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Critical ApparatusCritical ApparatusΓ.‎

  • 1 Editor’s NoteCritical ApparatusἘπεὶ δ' ἡ φύσις μέν ἐστιν ἀρχὴ κινήσεως καὶ μετα-
  • Critical Apparatusβολῆς, ἡ δὲ μέθοδος ἡμῖν περὶ φύσεώς ἐστι, δεῖ μὴ λαν-
  • Critical Apparatusθάνειν τί ἐστι κίνησις· ἀναγκαῖον γὰρ ἀγνοουμένης αὐτῆς ἀγ-
  • 15νοεῖσθαι καὶ τὴν φύσιν. διορισαμένοις δὲ περὶ κινήσεως πει-
  • Editor’s Noteρατέον τὸν αὐτὸν ἐπελθεῖν τρόπον περὶ τῶν ἐφεξῆς. δοκεῖ δ'
  • Editor’s Noteἡ κίνησις εἶναι τῶν συνεχῶν, τὸ δ' ἄπειρον ἐμφαίνεται πρῶ-
  • Editor’s NoteCritical Apparatusτον ἐν τῷ συνεχεῖ· διὸ καὶ τοῖς ὁριζομένοις τὸ συνεχὲς συμ-
  • Critical Apparatusβαίνει προσχρήσασθαι πολλάκις τῷ λόγῳ τῷ τοῦ ἀπείρου,
  • Editor’s Note20ὡς τὸ εἰς ἄπειρον διαιρετὸν συνεχὲς ὄν. πρὸς δὲ τούτοις ἄνευ
  • Editor’s NoteCritical Apparatusτόπου καὶ κενοῦ καὶ χρόνου κίνησιν ἀδύνατον εἶναι. δῆλον οὖν
  • Editor’s NoteCritical Apparatusὡς διά τε ταῦτα, καὶ διὰ τὸ πάντων εἶναι κοινὰ καὶ κα-
  • Critical Apparatusθόλου ταῦτα, σκεπτέον προχειρισαμένοις περὶ ἑκάστου
  • τούτων (ὑστέρα γὰρ ἡ περὶ τῶν ἰδίων θεωρία τῆς περὶ τῶν
  • Editor’s NoteCritical Apparatus25κοινῶν ἐστιν)· καὶ πρῶτον, καθάπερ εἴπαμεν, περὶ κινήσεως.
  • Editor’s NoteCritical Apparatusἔστι δὴ [τι] τὸ μὲν ἐντελεχείᾳ μόνον, τὸ δὲ δυνάμει καὶ ἐν-
  • Editor’s NoteCritical Apparatusτελεχείᾳ, τὸ μὲν τόδε τι, τὸ δὲ τοσόνδε, τὸ δὲ τοιόνδε, καὶ
  • Editor’s NoteCritical Apparatusτῶν ἄλλων τῶν τοῦ ὄντος κατηγοριῶν ὁμοίως. τοῦ δὲ πρός
  • pg 164Editor’s NoteCritical Apparatusτι τὸ μὲν καθ' ὑπεροχὴν λέγεται καὶ κατ' ἔλλειψιν, τὸ δὲ
  • Critical Apparatus30κατὰ τὸ ποιητικὸν καὶ παθητικόν, καὶ ὅλως κινητικόν τε
  • Critical Apparatusκαὶ κινητόν· τὸ γὰρ κινητικὸν κινητικὸν τοῦ κινητοῦ καὶ τὸ κι-
  • Editor’s NoteCritical Apparatusνητὸν κινητὸν ὑπὸ τοῦ κινητικοῦ. οὐκ ἔστι δὲ κίνησις παρὰ τὰ
  • Critical Apparatusπράγματα· μεταβάλλει γὰρ ἀεὶ τὸ μεταβάλλον ἢ κατ'
  • Critical Apparatusοὐσίαν ἢ κατὰ ποσὸν ἢ κατὰ ποιὸν ἢ κατὰ τόπον, κοινὸν δ'
  • Critical Apparatus35ἐπὶ τούτων οὐδὲν ἔστι λαβεῖν, ὡς φαμέν, ὃ οὔτε τόδε οὔτε πο-
  • Critical Apparatus201aσὸν οὔτε ποιὸν οὔτε τῶν ἄλλων κατηγορημάτων οὐθέν· ὥστ' οὐδὲ
  • Critical Apparatusκίνησις οὐδὲ μεταβολὴ οὐθενὸς ἔσται παρὰ τὰ εἰρημένα, μη-
  • Editor’s NoteCritical Apparatus Link θενός γε ὄντος παρὰ τὰ εἰρημένα. ἕκαστον δὲ διχῶς ὑπάρ-
  • χει πᾶσιν, οἷον τὸ τόδε (τὸ μὲν γὰρ μορφὴ αὐτοῦ, τὸ δὲ
  • 5στέρησις), καὶ κατὰ τὸ ποιόν (τὸ μὲν γὰρ λευκὸν τὸ δὲ
  • Critical Apparatus Link μέλαν), καὶ κατὰ τὸ ποσὸν τὸ μὲν τέλειον τὸ δ' ἀτελές.
  • ὁμοίως δὲ καὶ κατὰ τὴν φορὰν τὸ μὲν ἄνω τὸ δὲ κάτω,
  • Editor’s NoteCritical Apparatus Link ἢ τὸ μὲν κοῦφον τὸ δὲ βαρύ. ὥστε κινήσεως καὶ μεταβο-
  • Editor’s Note9λῆς ἔστιν εἴδη τοσαῦτα ὅσα τοῦ ὄντος.
