερον
δὲ πάλιν, ὅταν ἐπισκοπῶμεν περὶ τῆς οὐσίας αὐτῶν.
Βαρὺ μὲν οὖν ἔστω τὸ φέρεσθαι πεφυκὸς ἐπὶ τὸ μέσον,
κοῦφον δὲ τὸ ἀπὸ τοῦ μέσου, βαρύτατον δὲ τὸ πᾶσιν ὑφιστάμενον
25 τοῖς κάτω φερομένοις, κουφότατον δὲ τὸ πᾶσιν
ἐπιπολάζον τοῖς ἄνω φερομένοις. Ἀνάγκη δὴ πᾶν τὸ φερόμενον
ἢ κάτω ἢ ἄνω ἢ κουφότητ' ἔχειν ἢ βάρος ἢ ἄμφω,
μὴ πρὸς τὸ αὐτὸ δέ· πρὸς ἄλληλα γάρ ἐστι βαρέα
καὶ κοῦφα, οἷον ἀὴρ πρὸς ὕδωρ, καὶ πρὸς γῆν ὕδωρ. Τὸ
30 δὲ κύκλῳ σῶμα φερόμενον ἀδύνατον ἔχειν βάρος ἢ κουφότητα·
οὔτε γὰρ κατὰ φύσιν οὔτε παρὰ φύσιν ἐνδέχεται
αὐτῷ κινηθῆναι ἐπὶ τὸ μέσον ἢ ἀπὸ τοῦ μέσου. Κατὰ φύσιν
μὲν γὰρ οὐκ ἔστιν αὐτῷ ἡ ἐπ' εὐθείας φορά· μία γὰρ
ἦν ἑκάστου τῶν ἁπλῶν, ὥστ' ἔσται τὸ αὐτὸ τῶν οὕτω τινὶ
35 φερομένων. Παρὰ φύσιν δ' ἐνεχθέντος, εἰ μὲν ἡ κάτω
In consequence of what has been said, 20in part by way of assumption and in part by way of proof, it is clear that not every body either possesses lightness or heaviness. As a preliminary we must explain in what sense we are using the words 'heavy' and 'light', sufficiently, at least, for our present purpose: we can examine the terms more closely later, when we come to consider their essential nature. Let us then apply the 25term 'heavy' to that which naturally moves towards the centre, and 'light' to that which moves naturally away from the centre. The heaviest thing will be that which sinks to the bottom of all things that move downward, and the lightest that which rises to the surface of everything that moves upward. Now, necessarily, everything which moves either up or down possesses lightness or 30heaviness or both-but not both relatively to the same thing: for things are heavy and light relatively to one another; air, for instance, is light relatively to water, and water light relatively to earth. The body, then, which moves in a circle cannot possibly possess either heaviness or lightness. For neither naturally nor unnaturally can it move either towards or away from the centre.
270a
1 παρὰ φύσιν, ἡ ἄνω ἔσται κατὰ φύσιν, εἰ δ' ἡ ἄνω παρὰ
φύσιν, ἡ κάτω κατὰ φύσιν· ἔθεμεν γὰρ τῶν ἐναντίων ᾧ
ἡ ἑτέρα παρὰ φύσιν, τὴν ἑτέραν εἶναι κατὰ φύσιν. Ἐπεὶ
δ' εἰς τὸ αὐτὸ φέρεται τὸ ὅλον καὶ τὸ μόριον κατὰ φύσιν,
5 οἷον πᾶσα γῆ καὶ μικρὰ βῶλος, συμβαίνει πρῶτον μὲν
μήτε κουφότητ' ἔχειν αὐτὸ μηδεμίαν μήτε βάρος (ἢ γὰρ ἂν
πρὸς τὸ μέσον ἢ ἀπὸ τοῦ μέσου ἠδύνατο φέρεσθαι κατὰ τὴν
ἑαυτοῦ φύσιν), ἔπειθ' ὅτι ἀδύνατον κινηθῆναι τὴν κατὰ
τόπον κίνησιν ἢ ἄνω ἢ κάτω κατασπώμενον· οὔτε γὰρ
10 κατὰ φύσιν ἐνδέχεται κινηθῆναι κίνησιν αὐτῷ ἄλλην οὔτε
παρὰ φύσιν, οὔτ' αὐτῷ οὔτε τῶν μορίων οὐδενί· ὁ γὰρ αὐτὸς
λόγος περὶ ὅλου καὶ μέρους. Ὁμοίως δ' εὔλογον ὑπολαβεῖν
περὶ αὐτοῦ καὶ ὅτι ἀγένητον καὶ ἄφθαρτον καὶ ἀναυξὲς
καὶ ἀναλλοίωτον, διὰ τὸ γίγνεσθαι μὲν ἅπαν τὸ γιγνόμενον
15 ἐξ ἐναντίου τε καὶ ὑποκειμένου τινός, καὶ φθείρεσθαι
ὡσαύτως ὑποκειμένου τέ τινος καὶ ὑπ' ἐναντίου καὶ εἰς
ἐναντίον, καθάπερ ἐν τοῖς πρώτοις εἴρηται λόγοις· τῶν δ'
ἐναντίων καὶ αἱ φοραὶ ἐναντίαι. Εἰ δὴ τούτῳ μηδὲν ἐναντίον
ἐνδέχεται εἶναι διὰ τὸ καὶ τῇ φορᾷ τῇ κύκλῳ μὴ εἶναι
20 ἄν τιν' ἐναντίαν κίνησιν, ὀρθῶς ἔοικεν ἡ φύσις τὸ μέλλον
ἔσεσθαι ἀγένητον καὶ ἄφθαρτον ἐξελέσθαι ἐκ τῶν ἐναντίων·
ἐν τοῖς ἐναντίοις γὰρ ἡ γένεσις καὶ ἡ φθορά. Ἀλλὰ μὴν
καὶ τὸ αὐξανόμενον ἅπαν αὐξάνεται [καὶ τὸ φθῖνον φθίνει]
ὑπὸ συγγενοῦς προσιόντος καὶ ἀναλυομένου εἰς τὴν ὕλην·
25 τούτῳ δ' οὐκ ἔστιν ἐξ οὗ γέγονεν. Εἰ δ' ἐστὶ καὶ ἀναύξητον
καὶ ἄφθαρτον, τῆς αὐτῆς διανοίας ἐστὶν ὑπολαβεῖν καὶ ἀναλλοίωτον
εἶναι. Ἔστι μὲν γὰρ ἡ ἀλλοίωσις κίνησις κατὰ τὸ ποιόν,
τοῦ δὲ ποιοῦ αἱ μὲν ἕξεις καὶ διαθέσεις οὐκ ἄνευ τῶν κατὰ
τὰ πάθη γίγνονται μεταβολῶν, οἷον ὑγίεια καὶ νόσος. Κατὰ
30 δὲ πάθος ὅσα μεταβάλλει τῶν φυσικῶν σωμάτων, ἔχονθ'
ὁρῶμεν πάντα καὶ αὔξησιν καὶ φθίσιν, οἷον τά τε τῶν ζῴων
σώματα καὶ τὰ μόρια αὐτῶν καὶ τὰ τῶν φυτῶν, ὁμοίως
δὲ καὶ τὰ τῶν στοιχείων· ὥστ' εἴπερ τὸ κύκλῳ σῶμα μήτ'
αὔξησιν ἔχειν ἐνδέχεται μήτε φθίσιν, εὔλογον καὶ ἀναλλοίωτον
35 εἶναι.
1Movement in a straight line certainly does not belong to it naturally, since one sort of movement is, as we saw, appropriate to each simple body, and so we should be compelled to identify it with one of the bodies which move in this way. Suppose, then, that the movement is unnatural. In that case, 5if it is the downward movement which is unnatural, the upward movement will be natural; and if it is the upward which is unnatural, the downward will be natural. For we decided that of contrary movements, if the one is unnatural to anything, the other will be natural to it. But since the natural movement of the whole and of its part of earth, for instance, as a whole 10and of a small clod-have one and the same direction, it results, in the first place, that this body can possess no lightness or heaviness at all (for that would mean that it could move by its own nature either from or towards the centre, which, as we know, is impossible); and, secondly, that it cannot possibly move in the way of locomotion by being forced violently aside 15in an upward or downward direction. For neither naturally nor unnaturally can it move with any other motion but its own, either itself or any part of it, since the reasoning which applies to the whole applies also to the part.
It is equally reasonable to assume that this body will be ungenerated and indestructible and exempt from increase and alteration, since everything 20that comes to be comes into being from its contrary and in some substrate, and passes away likewise in a substrate by the action of the contrary into the contrary, as we explained in our opening discussions. Now the motions of contraries are contrary. If then this body can have no contrary, because there can be no contrary motion to the circular, nature seems justly to 25have exempted from contraries the body which was to be ungenerated and indestructible. For it is in contraries that generation and decay subsist. Again, that which is subject to increase increases upon contact with a kindred body, which is resolved into its matter. But there is nothing out of which this body can have been generated. And if it is exempt from increase and 30diminution, the same reasoning leads us to suppose that it is also unalterable. For alteration is movement in respect of quality; and qualitative states and dispositions, such as health and disease, do not come into being without changes of properties. But all natural bodies which change their properties we see to be subject without exception to increase and diminution.
It is equally reasonable to assume that this body will be ungenerated and indestructible and exempt from increase and alteration, since everything 20that comes to be comes into being from its contrary and in some substrate, and passes away likewise in a substrate by the action of the contrary into the contrary, as we explained in our opening discussions. Now the motions of contraries are contrary. If then this body can have no contrary, because there can be no contrary motion to the circular, nature seems justly to 25have exempted from contraries the body which was to be ungenerated and indestructible. For it is in contraries that generation and decay subsist. Again, that which is subject to increase increases upon contact with a kindred body, which is resolved into its matter. But there is nothing out of which this body can have been generated. And if it is exempt from increase and 30diminution, the same reasoning leads us to suppose that it is also unalterable. For alteration is movement in respect of quality; and qualitative states and dispositions, such as health and disease, do not come into being without changes of properties. But all natural bodies which change their properties we see to be subject without exception to increase and diminution.
270b
1 Διότι μὲν οὖν ἀΐδιον καὶ οὔτ' αὔξησιν ἔχον οὔτε φθίσιν,
ἀλλ' ἀγήρατον καὶ ἀναλλοίωτον καὶ ἀπαθές ἐστι τὸ πρῶτον
τῶν σωμάτων, εἴ τις τοῖς ὑποκειμένοις πιστεύει, φανερὸν
ἐκ τῶν εἰρημένων ἐστίν. Ἔοικε δ' ὅ τε λόγος τοῖς φαινομένοις
5 μαρτυρεῖν καὶ τὰ φαινόμενα τῷ λόγῳ· πάντες γὰρ
ἄνθρωποι περὶ θεῶν ἔχουσιν ὑπόληψιν, καὶ πάντες τὸν ἀνωτάτω
τῷ θείῳ τόπον ἀποδιδόασι, καὶ βάρβαροι καὶ Ἕλληνες,
ὅσοι περ εἶναι νομίζουσι θεούς, δῆλον ὅτι ὡς τῷ
ἀθανάτῳ τὸ ἀθάνατον συνηρτημένον· ἀδύνατον γὰρ ἄλλως.
10 Εἴπερ οὖν ἔστι τι θεῖον, ὥσπερ ἔστι, καὶ τὰ νῦν εἰρημένα περὶ
τῆς πρώτης οὐσίας τῶν σωμάτων εἴρηται καλῶς. Συμβαίνει
δὲ τοῦτο καὶ διὰ τῆς αἰσθήσεως ἱκανῶς, ὥς γε πρὸς ἀνθρωπίνην
εἰπεῖν πίστιν· ἐν ἅπαντι γὰρ τῷ παρεληλυθότι
χρόνῳ κατὰ τὴν παραδεδομένην ἀλλήλοις μνήμην οὐθὲν
15 φαίνεται μεταβεβληκὸς οὔτε καθ' ὅλον τὸν ἔσχατον οὐρανὸν
οὔτε κατὰ μόριον αὐτοῦ τῶν οἰκείων οὐθέν. Ἔοικε δὲ καὶ τοὔνομα
παρὰ τῶν ἀρχαίων παραδεδόσθαι μέχρι καὶ τοῦ νῦν
χρόνου, τοῦτον τὸν τρόπον ὑπολαμβανόντων ὅνπερ καὶ ἡμεῖς
λέγομεν· οὐ γὰρ ἅπαξ οὐδὲ δὶς ἀλλ' ἀπειράκις δεῖ νομίζειν
20 τὰς αὐτὰς ἀφικνεῖσθαι δόξας εἰς ἡμᾶς. Διόπερ ὡς ἑτέρου
τινὸς ὄντος τοῦ πρώτου σώματος παρὰ γῆν καὶ πῦρ καὶ
ἀέρα καὶ ὕδωρ, αἰθέρα προσωνόμασαν τὸν ἀνωτάτω τόπον,
ἀπὸ τοῦ θεῖν ἀεὶ τὸν ἀΐδιον χρόνον θέμενοι τὴν ἐπωνυμίαν
αὐτῷ. Ἀναξαγόρας δὲ καταχρῆται τῷ ὀνόματι τούτῳ οὐ
25 καλῶς· ὀνομάζει γὰρ αἰθέρα ἀντὶ πυρός.
Φανερὸν δ' ἐκ τῶν εἰρημένων καὶ διότι τὸν ἀριθμὸν
ἀδύνατον εἶναι πλείω τὸν τῶν λεγομένων σωμάτων ἁπλῶν·
τοῦ μὲν γὰρ ἁπλοῦ σώματος ἀνάγκη τὴν κίνησιν ἁπλῆν
εἶναι, μόνας δὲ ταύτας εἶναί φαμεν ἁπλᾶς, τήν τε κύκλῳ
30 καὶ τὴν ἐπ' εὐθείας, καὶ ταύτης τὰ δύο μόρια, τὴν μὲν
ἀπὸ τοῦ μέσου, τὴν δ' ἐπὶ τὸ μέσον.
1This is the case, for instance, with the bodies of animals and their parts and with vegetable bodies, and similarly also with those of the elements. And so, if the body which moves with a circular motion cannot admit of increase or diminution, it is reasonable to suppose that it is also unalterable.
The 5reasons why the primary body is eternal and not subject to increase or diminution, but unaging and unalterable and unmodified, will be clear from what has been said to any one who believes in our assumptions. Our theory seems to confirm experience and to be confirmed by it. For all men have some conception of the nature of the gods, and all who believe in the existence of gods at 10all, whether barbarian or Greek, agree in allotting the highest place to the deity, surely because they suppose that immortal is linked with immortal and regard any other supposition as inconceivable. If then there is, as there certainly is, anything divine, what we have just said about the primary bodily substance was well said. The mere evidence of the senses is enough to 15convince us of this, at least with human certainty. For in the whole range of time past, so far as our inherited records reach, no change appears to have taken place either in the whole scheme of the outermost heaven or in any of its proper parts. The common name, too, which has been handed down from our distant ancestors even to our own day, seems to show that they conceived of it 20in the fashion which we have been expressing. The same ideas, one must believe, recur in men's minds not once or twice but again and again. And so, implying that the primary body is something else beyond earth, fire, air, and water, they gave the highest place a name of its own, aither, derived from the fact that it 'runs always' for an eternity of time. Anaxagoras, however, 25scandalously misuses this name, taking aither as equivalent to fire.
It is also clear from what has been said why the number of what we call simple bodies cannot be greater than it is. The motion of a simple body must itself be simple, and we assert that there are only these two simple motions, the circular and the straight, the latter being subdivided into motion away from and motion 30towards the centre.
The 5reasons why the primary body is eternal and not subject to increase or diminution, but unaging and unalterable and unmodified, will be clear from what has been said to any one who believes in our assumptions. Our theory seems to confirm experience and to be confirmed by it. For all men have some conception of the nature of the gods, and all who believe in the existence of gods at 10all, whether barbarian or Greek, agree in allotting the highest place to the deity, surely because they suppose that immortal is linked with immortal and regard any other supposition as inconceivable. If then there is, as there certainly is, anything divine, what we have just said about the primary bodily substance was well said. The mere evidence of the senses is enough to 15convince us of this, at least with human certainty. For in the whole range of time past, so far as our inherited records reach, no change appears to have taken place either in the whole scheme of the outermost heaven or in any of its proper parts. The common name, too, which has been handed down from our distant ancestors even to our own day, seems to show that they conceived of it 20in the fashion which we have been expressing. The same ideas, one must believe, recur in men's minds not once or twice but again and again. And so, implying that the primary body is something else beyond earth, fire, air, and water, they gave the highest place a name of its own, aither, derived from the fact that it 'runs always' for an eternity of time. Anaxagoras, however, 25scandalously misuses this name, taking aither as equivalent to fire.
It is also clear from what has been said why the number of what we call simple bodies cannot be greater than it is. The motion of a simple body must itself be simple, and we assert that there are only these two simple motions, the circular and the straight, the latter being subdivided into motion away from and motion 30towards the centre.
Book 1,Chapter 4 (270b32–271a33)
Ὅτι δ' οὐκ ἔστι τῇ κύκλῳ φορᾷ ἐναντία ἄλλη φορά,
πλεοναχόθεν ἄν τις λάβοι τὴν πίστιν· πρῶτον μὲν ὅτι τῇ
περιφερεῖ τὴν εὐθεῖαν ἀντικεῖσθαι μάλιστα τίθεμεν· τὸ γὰρ
35 κοῖλον καὶ τὸ κυρτὸν οὐ μόνον ἀλλήλοις ἀντικεῖσθαι δοκεῖ
That there is no other form of motion opposed as contrary to the circular may be proved in various ways. In the first place, there is an obvious tendency to oppose the straight line to the circular. For concave and convex are a not only regarded as opposed to one another, but they are also coupled together and treated as a unity in opposition to the straight.
271a
1 ἀλλὰ καὶ τῷ εὐθεῖ, συνδυαζόμενα καὶ λαβόντα σύνθεσιν·
ὥστ' εἴπερ ἐναντία τίς ἐστι, τὴν ἐπὶ τῆς εὐθείας μάλιστα
ἀναγκαῖον ἐναντίαν εἶναι πρὸς τὴν κύκλῳ κίνησιν. Αἱ δ' ἐπὶ
τῆς εὐθείας ἀλλήλαις ἀντίκεινται διὰ τοὺς τόπους· τὸ γὰρ
5 ἄνω κάτω τόπου τέ ἐστι διαφορὰ καὶ ἐναντίωσις. Ἔπειτ'
εἴ τις ὑπολαμβάνει τὸν αὐτὸν εἶναι λόγον ὅνπερ ἐπὶ τῆς
εὐθείας καὶ ἐπὶ τῆς περιφεροῦς (τὴν γὰρ ἀπὸ τοῦ Α πρὸς
τὸ Β φορὰν ἐναντίαν εἶναι τῇ ἀπὸ τοῦ Β πρὸς τὸ Α), τὴν
ἐπὶ τῆς εὐθείας λέγει· αὕτη γὰρ πεπέρανται, περιφερεῖς
10 δ' ἄπειροι ἂν εἶεν περὶ τὰ αὐτὰ σημεῖα. Ὁμοίως δὲ καὶ
ἐπὶ τοῦ ἡμικυκλίου τοῦ ἑνός, οἷον ἀπὸ τοῦ Γ ἐπὶ τὸ Δ καὶ
ἀπὸ τοῦ Δ ἐπὶ τὸ Γ· ἡ γὰρ αὐτὴ τῇ ἐπὶ τῆς διαμέτρου
ἐστίν· ἀεὶ γὰρ ἕκαστον ἀπέχειν τὴν εὐθεῖαν τίθεμεν. Ὁμοίως
δὲ κἂν εἴ τις κύκλον ποιήσας τὴν ἐπὶ θατέρου ἡμικυκλίου
15 φορὰν ἐναντίαν θείη τῇ ἐπὶ θατέρου, οἷον ἐν τῷ ὅλῳ κύκλῳ
τὴν ἀπὸ τοῦ Ε πρὸς τὸ Ζ τοῦ Η ἡμικυκλίου τῇ ἀπὸ
τοῦ Ζ πρὸς τὸ Ε ἐν τῷ Θ ἡμικυκλίῳ. Εἰ δὲ καὶ αὗται
ἐναντίαι, ἀλλ' οὔτι γε αἱ ἐπὶ τοῦ ὅλου κύκλου φοραὶ ἀλλήλαις
διὰ τοῦτο ἐναντίαι. *—* Ἀλλὰ μὴν οὐδ' ἡ ἀπὸ τοῦ Α ἐπὶ
20 τὸ Β κύκλῳ φορὰ ἐναντία τῇ ἀπὸ τοῦ Α ἐπὶ τὸ Γ· ἐκ
ταὐτοῦ γὰρ εἰς ταὐτὸ ἡ κίνησις, ἡ δ' ἐναντία διωρίσθη φορὰ
ἐκ τοῦ ἐναντίου εἰς τὸ ἐναντίον. Εἰ δὲ καὶ ἦν ἡ κύκλῳ
τῇ κύκλῳ ἐναντία, μάτην ἂν ἦν ἡ ἑτέρα· *ἐπὶ τὸ αὐτὸ
γάρ, ὅτι ἀνάγκη τὸ κύκλῳ φερόμενον ὁποθενοῦν ἀρξάμενον
25 εἰς πάντας ὁμοίως ἀφικνεῖσθαι τοὺς ἐναντίους τόπους
(εἰσὶ δὲ τόπου ἐναντιότητες τὸ ἄνω καὶ κάτω καὶ τὸ πρόσθιον
καὶ ὀπίσθιον καὶ τὸ δεξιὸν καὶ ἀριστερόν), αἱ δὲ τῆς
φορᾶς ἐναντιώσεις κατὰ τὰς τῶν τόπων εἰσὶν ἐναντιώσεις·*
εἰ μὲν γὰρ ἴσαι ἦσαν, οὐκ ἂν ἦν κίνησις αὐτῶν, εἰ δ' ἡ
30 ἑτέρα κίνησις ἐκράτει, ἡ ἑτέρα οὐκ ἂν ἦν. Ὥστ' εἰ ἀμφότερα
ἦν, μάτην ἂν θάτερον ἦν σῶμα μὴ κινούμενον τὴν αὑτοῦ
κίνησιν· μάτην γὰρ ὑπόδημα τοῦτο λέγομεν, οὗ μή ἐστιν
ὑπόδεσις. Ὁ δὲ θεὸς καὶ ἡ φύσις οὐδὲν μάτην ποιοῦσιν.
1And so, if there is a contrary to circular motion, motion in a straight line must be recognized as having the best claim to that name. But the two forms of rectilinear motion are opposed to one another by reason of their places; for up and down is a difference and a contrary opposition in place. Secondly, it may 5be thought that the same reasoning which holds good of the rectilinear path applies also the circular, movement from A to B being opposed as contrary to movement from B to A. But what is meant is still rectilinear motion. For that is limited to a single path, while the circular paths which pass through the same two points are infinite in number. Even if we are confined to the single semicircle 10and the opposition is between movement from C to D and from D to C along that semicircle, the case is no better. For the motion is the same as that along the diameter, since we invariably regard the distance between two points as the length of the straight line which joins them. It is no more satisfactory to construct a circle and treat motion 'along one semicircle as contrary to motion 15along the other. For example, taking a complete circle, motion from E to F on the semicircle G may be opposed to motion from F to E on the semicircle H. But even supposing these are contraries, it in no way follows that the reverse motions on the complete circumference contraries. Nor again can motion along the circle from A to B be regarded as the contrary of motion from A to C: for the 20motion goes from the same point towards the same point, and contrary motion was distinguished as motion from a contrary to its contrary. And even if the motion round a circle is the contrary of the reverse motion, one of the two would be ineffective: for both move to the same point, because that which moves in a circle, at whatever point it begins, must necessarily pass through all the 25contrary places alike. (By contrarieties of place I mean up and down, back and front, and right and left; and the contrary oppositions of movements are determined by those of places.) One of the motions, then, would be ineffective, for if the two motions were of equal strength, there would be no movement either way, and if one of the two were preponderant, the other would be inoperative. So 30that if both bodies were there, one of them, inasmuch as it would not be moving with its own movement, would be useless, in the sense in which a shoe is useless when it is not worn. But God and nature create nothing that has not its use.
