sible, but it is among the impossible things for that which is going to be to be ungenerated, both without beginning and without end, both having and containing in itself infinite time, therefore he who says these things will be ignorant of the difference between a possible and an impossible thing. 15. From the first book of Aristotle's On the Heavens, at the end of the book. For nothing that comes from chance can be either incorruptible or ungenerated. How then could anyone believe him who says both things about the heaven? For in the eleventh chapter he says that chance is the cause of the heaven, but in the thirteenth he says that the heaven is without beginning and ungenerated. 10. From the second book of the Physics. There are two principles that move naturally, one of which is not natural; for it does not have the principle of motion in itself. Such a thing is whatever moves without being moved, so that it is both completely unmoved and the first of all things. How then could the principle move naturally, being neither natural nor moving according to nature? For it is consistent only for the natural principle that moves according to nature to move naturally. If the principle which is not natural does not have in itself a principle of motion, it is clear that the natural principle does have in itself a principle of motion; but the principle that has a principle is not a principle. If among eternally ungenerated things nothing can be before or after anything else, how is the unmoved principle, which is not moved, but moves, the first of all things or a principle at all? 17. From the third book of the same treatise. And they derive their belief in the infinite from time; for this is infinite; and further, because only in this way would generation and destruction not fail, if there were an infinite source from which that which is coming to be is taken. If time always has its being in coming to be, and that which is coming to be did not exist before it came to be, how is time infinite, whose existence is always preceded by non-existence? For that which is not yet is about to be present, and that which is future is about to pass away, and that which has passed was about to come to be. If, because generation and destruction do not fail, it is necessary for generation and destruction to be infinite, then generation and destruction will also be without beginning, just like that which is ungenerated and incorruptible; but if this is impossible, then generation and destruction are not infinite. 18. From the same book. But indeed, number is not infinite in the sense of being separate; for number is that which can be numbered or that which has number. If, therefore, it is possible to number that which is numerable, it would also be possible to traverse the infinite. If the number of that which can be numbered and of that which has number is not infinite, and past time is numerable, then past time would be finite. 19. From the same book.