  • 9                                                                        διῃρημένου δὲ καθ'
  • Editor’s NoteCritical Apparatus Link 10ἕκαστον γένος τοῦ μὲν ἐντελεχείᾳ τοῦ δὲ δυνάμει, ἡ τοῦ δυ-
  • Critical Apparatus Link νάμει ὄντος ἐντελέχεια, ᾗ τοιοῦτον, κίνησίς ἐστιν, οἷον τοῦ μὲν
  • Critical Apparatusἀλλοιωτοῦ, ᾗ ἀλλοιωτόν, ἀλλοίωσις, τοῦ δὲ αὐξητοῦ καὶ τοῦ
  • ἀντικειμένου φθιτοῦ (οὐδὲν γὰρ ὄνομα κοινὸν ἐπ' ἀμφοῖν) αὔ-
  • Critical Apparatusξησις καὶ φθίσις, τοῦ δὲ γενητοῦ καὶ φθαρτοῦ γένεσις καὶ
  • Editor’s NoteCritical Apparatus15φθορά, τοῦ δὲ φορητοῦ φορά. ὅτι δὲ τοῦτο ἔστιν ἡ κίνησις,
  • Editor’s NoteCritical Apparatusἐντεῦθεν δῆλον. ὅταν γὰρ τὸ οἰκοδομητόν, ᾗ τοιοῦτον αὐτὸ
  • pg 165λέγομεν εἶναι, ἐντελεχείᾳ ᾖ, οἰκοδομεῖται, καὶ ἔστιν τοῦτο
  • Critical Apparatusοἰκοδόμησις· ὁμοίως δὲ καὶ μάθησις καὶ ἰάτρευσις καὶ κύ-
  • Editor’s NoteCritical Apparatusλισις καὶ ἅλσις καὶ ἅδρυνσις καὶ γήρανσις. ἐπεὶ δ' ἔνια
  • Critical Apparatus Link 20ταὐτὰ καὶ δυνάμει καὶ ἐντελεχείᾳ ἐστίν, οὐχ ἅμα δὲ ἢ οὐ
  • Critical Apparatusκατὰ τὸ αὐτό, ἀλλ' οἷον θερμὸν μὲν ἐντελεχείᾳ ψυχρὸν δὲ
  • δυνάμει, πολλὰ ἤδη ποιήσει καὶ πείσεται ὑπ' ἀλλήλων·
  • ἅπαν γὰρ ἔσται ἅμα ποιητικὸν καὶ παθητικόν. ὥστε καὶ
  • Editor’s Noteτὸ κινοῦν φυσικῶς κινητόν· πᾶν γὰρ τὸ τοιοῦτον κινεῖ κινού-
  • Editor’s Note25μενον καὶ αὐτό. δοκεῖ μὲν οὖν τισιν ἅπαν κινεῖσθαι τὸ κι-
  • Editor’s NoteCritical Apparatusνοῦν, οὐ μὴν ἀλλὰ περὶ τούτου μὲν ἐξ ἄλλων ἔσται δῆλον
  • Editor’s NoteCritical Apparatusὅπως ἔχει (ἔστι γάρ τι κινοῦν καὶ ἀκίνητον), ἡ δὲ τοῦ δυνάμει
  • Editor’s NoteCritical Apparatusὄντος ⟨ἐντελέχεια⟩, ὅταν ἐντελεχείᾳ ὂν ἐνεργῇ οὐχ ᾗ αὐτὸ ἀλλ'
  • Critical Apparatus Link ᾗ κινητόν, κίνησίς ἐστιν. λέγω δὲ τὸ ᾗ ὡδί. ἔστι γὰρ ὁ χαλ-
  • 30κὸς δυνάμει ἀνδριάς, ἀλλ' ὅμως οὐχ ἡ τοῦ χαλκοῦ ἐντελέ-
  • Critical Apparatusχεια, ᾗ χαλκός, κίνησίς ἐστιν· οὐ γὰρ τὸ αὐτὸ τὸ χαλκῷ
  • Editor’s NoteCritical Apparatusεἶναι καὶ δυνάμει τινί [κινητῷ], ἐπεὶ εἰ ταὐτὸν ἦν ἁπλῶς
  • Critical Apparatusκαὶ κατὰ τὸν λόγον, ἦν ἂν ἡ τοῦ χαλκοῦ, ᾗ χαλκός, ἐν-
  • Editor’s NoteCritical Apparatusτελέχεια κίνησις· οὐκ ἔστιν δὲ ταὐτόν, ὡς εἴρηται (δῆλον δ'
  • Link 35ἐπὶ τῶν ἐναντίων· τὸ μὲν γὰρ δύνασθαι ὑγιαίνειν καὶ δύ-
  • Critical Apparatus201bνασθαι κάμνειν ἕτερον—καὶ γὰρ ἂν τὸ κάμνειν καὶ τὸ ὑγι-
  • αίνειν ταὐτὸν ἦν—τὸ δὲ ὑποκείμενον καὶ τὸ ὑγιαῖνον καὶ τὸ
  • Editor’s Noteνοσοῦν, εἴθ' ὑγρότης εἴθ' αἷμα, ταὐτὸν καὶ ἕν). ἐπεὶ δ' οὐ ταὐ-
  • Editor’s Note Link τόν, ὥσπερ οὐδὲ χρῶμα ταὐτὸν καὶ ὁρατόν, ἡ τοῦ δυνατοῦ,
  • pg 166Editor’s NoteCritical Apparatus5ᾗ δυνατόν, ἐντελέχεια φανερὸν ὅτι κίνησίς ἐστιν.