Book 1,Chapter 5 (271b1–273a6)
271b
1 Ἀλλ' ἐπεὶ δῆλον περὶ τούτων, περὶ τῶν λοιπῶν
σκεπτέον, καὶ πρῶτον πότερον ἔστι τι σῶμα ἄπειρον, ὥςπερ
οἱ πλεῖστοι τῶν ἀρχαίων φιλοσόφων ᾠήθησαν, ἢ τοῦτ'
ἔστιν ἕν τι τῶν ἀδυνάτων· τὸ γὰρ οὕτως ἢ ἐκείνως ἔχειν οὔ
5 τι μικρὸν ἀλλ' ὅλον διαφέρει καὶ πᾶν πρὸς τὴν περὶ τῆς
ἀληθείας θεωρίαν· σχεδὸν γὰρ αὕτη πασῶν ἀρχὴ τῶν ἐναντιώσεων
τοῖς ἀποφηναμένοις τι περὶ τῆς ὅλης φύσεως καὶ
γέγονε καὶ γένοιτ' ἄν, εἴπερ καὶ τὸ μικρὸν παραβῆναι τῆς
ἀληθείας ἀφισταμένοις γίνεται πόρρω μυριοπλάσιον. Οἷον εἴ
10 τις ἐλάχιστον εἶναί τι φαίη μέγεθος· οὗτος γὰρ τοὐλάχιστον
εἰσαγαγὼν τὰ μέγιστ' ἂν κινήσειε τῶν μαθηματικῶν. Τούτου
δ' αἴτιον ὅτι ἡ ἀρχὴ δυνάμει μείζων ἢ μεγέθει, διόπερ τὸ
ἐν ἀρχῇ μικρὸν ἐν τῇ τελευτῇ γίνεται παμμέγεθες. Τὸ δ'
ἄπειρον καὶ ἀρχῆς ἔχει δύναμιν καὶ τοῦ ποσοῦ τὴν μεγίστην,
15 ὥστ' οὐδὲν ἄτοπον οὐδ' ἄλογον τὸ θαυμαστὴν εἶναι τὴν
διαφορὰν ἐκ τοῦ λαβεῖν ὡς ἔστι τι σῶμα ἄπειρον. Διὸ περὶ
αὐτοῦ λεκτέον ἐξ ἀρχῆς ἀναλαβοῦσιν. Ἀνάγκη δὴ πᾶν σῶμα
ἤτοι τῶν ἁπλῶν εἶναι ἢ τῶν συνθέτων, ὥστε καὶ τὸ ἄπειρον
ἢ ἁπλοῦν ἔσται ἢ σύνθετον. Ἀλλὰ μὴν καὶ ὅτι γε πεπεραςμένων
20 τῶν ἁπλῶν ἀνάγκη πεπερασμένον εἶναι τὸ σύνθετον,
δῆλον· τὸ γὰρ ἐκ πεπερασμένων καὶ πλήθει καὶ μεγέθει
συγκείμενον πεπέρανται καὶ πλήθει καὶ μεγέθει· τοσοῦτον
γάρ ἐστιν ἐξ ὅσων ἐστὶ συγκείμενον. Λοιπὸν τοίνυν ἰδεῖν
πότερον ἐνδέχεταί τι τῶν ἁπλῶν ἄπειρον εἶναι τὸ μέγεθος,
25 ἢ τοῦτ' ἀδύνατον. Προχειρισάμενοι δὴ περὶ τοῦ πρώτου τῶν
σωμάτων, οὕτω σκοπῶμεν καὶ περὶ τῶν λοιπῶν. Ὅτι μὲν
τοίνυν ἀνάγκη τὸ σῶμα τὸ κύκλῳ φερόμενον πεπεράνθαι
πᾶν, ἐκ τῶνδε δῆλον. Εἰ γὰρ ἄπειρον τὸ κύκλῳ φερόμενον
σῶμα, ἄπειροι ἔσονται αἱ ἀπὸ τοῦ μέσου ἐκβαλλόμεναι.
30 Τῶν δ' ἀπείρων τὸ διάστημα ἄπειρον· διάστημα δὲ λέγω
τῶν γραμμῶν, οὗ μηδὲν ἔστιν ἔξω λαβεῖν μέγεθος ἁπτόμενον
τῶν γραμμῶν. Τοῦτ' οὖν ἀνάγκη ἄπειρον εἶναι· τῶν γὰρ
πεπερασμένων ἀεὶ ἔσται πεπερασμένον. Ἔτι δ' ἀεὶ ἔστι τοῦ
1This being clear, we must go on to consider the questions which remain. First, is there an infinite body, as the majority of the ancient philosophers thought, or is this an impossibility? The decision of this question, either way, is not unimportant, but rather all-important, to our search 5for the truth. It is this problem which has practically always been the source of the differences of those who have written about nature as a whole. So it has been and so it must be; since the least initial deviation from the truth is multiplied later a thousandfold. Admit, for instance, the existence of a minimum magnitude, and you will find that the minimum 10which you have introduced, small as it is, causes the greatest truths of mathematics to totter. The reason is that a principle is great rather in power than in extent; hence that which was small at the start turns out a giant at the end. Now the conception of the infinite possesses this power of principles, and indeed in the sphere of quantity possesses it in a 15higher degree than any other conception; so that it is in no way absurd or unreasonable that the assumption that an infinite body exists should be of peculiar moment to our inquiry. The infinite, then, we must now discuss, opening the whole matter from the beginning.
Every body is necessarily to be classed either as simple or as composite; the infinite body, 20therefore, will be either simple or composite.
But it is clear, further, that if the simple bodies are finite, the composite must also be finite, since that which is composed of bodies finite both in number and in magnitude is itself finite in respect of number and magnitude: its quantity is in fact the same as that of the bodies which compose it. What remains for 25us to consider, then, is whether any of the simple bodies can be infinite in magnitude, or whether this is impossible. Let us try the primary body first, and then go on to consider the others.
The body which moves in a circle must necessarily be finite in every respect, for the following reasons. (1) If the body so moving is infinite, the radii drawn from the 30centre will be infinite. But the space between infinite radii is infinite: and by the space between the radii I mean the area outside which no magnitude which is in contact with the two lines can be conceived as falling.
Every body is necessarily to be classed either as simple or as composite; the infinite body, 20therefore, will be either simple or composite.
But it is clear, further, that if the simple bodies are finite, the composite must also be finite, since that which is composed of bodies finite both in number and in magnitude is itself finite in respect of number and magnitude: its quantity is in fact the same as that of the bodies which compose it. What remains for 25us to consider, then, is whether any of the simple bodies can be infinite in magnitude, or whether this is impossible. Let us try the primary body first, and then go on to consider the others.
The body which moves in a circle must necessarily be finite in every respect, for the following reasons. (1) If the body so moving is infinite, the radii drawn from the 30centre will be infinite. But the space between infinite radii is infinite: and by the space between the radii I mean the area outside which no magnitude which is in contact with the two lines can be conceived as falling.
272a
1 δοθέντος μεῖζον λαβεῖν, ὥστε καθάπερ ἀριθμὸν λέγομεν
ἄπειρον, ὅτι μέγιστος οὐκ ἔστιν, ὁ αὐτὸς λόγος καὶ περὶ
τοῦ διαστήματος· εἰ οὖν τὸ μὲν ἄπειρον μὴ ἔστι διελθεῖν, ἀπείρου
δ' ὄντος ἀνάγκη τὸ διάστημα ἄπειρον εἶναι, οὐκ ἂν ἐνδέχοιτο
5 κινηθῆναι κύκλῳ· τὸν δ' οὐρανὸν ὁρῶμεν κύκλῳ στρεφόμενον,
καὶ τῷ λόγῳ δὲ διωρίσαμεν ὅτι ἐστί τινος ἡ κύκλῳ
κίνησις. Ἔτι ἀπὸ πεπερασμένου χρόνου ἐὰν ἀφέλῃς
πεπερασμένον, ἀνάγκη καὶ τὸν λοιπὸν εἶναι πεπερασμένον
καὶ ἔχειν ἀρχήν. Εἰ δ' ὁ χρόνος ὁ τῆς βαδίσεως ἔχει ἀρχήν,
10 ἔστιν ἀρχὴ καὶ τῆς κινήσεως, ὥστε καὶ τοῦ μεγέθους ὃ
βεβάδικεν. Ὁμοίως δὲ τοῦτο καὶ ἐπὶ τῶν ἄλλων. Ἔστω δὴ
γραμμὴ ἄπειρος, ἐφ' ᾗ ΑΓΕ, ἐπὶ θάτερα, ᾗ τὸ Ε· ἡ
δ' ἐφ' ᾗ τὰ ΒΒ, ἐπ' ἀμφότερα ἄπειρος. Εἰ δὴ γράψει
κύκλον ἡ τὸ ΑΓΕ ἀπὸ τοῦ Γ κέντρου, τέμνουσά ποτε
15 οἰσθήσεται κύκλῳ τὴν τὰ ΒΒ ἡ τὸ ΑΓΕ πεπερασμένον χρόνον·
ὁ γὰρ πᾶς χρόνος, ἐν ὅσῳ κύκλῳ ἠνέχθη ὁ οὐρανός,
πεπερασμένος. Καὶ ὁ ἀφῃρημένος ἄρα, ὃν ἡ τέμνουσα ἐφέρετο.
Ἔσται ἄρα τις ἀρχὴ ᾗ πρῶτον ἡ τὸ ΑΓΕ τὴν τὰ
ΒΒ ἔτεμεν. Ἀλλ' ἀδύνατον. Οὐκ ἄρα ἔστι κύκλῳ στραφῆναι
20 τὸ ἄπειρον. Ὥστ' οὐδὲ τὸν κόσμον, εἰ ἦν ἄπειρος.
Ἔτι δὲ καὶ ἐκ τῶνδε φανερόν, ὅτι τὸ ἄπειρον ἀδύνατον
κινηθῆναι. Ἔστω γὰρ ἡ τὸ Α φερομένη παρὰ τὴν Β, πεπερασμένη
παρὰ πεπερασμένην. Ἀνάγκη δὴ ἅμα τήν τε Α
τῆς Β ἀπολελύσθαι καὶ τὴν Β τῆς Α· ὅσον γὰρ ἡ ἑτέρα
25 ἐπιβάλλει τῆς ἑτέρας, καὶ ἡ ἑτέρα ἐκείνης τοσοῦτον. Εἰ μὲν
οὖν ἄμφω κινοῖντο εἰς τοὐναντίον, θᾶττον ἂν ἀπολύοιντο, εἰ
δὲ παρὰ μένουσαν φέροιτο, βραδύτερον, τῷ αὐτῷ τάχει
κινουμένου τοῦ παραφερομένου. Ἀλλ' ἐκεῖνό γε φανερόν, ὅτι
ἀδύνατον τὴν ἄπειρον διελθεῖν ἐν πεπερασμένῳ χρόνῳ. Ἐν
30 ἀπείρῳ ἄρα· δέδεικται γὰρ τοῦτο πρότερον ἐν τοῖς περὶ κινήσεως.
Διαφέρει δέ γε οὐθὲν ἢ τὴν πεπερασμένην φέρεσθαι
παρὰ τὴν ἄπειρον ἢ τὴν ἄπειρον παρ' ἐκείνην· ὅταν γὰρ
1This, I say, will be infinite: first, because in the case of finite radii it is always finite; and secondly, because in it one can always go on to a width greater than any given width; thus the reasoning which forces us to believe in infinite number, because there is no maximum, applies also to the space 5between the radii. Now the infinite cannot be traversed, and if the body is infinite the interval between the radii is necessarily infinite: circular motion therefore is an impossibility. Yet our eyes tell us that the heavens revolve in a circle, and by argument also we have determined that there is something to which circular movement belongs.
(2) Again, if from a finite time a 10finite time be subtracted, what remains must be finite and have a beginning. And if the time of a journey has a beginning, there must be a beginning also of the movement, and consequently also of the distance traversed. This applies universally. Take a line, ACE, infinite in one direction, E, and another line, BB, infinite in both directions. Let ACE describe a circle, revolving 15upon C as centre. In its movement it will cut BB continuously for a certain time. This will be a finite time, since the total time is finite in which the heavens complete their circular orbit, and consequently the time subtracted from it, during which the one line in its motion cuts the other, is also finite. Therefore there will be a point at which ACE began for the first time 20to cut BB. This, however, is impossible. The infinite, then, cannot revolve in a circle; nor could the world, if it were infinite.
(3) That the infinite cannot move may also be shown as follows. Let A be a finite line moving past the finite line, B. Of necessity A will pass clear of B and B of A at the same moment; for each overlaps the other to precisely the same extent. Now 25if the two were both moving, and moving in contrary directions, they would pass clear of one another more rapidly; if one were still and the other moving past it, less rapidly; provided that the speed of the latter were the same in both cases. This, however, is clear: that it is impossible to traverse an infinite line in a finite time. Infinite time, then, would be required. (This 30we demonstrated above in the discussion of movement.) And it makes no difference whether a finite is passing by an infinite or an infinite by a finite.
(2) Again, if from a finite time a 10finite time be subtracted, what remains must be finite and have a beginning. And if the time of a journey has a beginning, there must be a beginning also of the movement, and consequently also of the distance traversed. This applies universally. Take a line, ACE, infinite in one direction, E, and another line, BB, infinite in both directions. Let ACE describe a circle, revolving 15upon C as centre. In its movement it will cut BB continuously for a certain time. This will be a finite time, since the total time is finite in which the heavens complete their circular orbit, and consequently the time subtracted from it, during which the one line in its motion cuts the other, is also finite. Therefore there will be a point at which ACE began for the first time 20to cut BB. This, however, is impossible. The infinite, then, cannot revolve in a circle; nor could the world, if it were infinite.
(3) That the infinite cannot move may also be shown as follows. Let A be a finite line moving past the finite line, B. Of necessity A will pass clear of B and B of A at the same moment; for each overlaps the other to precisely the same extent. Now 25if the two were both moving, and moving in contrary directions, they would pass clear of one another more rapidly; if one were still and the other moving past it, less rapidly; provided that the speed of the latter were the same in both cases. This, however, is clear: that it is impossible to traverse an infinite line in a finite time. Infinite time, then, would be required. (This 30we demonstrated above in the discussion of movement.) And it makes no difference whether a finite is passing by an infinite or an infinite by a finite.
272b
1 ἐκείνη παρ' ἐκείνην, κἀκείνη παραλλάττει ἐκείνην,
ὁμοίως κινουμένη καὶ ἀκίνητος· πλὴν θᾶττον, ἐὰν κινῶνται ἀμφότεραι,
ἀπολυθήσονται. Καίτοι γ' ἐνίοτ' οὐθὲν κωλύει τὴν κινουμένην
παρ' ἠρεμοῦσαν θᾶττον παρελθεῖν ἢ τὴν ἀντικινουμένην,
5 ἐάν τις ποιήσῃ τὰς μὲν ἀντικινουμένας ἀμφοτέρας φερομένας
βραδέως, τὴν δὲ παρὰ τὴν ἠρεμοῦσαν πολλῷ ἐκείνων
θᾶττον φερομένην. Οὐδὲν οὖν πρὸς τὸν λόγον ἐμπόδιον ὅτι
παρ' ἠρεμοῦσαν, ἐπείπερ κινουμένην ἐνδέχεται τὴν Α παρὰ
κινουμένην τὴν Β βραδύτερον παρελθεῖν. Εἰ οὖν ἄπειρος ὁ
10 χρόνος ὃν ἡ πεπερασμένη ἀπολύεται κινουμένη, καὶ ἐν ᾧ ἡ
ἄπειρος τὴν πεπερασμένην ἐκινήθη ἀνάγκη ἄπειρον εἶναι.
Ἀδύνατον ἄρα τὸ ἄπειρον κινεῖσθαι ὅλον· ἐὰν γὰρ καὶ τοὐλάχιστον
κινηθῇ, ἀνάγκη ἄπειρον γίγνεσθαι χρόνον. Ἀλλὰ
μὴν ὅ γ' οὐρανὸς περιέρχεται καὶ στρέφεται ὅλος κύκλῳ ἐν
15 πεπερασμένῳ χρόνῳ, ὥστε περίεισιν ἅπασαν τὴν ἐντός, οἷον
τὴν ΑΒ πεπερασμένην. Ἀδύνατον ἄρα ἄπειρον εἶναι τὸ κύκλῳ.
Ἔτι ὥσπερ γραμμὴν ᾗ πέρας ἐστὶν ἀδύνατον εἶναι
ἄπειρον, ἀλλ' εἴπερ, ἐπὶ μῆκος, καὶ ἐπίπεδον ὡσαύτως ᾗ
πέρας οὐκ ἐνδέχεται· ὅταν δ' ὁρισθῇ, οὐθαμῇ, οἷον τετράγωνον
20 ἄπειρον ἢ κύκλον ἢ σφαῖραν, ὥσπερ οὐδὲ ποδιαίαν ἄπειρον.
Εἰ οὖν μήτε σφαῖρα [μήτε τετράγωνον] μήτε κύκλος ἐστὶν
ἄπειρος, μὴ ὄντος δὲ κύκλου οὐδ' ἂν ἡ κύκλῳ εἴη φορά,
ὁμοίως δὲ μηδ' ἀπείρου ὄντος οὐκ ἂν εἴη ἄπειρος, εἰ μηδ' ὁ
κύκλος ἄπειρός ἐστιν, οὐκ ἂν κινοῖτο κυκλικῶς ἄπειρον σῶμα.
25 Ἔτι εἰ τὸ Γ κέντρον, ἡ δὲ τὸ ΑΒ ἄπειρος καὶ ἡ τὸ Ε πρὸς
ὀρθὴν ἄπειρος καὶ ἡ τὸ ΓΔ κινουμένη, οὐδέποτ' ἀπολυθήσεται
τῆς Ε, ἀλλ' ἀεὶ ἕξει ὥσπερ ἡ ΓΕ· τέμνει γὰρ ᾗ τὸ
Ζ. Οὐκ ἄρα περίεισι κύκλῳ ἡ ἄπειρος. Ἔτι εἴπερ ἄπειρος ὁ
οὐρανός, κινεῖται δὲ κύκλῳ, ἐν πεπερασμένῳ χρόνῳ ἄπειρον
30 ἔσται διεληλυθώς. Ἔστω γὰρ ὁ μὲν μένων οὐρανὸς ἄπειρος,
ὁ δ' ἐν τούτῳ κινούμενος ἴσος. Ὥστ' εἴπερ περιελήλυθε κύκλῳ
ἄπειρος ὤν, ἄπειρον τὸν ἴσον αὑτῷ διελήλυθεν ἐν πεπερασμένῳ
1For when A is passing B, then B overlaps A and it makes no difference whether B is moved or unmoved, except that, if both move, they pass clear of one another more quickly. It is, however, quite possible that a moving line should in certain cases pass one which is stationary quicker than it passes one moving 5in an opposite direction. One has only to imagine the movement to be slow where both move and much faster where one is stationary. To suppose one line stationary, then, makes no difficulty for our argument, since it is quite possible for A to pass B at a slower rate when both are moving than when only one is. If, therefore, the time which the finite moving line takes to pass the other 10is infinite, then necessarily the time occupied by the motion of the infinite past the finite is also infinite. For the infinite to move at all is thus absolutely impossible; since the very smallest movement conceivable must take an infinity of time. Moreover the heavens certainly revolve, and they complete their circular orbit in a finite time; so that they pass round the whole extent 15of any line within their orbit, such as the finite line AB. The revolving body, therefore, cannot be infinite.
(4) Again, as a line which has a limit cannot be infinite, or, if it is infinite, is so only in length, so a surface cannot be infinite in that respect in which it has a limit; or, indeed, if it is completely determinate, in any respect whatever. Whether it be a square or a 20circle or a sphere, it cannot be infinite, any more than a foot-rule can. There is then no such thing as an infinite sphere or square or circle, and where there is no circle there can be no circular movement, and similarly where there is no infinite at all there can be no infinite movement; and from this it follows that, an infinite circle being itself an impossibility, there can be no 25circular motion of an infinite body.
(5) Again, take a centre C, an infinite line, AB, another infinite line at right angles to it, E, and a moving radius, CD. CD will never cease contact with E, but the position will always be something like CE, CD cutting E at F. The infinite line, therefore, refuses to complete the circle.
(6) Again, if the heaven is infinite and moves in a circle, we 30shall have to admit that in a finite time it has traversed the infinite. For suppose the fixed heaven infinite, and that which moves within it equal to it.
(4) Again, as a line which has a limit cannot be infinite, or, if it is infinite, is so only in length, so a surface cannot be infinite in that respect in which it has a limit; or, indeed, if it is completely determinate, in any respect whatever. Whether it be a square or a 20circle or a sphere, it cannot be infinite, any more than a foot-rule can. There is then no such thing as an infinite sphere or square or circle, and where there is no circle there can be no circular movement, and similarly where there is no infinite at all there can be no infinite movement; and from this it follows that, an infinite circle being itself an impossibility, there can be no 25circular motion of an infinite body.
(5) Again, take a centre C, an infinite line, AB, another infinite line at right angles to it, E, and a moving radius, CD. CD will never cease contact with E, but the position will always be something like CE, CD cutting E at F. The infinite line, therefore, refuses to complete the circle.
(6) Again, if the heaven is infinite and moves in a circle, we 30shall have to admit that in a finite time it has traversed the infinite. For suppose the fixed heaven infinite, and that which moves within it equal to it.
273a
1 χρόνῳ. Ἀλλὰ τοῦτ' ἦν ἀδύνατον. Ἔστι δὲ καὶ ἀντεστραμμένως
εἰπεῖν, ὅτι εἰ πεπερασμένος ὁ χρόνος ἐν ᾧ περιεστράφη,
καὶ τὸ μέγεθος ὃ διελήλυθεν ἀναγκαῖον εἶναι πεπερασμένον·
ἴσον δ' αὑτῷ διελήλυθεν· πεπέρανται ἄρα καὶ αὐτός.
5 Ὅτι μὲν οὖν τὸ κύκλῳ κινούμενον οὐκ ἔστιν ἀτελεύτητον
οὐδ' ἄπειρον, ἀλλ' ἔχει τέλος, φανερόν.
1It results that when the infinite body has completed its revolution, it has traversed an infinite equal to itself in a finite time. But that we know to be impossible.
(7) It can also be shown, conversely, that if the time of revolution is finite, the area traversed must also be finite; but the area traversed was 5equal to itself; therefore, it is itself finite.
We have now shown that the body which moves in a circle is not endless or infinite, but has its limit.
(7) It can also be shown, conversely, that if the time of revolution is finite, the area traversed must also be finite; but the area traversed was 5equal to itself; therefore, it is itself finite.
We have now shown that the body which moves in a circle is not endless or infinite, but has its limit.
Book 1,Chapter 6 (273a7–274a29)
Ἀλλὰ μὴν οὐδὲ τὸ ἐπὶ τὸ μέσον οὐδὲ τὸ ἀπὸ τοῦ μέσου
φερόμενον ἄπειρον ἔσται· ἐναντίαι γὰρ αἱ φοραὶ ἡ ἄνω καὶ
ἡ κάτω, αἱ δ' ἐναντίαι εἰς ἐναντίους τόπους. Τῶν δ' ἐναντίων
10 εἰ θάτερον ὥρισται, καὶ θάτερον ὡρισμένον ἔσται. Τὸ δὲ μέσον
ὥρισται· εἰ γὰρ ὁποθενοῦν φέροιτο κάτω τὸ ὑφιστάμενον,
οὐκ ἐνδέχεται πορρωτέρω διελθεῖν τοῦ μέσου. Ὡρισμένου οὖν
τοῦ μέσου, καὶ τὸν ἄνω τόπον ἀνάγκη ὡρίσθαι. Εἰ δ' οἱ
τόποι ὡρισμένοι καὶ πεπερασμένοι, καὶ τὰ σώματα ἔσται πεπερασμένα.
15 Ἔτι εἰ τὸ ἄνω καὶ τὸ κάτω ὥρισται, καὶ τὸ μεταξὺ
ἀνάγκη ὡρίσθαι. Εἰ γὰρ μὴ ὥρισται, ἄπειρος ἂν εἴη ἡ
κίνησις· τοῦτο δ' ὅτι ἀδύνατον, δέδεικται πρότερον. Ὥρισται
ἄρα τὸ μέσον, ὥστε καὶ τὸ ἐν τούτῳ σῶμα ἢ ὂν ἢ γενέσθαι
δυνατόν. Ἀλλὰ μὴν τὸ ἄνω καὶ κάτω φερόμενον σῶμα δύναται
20 ἐν τούτῳ γενέσθαι· πέφυκε γὰρ τὸ μὲν ἀπὸ τοῦ μέσου
κινεῖσθαι, τὸ δ' ἐπὶ τὸ μέσον. Ἔκ τε δὴ τούτων φανερὸν ὅτι
οὐκ ἐνδέχεται σῶμα εἶναι ἄπειρον, καὶ πρὸς τούτοις εἰ βάρος
μή ἐστιν ἄπειρον, οὐδ' ἂν τούτων τῶν σωμάτων οὐθὲν εἴη ἄπειρον·
ἀνάγκη γὰρ τοῦ ἀπείρου σώματος ἄπειρον εἶναι καὶ τὸ
25 βάρος. (Ὁ δ' αὐτὸς λόγος ἔσται καὶ ἐπὶ τοῦ κούφου· εἰ γάρ
ἐστιν ἄπειρος βαρύτης, ἔστι καὶ κουφότης, ἐὰν ἄπειρον ᾖ τὸ
ἐπιπολάζον). Δῆλον δ' ἐκ τῶνδε. Ἔστω γὰρ πεπερασμένον,
καὶ εἰλήφθω τὸ μὲν ἄπειρον σῶμα ἐφ' ᾧ τὸ ΑΒ, τὸ δὲ βάρος
αὐτοῦ ἐφ' ᾧ τὸ Γ. Ἀφῃρήσθω οὖν ἀπὸ τοῦ ἀπείρου πεπεραςμένον
30 μέγεθος ἐφ' ᾧ τὸ ΒΔ· καὶ τὸ βάρος αὐτοῦ ἔστω
ἐφ' ᾧ τὸ Ε. Τὸ δὴ Ε τοῦ Γ ἔλαττον ἔσται· τὸ γὰρ τοῦ ἐλάττονος
βάρος ἔλαττον. Καταμετρείτω δὴ τὸ ἔλαττον ὁποσακισοῦν,
Further, neither that which moves towards nor that which moves away from the centre can be infinite. For the upward and downward motions are contraries and are therefore motions towards contrary places. But if one of a pair of contraries is 10determinate, the other must be determinate also. Now the centre is determined; for, from whatever point the body which sinks to the bottom starts its downward motion, it cannot go farther than the centre. The centre, therefore, being determinate, the upper place must also be determinate. But if these two places are determined and finite, the corresponding bodies must also be finite. Further, if 15up and down are determinate, the intermediate place is also necessarily determinate. For, if it is indeterminate, the movement within it will be infinite; and that we have already shown to be an impossibility. The middle region then is determinate, and consequently any body which either is in it, or might be in it, is determinate. But the bodies which move up and down may be in it, since the 20one moves naturally away from the centre and the other towards it.