νατόν, ἐστὶ δὲ τῶν ἀδυνάτων τὸ μέλλον ἔσεσθαι ἀγένητον εἶναι, ἄναρχόν τε καὶ ἀτελεύτητον, ἔχον τε καὶ περιέχον ἐν ἑαυτῷ τὸν ἄπειρον χρόνον, ἔσται ἄρα ὁ ταῦτα λέγων δυνατοῦ τε καὶ ἀδυνάτου πράγματος ἀγνοῶν τὴν διαφοράν. ιε. Ἐκ τοῦ πρώτου Περὶ οὐρανοῦ λόγου Ἀριστοτέλους, ἐν τῷ τέλει τοῦ λόγου. Oὐθὲν γὰρ ἀπὸ ταὐτομάτου οὔτε ἄφθαρτον οὔτε ἀγένη τον οἷόν τε εἶναι. Πῶς οὖν ἄν τις πιστεύσειε τῷ ἀμφότερα λέγοντι περὶ τοῦ οὐρανοῦ; Ἐν μὲν τῷ ἑνδεκάτῳ κεφαλαίῳ τὸ αὐτόματον αἴτιον εἶναι λέγει τοῦ οὐρανοῦ, ἐν δὲ τῷ τρισκαιδεκάτῳ ἄναρ χόν τε καὶ ἀγένητον τὸν οὐρανὸν εἶναι λέγει. ι. Ἐκ τοῦ δευτέρου λόγου τῆς Φυσικῆς ἀκροάσεως. ∆ιτταὶ δὲ ἀρχαὶ αἱ κινοῦσαι φυσικῶς, ὧν ἡ ἑτέρα οὐ φυσική· οὐ γὰρ ἔχει κινήσεως ἀρχὴν ἐν ἑαυτῇ. Τοιοῦτον δέ ἐστιν εἴ τι κινεῖ μὴ κινούμενον, ὥστε τό τε παντελῶς ἀκίνη τον καὶ τὸ πάντων πρῶτον. Πῶς ἂν οὖν κινήσειε φυσικῶς ἡ ἀρχή, ἡ μήτε φυσικὴ οὖσα μήτε κατὰ φύσιν κινοῦσα; Τῇ γὰρ μόνῃ φυσικῇ ἀρχῇ τῇ κατὰ φύσιν κινούσῃ ἀκόλουθόν ἐστι τὸ φυσικῶς κινεῖν. Eἰ ἀρχὴ ἡ μὴ οὖσα φυσικὴ οὐκ ἔχει ἐν ἑαυτῇ ἀρχὴν κινήσεως, δῆλον ὅτι ἡ φυσικὴ ἀρχὴ ἔχει ἐν ἑαυτῇ ἀρχὴν κινήσεως· ἀλλ' ἡ ἀρχὴ ἡ ἀρχὴν ἔχουσα οὐκ ἔστιν ἀρχή. Eἰ ἐν τοῖς ἀϊδίως ἀγενήτοις οὐδὲν οὐδενὸς πρότερον ἢ ὕστερον εἶναι δύναται, πῶς ἡ ἀρχὴ ἀκίνητος, ἡ μὴ κινουμένη, κινοῦσα, πάντων πρῶτόν ἐστιν ἢ ὅλως ἀρχή; ιζ. Ἐκ τοῦ τρίτου λόγου τῆς αὐτῆς πραγματείας. Τοῦ δὲ εἶναι ἄπειρον τὴν πίστιν λαμβάνουσιν ἔκ τε τοῦ χρόνου· οὗτος γὰρ ἄπειρος· ἔτι τῷ οὕτως ἂν μόνως μὴ ὑπο λείπειν γένεσιν καὶ φθοράν, εἰ ἄπειρον εἴη ὅθεν ἀφαιρεῖται τὸ γινόμενον. Eἰ ὁ χρόνος ἀεὶ ἐν τῷ γίνεσθαι τὸ εἶναι ἔχει, τὸ δὲ γιγνόμενον πρὸ τοῦ γίνεσθαι οὐκ ἦν, πῶς ἄπειρος ὁ χρόνος, οὗ ἀεὶ τῆς ὑπάρξεως προηγεῖται ἡ ἀνυπαρξία; Καὶ γὰρ τὸ μήπω ὂν μέλλει παρεῖναι, καὶ τὸ μέλλον μέλλει παρελθεῖν, καὶ τὸ παρελθὸν ἔμελλε γίνεσθαι. Eἰ τῷ μὴ ὑπολείπεσθαι τὴν γένεσιν καὶ τὴν φθορὰν ἀνάγκη ἄπειρον εἶναι τὴν γένεσιν καὶ τὴν φθοράν, ἔσται ἄρα καὶ ἡ γένεσις καὶ ἡ φθορὰ ἄναρ χος, ὥσπερ τὸ ἀγένητον καὶ τὸ ἄφθαρτον· εἰ δὲ τοῦτο ἀδύνα τον, οὐκ ἄρα ἄπειρος ἡ γένεσις καὶ ἡ φθορά. ιη. Ἐκ τοῦ αὐτοῦ λόγου. Ἀλλὰ μὴν οὐδὲ ἀριθμὸς οὕτως ὡς κεχωρισμένος καὶ ἄπειρος· ἀριθμητὸν γὰρ ὁ ἀριθμὸς ἢ τὸ ἔχον ἀριθμόν. Eἰ οὖν τὸ ἀριθμητὸν ἐνδέχεται ἀριθμῆσαι, καὶ τὸ διεξελθεῖν ἂν εἴη δυνατὸν τὸ ἄπειρον. Eἰ τοῦ ἀριθμητοῦ καὶ τοῦ ἔχοντος ἀριθμὸν οὐκ ἔστιν ἄπει ρος ὁ ἀριθμός, ἀριθμητὸς δὲ ὁ γεγονὼς χρόνος, πεπερασμένος ἄρα ἂν εἴη γεγονὼς χρόνος. ιθ. Ἐκ τοῦ αὐτοῦ λόγου.