  • 5                                                                                    ὅτι μὲν οὖν
  • Critical Apparatus Link ἐστιν αὕτη, καὶ ὅτι συμβαίνει τότε κινεῖσθαι ὅταν ἡ ἐντελέ-
  • Critical Apparatus Link χεια ᾖ αὐτή, καὶ οὔτε πρότερον οὔτε ὕστερον, δῆλον· ἐνδέχεται
  • Critical Apparatusγὰρ ἕκαστον ὁτὲ μὲν ἐνεργεῖν ὁτὲ δὲ μή, οἷον τὸ οἰκοδομη-
  • Critical Apparatusτόν, καὶ ἡ τοῦ οἰκοδομητοῦ ἐνέργεια, ᾗ οἰκοδομητόν, οἰκοδό-
  • Editor’s NoteCritical Apparatus10μησίς ἐστιν (ἢ γὰρ οἰκοδόμησις ἡ ἐνέργεια [τοῦ οἰκοδομητοῦ]
  • Critical Apparatusἢ ἡ οἰκία· ἀλλ' ὅταν οἰκία ᾖ, οὐκέτ' οἰκοδομητὸν ἔστιν· οἰ-
  • Critical Apparatusκοδομεῖται δὲ τὸ οἰκοδομητόν· ἀνάγκη οὖν οἰκοδόμη-
  • Critical Apparatusσιν τὴν ἐνέργειαν εἶναι)· ἡ δ' οἰκοδόμησις κίνησίς τις.
  • ἀλλὰ μὴν ὁ αὐτὸς ἐφαρμόσει λόγος καὶ ἐπὶ τῶν ἄλλων
  • 15κινήσεων.
  • 2 Editor’s NoteὍτι δὲ καλῶς εἴρηται, δῆλον καὶ ἐξ ὧν οἱ ἄλλοι
  • Editor’s NoteCritical Apparatusπερὶ αὐτῆς λέγουσιν, καὶ ἐκ τοῦ μὴ ῥᾴδιον εἶναι διορίσαι ἄλ-
  • Editor’s NoteCritical Apparatusλως αὐτήν. οὔτε γὰρ τὴν κίνησιν καὶ τὴν μεταβολὴν ἐν ἄλ-
  • Editor’s NoteCritical Apparatusλῳ γένει θεῖναι δύναιτ' ἄν τις, δῆλόν τε σκοποῦσιν ὡς τι-
  • Critical Apparatus20θέασιν αὐτὴν ἔνιοι, ἑτερότητα καὶ ἀνισότητα καὶ τὸ μὴ ὂν
  • Editor’s Noteφάσκοντες εἶναι τὴν κίνησιν· ὧν οὐδὲν ἀναγκαῖον κινεῖσθαι,
  • Critical Apparatusοὔτ' ἂν ἕτερα ᾖ οὔτ' ἂν ἄνισα οὔτ' ἂν οὐκ ὄντα· ἀλλ' οὐδ' ἡ
  • Critical Apparatusμεταβολὴ οὔτ' εἰς ταῦτα οὔτ' ἐκ τούτων μᾶλλόν ἐστιν ἢ ἐκ
  • Editor’s Noteτῶν ἀντικειμένων. αἴτιον δὲ τοῦ εἰς ταῦτα τιθέναι ὅτι ἀόριστόν
  • Editor’s NoteCritical Apparatus25τι δοκεῖ εἶναι ἡ κίνησις, τῆς δὲ ἑτέρας συστοιχίας αἱ ἀρχαὶ
  • Critical Apparatusδιὰ τὸ στερητικαὶ εἶναι ἀόριστοι· οὔτε γὰρ τόδε οὔτε τοιόνδε
  • Editor’s NoteCritical Apparatusοὐδεμία αὐτῶν ἐστιν, [ὅτι] οὐδὲ τῶν ἄλλων κατηγοριῶν. τοῦ δὲ
  • Editor’s Noteδοκεῖν ἀόριστον εἶναι τὴν κίνησιν αἴτιον ὅτι οὔτε εἰς δύναμιν
  • pg 167Critical Apparatusτῶν ὄντων οὔτε εἰς ἐνέργειαν ἔστιν θεῖναι αὐτήν· οὔτε
  • Critical Apparatus30γὰρ τὸ δυνατὸν ποσὸν εἶναι κινεῖται ἐξ ἀνάγκης οὔτε τὸ ἐν-
  • Editor’s NoteCritical Apparatus Link εργείᾳ ποσόν, ἥ τε κίνησις ἐνέργεια μὲν εἶναί τις δοκεῖ,
  • Editor’s NoteCritical Apparatusἀτελὴς δέ· αἴτιον δ' ὅτι ἀτελὲς τὸ δυνατόν, οὗ ἐστιν ἐνέρ-
  • Editor’s NoteCritical Apparatusγεια. καὶ διὰ τοῦτο δὴ χαλεπὸν αὐτὴν λαβεῖν τί ἐστιν· ἢ
  • γὰρ εἰς στέρησιν ἀναγκαῖον θεῖναι ἢ εἰς δύναμιν ἢ εἰς ἐνέρ-
  • 35γειαν ἁπλῆν, τούτων δ' οὐδὲν φαίνεται ἐνδεχόμενον. λείπεται
  • Critical Apparatus202aCritical Apparatusτοίνυν ὁ εἰρημένος τρόπος, ἐνέργειαν μέν τινα εἶναι, τοιαύτην
  • Editor’s NoteCritical Apparatusδ' ἐνέργειαν οἵαν εἴπαμεν, χαλεπὴν μὲν ἰδεῖν, ἐνδεχομένην
  • Editor’s NoteCritical Apparatusδ' εἶναι.
  • 3κινεῖται δὲ καὶ τὸ κινοῦν ὥσπερ εἴρηται πᾶν, τὸ
  • Editor’s NoteCritical Apparatusδυνάμει ὂν κινητόν, καὶ οὗ ἡ ἀκινησία ἠρεμία ἐστίν (ᾧ γὰρ
  • Editor’s NoteCritical Apparatus Link 5ἡ κίνησις ὑπάρχει, τούτου ἡ ἀκινησία ἠρεμία). τὸ γὰρ πρὸς
  • τοῦτο ἐνεργεῖν, ᾗ τοιοῦτον, αὐτὸ τὸ κινεῖν ἐστι· τοῦτο δὲ ποιεῖ
  • θίξει, ὥστε ἅμα καὶ πάσχει· διὸ ἡ κίνησις ἐντελέχεια τοῦ
  • Critical Apparatusκινητοῦ, ᾗ κινητόν, συμβαίνει δὲ τοῦτο θίξει τοῦ κινητικοῦ, ὥσθ'
  • Editor’s NoteCritical Apparatus Link ἅμα καὶ πάσχει. εἶδος δὲ ἀεὶ οἴσεταί τι τὸ κινοῦν, ἤτοι τό-
  • Editor’s NoteCritical Apparatus Link 10δε ἢ τοιόνδε ἢ τοσόνδε, ὃ ἔσται ἀρχὴ καὶ αἴτιον τῆς κινή-
  • Critical Apparatus Link σεως, ὅταν κινῇ, οἷον ὁ ἐντελεχείᾳ ἄνθρωπος ποιεῖ ἐκ τοῦ
  • δυνάμει ὄντος ἀνθρώπου ἄνθρωπον.