From this alone it is clear that an infinite body is an impossibility; but there is a further point. If there is no such thing as infinite weight, then it follows that none of these bodies can be infinite. For the supposed infinite body would have to be infinite in weight. (The same argument applies to lightness: for as the 25one supposition involves infinite weight, so the infinity of the body which rises to the surface involves infinite lightness.) This is proved as follows. Assume the weight to be finite, and take an infinite body, AB, of the weight C. Subtract from the infinite body a finite mass, BD, the weight of which shall be E. E then is less than C, since it is the weight of a lesser mass. Suppose then 30that the smaller goes into the greater a certain number of times, and take BF bearing the same proportion to BD which the greater weight bears to the smaller.
From this alone it is clear that an infinite body is an impossibility; but there is a further point. If there is no such thing as infinite weight, then it follows that none of these bodies can be infinite. For the supposed infinite body would have to be infinite in weight. (The same argument applies to lightness: for as the 25one supposition involves infinite weight, so the infinity of the body which rises to the surface involves infinite lightness.) This is proved as follows. Assume the weight to be finite, and take an infinite body, AB, of the weight C. Subtract from the infinite body a finite mass, BD, the weight of which shall be E. E then is less than C, since it is the weight of a lesser mass. Suppose then 30that the smaller goes into the greater a certain number of times, and take BF bearing the same proportion to BD which the greater weight bears to the smaller.
273b
1 καὶ ὡς τὸ βάρος τοὔλαττον πρὸς τὸ μεῖζον, τὸ ΒΔ πρὸς
τὸ ΒΖ γεγενήσθω· ἐνδέχεται γὰρ ἀφελεῖν τοῦ ἀπείρου
ὁποσονοῦν. Εἰ τοίνυν ἀνάλογον τὰ μεγέθη τοῖς βάρεσι, τὸ δ'
ἔλαττον βάρος τοῦ ἐλάττονός ἐστι μεγέθους, καὶ τὸ μεῖζον
5 ἂν εἴη τοῦ μείζονος. Ἴσον ἄρα ἔσται τὸ τοῦ πεπερασμένου καὶ
τὸ τοῦ ἀπείρου βάρος. Ἔτι δ' εἰ τοῦ μείζονος σώματος μεῖζον
τὸ βάρος, τὸ τοῦ ΗΒ μεῖζον ἔσται βάρος ἢ τὸ τοῦ ΖΒ, ὥςτε
τὸ τοῦ πεπερασμένου ἢ τὸ τοῦ ἀπείρου [μεῖζον ἔσται βάρος].
Καὶ τὸ τῶν ἀνίσων δὲ μεγεθῶν ταὐτὸν ἔσται βάρος· ἄνισον
10 γὰρ τῷ πεπερασμένῳ τὸ ἄπειρον. Οὐθὲν δὲ διαφέρει τὰ
βάρη σύμμετρα εἶναι ἢ ἀσύμμετρα· καὶ γὰρ ἀσυμμέτρων ὄντων
ὁ αὐτὸς ἔσται λόγος· οἷον εἰ [τὸ Ε] τρίτον ὑπερβάλλει μετροῦν
τὸ βάρος· τῶν γὰρ ΒΔ μεγεθῶν τριῶν ὅλων ληφθέντων
μεῖζον ἔσται τὸ βάρος ἢ τὸ ἐφ' ᾧ τὸ Γ. Ὥστε τὸ αὐτὸ ἔσται
15 ἀδύνατον. Ἔτι δὲ καὶ ἐγχωρεῖ σύμμετρα λαβεῖν· οὐδὲν γὰρ
διαφέρει ἄρχεσθαι ἀπὸ τοῦ βάρους ἢ ἀπὸ τοῦ μεγέθους· οἷον
ἐὰν ληφθῇ σύμμετρον βάρος τῷ Γ τὸ ἐφ' ᾧ τὸ Ε, καὶ ἀπὸ
τοῦ ἀπείρου ἀφαιρεθῇ τὸ ἔχον τὸ ἐφ' ᾧ Ε βάρος, οἷον τὸ
ΒΔ, εἶτα ὡς τὸ βάρος πρὸς τὸ βάρος, τὸ ΒΔ πρὸς ἄλλο
20 γένηται μέγεθος, οἷον πρὸς τὸ ΒΖ· ἐνδέχεται γὰρ ἀπείρου
ὄντος τοῦ μεγέθους ὁποσονοῦν ἀφαιρεθῆναι· τούτων γὰρ ληφθέντων
σύμμετρα ἔσται καὶ τὰ μεγέθη καὶ τὰ βάρη ἀλλήλοις.
Οὐδὲ δὴ τὸ μέγεθος ὁμοιοβαρὲς εἶναι ἢ ἀνομοιοβαρὲς
οὐδὲν διοίσει πρὸς τὴν ἀπόδειξιν· ἀεὶ γὰρ ἔσται λαβεῖν ἰσοβαρῆ
25 σώματα τῷ ΒΔ, ἀπὸ τοῦ ἀπείρου ὁποσαοῦν ἢ ἀφαιροῦντας
ἢ προστιθέντας. Ὥστε δῆλον ἐκ τῶν εἰρημένων ὅτι οὐκ
ἔσται τοῦ ἀπείρου σώματος πεπερασμένον τὸ βάρος. Ἄπειρον
ἄρα. Εἰ τοίνυν τοῦτ' ἀδύνατον, καὶ τὸ ἄπειρόν τι εἶναι σῶμα
ἀδύνατον. Ἀλλὰ μὴν ὅτι ἄπειρόν τι εἶναι βάρος ἀδύνατον,
30 ἐκ τῶνδε φανερόν. Εἰ γὰρ τοσόνδε βάρος τὴν τοσήνδε
ἐν τῷδε τῷ χρόνῳ κινεῖται, τὸ τοσοῦτον καὶ ἔτι ἐν ἐλάττονι,
καὶ τὴν ἀναλογίαν ἣν τὰ βάρη ἔχει, οἱ χρόνοι ἀνάπαλιν ἕξουσιν,
1For you may subtract as much as you please from an infinite. If now the masses are proportionate to the weights, and the lesser weight is that of the lesser mass, the greater must be that of the greater. The weights, therefore, of the finite and of the infinite body are equal. Again, if the 5weight of a greater body is greater than that of a less, the weight of GB will be greater than that of FB; and thus the weight of the finite body is greater than that of the infinite. And, further, the weight of unequal masses will be the same, since the infinite and the finite cannot be equal. It does not matter whether the weights are commensurable or not. If (a) they 10are incommensurable the same reasoning holds. For instance, suppose E multiplied by three is rather more than C: the weight of three masses of the full size of BD will be greater than C. We thus arrive at the same impossibility as before. Again (b) we may assume weights which are commensurate; for it makes no difference whether we begin with the weight or with the 15mass. For example, assume the weight E to be commensurate with C, and take from the infinite mass a part BD of weight E. Then let a mass BF be taken having the same proportion to BD which the two weights have to one another. (For the mass being infinite you may subtract from it as much as you please.) These assumed bodies will be commensurate in mass and in weight 20alike. Nor again does it make any difference to our demonstration whether the total mass has its weight equally or unequally distributed. For it must always be Possible to take from the infinite mass a body of equal weight to BD by diminishing or increasing the size of the section to the necessary extent.
From what we have said, then, it is clear that the weight of 25the infinite body cannot be finite. It must then be infinite. We have therefore only to show this to be impossible in order to prove an infinite body impossible. But the impossibility of infinite weight can be shown in the following way. A given weight moves a given distance in a given time; a weight which is as great and more moves the same distance in a less time, 30the times being in inverse proportion to the weights. For instance, if one weight is twice another, it will take half as long over a given movement.
From what we have said, then, it is clear that the weight of 25the infinite body cannot be finite. It must then be infinite. We have therefore only to show this to be impossible in order to prove an infinite body impossible. But the impossibility of infinite weight can be shown in the following way. A given weight moves a given distance in a given time; a weight which is as great and more moves the same distance in a less time, 30the times being in inverse proportion to the weights. For instance, if one weight is twice another, it will take half as long over a given movement.
274a
1 οἷον εἰ τὸ ἥμισυ βάρος ἐν τῷδε, τὸ διπλάσιον ἐν
ἡμίσει τούτου. Ἔτι τὸ πεπερασμένον βάρος ἅπασαν πεπερασμένην
δίεισιν ἔν τινι χρόνῳ πεπερασμένῳ. Ἀνάγκη ἄρα ἐκ
τούτων, εἴ τι ἔστιν ἄπειρον βάρος, κινεῖσθαι μὲν ᾗ τοσόνδε
5 ὅσον τὸ πεπερασμένον καὶ ἔτι, μὴ κινεῖσθαι δέ, ᾗ ἀνάλογον
μὲν δεῖ κατὰ τὰς ὑπεροχὰς κινεῖσθαι, ἐναντίως δὲ τὸ
μεῖζον ἐν τῷ ἐλάττονι. Λόγος δ' οὐθείς ἐστι τοῦ ἀπείρου πρὸς
τὸ πεπερασμένον, τοῦ δ' ἐλάττονος χρόνου πρὸς τὸν μείζω
πεπερασμένον· ἀλλ' ἀεὶ ἐν ἐλάττονι. Ἐλάχιστος δ' οὐκ ἔστιν.
10 Οὐδ' εἰ ἦν, ὄφελός τι ἂν ἦν· ἄλλο γὰρ ἄν τι πεπερασμένον
ἐλήφθη ἐν τῷ αὐτῷ λόγῳ, ἐν ᾧ τὸ ἄπειρον πρὸς ἕτερον,
μεῖζον, ὥστ' ἐν ἴσῳ χρόνῳ τὴν ἴσην ἂν ἐκινεῖτο τὸ ἄπειρον
τῷ πεπερασμένῳ. Ἀλλ' ἀδύνατον. Ἀλλὰ μὴν ἀνάγκη γε,
εἴπερ ἐν ὁπηλικῳοῦν χρόνῳ πεπερασμένῳ δὲ κινεῖται τὸ ἄπειρον,
15 καὶ ἄλλο ἐν τῷ αὐτῷ τούτῳ πεπερασμένον βάρος κινεῖσθαί
τινα πεπερασμένην. Ἀδύνατον ἄρα ἄπειρον εἶναι βάρος,
ὁμοίως δὲ καὶ κουφότητα. Καὶ σώματα ἄρ' ἄπειρον
βάρος ἔχοντα καὶ κουφότητα ἀδύνατον.
Ὅτι μὲν οὖν οὐκ ἔστιν ἄπειρον σῶμα, δῆλον διά τε τῶν
20 κατὰ μέρος θεωροῦσι τοῦτον τὸν τρόπον, καὶ καθόλου σκοπουμένοις
μὴ μόνον κατὰ τοὺς λόγους τοὺς ἐν τοῖς περὶ τὰς
ἀρχὰς εἰρημένους ἡμῖν (διωρίσθη γὰρ κἀκεῖ καθόλου πρότερον
περὶ ἀπείρου πῶς ἔστι καὶ πῶς οὐκ ἔστιν) ἀλλὰ καὶ νῦν
ἄλλον τρόπον. Μετὰ δὲ ταῦτ' ἐπισκεπτέον κἂν εἰ μὴ ἄπειρον
25 μὲν τὸ σῶμα τὸ πᾶν, οὐ μὴν ἀλλὰ τοσοῦτόν γε ὥστ' εἶναι
πλείους οὐρανούς· τάχα γὰρ ἄν τις τοῦτ' ἀπορήσειεν, ὅτι καθάπερ
ὁ περὶ ἡμᾶς κόσμος συνέστηκεν, οὐδὲν κωλύει καὶ
ἑτέρους εἶναι πλείους μὲν ἑνός, μὴ μέντοι γε ἀπείρους. Πρῶτον
δ' εἴπωμεν καθόλου περὶ τοῦ ἀπείρου.
1Further, a finite weight traverses any finite distance in a finite time. It necessarily follows from this that infinite weight, if there is such a thing, being, on the one hand, as great and more than as great as the finite, will move accordingly, but being, on the other hand, compelled to move in a 5time inversely proportionate to its greatness, cannot move at all. The time should be less in proportion as the weight is greater. But there is no proportion between the infinite and the finite: proportion can only hold between a less and a greater finite time. And though you may say that the time of the movement can be continually diminished, yet there is no minimum. Nor, if 10there were, would it help us. For some finite body could have been found greater than the given finite in the same proportion which is supposed to hold between the infinite and the given finite; so that an infinite and a finite weight must have traversed an equal distance in equal time. But that is impossible. Again, whatever the time, so long as it is finite, in which the 15infinite performs the motion, a finite weight must necessarily move a certain finite distance in that same time. Infinite weight is therefore impossible, and the same reasoning applies also to infinite lightness. Bodies then of infinite weight and of infinite lightness are equally impossible.
That there is no infinite body may be shown, as we have shown it, by a detailed consideration 20of the various cases. But it may also be shown universally, not only by such reasoning as we advanced in our discussion of principles (though in that passage we have already determined universally the sense in which the existence of an infinite is to be asserted or denied), but also suitably to our present purpose in the following way. That will lead us to a further 25question. Even if the total mass is not infinite, it may yet be great enough to admit a plurality of universes. The question might possibly be raised whether there is any obstacle to our believing that there are other universes composed on the pattern of our own, more than one, though stopping short of infinity. First, however, let us treat of the infinite universally.
That there is no infinite body may be shown, as we have shown it, by a detailed consideration 20of the various cases. But it may also be shown universally, not only by such reasoning as we advanced in our discussion of principles (though in that passage we have already determined universally the sense in which the existence of an infinite is to be asserted or denied), but also suitably to our present purpose in the following way. That will lead us to a further 25question. Even if the total mass is not infinite, it may yet be great enough to admit a plurality of universes. The question might possibly be raised whether there is any obstacle to our believing that there are other universes composed on the pattern of our own, more than one, though stopping short of infinity. First, however, let us treat of the infinite universally.
Book 1,Chapter 7 (274a30–276a17)
30 Ἀνάγκη δὴ σῶμα πᾶν ἤτοι ἄπειρον εἶναι ἢ πεπερασμένον,
καὶ εἰ ἄπειρον, ἤτοι ἀνομοιομερὲς ἅπαν ἢ ὁμοιομερές,
κἂν εἰ ἀνομοιομερές, ἤτοι ἐκ πεπερασμένων εἰδῶν
ἢ ἐξ ἀπείρων. Ὅτι μὲν τοίνυν οὐχ οἷόν τε ἐξ ἀπείρων, φανερόν,
εἴ τις ἡμῖν ἐάσει μένειν τὰς πρώτας ὑποθέσεις· πεπεραςμένων
Every body 30must necessarily be either finite or infinite, and if infinite, either of similar or of dissimilar parts. If its parts are dissimilar, they must represent either a finite or an infinite number of kinds. That the kinds cannot be infinite is evident, if our original presuppositions remain unchallenged.
274b
1 γὰρ τῶν πρώτων κινήσεων οὐσῶν, ἀνάγκη καὶ
τὰς ἰδέας τῶν ἁπλῶν σωμάτων εἶναι πεπερασμένας. Ἁπλῆ
μὲν γὰρ ἡ τοῦ ἁπλοῦ σώματος κίνησις, αἱ δ' ἁπλαῖ πεπερασμέναι
κινήσεις εἰσίν· ἀνάγκη δὲ κίνησιν ἔχειν σῶμα
5 πᾶν φυσικόν. Ἀλλὰ μὴν εἴ γε ἐκ πεπερασμένων ἔσται τὸ
ἄπειρον, ἀνάγκη καὶ τῶν μορίων ἕκαστον εἶναι ἄπειρον,
λέγω δ' οἷον τὸ ὕδωρ ἢ τὸ πῦρ. Ἀλλ' ἀδύνατον· δέδεικται
γὰρ ὅτι οὔτε βάρος οὔτε κουφότης ἐστὶν ἄπειρος. Ἔτι ἀναγκαῖον
ἀπείρους τῷ μεγέθει εἶναι καὶ τοὺς τόπους αὐτῶν, ὥστε
10 καὶ τὰς κινήσεις ἀπείρους εἶναι πάντων. Τοῦτο δ' ἀδύνατον,
εἰ θήσομεν ἀληθεῖς εἶναι τὰς πρώτας ὑποθέσεις, καὶ μήτε
τὸ κάτω φερόμενον εἰς ἄπειρον ἐνδέχεσθαι φέρεσθαι μήτε
τὸ ἄνω κατὰ τὸν αὐτὸν λόγον. Ἀδύνατον γὰρ γίνεσθαι ὃ
μὴ ἐνδέχεται γενέσθαι, ὁμοίως ἐπὶ τοῦ τοιόνδε καὶ τοσόνδε
15 καὶ τοῦ ποῦ. Λέγω δ', εἰ ἀδύνατον γενέσθαι λευκὸν ἢ πηχυαῖον
ἢ ἐν Αἰγύπτῳ, καὶ γίνεσθαί τι τούτων ἀδύνατον.
Ἀδύνατον ἄρα καὶ φέρεσθαι ἐκεῖ οὗ μηθὲν δυνατὸν ἀφικέσθαι
φερόμενον. Ἔτι εἰ καὶ διεσπασμένα ἐστίν, οὐδὲν ἧττον
ἐνδέχοιτ' ἂν τὸ ἐξ ἁπάντων [πῦρ] ἄπειρον εἶναι. Ἀλλὰ σῶμα
20 ἦν τὸ πάντῃ διάστασιν ἔχον· ὥστε πῶς οἷόν τε πλείω μὲν
ἀνόμοια, ἕκαστον δ' αὐτῶν ἄπειρον εἶναι; πάντῃ γὰρ ἕκαστον
δεῖ ἄπειρον εἶναι. Ἀλλὰ μὴν οὐδὲ πᾶν ὁμοιομερὲς ἐνδέχεται
τὸ ἄπειρον εἶναι. Πρῶτον μὲν γὰρ οὐκ ἔστιν ἄλλη
παρὰ ταύτας κίνησις. Ἕξει οὖν μίαν τούτων. Εἰ δὲ τοῦτο,
25 συμβήσεται ἢ βάρος ἄπειρον ἢ κουφότητα εἶναι ἄπειρον.
Ἀλλὰ μὴν οὐδ' οἷόν τε τὸ κύκλῳ σῶμα φερόμενον [εἶναι ἄπειρον].
Ἀδύνατον γὰρ τὸ ἄπειρον φέρεσθαι κύκλῳ· οὐθὲν γὰρ
διαφέρει τοῦτο λέγειν ἢ τὸ τὸν οὐρανὸν φάναι ἄπειρον εἶναι,
τοῦτο δὲ δέδεικται ὅτι ἀδύνατον. Ἀλλὰ μὴν οὐδ' ὅλως γε τὸ
30 ἄπειρον ἐνδέχεται κινεῖσθαι. Ἢ γὰρ κατὰ φύσιν κινηθήσεται
ἢ βίᾳ· καὶ εἰ βίᾳ, ἔστιν αὐτῷ καὶ ἡ κατὰ φύσιν, ὥστε καὶ
τόπος ἄλλος ἴσος εἰς ὃν οἰσθήσεται. Τοῦτο δ' ἀδύνατον.
Ὅτι δ' ὅλως ἀδύνατον ἄπειρον ὑπὸ πεπερασμένου παθεῖν
τι ἢ ποιῆσαι τὸ πεπερασμένον, ἐκ τῶνδε φανερόν. Ἔστω
1For the primary movements being finite in number, the kinds of simple body are necessarily also finite, since the movement of a simple body is simple, and the simple movements are finite, and every natural body must always have its proper motion. Now if the infinite body is to be composed of a finite number of kinds, then 5each of its parts must necessarily be infinite in quantity, that is to say, the water, fire, &c., which compose it. But this is impossible, because, as we have already shown, infinite weight and lightness do not exist. Moreover it would be necessary also that their places should be infinite in extent, so that the movements too of all these bodies would be infinite. But this is not possible, if we 10are to hold to the truth of our original presuppositions and to the view that neither that which moves downward, nor, by the same reasoning, that which moves upward, can prolong its movement to infinity. For it is true in regard to quality, quantity, and place alike that any process of change is impossible which can have no end. I mean that if it is impossible for a thing to have come to be white, 15or a cubit long, or in Egypt, it is also impossible for it to be in process of coming to be any of these. It is thus impossible for a thing to be moving to a place at which in its motion it can never by any possibility arrive. Again, suppose the body to exist in dispersion, it may be maintained none the less that the total of all these scattered particles, say, of fire, is infinite. But body we saw to 20be that which has extension every way. How can there be several dissimilar elements, each infinite? Each would have to be infinitely extended every way.
It is no more conceivable, again, that the infinite should exist as a whole of similar parts. For, in the first place, there is no other (straight) movement beyond those mentioned: we must therefore give it one of them. And if so, we shall have to 25admit either infinite weight or infinite lightness. Nor, secondly, could the body whose movement is circular be infinite, since it is impossible for the infinite to move in a circle. This, indeed, would be as good as saying that the heavens are infinite, which we have shown to be impossible.
Moreover, in general, it is impossible that the infinite should move at all. If it did, it would move either 30naturally or by constraint: and if by constraint, it possesses also a natural motion, that is to say, there is another place, infinite like itself, to which it will move. But that is impossible.
That in general it is impossible for the infinite to be acted upon by the finite or to act upon it may be shown as follows.
(1.
It is no more conceivable, again, that the infinite should exist as a whole of similar parts. For, in the first place, there is no other (straight) movement beyond those mentioned: we must therefore give it one of them. And if so, we shall have to 25admit either infinite weight or infinite lightness. Nor, secondly, could the body whose movement is circular be infinite, since it is impossible for the infinite to move in a circle. This, indeed, would be as good as saying that the heavens are infinite, which we have shown to be impossible.
Moreover, in general, it is impossible that the infinite should move at all. If it did, it would move either 30naturally or by constraint: and if by constraint, it possesses also a natural motion, that is to say, there is another place, infinite like itself, to which it will move. But that is impossible.
That in general it is impossible for the infinite to be acted upon by the finite or to act upon it may be shown as follows.
(1.
275a
1 γὰρ ἄπειρον ἐφ' οὗ Α, πεπερασμένον ἐφ' οὗ Β, χρόνος
ἐν ᾧ ἐκίνησέ τι ἢ ἐκινήθη Γ. Εἰ δὴ ὑπὸ τοῦ Β τὸ Α ἐθερμάνθη
ἢ ὤσθη ἢ ἄλλο τι ἔπαθεν ἢ καὶ ὁτιοῦν ἐκινήθη ἐν τῷ χρόνῳ
ἐφ' οὗ Γ, ἔστω τὸ Δ τοῦ Β ἔλαττον, καὶ τὸ ἔλαττον ἐν τῷ
5 ἴσῳ χρόνῳ ἔλαττον κινείτω· ἔστω δὲ τὸ ἐφ' ᾧ Ε ὑπὸ τοῦ Δ
ἠλλοιωμένον. Ὃ δή ἐστι τὸ Δ πρὸς τὸ Β, τὸ Ε ἔσται πρὸς
πεπερασμένον τι. Ἔστω δὴ τὸ μὲν ἴσον ἐν ἴσῳ χρόνῳ ἴσον ἀλλοιοῦν,
τὸ δ' ἔλαττον ἐν τῷ ἴσῳ ἔλαττον, τὸ δὲ μεῖζον μεῖζον,
τοσοῦτον δὲ ὅσον ἀνάλογον ἔσται ὅπερ τὸ μεῖζον πρὸς τὸ
10 ἔλαττον. Οὐκ ἄρα τὸ ἄπειρον ὑπ' οὐδενὸς πεπερασμένου κινηθήσεται
ἐν οὐθενὶ χρόνῳ· ἔλαττον γὰρ ἄλλο ἐν τῷ ἴσῳ χρόνῳ
ὑπὸ ἐλάττονος κινηθήσεται, πρὸς ὃ τὸ ἀνάλογον πεπερασμένον
ἔσται· τὸ γὰρ ἄπειρον πρὸς τὸ πεπερασμένον ἐν οὐθενὶ λόγῳ
ἐστίν. Ἀλλὰ μὴν οὐδὲ τὸ ἄπειρον ἐν οὐθενὶ χρόνῳ κινήσει τὸ
15 πεπερασμένον. Ἔστω γὰρ ἐφ' ᾧ τὸ Α ἄπειρον, τὸ δὲ Β πεπερασμένον,
χρόνος ἐν ᾧ τὸ Γ. Οὐκοῦν τὸ Δ ἐν τῷ Γ ἔλαττον
τοῦ Β κινήσει· ἔστω τὸ Ζ. Ὃ δή ἐστι τὸ ΒΖ ὅλον πρὸς τὸ Ζ,
τὸ Ε ἔχον τὸν λόγον τοῦτον ἔστω πρὸς τὸ Δ. Κινήσει ἄρα τὸ
Ε τὸ ΒΖ ἐν τῷ Γ. Τὸ πεπερασμένον τοίνυν καὶ τὸ ἄπειρον
20 ἐν τῷ ἴσῳ χρόνῳ ἀλλοιώσει. Ἀλλ' ἀδύνατον· ἐν ἐλάττονι γὰρ
τὸ μεῖζον ὑπέκειτο. Ἀλλ' ἀεὶ ὁ ληφθεὶς χρόνος ταὐτὸ ποιήσει,
ὥστ' οὐκ ἔσται χρόνος οὐθεὶς ἐν ᾧ κινήσει. Ἀλλὰ μὴν ἐν
ἀπείρῳ γε οὐκ ἔστι κινῆσαι οὐδὲ κινηθῆναι· πέρας γὰρ οὐκ
ἔχει, ἡ δὲ ποίησις καὶ τὸ πάθος ἔχει. Οὐδ' ἄπειρον δὴ ὑπ' ἀπείρου
25 ἐνδέχεται οὐθὲν παθεῖν. Ἔστω γὰρ τὸ Α ἄπειρον καὶ τὸ
Β, χρόνος δ' ἐν ᾧ ἔπαθε τὸ Β ὑπὸ τοῦ Α, ἐφ' ᾧ ΓΔ. Τὸ δὴ
ἐφ' ᾧ τὸ Ε τοῦ ἀπείρου μέρος, ἐπεὶ ὅλον πέπονθε τὸ Β, οὐκ
ἐν ἴσῳ χρόνῳ τὸ αὐτό· ὑποκείσθω γὰρ ἐν ἐλάττονι κινεῖσθαι
τὸ ἔλαττον χρόνῳ. Ἔστω τὸ Ε κεκινημένον ὑπὸ τοῦ Α ἐν τῷ Δ.
