§1.2#12.
2.
Ὅλως τε δὴ περὶ γενέσεως καὶ φθορᾶς τῆς ἁπλῆς λεκτέον, πότερον ἔστιν ἢ οὐκ ἔστι καὶ πῶς ἐστίν, καὶ περὶ τῶν ἄλλων ἁπλῶν κινήσεων, οἶον περὶ αὐξήσεως καὶ ἀλλοιώσεως.
Generally, then, we must speak about simple generation and destruction, whether it exists or does not exist and how it exists, and about the other simple movements, such as growth and alteration.
Πλάτων μὲν οὖν μόνον περὶ γενέσεως ἐσκέψατο καὶ φθορᾶς, ὅπως ὑπάρχει τοῖς πράγμασι, καὶ περὶ γενέσεως οὐ πάσης ἀλλὰ τῆς τῶν στοιχείων· πῶς δὲ σάρκες ἢ ὀστᾶ ἢ τῶν ἄλλων τι τῶν τοιούτων, οὐδέν· ἔτι οὔτε περὶ ἀλλοιώσεως οὔτε περὶ αὐξήσεως, τίνα τρόπον ὑπάρχουσι τοῖς πράγμασιν.
Plato, then, investigated only generation and destruction, how they belong to things, and of generation not all, but only that of the elements; but how flesh or bones or any other such things come to be, he said nothing; further, neither concerning alteration nor growth, in what way they belong to things.
ὅλως δὲ παρὰ τὰ ἐπιπολῆς περὶ οὐδενὸς οὐδεὶς ἐπέστησεν ἔξω Δημοκρίτου.
In general, except in a superficial way, no one turned his attention to anything, except Democritus.
οὗτος δ᾿ ἔοικε μὲν περὶ ἁπάντων φροντίσαι, ἤδη δὲ ἐν τῷ πῶς διαφέρει.
And he seems to have thought about all things, but already differs in the 'how'.
οὔτε γὰρ περὶ αὐξήσεως οὐδεὶς οὐδὲν διώρισεν, ὥσπερ λέγομεν, ὅ τι μὴ κἂν ὁ τυχὼν εἴπειεν, ὅτι προσιόντος αὐξάνονται τοῦ ὁμοίου¹ τῷ ὁμοίῳ (πῶς δὲ τοῦτο, οὐκέτι), οὐδὲ περὶ μίξεως, οὐδὲ περὶ τῶν ἄλλων ὡς εἰπεῖν οὐδενός, οἷον τοῦ ποιεῖν καὶ τοῦ πάσχειν, τίνα τρόπον τὸ μὲν ποιεῖ τὸ δὲ πάσχει τὰς φυσικὰς ποιήσεις.
For neither concerning growth did anyone define anything, as we say, except what even any ordinary person might say, that things grow by the accession of like to like (but how this is so, they no longer explain), nor concerning mixture, nor about almost any of the other things, such as acting and being acted upon, in what way the one acts and the other undergoes natural actions.
Δημόκριτος δὲ καὶ Λεύκιππος ποιήσαντες τὰ σχήματα τὴν ἀλλοίωσιν καὶ τὴν γένεσιν ἐκ τούτων ποιοῦσι, διακρίσει μὲν καὶ συγκρίσει γένεσιν καὶ φθοράν, τάξει δὲ καὶ θέσει ἀλλοίωσιν.
But Democritus and Leucippus, having posited the shapes, produce alteration and generation from these: generation and destruction by dissociation and association, and alteration by order and position.
ἐπεὶ δ᾿ ᾤοντο τἀληθὲς ἐν τῷ φαίνεσθαι, ἐναντία δὲ καὶ ἄπειρα τὰ φαινόμενα, τὰ σχήματα ἄπειρα ἐποίησαν, ὥστε ταῖς μεταβολαῖς τοῦ συγκειμένου τὸ αὐτὸ ἐναντίον δοκεῖν ἄλλῳ καὶ ἄλλῳ, καὶ μετακινεῖσθαι μικροῦ ἐμμιγνυμένου, καὶ ὅλως ἕτερον φαίνεσθαι ἑνὸς μετακινηθέντος· ἐκ τῶν αὐτῶν γὰρ τραγῳδία καὶ κωμῳδία γίνεται γραμμάτων.
And since they thought that the truth is in appearance, and the appearances are contrary and infinite, they made the shapes infinite, so that by the changes of the compound, the same thing seems contrary to different people, and it shifts when a small thing is mixed in, and in general appears entirely different when one thing is shifted; for from the same letters come to be tragedy and comedy.