  • 3 Editor’s Note Link Καὶ τὸ ἀπορούμενον δὲ φανερόν, ὅτι ἐστὶν ἡ κίνησις ἐν
  • Critical Apparatus Link τῷ κινητῷ· ἐντελέχεια γάρ ἐστι τούτου [καὶ] ὑπὸ τοῦ κινητικοῦ.
  • Link 15καὶ ἡ τοῦ κινητικοῦ δὲ ἐνέργεια οὐκ ἄλλη ἐστίν· δεῖ μὲν γὰρ
  • Critical Apparatus Link εἶναι ἐντελέχειαν ἀμφοῖν· κινητικὸν μὲν γάρ ἐστιν τῷ δύνα-
  • Link σθαι, κινοῦν δὲ τῷ ἐνεργεῖν, ἀλλ' ἔστιν ἐνεργητικὸν τοῦ κινητοῦ,
  • pg 168Editor’s Note Link ὥστε ὁμοίως μία ἡ ἀμφοῖν ἐνέργεια ὥσπερ τὸ αὐτὸ διά-
  • Critical Apparatusστημα ἓν πρὸς δύο καὶ δύο πρὸς ἕν, καὶ τὸ ἄναντες καὶ τὸ
  • Editor’s Note Link 20κάταντες· ταῦτα γὰρ ἓν μέν ἐστιν, ὁ μέντοι λόγος οὐχ εἷς·
  • Editor’s Note21ὁμοίως δὲ καὶ ἐπὶ τοῦ κινοῦντος καὶ κινουμένου.
  • 21                                                                              ἔχει δ' ἀπορίαν
  • Critical Apparatus Link λογικήν· ἀναγκαῖον γὰρ ἴσως εἶναί τινα ἐνέργειαν τοῦ
  • Critical Apparatusποιητικοῦ καὶ τοῦ παθητικοῦ· τὸ μὲν δὴ ποίησις, τὸ δὲ πά-
  • θησις, ἔργον δὲ καὶ τέλος τοῦ μὲν ποίημα, τοῦ δὲ πάθος.
  • Editor’s NoteCritical Apparatus Link 25ἐπεὶ οὖν ἄμφω κινήσεις, εἰ μὲν ἕτεραι, ἐν τίνι; ἢ γὰρ ἄμ-
  • Critical Apparatus Link φω ἐν τῷ πάσχοντι καὶ κινουμένῳ, ἢ ἡ μὲν ποίησις ἐν τῷ
  • ποιοῦντι, ἡ δὲ πάθησις ἐν τῷ πάσχοντι (εἰ δὲ δεῖ καὶ ταύ-
  • Editor’s Noteτην ποίησιν καλεῖν, ὁμώνυμος ἂν εἴη). ἀλλὰ μὴν εἰ τοῦτο, ἡ
  • Editor’s Noteκίνησις ἐν τῷ κινοῦντι ἔσται (ὁ γὰρ αὐτὸς λόγος ἐπὶ κινοῦντος
  • 30καὶ κινουμένου), ὥστ' ἢ πᾶν τὸ κινοῦν κινήσεται, ἢ ἔχον κίνησιν
  • Editor’s Noteοὐ κινήσεται. εἰ δ' ἄμφω ἐν τῷ κινουμένῳ καὶ πάσχοντι,
  • καὶ ἡ ποίησις καὶ ἡ πάθησις, καὶ ἡ δίδαξις καὶ ἡ μάθη-
  • σις δύο οὖσαι ἐν τῷ μανθάνοντι, πρῶτον μὲν ἡ ἐνέργεια ἡ
  • Editor’s NoteCritical Apparatusἑκάστου οὐκ ἐν ἑκάστῳ ὑπάρξει, εἶτα ἄτοπον δύο κινήσεις ἅμα
  • Editor’s NoteCritical Apparatus35κινεῖσθαι· τίνες γὰρ ἔσονται ἀλλοιώσεις δύο τοῦ ἑνὸς καὶ εἰς
  • ἓν εἶδος; ἀλλ' ἀδύνατον. ἀλλὰ μία ἔσται ἡ ἐνέργεια. ἀλλ'
  • 202b Link ἄλογον δύο ἑτέρων τῷ εἴδει τὴν αὐτὴν καὶ μίαν εἶναι ἐνέρ-
  • Editor’s NoteCritical Apparatusγειαν· καὶ ἔσται, εἴπερ ἡ δίδαξις καὶ ἡ μάθησις τὸ αὐτὸ καὶ
  • Link ἡ ποίησις καὶ ἡ πάθησις, καὶ τὸ διδάσκειν τῷ μανθάνειν
  • τὸ αὐτὸ καὶ τὸ ποιεῖν τῷ πάσχειν, ὥστε τὸν διδάσκοντα ἀν-
  • Editor’s Note5άγκη ἔσται πάντα μανθάνειν καὶ τὸν ποιοῦντα πάσχειν.