30 Ὃ δὴ τὸ Δ πρὸς τὸ ΓΔ, τὸ Ε ἐστὶ πρός τι τοῦ Β πεπερασμένον.
Τοῦτο τοίνυν ἀνάγκη ὑπὸ τοῦ Α κινηθῆναι ἐν τῷ ΓΔ χρόνῳ·
ὑπὸ γὰρ τοῦ αὐτοῦ ὑποκείσθω ἐν τῷ πλείονι καὶ ἐλάττονι
1The infinite cannot be acted upon by the finite.) Let A be an infinite, B a finite, C the time of a given movement produced by one in the other. Suppose, then, that A was heated, or impelled, or modified in any way, or caused to undergo any sort of movement whatever, by in the time C. Let D be less than B; and, 5assuming that a lesser agent moves a lesser patient in an equal time, call the quantity thus modified by D, E. Then, as D is to B, so is E to some finite quantum. We assume that the alteration of equal by equal takes equal time, and the alteration of less by less or of greater by greater takes the same time, if the quantity of the patient is such as to keep the proportion which obtains 10between the agents, greater and less. If so, no movement can be caused in the infinite by any finite agent in any time whatever. For a less agent will produce that movement in a less patient in an equal time, and the proportionate equivalent of that patient will be a finite quantity, since no proportion holds between finite and infinite.
(2. The infinite cannot act upon the finite.) 15Nor, again, can the infinite produce a movement in the finite in any time whatever. Let A be an infinite, B a finite, C the time of action. In the time C, D will produce that motion in a patient less than B, say F. Then take E, bearing the same proportion to D as the whole BF bears to F. E will produce the motion in BF in the time C. Thus the finite and infinite effect the same alteration 20in equal times. But this is impossible; for the assumption is that the greater effects it in a shorter time. It will be the same with any time that can be taken, so that there will no time in which the infinite can effect this movement. And, as to infinite time, in that nothing can move another or be moved by it. For such time has no limit, while the action and reaction have.
(3. 25There is no interaction between infinites.) Nor can infinite be acted upon in any way by infinite. Let A and B be infinites, CD being the time of the action A of upon B. Now the whole B was modified in a certain time, and the part of this infinite, E, cannot be so modified in the same time, since we assume that a less quantity makes the movement in a less time. Let E then, when acted upon 30by A, complete the movement in the time D. Then, as D is to CD, so is E to some finite part of B. This part will necessarily be moved by A in the time CD.
(2. The infinite cannot act upon the finite.) 15Nor, again, can the infinite produce a movement in the finite in any time whatever. Let A be an infinite, B a finite, C the time of action. In the time C, D will produce that motion in a patient less than B, say F. Then take E, bearing the same proportion to D as the whole BF bears to F. E will produce the motion in BF in the time C. Thus the finite and infinite effect the same alteration 20in equal times. But this is impossible; for the assumption is that the greater effects it in a shorter time. It will be the same with any time that can be taken, so that there will no time in which the infinite can effect this movement. And, as to infinite time, in that nothing can move another or be moved by it. For such time has no limit, while the action and reaction have.
(3. 25There is no interaction between infinites.) Nor can infinite be acted upon in any way by infinite. Let A and B be infinites, CD being the time of the action A of upon B. Now the whole B was modified in a certain time, and the part of this infinite, E, cannot be so modified in the same time, since we assume that a less quantity makes the movement in a less time. Let E then, when acted upon 30by A, complete the movement in the time D. Then, as D is to CD, so is E to some finite part of B. This part will necessarily be moved by A in the time CD.
275b
1 χρόνῳ τὸ μεῖζον καὶ τὸ ἔλαττον πάσχειν, ὅσα ἀνάλογον
τῷ χρόνῳ διῄρηται. Ἐν οὐδενὶ ἄρα χρόνῳ δυνατὸν πεπερασμένῳ
ἄπειρον ὑπ' ἀπείρου κινηθῆναι· ἐν ἀπείρῳ ἄρα. Ἀλλ'
ὁ μὲν ἄπειρος χρόνος οὐκ ἔχει τέλος, τὸ δὲ κεκινημένον ἔχει.
5 Εἰ τοίνυν πᾶν σῶμα αἰσθητὸν ἔχει δύναμιν ποιητικὴν ἢ παθητικὴν
ἢ ἄμφω, ἀδύνατον σῶμα ἄπειρον αἰσθητὸν εἶναι. Ἀλλὰ
μὴν καὶ ὅσα γε σώματα ἐν τόπῳ, πάντα αἰσθητά. Οὐκ ἔςτιν
ἄρα σῶμα ἄπειρον ἔξω τοῦ οὐρανοῦ οὐθέν. Ἀλλὰ μὴν οὐδὲ
μέχρι τινός. Οὐθὲν ἄρα ὅλως σῶμα ἔξω τοῦ οὐρανοῦ. Εἰ μὲν
10 γὰρ νοητόν, ἔσται ἐν τόπῳ· τὸ γὰρ ἔξω καὶ ἔσω τόπον σημαίνει.
Ὥστ' ἔσται αἰσθητόν. Αἰσθητὸν δ' οὐθὲν μὴ ἐν τόπῳ.
Λογικώτερον δ' ἔστιν ἐπιχειρεῖν καὶ ὧδε. Οὔτε γὰρ
κύκλῳ οἷόν τε κινεῖσθαι τὸ ἄπειρον ὁμοιομερὲς ὄν· μέσον
μὲν γὰρ τοῦ ἀπείρου οὐκ ἔστι, τὸ δὲ κύκλῳ περὶ τὸ μέσον
15 κινεῖται. Ἀλλὰ μὴν οὐδ' ἐπ' εὐθείας οἷόν τε φέρεσθαι
τὸ ἄπειρον· δεήσει γὰρ ἕτερον εἶναι τοσοῦτον τόπον
ἄπειρον εἰς ὃν οἰσθήσεται κατὰ φύσιν, καὶ ἄλλον τοσοῦτον
εἰς ὃν παρὰ φύσιν. Ἔτι εἴτε φύσει ἔχει κίνησιν τοῦ εἰς εὐθὺ
εἴτε βίᾳ κινεῖται, ἀμφοτέρως δεήσει ἄπειρον εἶναι τὴν κινοῦσαν
20 ἰσχύν· ἥ τε γὰρ ἄπειρος ἀπείρου καὶ τοῦ ἀπείρου ἄπειρος
ἡ ἰσχύς· ὥστ' ἔσται καὶ τὸ κινοῦν ἄπειρον (λόγος δ' ἐν
τοῖς περὶ κινήσεως ὅτι οὐθὲν ἔχει ἄπειρον δύναμιν τῶν πεπερασμένων,
οὐδὲ τῶν ἀπείρων πεπερασμένην). Εἰ οὖν τὸ κατὰ
φύσιν καὶ παρὰ φύσιν ἐνδέχεται κινηθῆναι, ἔσται δύο ἄπειρα,
25 τό τε κινοῦν οὕτω καὶ τὸ κινούμενον. Ἔτι τὸ κινοῦν τὸ
ἄπειρον τί ἐστιν; εἰ μὲν γὰρ αὐτὸ ἑαυτό, ἔμψυχον ἔσται. Τοῦτο
δὲ πῶς δυνατόν, ἄπειρον εἶναι ζῷον; εἰ δ' ἄλλο [τι] τὸ κινοῦν,
δύο ἔσται ἄπειρα, τό τε κινοῦν καὶ τὸ κινούμενον, διαφέροντα
τὴν μορφὴν καὶ τὴν δύναμιν. Εἰ δὲ μὴ συνεχὲς τὸ πᾶν,
30 ἀλλ' ὥσπερ λέγει Δημόκριτος καὶ Λεύκιππος, διωρισμένα τῷ
κενῷ, μίαν ἀναγκαῖον εἶναι πάντων τὴν κίνησιν. Διώρισται μὲν
γὰρ τοῖς σχήμασιν· τὴν δὲ φύσιν φασὶν αὐτῶν εἶναι μίαν, ὥςπερ
1For we suppose that the same agent produces a given effect on a greater and a smaller mass in longer and shorter times, the times and masses varying proportionately. There is thus no finite time in which infinites can move one another. Is their time then infinite? No, for infinite time has no end, but the movement communicated 5has.
If therefore every perceptible body possesses the power of acting or of being acted upon, or both of these, it is impossible that an infinite body should be perceptible. All bodies, however, that occupy place are perceptible. There is therefore no infinite body beyond the heaven. Nor again is there anything of limited extent beyond it. And so beyond the heaven there is no body at all. For if 10you suppose it an object of intelligence, it will be in a place-since place is what 'within' and 'beyond' denote-and therefore an object of perception. But nothing that is not in a place is perceptible.
The question may also be examined in the light of more general considerations as follows. The infinite, considered as a whole of similar parts, cannot, on the one hand, move in a circle. For there is no 15centre of the infinite, and that which moves in a circle moves about the centre. Nor again can the infinite move in a straight line. For there would have to be another place infinite like itself to be the goal of its natural movement and another, equally great, for the goal of its unnatural movement. Moreover, whether its rectilinear movement is natural or constrained, in either case the force which 20causes its motion will have to be infinite. For infinite force is force of an infinite body, and of an infinite body the force is infinite. So the motive body also will be infinite. (The proof of this is given in our discussion of movement, where it is shown that no finite thing possesses infinite power, and no infinite thing finite power.) If then that which moves naturally can also move unnaturally, 25there will be two infinites, one which causes, and another which exhibits the latter motion. Again, what is it that moves the infinite? If it moves itself, it must be animate. But how can it possibly be conceived as an infinite animal? And if there is something else that moves it, there will be two infinites, that which moves and that which is moved, differing in their form and power.
If the whole is 30not continuous, but exists, as Democritus and Leucippus think, in the form of parts separated by void, there must necessarily be one movement of all the multitude.
If therefore every perceptible body possesses the power of acting or of being acted upon, or both of these, it is impossible that an infinite body should be perceptible. All bodies, however, that occupy place are perceptible. There is therefore no infinite body beyond the heaven. Nor again is there anything of limited extent beyond it. And so beyond the heaven there is no body at all. For if 10you suppose it an object of intelligence, it will be in a place-since place is what 'within' and 'beyond' denote-and therefore an object of perception. But nothing that is not in a place is perceptible.
The question may also be examined in the light of more general considerations as follows. The infinite, considered as a whole of similar parts, cannot, on the one hand, move in a circle. For there is no 15centre of the infinite, and that which moves in a circle moves about the centre. Nor again can the infinite move in a straight line. For there would have to be another place infinite like itself to be the goal of its natural movement and another, equally great, for the goal of its unnatural movement. Moreover, whether its rectilinear movement is natural or constrained, in either case the force which 20causes its motion will have to be infinite. For infinite force is force of an infinite body, and of an infinite body the force is infinite. So the motive body also will be infinite. (The proof of this is given in our discussion of movement, where it is shown that no finite thing possesses infinite power, and no infinite thing finite power.) If then that which moves naturally can also move unnaturally, 25there will be two infinites, one which causes, and another which exhibits the latter motion. Again, what is it that moves the infinite? If it moves itself, it must be animate. But how can it possibly be conceived as an infinite animal? And if there is something else that moves it, there will be two infinites, that which moves and that which is moved, differing in their form and power.
If the whole is 30not continuous, but exists, as Democritus and Leucippus think, in the form of parts separated by void, there must necessarily be one movement of all the multitude.
276a
1 ἂν εἰ χρυσὸς ἕκαστον εἴη κεχωρισμένος. Τούτων δέ,
καθάπερ λέγομεν, ἀναγκαῖον εἶναι τὴν αὐτὴν κίνησιν· ὅπου γὰρ
μία βῶλος, καὶ ἡ σύμπασα γῆ φέρεται, καὶ τό τε πᾶν πῦρ
καὶ σπινθὴρ εἰς τὸν αὐτὸν τόπον. Ὥστ' οὔτε κοῦφον ἁπλῶς
5 οὐθὲν ἔσται τῶν σωμάτων, εἰ πάντ' ἔχει βάρος· εἰ δὲ κουφότητα,
βαρὺ οὐδέν. Ἔτι εἰ βάρος ἔχει ἢ κουφότητα, ἔσται
ἢ ἔσχατόν τι τοῦ παντὸς ἢ μέσον. Τοῦτο δ' ἀδύνατον ἀπείρου
γ' ὄντος. Ὅλως δ', οὗ μή ἐστι μέσον μηδ' ἔσχατον, μηδὲ τὸ
μὲν ἄνω τὸ δὲ κάτω, τόπος οὐθεὶς ἔσται τοῖς σώμασι τῆς
10 φορᾶς. Τούτου δὲ μὴ ὄντος κίνησις οὐκ ἔσται· ἀνάγκη γὰρ
κινεῖσθαι ἤτοι κατὰ φύσιν ἢ παρὰ φύσιν, ταῦτα δ' ὥρισται
τοῖς τόποις τοῖς τ' οἰκείοις καὶ τοῖς ἀλλοτρίοις. Ἔτι εἰ οὗ παρὰ
φύσιν τι μένει ἢ φέρεται, ἀνάγκη ἄλλου τινὸς εἶναι
τοῦτον τὸν τόπον κατὰ φύσιν (τοῦτο δὲ πιστὸν ἐκ τῆς
15 ἐπαγωγῆς), ἀνάγκη δὴ μὴ πάντα ἢ βάρος ἔχειν ἢ κουφότητα,
ἀλλὰ τὰ μὲν τὰ δὲ μή. Ὅτι μὲν τοίνυν οὐκ ἔστι τὸ
σῶμα τοῦ παντὸς ἄπειρον, ἐκ τούτων φανερόν.
1They are distinguished, we are told, from one another by their figures; but their nature is one, like many pieces of gold separated from one another. But each piece must, as we assert, have the same motion. For a single clod moves to the same place as the whole mass of earth, and a spark to the same place 5as the whole mass of fire. So that if it be weight that all possess, no body is, strictly speaking, light: and if lightness be universal, none is heavy. Moreover, whatever possesses weight or lightness will have its place either at one of the extremes or in the middle region. But this is impossible while the world is conceived as infinite. And, generally, that which has no centre 10or extreme limit, no up or down, gives the bodies no place for their motion; and without that movement is impossible. A thing must move either naturally or unnaturally, and the two movements are determined by the proper and alien places. Again, a place in which a thing rests or to which it moves unnaturally, must be the natural place for some other body, as experience shows. 15Necessarily, therefore, not everything possesses weight or lightness, but some things do and some do not. From these arguments then it is clear that the body of the universe is not infinite.
Book 1,Chapter 8 (276a18–277b26)
Διότι δ' οὐδὲ πλείους οἷόν τ' οὐρανοὺς εἶναι, λέγωμεν·
τοῦτο γὰρ ἔφαμεν ἐπισκεπτέον, εἴ τις μὴ νομίζει καθόλου
20 δεδεῖχθαι περὶ τῶν σωμάτων ὅτι ἀδύνατον ἐκτὸς εἶναι τοῦ
κόσμου τοῦδε ὁτιοῦν αὐτῶν, ἀλλὰ μόνον ἐπὶ τῶν ἀορίστως
κειμένων εἰρῆσθαι τὸν λόγον. Ἅπαντα γὰρ καὶ μένει καὶ
κινεῖται καὶ κατὰ φύσιν καὶ βίᾳ, καὶ κατὰ φύσιν μέν, ἐν ᾧ
μένει μὴ βίᾳ, καὶ φέρεται, καὶ εἰς ὃν φέρεται, καὶ μένει·
25 ἐν ᾧ δὲ βίᾳ, καὶ φέρεται βίᾳ, καὶ εἰς ὃν βίᾳ φέρεται,
βίᾳ καὶ μένει. Ἔτι εἰ βίᾳ ἥδε ἡ φορά, ἡ ἐναντία κατὰ
φύσιν. Ἐπὶ δὴ τὸ μέσον τὸ ἐνταῦθα εἰ βίᾳ οἰσθήσεται ἡ γῆ
ἐκεῖθεν, ἐντεῦθεν οἰσθήσεται ἐκεῖ κατὰ φύσιν· καὶ εἰ μένει
ἐνταῦθα ἡ ἐκεῖθεν μὴ βίᾳ, καὶ οἰσθήσεται δεῦρο κατὰ
30 φύσιν. Μία γὰρ ἡ κατὰ φύσιν. Ἔτι ἀνάγκη πάντας τοὺς κόςμους
ἐκ τῶν αὐτῶν εἶναι σωμάτων, ὁμοίους γ' ὄντας τὴν φύσιν.
Ἀλλὰ μὴν καὶ τῶν σωμάτων ἕκαστον ἀναγκαῖον τὴν αὐτὴν
We must now proceed to explain why there cannot be more than one heaven-the further question mentioned above. For it may be thought that we have not proved universal of bodies that none whatever 20can exist outside our universe, and that our argument applied only to those of indeterminate extent.
Now all things rest and move naturally and by constraint. A thing moves naturally to a place in which it rests without constraint, and rests naturally in a place to which it moves without constraint. On the other hand, a thing moves by constraint to a place in which it rests by 25constraint, and rests by constraint in a place to which it moves by constraint. Further, if a given movement is due to constraint, its contrary is natural. If, then, it is by constraint that earth moves from a certain place to the centre here, its movement from here to there will be natural, and if earth from there rests here without constraint, its movement hither will be 30natural. And the natural movement in each case is one. Further, these worlds, being similar in nature to ours, must all be composed of the same bodies as it.
Now all things rest and move naturally and by constraint. A thing moves naturally to a place in which it rests without constraint, and rests naturally in a place to which it moves without constraint. On the other hand, a thing moves by constraint to a place in which it rests by 25constraint, and rests by constraint in a place to which it moves by constraint. Further, if a given movement is due to constraint, its contrary is natural. If, then, it is by constraint that earth moves from a certain place to the centre here, its movement from here to there will be natural, and if earth from there rests here without constraint, its movement hither will be 30natural. And the natural movement in each case is one. Further, these worlds, being similar in nature to ours, must all be composed of the same bodies as it.
276b
1 ἔχειν δύναμιν, οἷον λέγω πῦρ καὶ γῆν καὶ τὰ μεταξὺ
τούτων· εἰ γὰρ ὁμώνυμα ταῦτα καὶ μὴ κατὰ τὴν αὐτὴν ἰδέαν
λέγονται τἀκεῖ τοῖς παρ' ἡμῖν, καὶ τὸ πᾶν ὁμωνύμως ἂν
λέγοιτο κόσμος. Δῆλον τοίνυν ὅτι τὸ μὲν ἀπὸ τοῦ μέσου φέρεσθαι
5 πέφυκε, τὸ δ' ἐπὶ τὸ μέσον αὐτῶν, εἴπερ πᾶν ὁμοειδὲς
τὸ πῦρ τῷ πυρὶ καὶ τῶν ἄλλων ἕκαστον, ὥσπερ καὶ
τὰ ἐν τούτῳ μόρια τοῦ πυρός. Ὅτι δ' ἀναγκαῖον οὕτως ἔχειν,
ἐκ τῶν περὶ τὰς κινήσεις ὑποθέσεων φανερόν· αἵ τε γὰρ κινήσεις
πεπερασμέναι, ἕκαστόν τε τῶν στοιχείων λέγεται καθ' ἑκάστην
10 τῶν κινήσεων. Ὥστ' εἴπερ καὶ αἱ κινήσεις αἱ αὐταί, καὶ
τὰ στοιχεῖα ἀναγκαῖον εἶναι πανταχοῦ ταὐτά. Πέφυκεν ἄρα
φέρεσθαι καὶ ἐπὶ τόδε τὸ μέσον τὰ ἐν ἄλλῳ κόσμῳ τῆς
γῆς μόρια, καὶ πρὸς τόδε τὸ ἔσχατον τὸ ἐκεῖ πῦρ. Ἀλλ'
ἀδύνατον· τούτου γὰρ συμβαίνοντος ἀνάγκη φέρεσθαι ἄνω
15 μὲν τὴν γῆν ἐν τῷ οἰκείῳ κόσμῳ, τὸ δὲ πῦρ ἐπὶ τὸ μέσον,
ὁμοίως δὲ καὶ τὴν ἐντεῦθεν γῆν ἀπὸ τοῦ μέσου φέρεσθαι κατὰ
φύσιν πρὸς τὸ ἐκεῖ φερομένην μέσον, διὰ τὸ τοὺς κόσμους
οὕτω κεῖσθαι πρὸς ἀλλήλους. Ἢ γὰρ οὐ θετέον τὴν αὐτὴν εἶναι
φύσιν τῶν ἁπλῶν σωμάτων ἐν τοῖς πλείοσιν οὐρανοῖς, ἢ λέγοντας
20 οὕτως τὸ μέσον ἓν ποιεῖν ἀνάγκη καὶ τὸ ἔσχατον·
τούτου δ' ὄντος ἀδύνατον εἶναι κόσμους πλείους ἑνός.
Τὸ δ' ἀξιοῦν ἄλλην εἶναι φύσιν τῶν ἁπλῶν σωμάτων, ἂν ἀποσχῶσιν
ἔλαττον ἢ πλεῖον τῶν οἰκείων τόπων, ἄλογον· τί γὰρ
διαφέρει τὸ τοσονδὶ φάναι μῆκος ἀπέχειν ἢ τοσονδί; Διοίσει
25 γὰρ κατὰ λόγον, ὅσῳ πλεῖον μᾶλλον, τὸ δ' εἶδος τὸ αὐτό.
Ἀλλὰ μὴν ἀνάγκη γ' εἶναί τινα κίνησιν αὐτῶν· ὅτι μὲν γὰρ
κινοῦνται, φανερόν. Πότερον οὖν βίᾳ πάσας ἐροῦμεν κινεῖσθαι
καὶ τὰς ἐναντίας; ἀλλ' ὃ μὴ πέφυκεν ὅλως κινεῖσθαι, ἀδύνατον
τοῦτο κινεῖσθαι βίᾳ. Εἰ τοίνυν ἐστί τις κίνησις αὐτῶν
30 κατὰ φύσιν, ἀνάγκη τῶν ὁμοειδῶν καὶ τῶν καθ' ἕκαστον
πρὸς ἕνα ἀριθμῷ τόπον ὑπάρχειν τὴν κίνησιν, οἷον πρὸς τόδε
τι μέσον καὶ πρὸς τόδε τι ἔσχατον. Εἰ δὲ πρὸς εἴδει ταὐτά,
1Moreover each of the bodies, fire, I mean, and earth and their intermediates, must have the same power as in our world. For if these names are used equivocally, if the identity of name does not rest upon an identity of form in these elements and ours, then the whole to which they belong can only be called a world by equivocation. Clearly, then, 5one of the bodies will move naturally away from the centre and another towards the centre, since fire must be identical with fire, earth with earth, and so on, as the fragments of each are identical in this world. That this must be the case is evident from the principles laid down in our discussion of the movements, for these are limited in number, and the distinction of the elements depends upon the distinction of the movements. 10Therefore, since the movements are the same, the elements must also be the same everywhere. The particles of earth, then, in another world move naturally also to our centre and its fire to our circumference. This, however, is impossible, since, if it were true, earth must, in its own world, move upwards, and fire to the centre; in the same way the earth of our world must move naturally away from the centre when it moves towards 15the centre of another universe. This follows from the supposed juxtaposition of the worlds. For either we must refuse to admit the identical nature of the simple bodies in the various universes, or, admitting this, we must make the centre and the extremity one as suggested. This being so, it follows that there cannot be more worlds than one.
To postulate a difference of nature in the simple bodies according as they are more or less 20distant from their proper places is unreasonable. For what difference can it make whether we say that a thing is this distance away or that? One would have to suppose a difference proportionate to the distance and increasing with it, but the form is in fact the same. Moreover, the bodies must have some movement, since the fact that they move is quite evident. Are we to say then that all their movements, even those which are 25mutually contrary, are due to constraint? No, for a body which has no natural movement at all cannot be moved by constraint. If then the bodies have a natural movement, the movement of the particular instances of each form must necessarily have for goal a place numerically one, i.e. a particular centre or a particular extremity. If it be suggested that the goal in each case is one in form but numerically more than one, on the analogy 30of particulars which are many though each undifferentiated in form, we reply that the variety of goal cannot be limited to this portion or that but must extend to all alike.