Ἐπεὶ δὲ δοκεῖ σχεδὸν πᾶσιν ἕτερον εἶναι γένεσις καὶ ἀλλοίωσις, καὶ γίνεσθαι μὲν καὶ φθείρεσθαι συγκρινόμενα καὶ διακρινόμενα, ἀλλοιοῦσθαι δὲ μεταβαλλόντων τῶν παθημάτων, περὶ τούτων ἐπιστήσασι θεωρητέον.
And since it seems to almost everyone that generation and alteration are different, and that things come to be and are destroyed by being associated and dissociated, but are altered by the changing of their affections, we must consider this by focusing our attention upon these.
ἀπορίας γὰρ ἔχει ταῦτα καὶ πολλὰς καὶ εὐλόγους.
For these things contain difficulties, both many and reasonable.
εἰ μὲν γάρ ἐστι σύγκρισις ἡ γένεσις, πολλὰ ἀδύνατα συμβαίνει· εἰσὶ δ᾿ αὖ λόγοι ἕτεροι ἀναγκαστικοὶ καὶ οὐκ εὔποροι διαλύειν ὡς οὐκ ἐνδέχεται ἄλλως ἔχειν.
For if generation is association, many impossible consequences follow; and yet on the other hand, there are other arguments, compelling and not easy to dismantle, showing that it cannot be otherwise.
εἰ δὲ¹ μή ἐστι σύγκρισις ἡ γένεσις, ἢ ὅλως οὐκ ἔστι γένεσις ἢ ἀλλοίωσις, ἢ¹ καὶ τοῦτο διαλῦσαι χαλεπὸν ὃν πειρατέον.
But if generation is not association, either there is no generation at all, or it is alteration, or even this, being difficult, we must try to resolve.
Ἀρχὴ δὲ τούτων πάντων, πότερον οὕτω γίνεται καὶ ἀλλοιοῦται καὶ αὐξάνεται τὰ ὄντα καὶ τἀναττία τούτοις πάσχει, τῶν πρώτων ὑπαρχόντων μεγεθῶν ἀδιαιρέτων, ἢ οὐδέν ἐστι μέγεθος ἀδιαίρετον· διαφέρει γὰρ τοῦτο πλεῖστον.
And the starting point of all these is whether existing things come to be and are altered and grow in this way, and undergo the contraries of these, because there are primary indivisible magnitudes, or whether there is no indivisible magnitude at all; for this makes the greatest difference.
καὶ πάλιν εἰ μεγέθη, πότερον, ὡς Δημόκριτος καὶ Λεύκιππος, σώματα ταῦτ᾿ ἐστίν, ἢ ὥσπερ ἐν τῷ Τιμαίῳ, ἐπίπεδα.
And again, if there are magnitudes, whether, as Democritus and Leucippus say, these are bodies, or, as in the Timaeus, planes.
τοῦτο μὲν οὖν αὐτό, καθάπερ καὶ ἐν ἄλλοις εἰρήκαμεν, ἄλογον μέχρι ἐπιπέδων διαλῦσαι.
Now, to resolve bodies down to planes is itself unreasonable, as we have also said in other works.
διὸ μᾶλλον εὔλογον σώματα εἶναι ἀδιαίρετα.
Therefore, it is more reasonable that there are indivisible bodies.
ἀλλὰ καὶ ταῦτα πολλὴν ἔχει ἀλογίαν.
Yet these too involve much unreason.
ὅμως δὲ τούτοις ἀλλοίωσιν καὶ γένεσιν ἐνδέχεται ποιεῖν, καθάπερ εἴρηται, τροπῇ καὶ διαθιγῇ μετακινοῦντα τὸ αὐτὸ καὶ ταῖς τῶν σχημάτων διαφοραῖς, ὅπερ ποιεῖ Δημόκριτος (διὸ καὶ χροιὰν οὔ φησιν εἶναι· τροπῇ γὰρ χρωματίξεσθαι), τοῖς δ᾿ εἰς ἐπίπεδα διαιροῦσιν οὐκέτι· οὐδὲν γὰρ γίνεται πλὴν στερεὰ συντιθεμένων· πάθος γὰρ οὐδ᾿ ἐγχειροῦσι γεννᾶν οὐδὲν ἐξ αὐτῶν.
Nevertheless, with these it is possible to produce alteration and generation, as has been said, by shifting the same thing by turning and touching and by the differences of their shapes, which is what Democritus does (and for this reason he says that color does not exist, since things are colored by turning), but for those who divide into planes, this is no longer possible; for nothing comes to be except solids when they are put together, since they do not even attempt to generate any affection from them.
Αἴτιον δὲ τοῦ ἐπ᾿ ἔλαττον δύνασθαι τὰ ὁμολογούμενα συνορᾶν ἡ ἀπειρία.
And the cause of the inability to see the agreed facts comprehensively is inexperience.