  • 5                                                                                                        
  • οὔτε τὸ τὴν ἄλλου ἐνέργειαν ἐν ἑτέρῳ εἶναι ἄτοπον (ἔστι γὰρ
  • Critical Apparatus Link ἡ δίδαξις ἐνέργεια τοῦ διδασκαλικοῦ, ἔν τινι μέντοι, καὶ οὐκ
  • Editor’s NoteCritical Apparatus Link ἀποτετμημένη, ἀλλὰ τοῦδε ἐν τῷδε), οὔτε μίαν δυοῖν κωλύει οὐθὲν
  • pg 169Editor’s NoteCritical Apparatusτὴν αὐτὴν εἶναι (μὴ ὡς τῷ εἶναι τὸ αὐτό, ἀλλ' ὡς ὑπάρ-
  • Editor’s NoteCritical Apparatus Link 10χει τὸ δυνάμει ὂν πρὸς τὸ ἐνεργοῦν), οὔτ' ἀνάγκη τὸν διδά-
  • Critical Apparatus Link σκοντα μανθάνειν, οὐδ' εἰ τὸ ποιεῖν καὶ πάσχειν τὸ αὐτό ἐστιν,
  • Editor’s NoteCritical Apparatus Link μὴ μέντοι ὥστε τὸν λόγον εἶναι ἕνα τὸν ⟨τὸ⟩ τί ἦν εἶναι λέγοντα,
  • Critical Apparatusοἷον ὡς λώπιον καὶ ἱμάτιον, ἀλλ' ὡς ἡ ὁδὸς ἡ Θήβηθεν Ἀθήναζε
  • Editor’s Note Link καὶ ἡ Ἀθήνηθεν εἰς Θήβας, ὥσπερ εἴρηται καὶ πρότερον; οὐ γὰρ
  • Critical Apparatus Link 15ταὐτὰ πάντα ὑπάρχει τοῖς ὁπωσοῦν τοῖς αὐτοῖς, ἀλλὰ μόνον
  • Editor’s NoteCritical Apparatusοἷς τὸ εἶναι τὸ αὐτό. οὐ μὴν ἀλλ' οὐδ' εἰ ἡ δίδαξις τῇ μαθήσει
  • Critical Apparatusτὸ αὐτό, καὶ τὸ μανθάνειν τῷ διδάσκειν, ὥσπερ οὐδ' εἰ ἡ διά-
  • στασις μία τῶν διεστηκότων, καὶ τὸ διίστασθαι ἐνθένθε ἐκεῖσε
  • Editor’s Note Link κἀκεῖθεν δεῦρο ἓν καὶ τὸ αὐτό. ὅλως δ' εἰπεῖν οὐδ' ἡ δίδαξις
  • Critical Apparatus20τῇ μαθήσει οὐδ' ἡ ποίησις τῇ παθήσει τὸ αὐτὸ κυρίως, ἀλλ'
  • Critical Apparatusᾧ ὑπάρχει ταῦτα, ἡ κίνησις· τὸ γὰρ τοῦδε ἐν τῷδε καὶ τὸ
  • τοῦδε ὑπὸ τοῦδε ἐνέργειαν εἶναι ἕτερον τῷ λόγῳ.
  • Editor’s NoteCritical Apparatusτί μὲν οὖν ἐστιν κίνησις εἴρηται καὶ καθόλου καὶ κατὰ
  • Critical Apparatusμέρος· οὐ γὰρ ἄδηλον πῶς ὁρισθήσεται τῶν εἰδῶν ἕκαστον αὐ-
  • Link 25τῆς· ἀλλοίωσις μὲν γὰρ ἡ τοῦ ἀλλοιωτοῦ, ᾗ ἀλλοιωτόν, ἐν-
  • Link τελέχεια. ἔτι δὲ γνωριμώτερον, ἡ τοῦ δυνάμει ποιητικοῦ καὶ
  • Critical Apparatusπαθητικοῦ, ᾗ τοιοῦτον, ἁπλῶς τε καὶ πάλιν καθ' ἕκαστον, ἢ
  • Critical Apparatusοἰκοδόμησις ἢ ἰάτρευσις. τὸν αὐτὸν δὲ λεχθήσεται τρόπον
  • Link καὶ περὶ τῶν ἄλλων κινήσεων ἑκάστης.
  • 4 Editor’s NoteCritical Apparatus30Ἐπεὶ δ' ἐστὶν ἡ περὶ φύσεως ἐπιστήμη περὶ μεγέθη
  • καὶ κίνησιν καὶ χρόνον, ὧν ἕκαστον ἀναγκαῖον ἢ ἄπειρον ἢ
  • πεπερασμένον εἶναι, εἰ καὶ μὴ πᾶν ἐστιν ἄπειρον ἢ πεπε-
  • Editor’s Note Link ρασμένον, οἷον πάθος ἢ στιγμή (τῶν γὰρ τοιούτων ἴσως οὐ-
  • δὲν ἀναγκαῖον ἐν θατέρῳ τούτων εἶναι), προσῆκον ἂν εἴη τὸν
  • Link 35περὶ φύσεως πραγματευόμενον θεωρῆσαι περὶ ἀπείρου, εἰ ἔστιν
  • pg 170Editor’s NoteCritical Apparatus Link ἢ μή, καὶ εἰ ἔστιν, τί ἐστιν. σημεῖον δ' ὅτι ταύτης τῆς ἐπιστή-
  • 203aCritical Apparatus Link μης οἰκεία ἡ θεωρία ἡ περὶ αὐτοῦ· πάντες γὰρ οἱ δοκοῦντες ἀξιο-
  • Critical Apparatus Link λόγως ἧφθαι τῆς τοιαύτης φιλοσοφίας πεποίηνται λόγον