To postulate a difference of nature in the simple bodies according as they are more or less 20distant from their proper places is unreasonable. For what difference can it make whether we say that a thing is this distance away or that? One would have to suppose a difference proportionate to the distance and increasing with it, but the form is in fact the same. Moreover, the bodies must have some movement, since the fact that they move is quite evident. Are we to say then that all their movements, even those which are 25mutually contrary, are due to constraint? No, for a body which has no natural movement at all cannot be moved by constraint. If then the bodies have a natural movement, the movement of the particular instances of each form must necessarily have for goal a place numerically one, i.e. a particular centre or a particular extremity. If it be suggested that the goal in each case is one in form but numerically more than one, on the analogy 30of particulars which are many though each undifferentiated in form, we reply that the variety of goal cannot be limited to this portion or that but must extend to all alike.
277a
1 πλείω δέ, διότι καὶ τὰ καθ' ἕκαστα πλείω μέν, εἴδει δ'
ἕκαστον ἀδιάφορον, οὐ τῷ μὲν τῷ δ' οὐ τοιοῦτον ἔσται τῶν μορίων,
ἀλλ' ὁμοίως πᾶσιν· ὁμοίως γὰρ ἅπαντα κατ' εἶδος ἀδιάφορα
ἀλλήλων, ἀριθμῷ δ' ἕτερον ὁτιοῦν ὁτουοῦν. Λέγω δὲ
5 τοῦτο, ὅτι εἰ τὰ ἐνταῦθα μόρια πρὸς ἄλληλα καὶ τὰ ἐν ἑτέρῳ
κόσμῳ ὁμοίως ἔχει, καὶ τὸ ληφθὲν ἐντεῦθεν οὐδὲν διαφερόντως
πρὸς τῶν ἐν ἄλλῳ τινὶ κόσμῳ μορίων καὶ πρὸς τῶν ἐν
τῷ αὐτῷ, ἀλλ' ὡσαύτως· διαφέρουσι γὰρ οὐθὲν εἴδει ἀλλήλων.
Ὥστ' ἀναγκαῖον ἢ κινεῖν ταύτας τὰς ὑποθέσεις, ἢ τὸ
10 μέσον ἓν εἶναι καὶ τὸ ἔσχατον. Τούτου δ' ὄντος ἀνάγκη καὶ
τὸν οὐρανὸν ἕνα μόνον εἶναι καὶ μὴ πλείους, τοῖς αὐτοῖς τεκμηρίοις
τούτοις καὶ ταῖς αὐταῖς ἀνάγκαις. Ὅτι δ' ἔστι τι οὗ πέφυκεν
ἡ γῆ φέρεσθαι καὶ τὸ πῦρ, δῆλον καὶ ἐκ τῶν ἄλλων.
Ὅλως γὰρ τὸ κινούμενον ἔκ τινος εἴς τι μεταβάλλει,
15 καὶ ταῦτα ἐξ οὗ καὶ εἰς ὃ εἴδει διαφέρει· πᾶσα δὲ πεπερασμένη
μεταβολή· οἷον τὸ ὑγιαζόμενον ἐκ νόσου εἰς ὑγίειαν
καὶ τὸ αὐξανόμενον ἐκ μικρότητος εἰς μέγεθος. Καὶ τὸ φερόμενον
ἄρα· καὶ γὰρ τοῦτο γίνεταί ποθέν ποι. Δεῖ ἄρα εἴδει
διαφέρειν ἐξ οὗ καὶ εἰς ὃ πέφυκε φέρεσθαι, ὥσπερ τὸ ὑγιαζόμενον
20 οὐχ οὗ ἔτυχεν, οὐδ' οὗ βούλεται ὁ κινῶν. Καὶ τὸ πῦρ
ἄρα καὶ ἡ γῆ οὐκ εἰς ἄπειρον φέρονται, ἀλλ' εἰς ἀντικείμενα·
ἀντίκειται δὲ κατὰ τόπον τὸ ἄνω τῷ κάτω, ὥστε ταῦτα ἔσται
πέρατα τῆς φορᾶς. Ἐπεὶ καὶ ἡ κύκλῳ ἔχει πως ἀντικείμενα
τὰ κατὰ διάμετρον, τῇ δ' ὅλῃ οὐκ ἔστιν ἐναντίον οὐδέν,
25 ὥστε καὶ τούτοις τρόπον τινὰ ἡ κίνησις εἰς ἀντικείμενα
καὶ πεπερασμένα. Ἀνάγκη ἄρα εἶναί τι τέλος καὶ μὴ εἰς
ἄπειρον φέρεσθαι. Τεκμήριον δὲ τοῦ μὴ εἰς ἄπειρον φέρεσθαι
καὶ τὸ τὴν γῆν μέν, ὅσῳ ἂν ἐγγυτέρω ᾖ τοῦ μέσου,
θᾶττον φέρεσθαι, τὸ δὲ πῦρ, ὅσῳ ἂν τοῦ ἄνω. Εἰ δ' ἄπειρον
30 ἦν, ἄπειρος ἂν ἦν καὶ ἡ ταχυτής, εἰ δ' ἡ ταχυτής, καὶ τὸ βάρος
καὶ ἡ κουφότης· ὡς γὰρ <εἰ> τῷ κατωτέρω ταχὺ ἦν τι,
ἕτερον τῷ βάρει ἂν ἦν ταχύ, οὕτως εἰ ἄπειρος ἦν ἡ τούτου
ἐπίδοσις, καὶ ἡ τῆς ταχυτῆτος ἐπίδοσις ἄπειρος ἂν ἦν. Ἀλλὰ
1For all are equally undifferentiated in form, but any one is different numerically from any other. What I mean is this: if the portions in this world behave similarly both to one another and to those in another world, then the portion which is taken hence will not behave differently either from the portions 5in another world or from those in the same world, but similarly to them, since in form no portion differs from another. The result is that we must either abandon our present assumption or assert that the centre and the extremity are each numerically one. But this being so, the heaven, by the same evidence and the same necessary inferences, must be one only and no more.
A consideration 10of the other kinds of movement also makes it plain that there is some point to which earth and fire move naturally. For in general that which is moved changes from something into something, the starting-point and the goal being different in form, and always it is a finite change. For instance, to recover health is to change from disease to health, to increase is to change from 15smallness to greatness. Locomotion must be similar: for it also has its goal and starting-point--and therefore the starting-point and the goal of the natural movement must differ in form-just as the movement of coming to health does not take any direction which chance or the wishes of the mover may select. Thus, too, fire and earth move not to infinity but to opposite points; and 20since the opposition in place is between above and below, these will be the limits of their movement. (Even in circular movement there is a sort of opposition between the ends of the diameter, though the movement as a whole has no contrary: so that here too the movement has in a sense an opposed and finite goal.) There must therefore be some end to locomotion: it cannot continue to 25infinity.
This conclusion that local movement is not continued to infinity is corroborated by the fact that earth moves more quickly the nearer it is to the centre, and fire the nearer it is to the upper place. But if movement were infinite speed would be infinite also; and if speed then weight and lightness. For as superior speed in downward movement implies superior weight, so 30infinite increase of weight necessitates infinite increase of speed.
Further, it is not the action of another body that makes one of these bodies move up and the other down; nor is it constraint, like the 'extrusion' of some writers.
A consideration 10of the other kinds of movement also makes it plain that there is some point to which earth and fire move naturally. For in general that which is moved changes from something into something, the starting-point and the goal being different in form, and always it is a finite change. For instance, to recover health is to change from disease to health, to increase is to change from 15smallness to greatness. Locomotion must be similar: for it also has its goal and starting-point--and therefore the starting-point and the goal of the natural movement must differ in form-just as the movement of coming to health does not take any direction which chance or the wishes of the mover may select. Thus, too, fire and earth move not to infinity but to opposite points; and 20since the opposition in place is between above and below, these will be the limits of their movement. (Even in circular movement there is a sort of opposition between the ends of the diameter, though the movement as a whole has no contrary: so that here too the movement has in a sense an opposed and finite goal.) There must therefore be some end to locomotion: it cannot continue to 25infinity.
This conclusion that local movement is not continued to infinity is corroborated by the fact that earth moves more quickly the nearer it is to the centre, and fire the nearer it is to the upper place. But if movement were infinite speed would be infinite also; and if speed then weight and lightness. For as superior speed in downward movement implies superior weight, so 30infinite increase of weight necessitates infinite increase of speed.
Further, it is not the action of another body that makes one of these bodies move up and the other down; nor is it constraint, like the 'extrusion' of some writers.
277b
1 μὴν οὐδ' ὑπ' ἄλλου φέρεται αὐτῶν τὸ μὲν ἄνω τὸ δὲ κάτω·
οὐδὲ βίᾳ, ὥσπερ τινές φασι τῇ ἐκθλίψει. Βραδύτερον γὰρ
ἂν ἐκινεῖτο τὸ πλεῖον πῦρ ἄνω καὶ ἡ πλείων γῆ κάτω· νῦν
δὲ τοὐναντίον ἀεὶ τὸ πλεῖον πῦρ θᾶττον φέρεται καὶ ἡ πλείων
5 γῆ εἰς τὸν αὑτῶν τόπον. Οὐδὲ θᾶττον ἂν πρὸς τῷ τέλει ἐφέρετο,
εἰ βίᾳ καὶ ἐκθλίψει· πάντα γὰρ τοῦ βιασαμένου
πορρωτέρω γιγνόμενα βραδύτερον φέρεται, καὶ ὅθεν βίᾳ,
ἐκεῖ φέρεται οὐ βίᾳ. Ὥστ' ἐκ τούτων θεωροῦσιν ἔστι λαβεῖν
τὴν πίστιν περὶ τῶν λεγομένων ἱκανῶς. Ἔτι δὲ καὶ διὰ τῶν ἐκ
10 τῆς πρώτης φιλοσοφίας λόγων δειχθείη ἄν, καὶ ἐκ τῆς
κύκλῳ κινήσεως, ἣν ἀναγκαῖον ἀΐδιον ὁμοίως ἐνταῦθά τ' εἶναι
καὶ ἐν τοῖς ἄλλοις κόσμοις. Δῆλον δὲ κἂν ὧδε γένοιτο
σκοπουμένοις ὅτι ἀνάγκη ἕνα εἶναι τὸν οὐρανόν. Τριῶν γὰρ
ὄντων τῶν σωματικῶν στοιχείων, τρεῖς ἔσονται καὶ οἱ τόποι
15 τῶν στοιχείων, εἷς μὲν ὁ τοῦ ὑφισταμένου σώματος ὁ περὶ τὸ
μέσον, ἄλλος δὲ ὁ τοῦ κύκλῳ φερομένου, ὅσπερ ἐστὶν ἔσχατος,
τρίτος δ' ὁ μεταξὺ τούτων ὁ τοῦ μέσου σώματος. Ἀνάγκη γὰρ
ἐν τούτῳ εἶναι τὸ ἐπιπολάζον. Εἰ γὰρ μὴ ἐν τούτῳ, ἔξω ἔσται·
ἀλλ' ἀδύνατον ἔξω. Τὸ μὲν γὰρ ἀβαρὲς τὸ δ' ἔχον βάρος,
20 κατωτέρω δὲ ὁ τοῦ βάρος ἔχοντος σώματος τόπος, εἴπερ ὁ
πρὸς τῷ μέσῳ τοῦ βαρέος. Ἀλλὰ μὴν οὐδὲ παρὰ φύσιν·
ἄλλῳ γὰρ ἔσται κατὰ φύσιν, ἄλλο δ' οὐκ ἦν. Ἀνάγκη ἄρα ἐν
τῷ μεταξὺ εἶναι. Τούτου δ' αὐτοῦ τίνες εἰσὶ διαφοραί, ὕστερον
ἐροῦμεν. Περὶ μὲν οὖν τῶν σωματικῶν στοιχείων, ποῖά τ' ἐστὶ
25 καὶ πόσα, καὶ τίς ἑκάστου τόπος, ἔτι δ' ὅλως πόσοι τὸ
πλῆθος οἱ τόποι, δῆλον ἡμῖν ἐκ τῶν εἰρημένων.
1For in that case the larger the mass of fire or earth the slower would be the upward or downward movement; but the fact is the reverse: the greater the mass of fire or earth the quicker always is its movement towards its own place. Again, the speed of the movement would not increase towards the end if 5it were due to constraint or extrusion; for a constrained movement always diminishes in speed as the source of constraint becomes more distant, and a body moves without constraint to the place whence it was moved by constraint.
A consideration of these points, then, gives adequate assurance of the truth of our contentions. The same could also be shown with the aid of the discussions 10which fall under First Philosophy, as well as from the nature of the circular movement, which must be eternal both here and in the other worlds. It is plain, too, from the following considerations that the universe must be one.
The bodily elements are three, and therefore the places of the elements will be three also; the place, first, of the body which sinks to the bottom, 15namely the region about the centre; the place, secondly, of the revolving body, namely the outermost place, and thirdly, the intermediate place, belonging to the intermediate body. Here in this third place will be the body which rises to the surface; since, if not here, it will be elsewhere, and it cannot be elsewhere: for we have two bodies, one weightless, one endowed with 20weight, and below is place of the body endowed with weight, since the region about the centre has been given to the heavy body. And its position cannot be unnatural to it, for it would have to be natural to something else, and there is nothing else. It must then occupy the intermediate place. What distinctions there are within the intermediate itself we will explain later on.
We 25have now said enough to make plain the character and number of the bodily elements, the place of each, and further, in general, how many in number the various places are.
A consideration of these points, then, gives adequate assurance of the truth of our contentions. The same could also be shown with the aid of the discussions 10which fall under First Philosophy, as well as from the nature of the circular movement, which must be eternal both here and in the other worlds. It is plain, too, from the following considerations that the universe must be one.
The bodily elements are three, and therefore the places of the elements will be three also; the place, first, of the body which sinks to the bottom, 15namely the region about the centre; the place, secondly, of the revolving body, namely the outermost place, and thirdly, the intermediate place, belonging to the intermediate body. Here in this third place will be the body which rises to the surface; since, if not here, it will be elsewhere, and it cannot be elsewhere: for we have two bodies, one weightless, one endowed with 20weight, and below is place of the body endowed with weight, since the region about the centre has been given to the heavy body. And its position cannot be unnatural to it, for it would have to be natural to something else, and there is nothing else. It must then occupy the intermediate place. What distinctions there are within the intermediate itself we will explain later on.
We 25have now said enough to make plain the character and number of the bodily elements, the place of each, and further, in general, how many in number the various places are.
Book 1,Chapter 9 (277b27–279b3)
Ὅτι δ' οὐ μόνον εἷς ἐστίν, ἀλλὰ καὶ ἀδύνατον
γενέσθαι πλείους, ἔτι δ' ὡς ἀΐδιος ἄφθαρτος ὢν καὶ ἀγένητος,
λέγωμεν, πρῶτον διαπορήσαντες περὶ αὐτοῦ. Δόξειε γὰρ
30 ἂν ὡδὶ σκοπουμένοις ἀδύνατον ἕνα καὶ μόνον εἶναι αὐτόν· ἐν
ἅπασι γὰρ καὶ τοῖς φύσει καὶ τοῖς ἀπὸ τέχνης συνεστῶσι
καὶ γεγενημένοις ἕτερόν ἐστιν αὐτή τε καθ' αὑτὴν ἡ μορφὴ καὶ
μεμιγμένη μετὰ τῆς ὕλης· οἷον τῆς σφαίρας ἕτερον τὸ εἶδος
We must show not only that the heaven is one, but also that more than one heaven is and, further, that, as exempt from decay and generation, the heaven is eternal. We may begin by raising a difficulty. From 30one point of view it might seem impossible that the heaven should be one and unique, since in all formations and products whether of nature or of art we can distinguish the shape in itself and the shape in combination with matter.
278a
1 καὶ ἡ χρυσῆ καὶ ἡ χαλκῆ σφαῖρα, καὶ πάλιν τοῦ κύκλου
ἑτέρα ἡ μορφὴ καὶ ὁ χαλκοῦς καὶ ὁ ξύλινος κύκλος· τὸ
γὰρ τί ἦν εἶναι λέγοντες σφαίρᾳ ἢ κύκλῳ οὐκ ἐροῦμεν ἐν τῷ
λόγῳ χρυσὸν ἢ χαλκόν, ὡς οὐκ ὄντα ταῦτα τῆς οὐσίας· ἂν
5 δὲ τὴν χαλκῆν ἢ χρυσῆν, ἐροῦμεν, καὶ ἐὰν μὴ δυνώμεθα
νοῆσαι μηδὲ λαβεῖν ἄλλο τι παρὰ τὸ καθ' ἕκαστον. Ἐνίοτε
γὰρ οὐθὲν κωλύει τοῦτο συμβαίνειν, οἷον εἰ μόνος εἷς ληφθείη
κύκλος· οὐθὲν γὰρ ἧττον ἄλλο ἔσται τὸ κύκλῳ εἶναι καὶ τῷδε
τῷ κύκλῳ, καὶ τὸ μὲν εἶδος, τὸ δ' εἶδος ἐν τῇ ὕλῃ καὶ
10 τῶν καθ' ἕκαστον. Ἐπεὶ οὖν ἐστὶν ὁ οὐρανὸς αἰσθητός, τῶν καθ'
ἕκαστον ἂν εἴη· τὸ γὰρ αἰσθητὸν ἅπαν ἐν τῇ ὕλῃ ὑπῆρχεν.
Εἰ δὲ τῶν καθ' ἕκαστον, ἕτερον ἂν εἴη τῷδε τῷ οὐρανῷ εἶναι
καὶ οὐρανῷ ἁπλῶς. Ἕτερον ἄρα ὅδε ὁ οὐρανὸς καὶ οὐρανὸς ἁπλῶς,
καὶ τὸ μὲν ὡς εἶδος καὶ μορφή, τὸ δ' ὡς τῇ ὕλῃ μεμιγμένον.
15 Ὧν δ' ἐστὶ μορφή τις καὶ εἶδος, ἤτοι ἔστιν ἢ ἐνδέχεται
πλείω γενέσθαι τὰ καθ' ἕκαστα. Εἴτε γὰρ ἔστιν εἴδη, καθάπερ
φασί τινες, ἀνάγκη τοῦτο συμβαίνειν, εἴτε καὶ χωριστὸν μηθὲν
τῶν τοιούτων, οὐθὲν ἧττον· ἐπὶ πάντων γὰρ οὕτως ὁρῶμεν,
ὅσων ἡ οὐσία ἐν ὕλῃ ἐστίν, πλείω καὶ ἄπειρα ὄντα τὰ ὁμοειδῆ.
20 Ὥστε ἤτοι εἰσὶ πλείους οὐρανοὶ ἢ ἐνδέχεται πλείους εἶναι.
Ἐκ μὲν δὴ τούτων ὑπολάβοι τις ἂν καὶ εἶναι καὶ ἐνδέχεσθαι
πλείους εἶναι οὐρανούς· σκεπτέον δὲ πάλιν τί τούτων λέγεται
καλῶς καὶ τί οὐ καλῶς. Τὸ μὲν οὖν ἕτερον εἶναι τὸν
λόγον τὸν ἄνευ τῆς ὕλης καὶ τὸν ἐν τῇ ὕλῃ τῆς μορφῆς καλῶς
25 τε λέγεται, καὶ ἔστω τοῦτ' ἀληθές. Ἀλλ' οὐδὲν ἧττον οὐδεμία
ἀνάγκη διὰ τοῦτο πλείους εἶναι κόσμους, οὐδ' ἐνδέχεται
γενέσθαι πλείους, εἴπερ οὗτος ἐξ ἁπάσης ἐστὶ τῆς ὕλης, ὥσπερ
ἔστιν. Ὡδὶ δὲ μᾶλλον ἴσως τὸ λεγόμενον ἔσται δῆλον. Εἰ γάρ
ἐστιν ἡ γρυπότης καμπυλότης ἐν ῥινὶ ἢ σαρκί, καὶ ἔστιν ὕλη
30 τῇ γρυπότητι ἡ σάρξ, εἰ ἐξ ἁπασῶν τῶν σαρκῶν μία γένοιτο
σὰρξ καὶ ὑπάρξειεν ταύτῃ τὸ γρυπόν, οὐθὲν ἂν ἄλλ'
οὔτ' εἴη γρυπὸν οὔτ' ἐνδέχοιτο γενέσθαι. Ὁμοίως δὲ καὶ εἰ τῷ
ἀνθρώπῳ ἐστὶν ὕλη σάρκες καὶ ὀστᾶ, εἰ ἐκ πάσης τῆς σαρκὸς
καὶ πάντων τῶν ὀστῶν ἄνθρωπος γένοιτο ἀδυνάτων ὄντων
35 διαλυθῆναι, οὐκ ἂν ἐνδέχοιτο εἶναι ἄλλον ἄνθρωπον. Ὡσαύτως
1For instance the form of the sphere is one thing and the gold or bronze sphere another; the shape of the circle again is one thing, the bronze or wooden circle another. For when we state the essential nature of the sphere or circle we do not include in the formula gold or bronze, because they do 5not belong to the essence, but if we are speaking of the copper or gold sphere we do include them. We still make the distinction even if we cannot conceive or apprehend any other example beside the particular thing. This may, of course, sometimes be the case: it might be, for instance, that only one circle could be found; yet none the less the difference will remain between 10the being of circle and of this particular circle, the one being form, the other form in matter, i.e. a particular thing. Now since the universe is perceptible it must be regarded as a particular; for everything that is perceptible subsists, as we know, in matter. But if it is a particular, there will be a distinction between the being of 'this universe' and of 'universe' 15unqualified. There is a difference, then, between 'this universe' and simple 'universe'; the second is form and shape, the first form in combination with matter; and any shape or form has, or may have, more than one particular instance.
On the supposition of Forms such as some assert, this must be the case, and equally on the view that no such entity has a separate 20existence. For in every case in which the essence is in matter it is a fact of observation that the particulars of like form are several or infinite in number. Hence there either are, or may be, more heavens than one. On these grounds, then, it might be inferred either that there are or that there might be several heavens. We must, however, return and ask how much of this 25argument is correct and how much not.
Now it is quite right to say that the formula of the shape apart from the matter must be different from that of the shape in the matter, and we may allow this to be true. We are not, however, therefore compelled to assert a plurality of worlds. Such a plurality is in fact impossible if this world contains the entirety of matter, as in 30fact it does. But perhaps our contention can be made clearer in this way. Suppose 'aquilinity' to be curvature in the nose or flesh, and flesh to be the matter of aquilinity. Suppose further, that all flesh came together into a single whole of flesh endowed with this aquiline quality. Then neither would there be, nor could there arise, any other thing that was aquiline.
On the supposition of Forms such as some assert, this must be the case, and equally on the view that no such entity has a separate 20existence. For in every case in which the essence is in matter it is a fact of observation that the particulars of like form are several or infinite in number. Hence there either are, or may be, more heavens than one. On these grounds, then, it might be inferred either that there are or that there might be several heavens. We must, however, return and ask how much of this 25argument is correct and how much not.
Now it is quite right to say that the formula of the shape apart from the matter must be different from that of the shape in the matter, and we may allow this to be true. We are not, however, therefore compelled to assert a plurality of worlds. Such a plurality is in fact impossible if this world contains the entirety of matter, as in 30fact it does. But perhaps our contention can be made clearer in this way. Suppose 'aquilinity' to be curvature in the nose or flesh, and flesh to be the matter of aquilinity. Suppose further, that all flesh came together into a single whole of flesh endowed with this aquiline quality. Then neither would there be, nor could there arise, any other thing that was aquiline.
278b
1 δὲ καὶ ἐπὶ τῶν ἄλλων· ὅλως γὰρ ὅσων ἐστὶν ἡ οὐσία ἐν
ὑποκειμένῃ τινὶ ὕλῃ, τούτων οὐδὲν ἐνδέχεται γίγνεσθαι μὴ
ὑπαρχούσης τινὸς ὕλης. Ὁ δ' οὐρανὸς ἔστι μὲν τῶν καθ' ἕκαστα
καὶ τῶν ἐκ τῆς ὕλης· ἀλλ' εἰ μὴ ἐκ μορίου αὐτῆς συνέστηκεν
5 ἀλλ' ἐξ ἁπάσης, τὸ μὲν εἶναι αὐτῷ οὐρανῷ καὶ τῷδε τῷ
οὐρανῷ ἕτερόν ἐστιν, οὐ μέντοι οὔτ' ἂν εἴη ἄλλος οὔτ' ἂν ἐνδέχοιτο
γενέσθαι πλείους, διὰ τὸ πᾶσαν τὴν ὕλην περιειληφέναι
τοῦτον. Λείπεται ἄρα αὐτὸ τοῦτο δεῖξαι, ὅτι ἐξ ἅπαντος τοῦ
φυσικοῦ καὶ τοῦ αἰσθητοῦ συνέστηκε σώματος. Εἴπωμεν δὲ πρῶτον
10 τί λέγομεν εἶναι τὸν οὐρανὸν καὶ ποσαχῶς, ἵνα μᾶλλον
ἡμῖν δῆλον γένηται τὸ ζητούμενον. Ἕνα μὲν οὖν τρόπον οὐρανὸν
λέγομεν τὴν οὐσίαν τὴν τῆς ἐσχάτης τοῦ παντὸς περιφορᾶς,
ἢ σῶμα φυσικὸν τὸ ἐν τῇ ἐσχάτῃ περιφορᾷ τοῦ
παντός· εἰώθαμεν γὰρ τὸ ἔσχατον καὶ τὸ ἄνω μάλιστα
15 καλεῖν οὐρανόν, ἐν ᾧ καὶ τὸ θεῖον πᾶν ἱδρῦσθαί φαμεν.