διὸ ὅσοι ἐνῳκήκασι μᾶλλον ἐν τοῖς φυσικοῖς, μᾶλλον δύνανται ὑποτίθεσθαι τοιαύτας ἀρχὰς αἳ ἐπὶ πολὺ δύνανται συνείρειν· οἱ δ᾿ ἐκ τῶν πολλῶν λόγων ἀθεώρητοι τῶν ὑπαρχόντων ὄντες, πρὸς ὀλίγα βλέψαντες ἀποφαίνονται ῥᾷον.
Therefore, those who have lived more in natural inquiries are better able to posit such principles as can cohere over a wide range; whereas those who, from much verbal discussion, are unobservant of existing things, look at only a few things and declare too easily.
ἴδοι δ᾿ ἄν τις καὶ ἐκ τούτων ὅσον διαφέρουσιν οἱ φυσικῶς καὶ λογικῶς σκοποῦντες· περὶ γὰρ τοῦ ἄτομα εἶναι μεγέθη οἱ μέν φασιν ὅτι τὸ αὐτοτρίγωνον πολλὰ ἔσται, Δημόκριτος δ᾿ ἂν φανείη οἰκείοις καὶ φυσικοῖς λόγοις πεπεῖσθαι.
And one might see from this too how much those who investigate physically and those who investigate logically differ; for concerning the existence of indivisible magnitudes, the latter say that the 'triangle-itself' will be many, while Democritus would appear to have been persuaded by appropriate and physical arguments.
δῆλον δ᾿ ἔσται ὃ λέγομεν προϊοῦσιν.
And what we mean will be clear as we proceed.
Ἔχει γὰρ ἀπορίαν, εἴ τις θείη σῶμά τι εἶναι καὶ μέγεθος πάντῃ διαιρετόν, καὶ τοῦτο δυνατόν.
For it contains a difficulty if one should posit some body and magnitude to be divisible everywhere, and this to be possible.
τί γὰρ ἔσται ὅπερ τὴν διαίρεσιν διαφεύγει;
For what will there be that escapes the division?
εἰ γὰρ πάντῃ διαιρετόν, καὶ τοῦτο δυνατόν, κἂν ἄμα εἴη τοῦτο πάντῃ διῃρημένον, καὶ εἰ μὴ ἄμα διήρηται· κὲν εἰ τοῦτο γένοιτο, οὐδὲν ἂν εἴη ἀδύνατον.
For if it is divisible everywhere, and this is possible, then even if it has not been divided simultaneously, it could be simultaneously divided everywhere; and if this should happen, nothing impossible would occur.
οὐκοῦν καὶ κατὰ τὸ μέσον ὡσαύτως, καὶ ὅλως δέ, εἰ πάντῃ πέφυκε διαιρετόν, κἂν διαιρεθῇ, οὐδὲν ἔσται ἀδύνατον γεγονός, ἐπεὶ οὐδ᾿ ἂν εἰς μυρία μυριάκις διῃρημένα ᾗ, οὐδὲν ἀδύνατον· καίτοι ἴσως οὐδεὶς ἄν διέλοι.
Therefore, also in the middle likewise, and in general, if it is by nature divisible everywhere, even if it is divided, nothing impossible will have happened, since even if it has been divided into ten thousand times ten thousand pieces, there is nothing impossible, although perhaps no one would actually divide it.
ἐπεὶ τοίνυν πάντῃ τοιοῦτόν ἐστι τὸ σῶμα, διῃρήσθω.
Since, therefore, the body is such everywhere, let it be divided.
τί οὖν ἔσται λοιπόν;
What, then, will remain?
μέγεθος;
A magnitude?
οὐ γὰρ οἶόν τε· ἔσται γάρ τι οὐ διῃρημένον, ἦν δὲ πάντῃ διαιρετόν.
For that is not possible; for there will be something not divided, whereas it was divisible everywhere.
ἀλλὰ μὴν εἰ μηδὲν ἔσται σῶμα μηδὲ μέγεθος, διαίρεσις δ᾿ ἔσται, ἢ ἐκ στιγμῶν ἔσται, καὶ ἀμεγέθη ἐξ ὧν σύγκειται, ἢ οὐδὲν παντάπασιν, ὥστε κἂν γίνοιτο ἐκ μηδενὸς κἂν εἴη συγκείμενον, καὶ τὸ πᾶν δὴ οὐδὲν ἀλλ᾿ ἢ φαινόμενον.
But indeed, if there is to be no body nor magnitude, but division is to exist, either it will consist of points, and the things from which it is composed will be without magnitude, or it will be absolutely nothing, so that it would come to be from nothing and be composed of nothing, and the whole would indeed be nothing but an appearance.
ὁμοίως δὲ κἄν ᾗ ἐκ στιγμῶν, οὐκ ἔσται ποσόν.
And likewise, even if it is composed of points, it will not be a quantity.