  • Critical Apparatusπερὶ τοῦ ἀπείρου, καὶ πάντες ὡς ἀρχήν τινα τιθέασι τῶν ὄν-
  • Editor’s NoteCritical Apparatusτων, οἱ μέν, ὥσπερ οἱ Πυθαγόρειοι καὶ Πλάτων, καθ' αὑτό,
  • Critical Apparatus5οὐχ ὡς συμβεβηκός τινι ἑτέρῳ ἀλλ' οὐσίαν αὐτὸ ὂν τὸ ἄπει-
  • Editor’s Noteρον. πλὴν οἱ μὲν Πυθαγόρειοι ἐν τοῖς αἰσθητοῖς (οὐ γὰρ χω-
  • Editor’s NoteCritical Apparatusριστὸν ποιοῦσιν τὸν ἀριθμόν), καὶ εἶναι τὸ ἔξω τοῦ οὐρανοῦ ἄπει-
  • Critical Apparatus Link ρον, Πλάτων δὲ ἔξω μὲν οὐδὲν εἶναι σῶμα, οὐδὲ τὰς ἰδέας,
  • Critical Apparatus Link διὰ τὸ μηδὲ ποὺ εἶναι αὐτάς, τὸ μέντοι ἄπειρον καὶ ἐν τοῖς
  • Editor’s NoteCritical Apparatus Link 10αἰσθητοῖς καὶ ἐν ἐκείναις εἶναι· καὶ οἱ μὲν τὸ ἄπειρον εἶναι
  • Critical Apparatusτὸ ἄρτιον (τοῦτο γὰρ ἐναπολαμβανόμενον καὶ ὑπὸ τοῦ περιτ-
  • Critical Apparatusτοῦ περαινόμενον παρέχειν τοῖς οὖσι τὴν ἀπειρίαν· σημεῖον
  • Editor’s Noteδ' εἶναι τούτου τὸ συμβαῖνον ἐπὶ τῶν ἀριθμῶν· περιτιθεμένων
  • Critical Apparatusγὰρ τῶν γνωμόνων περὶ τὸ ἓν καὶ χωρὶς ὁτὲ μὲν ἄλλο ἀεὶ
  • Editor’s Note Link 15γίγνεσθαι τὸ εἶδος, ὁτὲ δὲ ἕν), Πλάτων δὲ δύο τὰ ἄπειρα,
  • Editor’s NoteCritical Apparatus16τὸ μέγα καὶ τὸ μικρόν.
  • 16                                                οἱ δὲ περὶ φύσεως πάντες [ἀεὶ]
  • Editor’s Noteὑποτιθέασιν ἑτέραν τινὰ φύσιν τῷ ἀπείρῳ τῶν λεγομένων
  • Editor’s NoteCritical Apparatusστοιχείων, οἷον ὕδωρ ἢ ἀέρα ἢ τὸ μεταξὺ τούτων. τῶν δὲ πε-
  • περασμένα ποιούντων στοιχεῖα οὐθεὶς ἄπειρα ποιεῖ· ὅσοι δ'
  • 20ἄπειρα ποιοῦσι τὰ στοιχεῖα, καθάπερ Ἀναξαγόρας καὶ Δη-
  • Editor’s Noteμόκριτος, ὁ μὲν ἐκ τῶν ὁμοιομερῶν, ὁ δ' ἐκ τῆς πανσπερ-
  • Editor’s NoteCritical Apparatusμίας τῶν σχημάτων, τῇ ἁφῇ συνεχὲς τὸ ἄπειρον εἶναι
  • Editor’s NoteCritical Apparatusφασίν· καὶ ὁ μὲν ὁτιοῦν τῶν μορίων εἶναι μίγμα ὁμοίως τῷ
  • Critical Apparatusπαντὶ διὰ τὸ ὁρᾶν ὁτιοῦν ἐξ ὁτουοῦν γιγνόμενον· ἐντεῦθεν γὰρ
  • Editor’s NoteCritical Apparatus25ἔοικε καὶ ὁμοῦ ποτὲ πάντα χρήματα φάναι εἶναι, οἷον ἥδε
  • pg 171Critical Apparatusἡ σὰρξ καὶ τόδε τὸ ὁστοῦν, καὶ οὕτως ὁτιοῦν· καὶ πάντα ἄρα·
  • Editor’s Noteκαὶ ἅμα τοίνυν· ἀρχὴ γὰρ οὐ μόνον ἐν ἑκάστῳ ἔστι τῆς δια-
  • Editor’s NoteCritical Apparatusκρίσεως, ἀλλὰ καὶ πάντων. ἐπεὶ γὰρ τὸ γιγνόμενον ἐκ τοῦ
  • τοιούτου γίγνεται σώματος, πάντων δ' ἔστι γένεσις πλὴν οὐχ
  • Critical Apparatus30ἅμα, καί τινα ἀρχὴν δεῖ εἶναι τῆς γενέσεως, αὕτη δ' ἐστὶν
  • Editor’s NoteCritical Apparatusμία, οἷον ἐκεῖνος καλεῖ νοῦν, ὁ δὲ νοῦς ἀπ' ἀρχῆς τινος ἐργάζε-
  • Critical Apparatusται νοήσας· ὥστε ἀνάγκη ὁμοῦ ποτε πάντα εἶναι καὶ ἄρξα-
  • Editor’s Noteσθαί ποτε κινούμενα. Δημόκριτος δ' οὐδὲν ἕτερον ἐξ ἑτέρου
  • Critical Apparatusγίγνεσθαι τῶν πρώτων φησίν· ἀλλ' ὅμως γε αὐτῷ τὸ κοινὸν
  • 203bCritical Apparatusσῶμα πάντων ἐστὶν ἀρχή, μεγέθει κατὰ μόρια καὶ σχή-
  • ματι διαφέρον.