Ἄλλον δ' αὖ τρόπον τὸ συνεχὲς σῶμα τῇ ἐσχάτῃ περιφορᾷ
τοῦ παντός, ἐν ᾧ σελήνη καὶ ἥλιος καὶ ἔνια τῶν
ἄστρων· καὶ γὰρ ταῦτα ἐν τῷ οὐρανῷ εἶναί φαμεν. Ἔτι δ'
ἄλλως λέγομεν οὐρανὸν τὸ περιεχόμενον σῶμα ὑπὸ τῆς
20 ἐσχάτης περιφορᾶς· τὸ γὰρ ὅλον καὶ τὸ πᾶν εἰώθαμεν λέγειν
οὐρανόν. Τριχῶς δὴ λεγομένου τοῦ οὐρανοῦ, τὸ ὅλον τὸ ὑπὸ
τῆς ἐσχάτης περιεχόμενον περιφορᾶς ἐξ ἅπαντος ἀνάγκη
συνεστάναι τοῦ φυσικοῦ καὶ τοῦ αἰσθητοῦ σώματος διὰ τὸ μήτ'
εἶναι μηδὲν ἔξω σῶμα τοῦ οὐρανοῦ μήτ' ἐνδέχεσθαι γενέσθαι.
25 Εἰ γὰρ ἔστιν ἔξω τῆς ἐσχάτης περιφορᾶς σῶμα φυσικόν,
ἀνάγκη αὐτὸ ἤτοι τῶν ἁπλῶν εἶναι σωμάτων ἢ τῶν συνθέτων,
καὶ ἢ κατὰ φύσιν ἢ παρὰ φύσιν ἔχειν. Τῶν μὲν οὖν
ἁπλῶν οὐθὲν ἂν εἴη. Τὸ μὲν γὰρ κύκλῳ φερόμενον δέδεικται
ὅτι οὐκ ἐνδέχεται μεταλλάξαι τὸν αὑτοῦ τόπον. Ἀλλὰ μὴν
30 οὐδὲ τὸ ἀπὸ τοῦ μέσου δυνατόν, οὐδὲ τὸ ὑφιστάμενον. Κατὰ
φύσιν μὲν γὰρ οὐκ ἂν εἴησαν (ἄλλοι γὰρ αὐτῶν οἰκεῖοι τόποι),
παρὰ φύσιν δ' εἴπερ εἰσίν, ἄλλῳ τινὶ ἔσται κατὰ φύσιν
ὁ ἔξω τόπος· τὸν γὰρ τούτῳ παρὰ φύσιν ἀναγκαῖον
ἄλλῳ εἶναι κατὰ φύσιν. Ἀλλ' οὐκ ἦν ἄλλο σῶμα παρὰ
35 ταῦτα. Οὐκ ἄρ' ἐστὶ δυνατὸν οὐθὲν τῶν ἁπλῶν ἔξω εἶναι τοῦ
1Similarly, suppose flesh and bones to be the matter of man, and suppose a man to be created of all flesh and all bones in indissoluble union. The possibility of another man would be removed. Whatever case you took it would be the same. The general rule is this: a thing whose essence resides in a substratum 5of matter can never come into being in the absence of all matter. Now the universe is certainly a particular and a material thing: if however, it is composed not of a part but of the whole of matter, then though the being of 'universe' and of 'this universe' are still distinct, yet there is no other universe, and no possibility of others being made, because all the matter 10is already included in this. It remains, then, only to prove that it is composed of all natural perceptible body.
First, however, we must explain what we mean by 'heaven' and in how many senses we use the word, in order to make clearer the object of our inquiry. (a) In one sense, then, we call 'heaven' the substance of the extreme circumference of the whole, or that natural 15body whose place is at the extreme circumference. We recognize habitually a special right to the name 'heaven' in the extremity or upper region, which we take to be the seat of all that is divine. (b) In another sense, we use this name for the body continuous with the extreme circumference which contains the moon, the sun, and some of the stars; these we say are 'in the heaven'. 20(c) In yet another sense we give the name to all body included within extreme circumference, since we habitually call the whole or totality 'the heaven'. The word, then, is used in three senses.
Now the whole included within the extreme circumference must be composed of all physical and sensible body, because there neither is, nor can come into being, any body outside the 25heaven. For if there is a natural body outside the extreme circumference it must be either a simple or a composite body, and its position must be either natural or unnatural. But it cannot be any of the simple bodies. For, first, it has been shown that that which moves in a circle cannot change its place. And, secondly, it cannot be that which moves from the centre or that which 30lies lowest. Naturally they could not be there, since their proper places are elsewhere; and if these are there unnaturally, the exterior place will be natural to some other body, since a place which is unnatural to one body must be natural to another: but we saw that there is no other body besides these. Then it is not possible that any simple body should be outside the heaven.
First, however, we must explain what we mean by 'heaven' and in how many senses we use the word, in order to make clearer the object of our inquiry. (a) In one sense, then, we call 'heaven' the substance of the extreme circumference of the whole, or that natural 15body whose place is at the extreme circumference. We recognize habitually a special right to the name 'heaven' in the extremity or upper region, which we take to be the seat of all that is divine. (b) In another sense, we use this name for the body continuous with the extreme circumference which contains the moon, the sun, and some of the stars; these we say are 'in the heaven'. 20(c) In yet another sense we give the name to all body included within extreme circumference, since we habitually call the whole or totality 'the heaven'. The word, then, is used in three senses.
Now the whole included within the extreme circumference must be composed of all physical and sensible body, because there neither is, nor can come into being, any body outside the 25heaven. For if there is a natural body outside the extreme circumference it must be either a simple or a composite body, and its position must be either natural or unnatural. But it cannot be any of the simple bodies. For, first, it has been shown that that which moves in a circle cannot change its place. And, secondly, it cannot be that which moves from the centre or that which 30lies lowest. Naturally they could not be there, since their proper places are elsewhere; and if these are there unnaturally, the exterior place will be natural to some other body, since a place which is unnatural to one body must be natural to another: but we saw that there is no other body besides these. Then it is not possible that any simple body should be outside the heaven.
279a
1 οὐρανοῦ σῶμα. Εἰ δὲ μὴ τῶν ἁπλῶν, οὐδὲ τῶν μικτῶν·
ἀνάγκη γὰρ εἶναι καὶ τὰ ἁπλᾶ τοῦ μικτοῦ ὄντος. Ἀλλὰ μὴν οὐδὲ
γενέσθαι δυνατόν· ἤτοι γὰρ κατὰ φύσιν ἔσται ἢ παρὰ φύσιν,
καὶ ἢ ἁπλοῦν ἢ μικτόν. Ὥστε πάλιν ὁ αὐτὸς ἥξει λόγος·
5 οὐδὲν γὰρ διαφέρει σκοπεῖν εἰ ἔστιν ἢ εἰ γενέσθαι δυνατόν.
Φανερὸν τοίνυν ἐκ τῶν εἰρημένων ὅτι οὔτ' ἔστιν ἔξω οὔτ' ἐγχωρεῖ
γενέσθαι σώματος ὄγκον οὐθενός· ἐξ ἁπάσης ἄρ' ἐστὶ
τῆς οἰκείας ὕλης ὁ πᾶς κόσμος· ὕλη γὰρ ἦν αὐτῷ τὸ φυσικὸν
σῶμα καὶ αἰσθητόν. Ὥστ' οὔτε νῦν εἰσὶ πλείους οὐρανοὶ
10 οὔτ' ἐγένοντο, οὔτ' ἐνδέχεται γενέσθαι πλείους· ἀλλ' εἷς καὶ
μόνος καὶ τέλειος οὗτος οὐρανός ἐστιν. Ἅμα δὲ δῆλον ὅτι οὐδὲ
τόπος οὐδὲ κενὸν οὐδὲ χρόνος ἐστὶν ἔξω τοῦ οὐρανοῦ. Ἐν ἅπαντι
γὰρ τόπῳ δυνατὸν ὑπάρξαι σῶμα· κενὸν δ' εἶναί φασιν ἐν
ᾧ μὴ ἐνυπάρχει σῶμα, δυνατὸν δ' ἐστὶ γενέσθαι· χρόνος
15 δὲ ἀριθμὸς κινήσεως· κίνησις δ' ἄνευ φυσικοῦ σώματος οὐκ
ἔστιν. Ἔξω δὲ τοῦ οὐρανοῦ δέδεικται ὅτι οὔτ' ἔστιν οὔτ' ἐνδέχεται
γενέσθαι σῶμα. Φανερὸν ἄρα ὅτι οὔτε τόπος οὔτε κενὸν οὔτε
χρόνος ἐστὶν ἔξω. Διόπερ οὔτ' ἐν τόπῳ τἀκεῖ πέφυκεν, οὔτε
χρόνος αὐτὰ ποιεῖ γηράσκειν, οὐδ' ἐστὶν οὐδενὸς οὐδεμία μεταβολὴ
20 τῶν ὑπὲρ τὴν ἐξωτάτω τεταγμένων φοράν, ἀλλ' ἀναλλοίωτα
καὶ ἀπαθῆ τὴν ἀρίστην ἔχοντα ζωὴν καὶ τὴν αὐταρκεστάτην
διατελεῖ τὸν ἅπαντα αἰῶνα. (Καὶ γὰρ τοῦτο τοὔνομα
θείως ἔφθεγκται παρὰ τῶν ἀρχαίων. Τὸ γὰρ τέλος τὸ περιέχον
τὸν τῆς ἑκάστου ζωῆς χρόνον, οὗ μηθὲν ἔξω κατὰ φύσιν,
25 αἰὼν ἑκάστου κέκληται. Κατὰ τὸν αὐτὸν δὲ λόγον καὶ τὸ τοῦ
παντὸς οὐρανοῦ τέλος καὶ τὸ τὸν πάντα χρόνον καὶ τὴν ἀπειρίαν
περιέχον τέλος αἰών ἐστιν, ἀπὸ τοῦ αἰεὶ εἶναι τὴν ἐπωνυμίαν
εἰληφώς, ἀθάνατος καὶ θεῖος). Ὅθεν καὶ τοῖς ἄλλοις
ἐξήρτηται, τοῖς μὲν ἀκριβέστερον τοῖς δ' ἀμαυρῶς, τὸ εἶναί
30 τε καὶ ζῆν. Καὶ γάρ, καθάπερ ἐν τοῖς ἐγκυκλίοις φιλοσοφήμασι
περὶ τὰ θεῖα, πολλάκις προφαίνεται τοῖς λόγοις ὅτι
τὸ θεῖον ἀμετάβλητον ἀναγκαῖον εἶναι πᾶν τὸ πρῶτον καὶ
ἀκρότατον· ὃ οὕτως ἔχον μαρτυρεῖ τοῖς εἰρημένοις. Οὔτε γὰρ ἄλλο
κρεῖττόν ἐστιν ὅ τι κινήσει (ἐκεῖνο γὰρ ἂν εἴη θειότερον) οὔτ'
35 ἔχει φαῦλον οὐδέν, οὔτ' ἐνδεὲς τῶν αὑτοῦ καλῶν οὐδενός ἐστιν.
1But, if no simple body, neither can any mixed body be there: for the presence of the simple body is involved in the presence of the mixture. Further neither can any body come into that place: for it will do so either naturally or unnaturally, and will be either simple or composite; so that the same 5argument will apply, since it makes no difference whether the question is 'does A exist?' or 'could A come to exist?' From our arguments then it is evident not only that there is not, but also that there could never come to be, any bodily mass whatever outside the circumference. The world as a whole, therefore, includes all its appropriate matter, which is, as we saw, natural 10perceptible body. So that neither are there now, nor have there ever been, nor can there ever be formed more heavens than one, but this heaven of ours is one and unique and complete.
It is therefore evident that there is also no place or void or time outside the heaven. For in every place body can be present; and void is said to be that in which the presence of body, though 15not actual, is possible; and time is the number of movement. But in the absence of natural body there is no movement, and outside the heaven, as we have shown, body neither exists nor can come to exist. It is clear then that there is neither place, nor void, nor time, outside the heaven. Hence whatever is there, is of such a nature as not to occupy any place, nor does time age 20it; nor is there any change in any of the things which lie beyond the outermost motion; they continue through their entire duration unalterable and unmodified, living the best and most selfsufficient of lives. As a matter of fact, this word 'duration' possessed a divine significance for the ancients, for the fulfilment which includes the period of life of any creature, outside 25of which no natural development can fall, has been called its duration. On the same principle the fulfilment of the whole heaven, the fulfilment which includes all time and infinity, is 'duration'-a name based upon the fact that it is always-duration immortal and divine. From it derive the being and life which other things, some more or less articulately but others feebly, 30enjoy. So, too, in its discussions concerning the divine, popular philosophy often propounds the view that whatever is divine, whatever is primary and supreme, is necessarily unchangeable. This fact confirms what we have said. For there is nothing else stronger than it to move it-since that would mean more divine-and it has no defect and lacks none of its proper excellences.
It is therefore evident that there is also no place or void or time outside the heaven. For in every place body can be present; and void is said to be that in which the presence of body, though 15not actual, is possible; and time is the number of movement. But in the absence of natural body there is no movement, and outside the heaven, as we have shown, body neither exists nor can come to exist. It is clear then that there is neither place, nor void, nor time, outside the heaven. Hence whatever is there, is of such a nature as not to occupy any place, nor does time age 20it; nor is there any change in any of the things which lie beyond the outermost motion; they continue through their entire duration unalterable and unmodified, living the best and most selfsufficient of lives. As a matter of fact, this word 'duration' possessed a divine significance for the ancients, for the fulfilment which includes the period of life of any creature, outside 25of which no natural development can fall, has been called its duration. On the same principle the fulfilment of the whole heaven, the fulfilment which includes all time and infinity, is 'duration'-a name based upon the fact that it is always-duration immortal and divine. From it derive the being and life which other things, some more or less articulately but others feebly, 30enjoy. So, too, in its discussions concerning the divine, popular philosophy often propounds the view that whatever is divine, whatever is primary and supreme, is necessarily unchangeable. This fact confirms what we have said. For there is nothing else stronger than it to move it-since that would mean more divine-and it has no defect and lacks none of its proper excellences.
279b
1 Καὶ ἄπαυστον δὴ κίνησιν κινεῖται εὐλόγως· πάντα γὰρ
παύεται κινούμενα ὅταν ἔλθῃ εἰς τὸν οἰκεῖον τόπον, τοῦ δὲ κύκλῳ
σώματος ὁ αὐτὸς τόπος ὅθεν ἤρξατο καὶ εἰς ὃν τελευτᾷ.
1Its unceasing movement, then, is also reasonable, since everything ceases to move when it comes to its proper place, but the body whose path is the circle has one and the same place for starting-point and goal.
Book 1,Chapter 10 (279b4–280a34)
Τούτων δὲ διωρισμένων λέγωμεν μετὰ ταῦτα πότερον
5 ἀγένητος ἢ γενητὸς καὶ ἄφθαρτος ἢ φθαρτός, διεξελθόντες
πρότερον τὰς τῶν ἄλλων ὑπολήψεις· αἱ γὰρ τῶν ἐναντίων
ἀποδείξεις ἀπορίαι περὶ τῶν ἐναντίων εἰσίν. Ἅμα δὲ καὶ
μᾶλλον ἂν εἴη πιστὰ τὰ μέλλοντα λεχθήσεσθαι προακηκοόσι
τὰ τῶν ἀμφισβητούντων λόγων δικαιώματα. Τὸ γὰρ
10 ἐρήμην καταδικάζεσθαι δοκεῖν ἧττον ἂν ἡμῖν ὑπάρχοι· καὶ
γὰρ δεῖ διαιτητὰς ἀλλ' οὐκ ἀντιδίκους εἶναι τοὺς μέλλοντας
τἀληθὲς κρίνειν ἱκανῶς. Γενόμενον μὲν οὖν ἅπαντες εἶναί φασιν,
ἀλλὰ γενόμενον οἱ μὲν ἀΐδιον, οἱ δὲ φθαρτὸν ὥσπερ
ὁτιοῦν ἄλλο τῶν συνισταμένων, οἱ δ' ἐναλλὰξ ὁτὲ μὲν
15 οὕτως ὁτὲ δὲ ἄλλως ἔχειν [φθειρόμενον], καὶ τοῦτο αἰεὶ διατελεῖν
οὕτως, ὥσπερ Ἐμπεδοκλῆς ὁ Ἀκραγαντῖνος καὶ Ἡράκλειτος
ὁ Ἐφέσιος. Τὸ μὲν οὖν γενέσθαι μὲν ἀΐδιον δ' ὅμως
εἶναι φάναι τῶν ἀδυνάτων. Μόνα γὰρ ταῦτα θετέον εὐλόγως
ὅσα ἐπὶ πολλῶν ἢ πάντων ὁρῶμεν ὑπάρχοντα, περὶ δὲ τούτου
20 συμβαίνει τοὐναντίον· ἅπαντα γὰρ τὰ γινόμενα καὶ φθειρόμενα
φαίνεται. Ἔτι δὲ τὸ μὴ ἔχον ἀρχὴν τοῦ ὡδὶ ἔχειν, ἀλλ'
ἀδύνατον ἄλλως ἔχειν πρότερον τὸν ἅπαντα αἰῶνα, ἀδύνατον
καὶ μεταβάλλειν· ἔσται γάρ τι αἴτιον, ὃ εἰ ὑπῆρχε πρότερον,
δυνατὸν ἂν ἦν ἄλλως ἔχειν τὸ ἀδύνατον ἄλλως ἔχειν. Εἰ δὲ
25 πρότερον ἐξ ἄλλως ἐχόντων συνέστη ὁ κόσμος, εἰ μὲν ἀεὶ οὕτως
ἐχόντων καὶ ἀδυνάτων ἄλλως ἔχειν, οὐκ ἂν ἐγένετο· εἰ δὲ
γέγονεν, ἀνάγκη δηλονότι κἀκεῖνα δυνατὰ εἶναι ἄλλως ἔχειν
καὶ μὴ ἀεὶ οὕτως ἔχειν, ὥστε καὶ συνεστῶτα διαλυθήσεται
καὶ διαλελυμένα συνέστη ἔμπροσθεν, καὶ τοῦτ' ἀπειράκις ἢ
30 οὕτως εἶχεν ἢ δυνατὸν ἦν. Εἰ δὲ τοῦτ', οὐκ ἂν εἴη ἄφθαρτος,
οὔτ' εἰ ἄλλως εἶχέ ποτε οὔτ' εἰ δυνατὸν ἄλλως ἔχειν.
Ἣν δέ τινες βοήθειαν ἐπιχειροῦσι φέρειν ἑαυτοῖς τῶν λεγόντων
ἄφθαρτον μὲν εἶναι γενόμενον δέ, οὐκ ἔστιν ἀληθής· ὁμοίως
γάρ φασι τοῖς τὰ διαγράμματα γράφουσι καὶ σφᾶς εἰρηκέναι
35 περὶ τῆς γενέσεως, οὐχ ὡς γενομένου ποτέ, ἀλλὰ
Having established these distinctions, we may now proceed to the question whether the heaven is ungenerated 5or generated, indestructible or destructible. Let us start with a review of the theories of other thinkers; for the proofs of a theory are difficulties for the contrary theory. Besides, those who have first heard the pleas of our adversaries will be more likely to credit the assertions which we are going to make. We shall be less open to the charge of procuring judgement by default. To give a 10satisfactory decision as to the truth it is necessary to be rather an arbitrator than a party to the dispute.
That the world was generated all are agreed, but, generation over, some say that it is eternal, others say that it is destructible like any other natural formation. Others again, with Empedliocles of Acragas and Heraclitus of Ephesus, believe that there is alternation in the destructive process, 15which takes now this direction, now that, and continues without end.
Now to assert that it was generated and yet is eternal is to assert the impossible; for we cannot reasonably attribute to anything any characteristics but those which observation detects in many or all instances. But in this case the facts point the other way: generated things are seen always to be destroyed. Further, a thing 20whose present state had no beginning and which could not have been other than it was at any previous moment throughout its entire duration, cannot possibly be changed. For there will have to be some cause of change, and if this had been present earlier it would have made possible another condition of that to which any other condition was impossible. Suppose that the world was formed out of elements 25which were formerly otherwise conditioned than as they are now. Then (1) if their condition was always so and could not have been otherwise, the world could never have come into being. And (2) if the world did come into being, then, clearly, their condition must have been capable of change and not eternal: after combination therefore they will be dispersed, just as in the past after dispersion 30they came into combination, and this process either has been, or could have been, indefinitely repeated. But if this is so, the world cannot be indestructible, and it does not matter whether the change of condition has actually occurred or remains a possibility.
Some of those who hold that the world, though indestructible, was yet generated, try to support their case by a parallel which is illusory.
That the world was generated all are agreed, but, generation over, some say that it is eternal, others say that it is destructible like any other natural formation. Others again, with Empedliocles of Acragas and Heraclitus of Ephesus, believe that there is alternation in the destructive process, 15which takes now this direction, now that, and continues without end.
Now to assert that it was generated and yet is eternal is to assert the impossible; for we cannot reasonably attribute to anything any characteristics but those which observation detects in many or all instances. But in this case the facts point the other way: generated things are seen always to be destroyed. Further, a thing 20whose present state had no beginning and which could not have been other than it was at any previous moment throughout its entire duration, cannot possibly be changed. For there will have to be some cause of change, and if this had been present earlier it would have made possible another condition of that to which any other condition was impossible. Suppose that the world was formed out of elements 25which were formerly otherwise conditioned than as they are now. Then (1) if their condition was always so and could not have been otherwise, the world could never have come into being. And (2) if the world did come into being, then, clearly, their condition must have been capable of change and not eternal: after combination therefore they will be dispersed, just as in the past after dispersion 30they came into combination, and this process either has been, or could have been, indefinitely repeated. But if this is so, the world cannot be indestructible, and it does not matter whether the change of condition has actually occurred or remains a possibility.
Some of those who hold that the world, though indestructible, was yet generated, try to support their case by a parallel which is illusory.
280a
1 διδασκαλίας χάριν ὡς μᾶλλον γνωριζόντων, ὥσπερ τὸ
διάγραμμα γιγνόμενον θεασαμένους. Τοῦτο δ' ἐστίν, ὥσπερ
λέγομεν, οὐ τὸ αὐτό· ἐν μὲν γὰρ τῇ ποιήσει τῶν διαγραμμάτων
πάντων τεθέντων εἶναι ἅμα τὸ αὐτὸ συμβαίνει, ἐν
5 δὲ ταῖς τούτων ἀποδείξεσιν οὐ ταὐτόν, ἀλλ' ἀδύνατον· τὰ
γὰρ λαμβανόμενα πρότερον καὶ ὕστερον ὑπεναντία ἐστίν·
ἐξ ἀτάκτων γὰρ τεταγμένα γενέσθαι φασίν, ἅμα δὲ
ἄτακτον εἶναι καὶ τεταγμένον ἀδύνατον, ἀλλ' ἀνάγκη
γένεσιν εἶναι τὴν χωρίζουσαν καὶ χρόνον· ἐν δὲ τοῖς διαγράμμασιν
10 οὐδὲν τῷ χρόνῳ κεχώρισται. Ὅτι μὲν οὖν ἀδύνατον
ἅμ' ἀΐδιον αὐτὸν εἶναι καὶ γενέσθαι, φανερόν. Τὸ δ' ἐναλλὰξ
συνιστάναι καὶ διαλύειν οὐδὲν ἀλλοιότερον ποιεῖν ἐστὶν ἢ
τὸ κατασκευάζειν αὐτὸν ἀΐδιον μέν, ἀλλὰ μεταβάλλοντα
τὴν μορφήν, ὥσπερ εἴ τις ἐκ παιδὸς ἄνδρα γινόμενον καὶ
15 ἐξ ἀνδρὸς παῖδα ὁτὲ μὲν φθείρεσθαι ὁτὲ δ' εἶναι οἴοιτο·
δῆλον γὰρ ὅτι καὶ εἰς ἄλληλα τῶν στοιχείων συνιόντων οὐχ
ἡ τυχοῦσα τάξις γίγνεται καὶ σύστασις, ἀλλ' ἡ αὐτή, ἄλλως
τε καὶ κατὰ τοὺς τοῦτον τὸν λόγον εἰρηκότας, οἳ τῆς
διαθέσεως ἑκατέρας αἰτιῶνται τὸ ἐναντίον. Ὥστ' εἰ τὸ ὅλον
20 σῶμα συνεχὲς ὂν ὁτὲ μὲν οὕτως ὁτὲ δ' ἐκείνως διατίθεται
καὶ διακεκόσμηται, ἡ δὲ τοῦ ὅλου σύστασίς ἐστι κόσμος καὶ
οὐρανός, οὐκ ἂν ὁ κόσμος γίγνοιτο καὶ φθείροιτο, ἀλλ' αἱ
διαθέσεις αὐτοῦ. Τὸ δ' ὅλως γενόμενον φθαρῆναι καὶ μὴ
ἀνακάμπτειν ὄντος μὲν ἑνὸς ἀδύνατόν ἐστιν· πρὶν γὰρ γενέσθαι
25 ἀεὶ ὑπῆρχεν ἡ πρὸ αὐτοῦ σύστασις, ἣν μὴ γενομένην
οὐχ οἷόν τ' εἶναί φαμεν μεταβάλλειν· ἀπείρων δ' ὄντων ἐνδέχεται
μᾶλλον. Οὐ μὴν ἀλλὰ καὶ τοῦτο πότερον ἀδύνατον ἢ
δυνατόν, ἔσται δῆλον ἐκ τῶν ὕστερον· εἰσὶ γάρ τινες οἷς ἐνδέχεσθαι
δοκεῖ καὶ ἀγένητόν τι ὂν φθαρῆναι καὶ γενόμενον
30 ἄφθαρτον διατελεῖν, ὥσπερ ἐν τῷ Τιμαίῳ· ἐκεῖ γάρ φησι
τὸν οὐρανὸν γενέσθαι μέν, οὐ μὴν ἀλλ' ἔσεσθαί γε τὸν λοιπὸν
ἀεὶ χρόνον. Πρὸς οὓς φυσικῶς μὲν περὶ οὐρανοῦ μόνον εἴρηται,
καθόλου δὲ περὶ ἅπαντος σκεψαμένοις ἔσται καὶ περὶ τούτου
δῆλον.
1They say that in their statements about its generation they are doing what geometricians do when they construct their figures, not implying that the universe really had a beginning, but for didactic reasons facilitating understanding by exhibiting the object, like the figure, as in course of formation. The two cases, as we 5said, are not parallel; for, in the construction of the figure, when the various steps are completed the required figure forthwith results; but in these other demonstrations what results is not that which was required. Indeed it cannot be so; for antecedent and consequent, as assumed, are in contradiction. The ordered, it is said, arose out of the unordered; and the same thing cannot be at the same time 10both ordered and unordered; there must be a process and a lapse of time separating the two states. In the figure, on the other hand, there is no temporal separation. It is clear then that the universe cannot be at once eternal and generated.
To say that the universe alternately combines and dissolves is no more paradoxical than to make it eternal but varying in shape. It is as if one were to think that 15there was now destruction and now existence when from a child a man is generated, and from a man a child. For it is clear that when the elements come together the result is not a chance system and combination, but the very same as before-especially on the view of those who hold this theory, since they say that the contrary is the cause of each state. So that if the totality of body, which is a continuum, 20is now in this order or disposition and now in that, and if the combination of the whole is a world or heaven, then it will not be the world that comes into being and is destroyed, but only its dispositions.
If the world is believed to be one, it is impossible to suppose that it should be, as a whole, first generated and then destroyed, never to reappear; since before it came into being there was 25always present the combination prior to it, and that, we hold, could never change if it was never generated. If, on the other hand, the worlds are infinite in number the view is more plausible. But whether this is, or is not, impossible will be clear from what follows. For there are some who think it possible both for the ungenerated to be destroyed and for the generated to persist undestroyed. (This is 30held in the Timaeus, where Plato says that the heaven, though it was generated, will none the less exist to eternity.) So far as the heaven is concerned we have answered this view with arguments appropriate to the nature of the heaven: on the general question we shall attain clearness when we examine the matter universally.
To say that the universe alternately combines and dissolves is no more paradoxical than to make it eternal but varying in shape. It is as if one were to think that 15there was now destruction and now existence when from a child a man is generated, and from a man a child. For it is clear that when the elements come together the result is not a chance system and combination, but the very same as before-especially on the view of those who hold this theory, since they say that the contrary is the cause of each state. So that if the totality of body, which is a continuum, 20is now in this order or disposition and now in that, and if the combination of the whole is a world or heaven, then it will not be the world that comes into being and is destroyed, but only its dispositions.
If the world is believed to be one, it is impossible to suppose that it should be, as a whole, first generated and then destroyed, never to reappear; since before it came into being there was 25always present the combination prior to it, and that, we hold, could never change if it was never generated. If, on the other hand, the worlds are infinite in number the view is more plausible. But whether this is, or is not, impossible will be clear from what follows. For there are some who think it possible both for the ungenerated to be destroyed and for the generated to persist undestroyed. (This is 30held in the Timaeus, where Plato says that the heaven, though it was generated, will none the less exist to eternity.) So far as the heaven is concerned we have answered this view with arguments appropriate to the nature of the heaven: on the general question we shall attain clearness when we examine the matter universally.
Book 1,Chapter 11 (280b1–281a27)
280b
1 Πρῶτον δὲ διαιρετέον πῶς ἀγένητα καὶ γενητά φαμεν
καὶ φθαρτὰ καὶ ἄφθαρτα· πολλαχῶς γὰρ λεγομένων, κἂν
μηδὲν διαφέρῃ πρὸς τὸν λόγον, ἀνάγκη τὴν διάνοιαν ἀορίστως
ἔχειν, ἄν τις τῷ διαιρουμένῳ πολλαχῶς ὡς ἀδιαιρέτῳ χρῆται·
5 ἄδηλον γὰρ κατὰ ποίαν φύσιν αὐτῶν συμβαίνει τὸ
λεχθέν. Λέγεται δ' ἀγένητον ἕνα μὲν τρόπον ἐὰν ᾖ τι νῦν
πρότερον μὴ ὂν ἄνευ γενέσεως καὶ μεταβολῆς, καθάπερ ἔνιοι
τὸ ἅπτεσθαι καὶ τὸ κινεῖσθαι λέγουσιν· οὐ γὰρ εἶναι γενέσθαι
φασὶν ἁπτόμενον, οὐδὲ κινούμενον. Ἕνα δ' εἴ τι ἐνδεχόμενον
10 γίνεσθαι ἢ γενέσθαι μή ἐστιν· ὁμοίως γὰρ καὶ τοῦτο ἀγένητον,
ὅτι ἐνδέχεται γενέσθαι. Ἕνα δ' εἴ τι ὅλως ἀδύνατον γενέσθαι,
ὥσθ' ὁτὲ μὲν εἶναι ὁτὲ δὲ μή. (Τὸ δ' ἀδύνατον λέγεται διχῶς.
Ἢ γὰρ τῷ μὴ ἀληθὲς εἶναι εἰπεῖν ὅτι γένοιτ' ἄν, ἢ τῷ μὴ
ῥᾳδίως μηδὲ ταχὺ ἢ καλῶς.) Τὸν αὐτὸν δὲ τρόπον καὶ τὸ
15 γενητὸν ἕνα μὲν εἰ μὴ ὂν πρότερον ὕστερον ἔστιν, εἴτε γινόμενον
εἴτ' ἄνευ τοῦ γίνεσθαι, ὁτὲ μὲν μὴ ὄν, πάλιν δ' ὄν. Ἕνα δ' εἰ
δυνατόν, εἴτε τῷ ἀληθεῖ διορισθέντος τοῦ δυνατοῦ εἴτε τῷ ῥᾳδίως.
Ἕνα δ' ἐὰν ἡ γένεσις αὐτοῦ ἐκ τοῦ μὴ ὄντος εἰς τὸ ὄν,
εἴτ' ἤδη ὄντος, διὰ τοῦ γίνεσθαι δ' ὄντος, εἴτε καὶ μήπω ὄντος,
20 ἀλλ' ἐνδεχομένου. Καὶ φθαρτὸν δὲ καὶ ἄφθαρτον ὡσαύτως· εἴτε
γὰρ πρότερόν τι ὂν ὕστερον ἢ μή ἐστιν ἢ ἐνδέχεται μὴ εἶναι,
φθαρτὸν εἶναί φαμεν, εἴτε φθειρόμενόν ποτε καὶ μεταβάλλον,
εἴτε μή. Ἔστι δ' ὅτε καὶ τὸ διὰ τοῦ φθείρεσθαι ἐνδεχόμενον
μὴ εἶναι φθαρτὸν εἶναί φαμεν, καὶ ἔτι ἄλλως τὸ
25 ῥᾳδίως φθειρόμενον, ὃ εἴποι ἄν τις εὔφθαρτον. Καὶ περὶ τοῦ
ἀφθάρτου ὁ αὐτὸς λόγος· Ἢ γὰρ τὸ ἄνευ φθορᾶς ὁτὲ μὲν
ὂν ὁτὲ δὲ μὴ ὄν, οἷον τὰς ἁφάς, ὅτι ἄνευ τοῦ φθείρεσθαι
πρότερον οὖσαι ὕστερον οὐκ εἰσίν. Ἢ τὸ ὂν μέν, δυνατὸν δὲ μὴ
εἶναι, ἢ καὶ οὐκ ἐσόμενόν ποτε, νῦν δ' ὄν· σὺ γὰρ εἶ, καὶ ἡ
30 ἁφὴ νῦν· ἀλλ' ὅμως φθαρτόν, ὅτι ἔσται ποτὲ ὅτε οὐκ ἀληθὲς
εἰπεῖν ὅτι εἶ, οὐδὲ ταῦτα ἅπτεσθαι. Τὸ δὲ μάλιστα
κυρίως, τὸ ὂν μέν, ἀδύνατον δὲ φθαρῆναι οὕτως ὥστε νῦν ὂν
ὕστερον μὴ εἶναι ἢ ἐνδέχεσθαι μὴ εἶναι. Ἢ καὶ τὸ μήπω
ἐφθαρμένον, ἐνδεχόμενον δ' ὕστερον μὴ εἶναι. Λέγεται δ'
1We must first distinguish the senses in which we use the words 'ungenerated' and 'generated', 'destructible' and 'indestructible'. These have many meanings, and though it may make no difference to the argument, yet some confusion of mind must result from treating as uniform in its use a word which has several distinct 5applications. The character which is the ground of the predication will always remain obscure.
The word 'ungenerated' then is used (a) in one sense whenever something now is which formerly was not, no process of becoming or change being involved. Such is the case, according to some, with contact and motion, since there is no process of coming to be in contact or in motion. (b) It is used in another sense, 10when something which is capable of coming to be, with or without process, does not exist; such a thing is ungenerated in the sense that its generation is not a fact but a possibility. (c) It is also applied where there is general impossibility of any generation such that the thing now is which then was not. And 'impossibility' has two uses: first, where it is untrue to say that the thing can ever come 15into being, and secondly, where it cannot do so easily, quickly, or well. In the same way the word 'generated' is used, (a) first, where what formerly was not afterwards is, whether a process of becoming was or was not involved, so long as that which then was not, now is; (b) secondly, of anything capable of existing, 'capable' being defined with reference either to truth or to facility; (c) thirdly, 20of anything to which the passage from not being to being belongs, whether already actual, if its existence is due to a past process of becoming, or not yet actual but only possible. The uses of the words 'destructible' and 'indestructible' are similar. 'Destructible' is applied (a) to that which formerly was and afterwards either is not or might not be, whether a period of being destroyed and changed 25intervenes or not; and (b) sometimes we apply the word to that which a process of destruction may cause not to be; and also (c) in a third sense, to that which is easily destructible, to the 'easily destroyed', so to speak. Of the indestructible the same account holds good. It is either (a) that which now is and now is not, without any process of destruction, like contact, which without being destroyed 30afterwards is not, though formerly it was; or (b) that which is but might not be, or which will at some time not be, though it now is. For you exist now and so does the contact; yet both are destructible, because a time will come when it will not be true of you that you exist, nor of these things that they are in contact.
The word 'ungenerated' then is used (a) in one sense whenever something now is which formerly was not, no process of becoming or change being involved. Such is the case, according to some, with contact and motion, since there is no process of coming to be in contact or in motion. (b) It is used in another sense, 10when something which is capable of coming to be, with or without process, does not exist; such a thing is ungenerated in the sense that its generation is not a fact but a possibility. (c) It is also applied where there is general impossibility of any generation such that the thing now is which then was not. And 'impossibility' has two uses: first, where it is untrue to say that the thing can ever come 15into being, and secondly, where it cannot do so easily, quickly, or well. In the same way the word 'generated' is used, (a) first, where what formerly was not afterwards is, whether a process of becoming was or was not involved, so long as that which then was not, now is; (b) secondly, of anything capable of existing, 'capable' being defined with reference either to truth or to facility; (c) thirdly, 20of anything to which the passage from not being to being belongs, whether already actual, if its existence is due to a past process of becoming, or not yet actual but only possible. The uses of the words 'destructible' and 'indestructible' are similar. 'Destructible' is applied (a) to that which formerly was and afterwards either is not or might not be, whether a period of being destroyed and changed 25intervenes or not; and (b) sometimes we apply the word to that which a process of destruction may cause not to be; and also (c) in a third sense, to that which is easily destructible, to the 'easily destroyed', so to speak. Of the indestructible the same account holds good. It is either (a) that which now is and now is not, without any process of destruction, like contact, which without being destroyed 30afterwards is not, though formerly it was; or (b) that which is but might not be, or which will at some time not be, though it now is. For you exist now and so does the contact; yet both are destructible, because a time will come when it will not be true of you that you exist, nor of these things that they are in contact.
281a
1 ἄφθαρτον καὶ τὸ μὴ ῥᾳδίως φθειρόμενον. Εἰ δὴ ταῦθ'
οὕτως ἔχει, σκεπτέον πῶς λέγομεν τὸ δυνατὸν καὶ ἀδύνατον·
τό τε γὰρ κυριώτατα λεγόμενον ἄφθαρτον τῷ μὴ δύνασθαι
ἂν φθαρῆναι, μηδ' ὁτὲ μὲν εἶναι ὁτὲ δὲ μή· λέγεται δὲ
5 καὶ τὸ ἀγένητον τὸ ἀδύνατον καὶ μὴ δυνάμενον γενέσθαι
οὕτως ὥστε πρότερον μὲν μὴ εἶναι ὕστερον δὲ εἶναι, οἷον
τὴν διάμετρον σύμμετρον. Εἰ δή τι δύναται κινηθῆναι [στάδια
ἑκατὸν] ἢ ἆραι βάρος, ἀεὶ πρὸς τὸ πλεῖστον λέγομεν, οἷον
τάλαντα ἆραι ἑκατὸν ἢ στάδια βαδίσαι ἑκατόν (καίτοι καὶ
10 τὰ μόρια δύναται τὰ ἐντός, εἴπερ καὶ τὴν ὑπεροχήν), ὡς
δέον ὁρίζεσθαι πρὸς τὸ τέλος καὶ τὴν ὑπεροχὴν τὴν δύναμιν.
Ἀνάγκη μὲν οὖν τὸ δυνατὸν καθ' ὑπεροχὴν τοσαδὶ καὶ
τὰ ἐντὸς δύνασθαι, οἷον εἰ τάλαντα ἑκατὸν ἆραι, καὶ δύο,
κἂν εἰ στάδια ἑκατόν, καὶ δύο δύνασθαι βαδίσαι. Ἡ δὲ δύναμις
15 τῆς ὑπεροχῆς ἐστίν· κἂν εἴ τι ἀδύνατον τοσονδὶ καθ'
ὑπερβολὴν εἰπόντων, καὶ τὰ πλείω ἀδύνατον, οἷον ὁ χίλια
βαδίσαι στάδια μὴ δυνάμενος δῆλον ὅτι καὶ χίλια καὶ ἕν.
Μηδὲν δ' ἡμᾶς παρενοχλείτω· διωρίσθω γὰρ κατὰ τῆς
ὑπεροχῆς τὸ τέλος λεγόμενον τὸ κυρίως δυνατόν. Τάχα
20 γὰρ ἐνσταίη τις ἂν ὡς οὐκ ἀνάγκη τὸ λεχθέν· ὁ γὰρ ὁρῶν
στάδιον οὐ καὶ τὰ ἐντὸς ὄψεται μεγέθη, ἀλλὰ τοὐναντίον
μᾶλλον ὁ δυνάμενος ἰδεῖν στιγμὴν ἢ ἀκοῦσαι μικροῦ ψόφου
καὶ τῶν μειζόνων ἕξει αἴσθησιν. Ἀλλ' οὐδὲν διαφέρει πρὸς
τὸν λόγον· διωρίσθω γὰρ ἤτοι ἐπὶ τῆς δυνάμεως ἢ ἐπὶ τοῦ
25 πράγματος ἡ ὑπερβολή. Τὸ γὰρ λεγόμενον δῆλον· ἡ μὲν
γὰρ ὄψις ἡ τοῦ ἐλάττονος ὑπερέχει, ἡ δὲ ταχυτὴς ἡ τοῦ
πλείονος.
1Thirdly (c) in its most proper use, it is that which is, but is incapable of any destruction such that the thing which now is later ceases to be or might cease to be; or again, that which has not yet been destroyed, but in the future may cease to be. For indestructible is also used of that which is 5destroyed with difficulty.
This being so, we must ask what we mean by 'possible' and 'impossible'. For in its most proper use the predicate 'indestructible' is given because it is impossible that the thing should be destroyed, i.e. exist at one time and not at another. And 'ungenerated' also involves impossibility when used for that which cannot be generated, in such fashion that, 10while formerly it was not, later it is. An instance is a commensurable diagonal. Now when we speak of a power to move or to lift weights, we refer always to the maximum. We speak, for instance, of a power to lift a hundred talents or walk a hundred stades-though a power to effect the maximum is also a power to effect any part of the maximum-since we feel obliged in defining the 15power to give the limit or maximum. A thing, then, which is within it. If, for example, a man can lift a hundred talents, he can also lift two, and if he can walk a hundred stades, he can also walk two. But the power is of the maximum, and a thing said, with reference to its maximum, to be incapable of so much is also incapable of any greater amount. It is, for instance, clear 20that a person who cannot walk a thousand stades will also be unable to walk a thousand and one. This point need not trouble us, for we may take it as settled that what is, in the strict sense, possible is determined by a limiting maximum. Now perhaps the objection might be raised that there is no necessity in this, since he who sees a stade need not see the smaller measures 25contained in it, while, on the contrary, he who can see a dot or hear a small sound will perceive what is greater. This, however, does not touch our argument. The maximum may be determined either in the power or in its object. The application of this is plain. Superior sight is sight of the smaller body, but superior speed is that of the greater body.
This being so, we must ask what we mean by 'possible' and 'impossible'. For in its most proper use the predicate 'indestructible' is given because it is impossible that the thing should be destroyed, i.e. exist at one time and not at another. And 'ungenerated' also involves impossibility when used for that which cannot be generated, in such fashion that, 10while formerly it was not, later it is. An instance is a commensurable diagonal. Now when we speak of a power to move or to lift weights, we refer always to the maximum. We speak, for instance, of a power to lift a hundred talents or walk a hundred stades-though a power to effect the maximum is also a power to effect any part of the maximum-since we feel obliged in defining the 15power to give the limit or maximum. A thing, then, which is within it. If, for example, a man can lift a hundred talents, he can also lift two, and if he can walk a hundred stades, he can also walk two. But the power is of the maximum, and a thing said, with reference to its maximum, to be incapable of so much is also incapable of any greater amount. It is, for instance, clear 20that a person who cannot walk a thousand stades will also be unable to walk a thousand and one. This point need not trouble us, for we may take it as settled that what is, in the strict sense, possible is determined by a limiting maximum. Now perhaps the objection might be raised that there is no necessity in this, since he who sees a stade need not see the smaller measures 25contained in it, while, on the contrary, he who can see a dot or hear a small sound will perceive what is greater. This, however, does not touch our argument. The maximum may be determined either in the power or in its object. The application of this is plain. Superior sight is sight of the smaller body, but superior speed is that of the greater body.
Book 1,Chapter 12 (281a28–283b22)
Διωρισμένων δὲ τούτων λεκτέον τὸ ἐφεξῆς. Εἰ δή ἐστιν
ἔνια δυνατὰ καὶ εἶναι καὶ μή, ἀνάγκη χρόνον τινὰ ὡρίσθαι
30 τὸν πλεῖστον καὶ τοῦ εἶναι καὶ τοῦ μή, λέγω δ' ὃν δυνατὸν
τὸ πρᾶγμα εἶναι καὶ ὃν δυνατὸν μὴ εἶναι καθ' ὁποιανοῦν
κατηγορίαν, οἷον ἄνθρωπον ἢ λευκὸν ἢ τρίπηχυ ἢ ἄλλ'
ὁτιοῦν τῶν τοιούτων. Εἰ γὰρ μὴ ἔσται ποσός τις, ἀλλ' ἀεὶ
πλείων τοῦ προτεθέντος καὶ οὐκ ἔστιν οὗ ἐλάττων, ἄπειρον
Having established these 30distinctions we car now proceed to the sequel. If there are thing! capable both of being and of not being, there must be some definite maximum time of their being and not being; a time, I mean, during which continued existence is possible to them and a time during which continued nonexistence is possible.
281b
1 ἔσται χρόνον δυνατὸν εἶναι, καὶ μὴ εἶναι ἄλλον
ἄπειρον· ἀλλὰ τοῦτ' ἀδύνατον. Ἀρχὴ δ' ἔστω ἐντεῦθεν· τὸ
γὰρ ἀδύνατον καὶ τὸ ψεῦδος οὐ ταὐτὸ σημαίνει. Ἔστι δὲ τὸ
ἀδύνατον καὶ δυνατὸν καὶ ψεῦδος καὶ ἀληθὲς τὸ μὲν
5 ἐξ ὑποθέσεως (λέγω δ', οἷον τὸ τρίγωνον ἀδύνατον δύο
ὀρθὰς ἔχειν, εἰ τάδε, καὶ ἡ διάμετρος σύμμετρος). Ἔςτι
δ' ἁπλῶς καὶ δυνατὰ καὶ ἀδύνατα καὶ ψευδῆ καὶ
ἀληθῆ. Οὐ δὴ ταὐτό ἐστι ψεῦδός τέ τι εἶναι ἁπλῶς
καὶ ἀδύνατον ἁπλῶς. Τὸ γάρ σε μὴ ἑστῶτα φάναι ἑστάναι
10 ψεῦδος μέν, οὐκ ἀδύνατον δέ. Ὁμοίως δὲ τὸν κιθαρίζοντα,
μὴ ᾄδοντα δέ, ᾄδειν φάναι ψεῦδος, ἀλλ' οὐκ
ἀδύνατον. Τὸ δ' ἅμα ἑστάναι καὶ καθῆσθαι, καὶ τὴν διάμετρον
σύμμετρον εἶναι, οὐ μόνον ψεῦδος, ἀλλὰ καὶ ἀδύνατον.
Οὐ δὴ ταὐτόν ἐστιν ὑποθέσθαι ψεῦδος καὶ ἀδύνατον.
15 Συμβαίνει δ' ἀδύνατον ἐξ ἀδυνάτου. Τοῦ μὲν οὖν καθῆσθαι
καὶ ἑστάναι ἅμα ἔχει τὴν δύναμιν, ὅτι ὅτε ἔχει ἐκείνην,
καὶ τὴν ἑτέραν· ἀλλ' οὐχ ὥστε ἅμα καθῆσθαι καὶ ἑστάναι,
ἀλλ' ἐν ἄλλῳ χρόνῳ. Εἰ δέ τι ἄπειρον χρόνον ἔχει πλειόνων
δύναμιν, οὐκ ἔστιν ἐν ἄλλῳ χρόνῳ, ἀλλὰ τοῦθ' ἅμα.
20 Ὥστ' εἴ τι ἄπειρον χρόνον ὂν φθαρτόν ἐστι, δύναμιν ἔχοι ἂν
τοῦ μὴ εἶναι. Εἰ δὴ ἄπειρον χρόνον, ἔστω ὑπάρχον
ὃ δύναται. Ἅμα ἄρ' ἔσται τε καὶ οὐκ ἔσται κατ' ἐνέργειαν.
Ψεῦδος μὲν οὖν συμβαίνοι ἄν, ὅτι ψεῦδος ἐτέθη.
Ἀλλ' εἰ μὴ ἀδύνατον ἦν, οὐκ ἂν καὶ ἀδύνατον ἦν τὸ συμβαῖνον.
25 Ἅπαν ἄρα τὸ ἀεὶ ὂν ἁπλῶς ἄφθαρτον. Ὁμοίως δὲ
καὶ ἀγένητον· εἰ γὰρ γενητόν, ἔσται δυνατὸν χρόνον τινὰ μὴ
εἶναι—φθαρτὸν μὲν γάρ ἐστι τὸ πρότερον μὲν ὄν, νῦν δὲ μὴ
ὂν ἢ ἐνδεχόμενόν ποτε ὕστερον μὴ εἶναι· γενητὸν δὲ ὃ ἐνδέχεται
πρότερον μὴ εἶναι—ἀλλ' οὐκ ἔστιν ἐν ᾧ χρόνῳ δυνατὸν
30 τὸ ἀεὶ ὂν ὥστε μὴ εἶναι, οὔτ' ἄπειρον οὔτε πεπερασμένον· καὶ
γὰρ τὸν πεπερασμένον χρόνον δύναται εἶναι, εἴπερ καὶ τὸν
ἄπειρον. Οὐκ ἄρα ἐνδέχεται τὸ αὐτὸ καὶ ἓν ἀεί τε δύνασθαι
εἶναι καὶ ἀεὶ μὴ εἶναι. Ἀλλὰ μὴν οὐδὲ τὴν ἀπόφασιν, οἷον λέγω
μὴ ἀεὶ εἶναι. Ἀδύνατον ἄρα καὶ ἀεὶ μέν τι εἶναι, φθαρτὸν
1And this is true in every category, whether the thing is, for example, 'man', or 'white', or 'three cubits long', or whatever it may be. For if the time is not definite in quantity, but longer than any that 5can be suggested and shorter than none, then it will be possible for one and the same thing to exist for infinite time and not to exist for another infinity. This, however, is impossible.