  • Editor’s Noteὅτι μὲν οὖν προσήκουσα τοῖς φυσικοῖς ἡ θεωρία, δῆλον
  • ἐκ τούτων. εὐλόγως δὲ καὶ ἀρχὴν αὐτὸ τιθέασι πάντες· οὔτε
  • Critical Apparatus5γὰρ μάτην οἷόν τε αὐτὸ εἶναι, οὔτε ἄλλην ὑπάρχειν αὐτῷ
  • δύναμιν πλὴν ὡς ἀρχήν· ἅπαντα γὰρ ἢ ἀρχὴ ἢ ἐξ ἀρχῆς,
  • Editor’s NoteCritical Apparatusτοῦ δὲ ἀπείρου οὐκ ἔστιν ἀρχή· εἴη γὰρ ἂν αὐτοῦ πέρας. ἔτι δὲ καὶ
  • Critical Apparatusἀγένητον καὶ ἄφθαρτον ὡς ἀρχή τις οὖσα· τό τε γὰρ γενό-
  • Critical Apparatusμενον ἀνάγκη τέλος λαβεῖν, καὶ τελευτὴ πάσης ἔστιν φθο-
  • Critical Apparatus Link 10ρᾶς. διό, καθάπερ λέγομεν, οὐ ταύτης ἀρχή, ἀλλ' αὕτη τῶν
  • Editor’s Note Link ἄλλων εἶναι δοκεῖ καὶ περιέχειν ἅπαντα καὶ πάντα κυβερ-
  • νᾶν, ὥς φασιν ὅσοι μὴ ποιοῦσι παρὰ τὸ ἄπειρον ἄλλας αἰ-
  • Editor’s NoteCritical Apparatusτίας, οἷον νοῦν ἢ φιλίαν· καὶ τοῦτ' εἶναι τὸ θεῖον· ἀθάνατον
  • Critical Apparatusγὰρ καὶ ἀνώλεθρον, ὥσπερ φησὶν Ἀναξίμανδρος καὶ οἱ πλεῖ-
  • Editor’s NoteCritical Apparatus15στοι τῶν φυσιολόγων.
  • 15                                          τοῦ δ' εἶναί τι ἄπειρον ἡ πίστις ἐκ πέντε
  • Critical Apparatus Link μάλιστ' ἂν συμβαίνοι σκοποῦσιν, ἔκ τε τοῦ χρόνου (οὗτος γὰρ
  • Editor’s Note Link ἄπειρος) καὶ ἐκ τῆς ἐν τοῖς μεγέθεσι διαιρέσεως (χρῶνται
  • Editor’s NoteCritical Apparatusγὰρ καὶ οἱ μαθηματικοὶ τῷ ἀπείρῳ)· ἔτι τῷ οὕτως ἂν μό-
  • Critical Apparatusνως μὴ ὑπολείπειν γένεσιν καὶ φθοράν, εἰ ἄπειρον εἴη ὅθεν
  • pg 172Critical Apparatus20ἀφαιρεῖται τὸ γιγνόμενον· ἔτι τῷ τὸ πεπερασμένον ἀεὶ πρός
  • Critical Apparatusτι περαίνειν, ὥστε ἀνάγκη μηδὲν εἶναι πέρας, εἰ ἀεὶ πε-
  • Editor’s Note Link ραίνειν ἀνάγκη ἕτερον πρὸς ἕτερον. μάλιστα δὲ καὶ κυ-
  • Link ριώτατον, ὃ τὴν κοινὴν ποιεῖ ἀπορίαν πᾶσι· διὰ γὰρ τὸ ἐν
  • τῇ νοήσει μὴ ὑπολείπειν καὶ ὁ ἀριθμὸς δοκεῖ ἄπειρος εἶναι
  • Editor’s NoteCritical Apparatus Link 25καὶ τὰ μαθηματικὰ μεγέθη καὶ τὸ ἔξω τοῦ οὐρανοῦ. ἀπείρου
  • Editor’s Noteδ' ὄντος τοῦ ἔξω, καὶ σῶμα ἄπειρον εἶναι δοκεῖ καὶ κόσμοι·
  • τί γὰρ μᾶλλον τοῦ κενοῦ ἐνταῦθα ἢ ἐνταῦθα; ὥστ' εἴπερ μο-
  • Editor’s Noteναχοῦ, καὶ πανταχοῦ εἶναι τὸν ὄγκον. ἅμα δ' εἰ καὶ ἔστι κε-
  • Critical Apparatusνὸν καὶ τόπος ἄπειρος, καὶ σῶμα εἶναι ἀναγκαῖον·
  • Editor’s NoteCritical Apparatus30ἐνδέχεσθαι γὰρ ἢ εἶναι οὐδὲν διαφέρει ἐν τοῖς ἀϊδίοις.
  • 30                                                                                                  ἔχει
  • Critical Apparatusδ' ἀπορίαν ἡ περὶ τοῦ ἀπείρου θεωρία· καὶ γὰρ μὴ εἶναι τι-
  • θεμένοις πόλλ' ἀδύνατα συμβαίνει καὶ εἶναι. ἔτι δὲ ποτέ-
  • Critical Apparatusρως ἔστιν, πότερον ὡς οὐσία ἢ ὡς συμβεβηκὸς καθ' αὑτὸ φύσει
  • Editor’s NoteCritical Apparatusτινί; ἢ οὐδετέρως, ἀλλ' οὐδὲν ἧττον ἔστιν ἄπειρον ἢ ἄπειρα
  • Critical Apparatus204aEditor’s NoteCritical Apparatus Link τῷ πλήθει; μάλιστα δὲ φυσικοῦ ἐστιν σκέψασθαι εἰ ἔστι μέ-
  • Editor’s NoteCritical Apparatus Link γεθος αἰσθητὸν ἄπειρον. πρῶτον οὖν διοριστέον ποσαχῶς λέγε-
  • Editor’s Noteται τὸ ἄπειρον. ἕνα μὲν δὴ τρόπον τὸ ἀδύνατον διελθεῖν τῷ
  • Critical Apparatusμὴ πεφυκέναι διιέναι, ὥσπερ ἡ φωνὴ ἀόρατος· ἄλλως δὲ
  • Editor’s NoteCritical Apparatus Link 5τὸ διέξοδον ἔχον ἀτελεύτητον, ἢ ὃ μόγις, ἢ ὃ πεφυκὸς
  • Editor’s Note Link ἔχειν μὴ ἔχει διέξοδον ἢ πέρας. ἔτι ἄπειρον ἅπαν ἢ κατὰ
  • πρόσθεσιν ἢ κατὰ διαίρεσιν ἢ ἀμφοτέρως.