Let us take our start from this point. The impossible and the false 10have not the same significance. One use of 'impossible' and 'possible', and 'false' and 'true', is hypothetical. It is impossible, for instance, on a certain hypothesis that the triangle should have its angles equal to two right angles, and on another the 15diagonal is commensurable. But there are also things possible and impossible, false and true, absolutely. Now it is one thing to be absolutely false, and another thing to be absolutely impossible. To say that you are standing when you are not standing is 20to assert a falsehood, but not an impossibility. Similarly to say that a man who is playing the harp, but not singing, is singing, is to say what is false but not impossible. To say, however, that you are at once standing and sitting, or that the diagonal 25is commensurable, is to say what is not only false but also impossible. Thus it is not the same thing to make a false and to make an impossible hypothesis, and from the impossible hypothesis impossible results follow. A man has, it is true, the capacity at 30once of sitting and of standing, because when he possesses the one he also possesses the other; but it does not follow that he can at once sit and stand, only that at another time he can do the other also.
Let us take our start from this point. The impossible and the false 10have not the same significance. One use of 'impossible' and 'possible', and 'false' and 'true', is hypothetical. It is impossible, for instance, on a certain hypothesis that the triangle should have its angles equal to two right angles, and on another the 15diagonal is commensurable. But there are also things possible and impossible, false and true, absolutely. Now it is one thing to be absolutely false, and another thing to be absolutely impossible. To say that you are standing when you are not standing is 20to assert a falsehood, but not an impossibility. Similarly to say that a man who is playing the harp, but not singing, is singing, is to say what is false but not impossible. To say, however, that you are at once standing and sitting, or that the diagonal 25is commensurable, is to say what is not only false but also impossible. Thus it is not the same thing to make a false and to make an impossible hypothesis, and from the impossible hypothesis impossible results follow. A man has, it is true, the capacity at 30once of sitting and of standing, because when he possesses the one he also possesses the other; but it does not follow that he can at once sit and stand, only that at another time he can do the other also.
282a
1 δ' εἶναι. Ὁμοίως δ' οὐδὲ γενητόν· δυοῖν γὰρ ὅροιν εἰ ἀδύνατον
τὸ ὕστερον ἄνευ τοῦ προτέρου ὑπάρξαι, ἐκεῖνο δ' ἀδύνατον
ὑπάρχειν, καὶ τὸ ὕστερον. Ὥστ' εἰ τὸ ἀεὶ ὂν μὴ ἐνδέχεταί
ποτε μὴ εἶναι, ἀδύνατον καὶ γενητὸν εἶναι. Ἐπεὶ δ' ἀπόφασις
5 τοῦ μὲν ἀεὶ δυναμένου εἶναι τὸ μὴ ἀεὶ δυνάμενον εἶναι,
τὸ δ' ἀεὶ δυνατὸν μὴ εἶναι ἐναντίον, οὗ ἀπόφασις τὸ
μὴ ἀεὶ δυνάμενον μὴ εἶναι, ἀνάγκη τὰς ἀποφάσεις ἀμφοῖν
τῷ αὐτῷ ὑπάρχειν, καὶ εἶναι μέσον τοῦ ἀεὶ ὄντος καὶ
τοῦ ἀεὶ μὴ ὄντος τὸ δυνάμενον εἶναι καὶ μὴ εἶναι· ἡ γὰρ
10 ἑκατέρου ἀπόφασίς ποτε ὑπάρξει, εἰ μὴ ἀεί. Ὥστ' εἰ
τὸ μὴ ἀεὶ μὴ ὂν ἔσται ποτὲ καὶ οὐκ ἔσται, καὶ τὸ μὴ ἀεὶ
δυνάμενον εἶναι δηλονότι, ἀλλά ποτε ὄν, ὥστε καὶ μὴ εἶναι.
Τὸ αὐτὸ ἄρ' ἔσται δυνατὸν εἶναι καὶ μή, καὶ τοῦτ' ἔστιν ἀμφοῖν
μέσον. Λόγος δὲ καθόλου ὅδε. Ἔστω γὰρ τὸ Α καὶ τὸ
15 Β μηδενὶ τῷ αὐτῷ δυνάμενα ὑπάρχειν, ἅπαντι δὲ τὸ Α ἢ
τὸ Γ καὶ τὸ Β ἢ τὸ Δ. Ἀνάγκη δὴ ᾧ μήτε τὸ Α ὑπάρχει
μήτε τὸ Β, παντὶ ὑπάρχειν τὰ ΓΔ. Ἔστω δὴ τὸ Ε τὸ μεταξὺ
τῶν ΑΒ· ἐναντίων γὰρ τὸ μηθέτερον μέσον. Τούτῳ δὴ
ἀνάγκη ἄμφω ὑπάρχειν τό τε Γ καὶ τὸ Δ. Παντὶ γὰρ ἢ
20 τὸ Α ἢ τὸ Γ, ὥστε καὶ τῷ Ε· ἐπεὶ οὖν τὸ Α ἀδύνατον, τὸ
Γ ὑπάρξει. Ὁ δ' αὐτὸς λόγος καὶ ἐπὶ τοῦ Δ. Οὔτε δὴ τὸ ἀεὶ
ὂν γενητὸν οὐδὲ φθαρτόν, οὔτε τὸ ἀεὶ μὴ ὄν. Δῆλον δ' ὅτι καὶ
εἰ γενητὸν ἢ φθαρτόν, οὐκ ἀΐδιον. Ἅμα γὰρ ἔσται δυνάμενον
ἀεὶ εἶναι καὶ δυνάμενον μὴ ἀεὶ εἶναι· τοῦτο δ' ὅτι ἀδύνατον,
25 δέδεικται πρότερον. ἀεὶ ὄν ἀεὶ μὴ ὄν Α Β γενητόν Ε μὴ ἀεὶ ὄν μὴ ἀεὶ μὴ ὄν Γ Δ Ἆρ' οὖν εἰ καὶ ἀγένητον, ὂν δέ, τοῦτ'
ἀνάγκη ἀΐδιον εἶναι, ὁμοίως δὲ καὶ εἰ ἄφθαρτον, ὂν δέ;
(Λέγω δὲ τὸ ἀγένητον καὶ ἄφθαρτον τὰ κυρίως λεγόμενα,
ἀγένητον μὲν ὃ ἔστι νῦν, καὶ πρότερον οὐκ ἀληθὲς ἦν εἰπεῖν
τὸ μὴ εἶναι, ἄφθαρτον δὲ ὃ νῦν ὂν ὕστερον μὴ ἀληθὲς ἔσται
30 εἰπεῖν μὴ εἶναι). Ἢ εἰ μὲν ταῦτα ἀλλήλοις ἀκολουθεῖ καὶ
τό τε ἀγένητον ἄφθαρτον καὶ τὸ ἄφθαρτον ἀγένητον, ἀνάγκη
καὶ τὸ ἀΐδιον ἑκατέρῳ ἀκολουθεῖν, καὶ εἴτε ἀγένητον,
1But if a thing has for infinite time more than one capacity, another time is impossible and the times must coincide. Thus if a thing which exists for infinite time is destructible, it will have the capacity 5of not being. Now if it exists for infinite time let this capacity be actualized; and it will be in actuality at once existent and non-existent. Thus a false conclusion would follow because a false assumption was made, but if what was assumed had not been 10impossible its consequence would not have been impossible.
Anything then which always exists is absolutely imperishable. It is also ungenerated, since if it was generated it will have the power for some time of not being. For as that which formerly was, 15but now is not, or is capable at some future time of not being, is destructible, so that which is capable of formerly not having been is generated. But in the case of that which always is, there is no time for such a capacity of not being, whether the supposed 20time is finite or infinite; for its capacity of being must include the finite time since it covers infinite time.
It is therefore impossible that one and the same thing should be capable of always existing and of always not-existing. And 'not always 25existing', the contradictory, is also excluded. Thus it is impossible for a thing always to exist and yet to be destructible. Nor, similarly, can it be generated. For of two attributes if B cannot be present without A, the impossibility A of proves the impossibility 30of B. What always is, then, since it is incapable of ever not being, cannot possibly be generated.
Anything then which always exists is absolutely imperishable. It is also ungenerated, since if it was generated it will have the power for some time of not being. For as that which formerly was, 15but now is not, or is capable at some future time of not being, is destructible, so that which is capable of formerly not having been is generated. But in the case of that which always is, there is no time for such a capacity of not being, whether the supposed 20time is finite or infinite; for its capacity of being must include the finite time since it covers infinite time.
It is therefore impossible that one and the same thing should be capable of always existing and of always not-existing. And 'not always 25existing', the contradictory, is also excluded. Thus it is impossible for a thing always to exist and yet to be destructible. Nor, similarly, can it be generated. For of two attributes if B cannot be present without A, the impossibility A of proves the impossibility 30of B. What always is, then, since it is incapable of ever not being, cannot possibly be generated.
282b
1 ἀΐδιον, εἴτε ἄφθαρτον, ἀΐδιον. Δῆλον δὲ καὶ ἐκ τοῦ
ὁρισμοῦ αὐτῶν· καὶ γὰρ ἀνάγκη, εἰ φθαρτόν, γενητόν. Ἢ γὰρ
ἀγένητον ἢ γενητόν· εἰς δὲ ἀγένητον, ἄφθαρτον ὑπόκειται.
Καὶ εἰ γενητὸν δή, φθαρτὸν ἀνάγκη· ἢ γὰρ φθαρτὸν ἢ
5 ἄφθαρτον· ἀλλ' εἰ ἄφθαρτον, ἀγένητον ὑπέκειτο. Εἰ δὲ μὴ
ἀκολουθοῦσιν ἀλλήλοις τὸ ἄφθαρτον καὶ τὸ ἀγένητον, οὐκ
ἀνάγκη οὔτε τὸ ἀγένητον οὔτε τὸ ἄφθαρτον ἀΐδιον εἶναι. Ὅτι
δ' ἀνάγκη ἀκολουθεῖν, ἐκ τῶνδε φανερόν. Τὸ γὰρ γενητὸν
καὶ τὸ φθαρτὸν ἀκολουθοῦσιν ἀλλήλοις. Δῆλον δὲ καὶ τοῦτο
10 ἐκ τῶν πρότερον· τοῦ γὰρ ἀεὶ ὄντος καὶ τοῦ ἀεὶ μὴ ὄντος ἐστὶ
μεταξὺ ᾧ μηδέτερον ἀκολουθεῖ, τοῦτο δ' ἐστὶ τὸ γενητὸν καὶ
φθαρτόν. Δυνατὸν γὰρ καὶ εἶναι καὶ μὴ εἶναι ὡρισμένον
χρόνον ἑκάτερον· λέγω δ' ἑκάτερον καὶ εἶναι ποσόν τινα
χρόνον καὶ μὴ εἶναι. Εἰ τοίνυν ἐστί τι γενητὸν ἢ φθαρτόν,
15 ἀνάγκη τοῦτο μεταξὺ εἶναι. Ἔστω γὰρ τὸ Α τὸ ἀεὶ ὄν, τὸ
δὲ Β τὸ ἀεὶ μὴ ὄν, τὸ δὲ Γ γενητόν, τὸ δὲ Δ φθαρτόν.
Ἀνάγκη δὴ τὸ Γ μεταξὺ εἶναι τοῦ Α καὶ τοῦ Β. Τῶν μὲν
γὰρ οὐκ ἔστι χρόνος ἐπ' οὐδέτερον τὸ πέρας ἐν ᾧ ἢ τὸ Α οὐκ
ἦν ἢ τὸ Β ἦν· τῷ δὲ γενητῷ ἀνάγκη ἢ ἐνεργείᾳ εἶναι ἢ
20 δυνάμει, τοῖς δὲ ΑΒ οὐδετέρως. Ποσὸν ἄρα τινὰ καὶ ὡριςμένον
χρόνον καὶ ἔσται καὶ πάλιν οὐκ ἔσται. Ὁμοίως δὲ
καὶ ἐπὶ τοῦ Δ. Γενητὸν ἄρα καὶ φθαρτὸν ἑκάτερον.
Ἀκολουθοῦσιν ἄρα ἀλλήλοις τὸ γενητὸν καὶ τὸ φθαρτόν. ἀεὶ ὄν γενητόν Α Γ φθαρτόν ἀεὶ μὴ ὄν Δ Β Ἔστω
δὴ τὸ ἐφ' ᾧ Ε ἀγένητον, τὸ δ' ἐφ' ᾧ Ζ γενητόν, τὸ δ' ἐφ'
25 ᾧ Η ἄφθαρτον, τὸ δ' ἐφ' ᾧ Θ φθαρτόν. Τὰ δὴ ΖΘ δέδεικται
ὅτι ἀκολουθεῖ ἀλλήλοις. Ὅταν δ' ᾖ οὕτω κείμενα ὡς
ταῦτα, οἷον τὸ μὲν Ζ καὶ τὸ Θ ἀκολουθοῦντα, τὸ δὲ Ε
καὶ τὸ Ζ μηθενὶ τῷ αὐτῷ, ἅπαντι δὲ θάτερον, ὁμοίως δὲ
καὶ τὰ ΗΘ, ἀνάγκη καὶ τὰ ΕΗ ἀκολουθεῖν ἀλλήλοις.
30 Ἔστω γὰρ τῷ Η τὸ Ε μὴ ἀκολουθοῦν. Τὸ ἄρα Ζ ἀκολουθήσει·
παντὶ γὰρ τὸ Ε ἢ τὸ Ζ. Ἀλλὰ μὴν ᾧ τὸ Ζ, καὶ τὸ
Θ. Τῷ ἄρα Η τὸ Θ ἀκολουθήσει. Ἀλλ' ὑπέκειτο ἀδύνατον
1But since the contradictory of 'that which is always capable of being' 'that which is not always capable of being'; while 'that which is always capable of not being' is the contrary, whose contradictory in turn 5is 'that which is not always capable of not being', it is necessary that the contradictories of both terms should be predicable of one and the same thing, and thus that, intermediate between what always is and what always is not, there should be that to which being 10and not-being are both possible; for the contradictory of each will at times be true of it unless it always exists. Hence that which not always is not will sometimes be and sometimes not be; and it is clear that this is true also of that which cannot always be but 15sometimes is and therefore sometimes is not. One thing, then, will have the power of being, and will thus be intermediate between the other two.
Expresed universally our argument is as follows. Let there be two attributes, A and B, not capable of being present in 20any one thing together, while either A or C and either B or D are capable of being present in everything. Then C and D must be predicated of everything of which neither A nor B is predicated. Let E lie between A and B; for that which is neither of two contraries 25is a mean between them. In E both C and D must be present, for either A or C is present everywhere and therefore in E. Since then A is impossible, C must be present, and the same argument holds of D.
Neither that which always is, therefore, nor that which always is 30not is either generated or destructible. And clearly whatever is generated or destructible is not eternal.
Expresed universally our argument is as follows. Let there be two attributes, A and B, not capable of being present in 20any one thing together, while either A or C and either B or D are capable of being present in everything. Then C and D must be predicated of everything of which neither A nor B is predicated. Let E lie between A and B; for that which is neither of two contraries 25is a mean between them. In E both C and D must be present, for either A or C is present everywhere and therefore in E. Since then A is impossible, C must be present, and the same argument holds of D.
Neither that which always is, therefore, nor that which always is 30not is either generated or destructible. And clearly whatever is generated or destructible is not eternal.
283a
1 εἶναι. Ὁ δ' αὐτὸς λόγος καὶ ὅτι τὸ Η τῷ Ε. Ἀλλὰ μὴν
οὕτως ἔχει τὸ ἀγένητον, ἐφ' ᾧ Ε, πρὸς τὸ γενητόν, ἐφ' ᾧ
Ζ, καὶ τὸ ἄφθαρτον, ἐφ' ᾧ Η, πρὸς τὸ φθαρτόν, ἐφ' ᾧ Θ. ἀγένητον γενητόν Ε Ζ ἄφθαρτον φθαρτόν Η Θ
Τὸ δὲ φάναι μηδὲν κωλύειν γινόμενόν τι ἄφθαρτον εἶναι
5 καὶ ἀγένητον ὂν φθαρῆναι, ἅπαξ ὑπαρχούσης τῷ μὲν
τῆς γενέσεως τῷ δὲ τῆς φθορᾶς, ἀναιρεῖν ἐστι τῶν δεδομένων
τι. Ἢ γὰρ ἄπειρον ἢ ποσόν τινα ὡρισμένον χρόνον δύναται
ἅπαντα ἢ ποιεῖν ἢ πάσχειν, ἢ εἶναι ἢ μὴ εἶναι *** καὶ
τὸν ἄπειρον διὰ τοῦτο, ὅτι ὥρισταί πως ὁ ἄπειρος, οὗ οὐκ
10 ἔστι πλείων. Τὸ δὴ πῇ ἄπειρον οὔτ' ἄπειρον οὔθ' ὡρισμένον.
Ἔτι τί μᾶλλον ἐπὶ τῷδε τῷ σημείῳ ἀεὶ ὂν πρότερον ἐφθάρη
ἢ μὴ ὂν ἄπειρον ἐγένετο; εἰ γὰρ μηθὲν μᾶλλον, ἄπειρα δὲ
τὰ σημεῖα, δῆλον ὅτι ἄπειρον χρόνον ἦν τι γενητὸν καὶ
φθαρτόν. Δύναται ἄρα μὴ εἶναι ἄπειρον χρόνον· ἅμα
15 γὰρ ἕξει δύναμιν τοῦ μὴ εἶναι καὶ εἶναι, τὸ μὲν πρότερον,
εἰ φθαρτόν, τὸ δ' ὕστερον, εἰ γενητόν. Ὥστ' ἐὰν ὑπάρχειν
θῶμεν ἃ δύναται, τὰ ἀντικείμενα ἅμα ὑπάρξει. Ἔτι δὲ καὶ
τοῦθ' ὁμοίως ἐν ἅπαντι σημείῳ ὑπάρξει, ὥστ' ἄπειρον χρόνον
τοῦ μὴ εἶναι καὶ τοῦ εἶναι ἕξει δύναμιν· ἀλλὰ δέδεικται ὅτι
20 ἀδύνατον τοῦτο. Ἔτι εἰ πρότερον ἡ δύναμις ὑπάρχει τῆς ἐνεργείας,
ἅπανθ' ὑπάρξει τὸν χρόνον, καὶ ὃν ἀγένητον ἦν καὶ
μὴ ὄν [τὸν ἄπειρον χρόνον], γίγνεσθαι δὲ δυνάμενον. Ἅμα δὴ
οὐκ ἦν καὶ τοῦ εἶναι δύναμιν εἶχε, καὶ τοῦ τότε εἶναι καὶ
ὕστερον· ἄπειρον ἄρα χρόνον. Φανερὸν δὲ καὶ ἄλλως ὅτι ἀδύνατον
25 φθαρτὸν ὂν μὴ φθαρῆναί ποτε. Ἀεὶ γὰρ ἔσται ἅμα
καὶ φθαρτὸν καὶ ἄφθαρτον ἐντελεχείᾳ, ὥστε ἅμα ἔσται δυνατὸν
ἀεί τε εἶναι καὶ μὴ ἀεί· φθείρεται ἄρα ποτὲ τὸ
φθαρτόν. Καὶ εἰ γενητόν, γέγονεν· δυνατὸν γὰρ γεγονέναι,
καὶ μὴ ἀεὶ ἄρα εἶναι. Ἔστι δὲ καὶ ὧδε θεωρῆσαι ὅτι ἀδύνατον
30 ἢ γενόμενόν ποτε ἄφθαρτον διατελεῖν, ἢ ἀγένητον ὂν
καὶ ἀεὶ πρότερον ὂν φθαρῆναι. Οὐδὲν γὰρ ἀπὸ τοῦ αὐτομάτου
οὔτ' ἄφθαρτον οὔτ' ἀγένητον οἷόν τ' εἶναι. Τὸ μὲν γὰρ αὐτόματόν
ἐστι καὶ τὸ ἀπὸ τύχης παρὰ τὸ ἀεὶ καὶ τὸ ὡς ἐπὶ
1If it were, it would be at once capable of always being and capable of not always being, but it has already been shown that this is impossible. Surely then whatever is ungenerated and in being must be 5eternal, and whatever is indestructible and in being must equally be so. (I use the words 'ungenerated' and 'indestructible' in their proper sense, 'ungenerated' for that which now is and could not at any previous time have been truly said not to be; 10'indestructible' for that which now is and cannot at any future time be truly said not to be.) If, again, the two terms are coincident, if the ungenerated is indestructible, and the indestructible ungenearted, then each of them is coincident with 15'eternal'; anything ungenerated is eternal and anything indestructible is eternal. This is clear too from the definition of the terms, Whatever is destructible must be generated; for it is either ungenerated, or generated, but, if ungenerated, it is by 20hypothesis indestructible. Whatever, further, is generated must be destructible. For it is either destructible or indestructible, but, if indestructible, it is by hypothesis ungenerated.
If, however, 'indestructible' and 'ungenerated' are not coincident, 25there is no necessity that either the ungenerated or the indestructible should be eternal. But they must be coincident, for the following reasons. The terms 'generated' and 'destructible' are coincident; this is obvious from our former remarks, 30since between what always is and what always is not there is an intermediate which is neither, and that intermediate is the generated and destructible.
If, however, 'indestructible' and 'ungenerated' are not coincident, 25there is no necessity that either the ungenerated or the indestructible should be eternal. But they must be coincident, for the following reasons. The terms 'generated' and 'destructible' are coincident; this is obvious from our former remarks, 30since between what always is and what always is not there is an intermediate which is neither, and that intermediate is the generated and destructible.
283b
1 τὸ πολὺ ἢ ὂν ἢ γινόμενον· τὸ δ' ἄπειρον χρόνον ἢ ἁπλῶς
ἢ ἀπό τινος, ἢ ἀεὶ ἢ ὡς ἐπὶ τὸ πολὺ ὑπάρχει ὄν.
Ἀνάγκη τοίνυν φύσει τὰ τοιαῦτα ὁτὲ μὲν εἶναι ὁτὲ δὲ μή.
Τῶν δὲ τοιούτων ἡ αὐτὴ δύναμις τῆς ἀντιφάσεως, καὶ ἡ
5 ὕλη αἰτία τοῦ εἶναι καὶ μή. Ὥστ' ἀνάγκη ἅμα ὑπάρχειν
ἐνεργείᾳ τὰ ἀντικείμενα. Ἀλλὰ μὴν οὐδέν γ' ἀληθὲς εἰπεῖν νῦν
ὅτι ἔστι πέρυσιν, οὐδὲ πέρυσιν ὅτι νῦν ἔστιν. Ἀδύνατον ἄρα μὴ
ὄν ποτε ὕστερον ἀΐδιον εἶναι· ἕξει γὰρ ὕστερον καὶ τὴν τοῦ
μὴ εἶναι δύναμιν, πλὴν οὐ τοῦ τότε μὴ εἶναι ὅτε ἔστιν (ὑπάρχει
10 γὰρ ἐνεργείᾳ ὄν), ἀλλὰ τοῦ πέρυσιν καὶ ἐν τῷ παρελθόντι
χρόνῳ. Ἔστω δὴ οὗ ἔχει τὴν δύναμιν ὑπάρχον ἐνεργείᾳ·
ἔσται ἄρα ἀληθὲς εἰπεῖν νῦν ὅτι οὐκ ἔστι πέρυσιν. Ἀλλ' ἀδύνατον·
οὐδεμία γὰρ δύναμις τοῦ γεγονέναι ἐστίν, ἀλλὰ τοῦ
εἶναι ἢ ἔσεσθαι. Ὁμοίως δὲ καὶ εἰ πρότερον ὂν ἀΐδιον ὕστερον
15 μὴ ἔσται· ἕξει γὰρ δύναμιν οὗ ἐνεργείᾳ οὐκ ἔστιν. Ὥστ' ἂν θῶμεν
τὸ δυνατόν, ἀληθὲς ἔσται εἰπεῖν νῦν ὅτι τοῦτ' ἔστι πέρυσιν
καὶ ὅλως ἐν τῷ παρελθόντι χρόνῳ. Καὶ φυσικῶς δὲ καὶ μὴ
καθόλου σκοποῦσιν ἀδύνατον ἢ ἀΐδιον ὂν πρότερον φθαρῆναι
ὕστερον, ἢ πρότερον μὴ ὂν ὕστερον ἀΐδιον εἶναι. Τὰ γὰρ
20 φθαρτὰ καὶ γενητὰ καὶ ἀλλοιωτὰ πάντα· ἀλλοιοῦται δὲ
τοῖς ἐναντίοις, καὶ ἐξ ὧν συνίσταται τὰ φύσει ὄντα, καὶ ὑπὸ
τῶν αὐτῶν τούτων φθείρεται.
1For whatever is either of these is capable both of being and of not being for a definite time: in either case, I mean, there is a certain period of time during which the thing is and another during which it is not. 5Anything therefore which is generated or destructible must be intermediate. Now let A be that which always is and B that which always is not, C the generated, and D the destructible. Then C must be intermediate between A and B. For in their case there is no time in 10the direction of either limit, in which either A is not or B is. But for the generated there must be such a time either actually or potentially, though not for A and B in either way. C then will be, and also not be, for a limited length of time, and this is true also 15of D, the destructible. Therefore each is both generated and destructible. Therefore 'generated' and 'destructible' are coincident. Now let E stand for the ungenerated, F for the generated, G for the indestructible, and H for the destructible. As for F and H, it 20has been shown that they are coincident. But when terms stand to one another as these do, F and H coincident,