  • 5 Editor’s NoteΧωριστὸν μὲν οὖν εἶναι τὸ ἄπειρον τῶν αἰσθητῶν, αὐτό
  • τι ὂν ἄπειρον, οὐχ οἷόν τε. εἰ γὰρ μήτε μέγεθός ἐστιν μήτε
  • Critical Apparatus10πλῆθος, ἀλλ' οὐσία αὐτό ἐστι τὸ ἄπειρον καὶ μὴ συμβεβη-
  • Critical Apparatusκός, ἀδιαίρετον ἔσται (τὸ γὰρ διαιρετὸν ἢ μέγεθος ἔσται ἢ
  • Editor’s NoteCritical Apparatusπλῆθος)· εἰ δὲ τοιοῦτον, οὐκ ἄπειρον, εἰ μὴ ὡς ἡ φωνὴ
  • Critical Apparatus Link ἀόρατος. ἀλλ' οὐχ οὕτως οὔτε φασὶν εἶναι οἱ φάσκοντες εἶναι
  • pg 173Editor’s NoteCritical Apparatus Link τὸ ἄπειρον οὔτε ἡμεῖς ζητοῦμεν, ἀλλ' ὡς ἀδιεξίτητον. εἰ δὲ
  • Critical Apparatus15κατὰ συμβεβηκὸς ἔστιν τὸ ἄπειρον, οὐκ ἂν εἴη στοιχεῖον τῶν
  • Editor’s NoteCritical Apparatusὄντων, ᾗ ἄπειρον, ὥσπερ οὐδὲ τὸ ἀόρατον τῆς διαλέκτου, καί-
  • Editor’s NoteCritical Apparatus Link τοι ἡ φωνή ἐστιν ἀόρατος. ἔτι πῶς ἐνδέχεται εἶναί τι αὐτὸ
  • Critical Apparatusἄπειρον, εἴπερ μὴ καὶ ἀριθμὸν καὶ μέγεθος, ὧν ἐστι καθ'
  • Editor’s NoteCritical Apparatusαὑτὸ πάθος τι τὸ ἄπειρον; ἔτι γὰρ ἧττον ἀνάγκη ἢ τὸν
  • Editor’s NoteCritical Apparatus Link 20ἀριθμὸν ἢ τὸ μέγεθος. φανερὸν δὲ καὶ ὅτι οὐκ ἐνδέχεται εἶ-
  • Editor’s NoteCritical Apparatusναι τὸ ἄπειρον ὡς ἐνεργείᾳ ὂν καὶ ὡς οὐσίαν καὶ ἀρχήν·
  • ἔσται γὰρ ὁτιοῦν αὐτοῦ ἄπειρον τὸ λαμβανόμενον, εἰ μεριστόν
  • (τὸ γὰρ ἀπείρῳ εἶναι καὶ ἄπειρον τὸ αὐτό, εἴπερ οὐσία τὸ
  • ἄπειρον καὶ μὴ καθ' ὑποκειμένου), ὥστ' ἢ ἀδιαίρετον ἢ εἰς
  • Editor’s NoteCritical Apparatus25ἄπειρα διαιρετόν· πολλὰ δ' ἄπειρα εἶναι τὸ αὐτὸ ἀδύνα-
  • Critical Apparatusτον (ἀλλὰ μὴν ὥσπερ ἀέρος ἀὴρ μέρος, οὕτω καὶ ἄπειρον
  • Critical Apparatusἀπείρου, εἴ γε οὐσία ἐστὶ καὶ ἀρχή)· ἀμέριστον ἄρα καὶ ἀδιαί-
  • Editor’s Noteρετον. ἀλλ' ἀδύνατον τὸ ἐντελεχείᾳ ὂν ἄπειρον· ποσὸν γάρ
  • Link τι εἶναι ἀναγκαῖον. κατὰ συμβεβηκὸς ἄρα ὑπάρχει τὸ
  • Editor’s NoteCritical Apparatus30ἄπειρον. ἀλλ' εἰ οὕτως, εἴρηται ὅτι οὐκ ἐνδέχεται αὐτὸ λέ-
  • Editor’s NoteCritical Apparatusγειν ἀρχήν, ἀλλ' ᾧ συμβέβηκε, τὸν ἀέρα ἢ τὸ ἄρτιον.
  • Editor’s NoteCritical Apparatusὥστε ἀτόπως ἂν ἀποφαίνοιντο οἱ λέγοντες οὕτως ὥσπερ
  • οἱ Πυθαγόρειοί φασιν· ἅμα γὰρ οὐσίαν ποιοῦσι τὸ ἄπειρον
  • Editor’s NoteCritical Apparatus34καὶ μερίζουσιν.
  • 34                                  ἀλλ' ἴσως αὕτη μὲν [ἐστι] καθόλου ἡ ζήτη-
  • Critical Apparatus35σις, εἰ ἐνδέχεται ἄπειρον καὶ ἐν τοῖς μαθηματικοῖς
  • pg 174Critical Apparatus204bCritical Apparatus Link εἶναι καὶ ἐν τοῖς νοητοῖς καὶ μηδὲν ἔχουσι μέγεθος· ἡμεῖς
  • δ' ἐπισκοποῦμεν περὶ τῶν αἰσθητῶν καὶ περὶ ὧν ποιούμεθα
  • Critical Apparatusτὴν μέθοδον, ἆρ' ἔστιν ἐν αὐτοῖς ἢ οὐκ ἔστι σῶμα ἄπειρον
  • Editor’s NoteCritical Apparatus Link ἐπὶ τὴν αὔξησιν. λογικῶς μὲν οὖν σκοπουμένοις ἐκ τῶν τοι-
  • Critical Apparatus Link 5ῶνδε δόξειεν ἂν οὐκ εἶναι· εἰ γάρ ἐστι σώματος λόγος τὸ
  • Editor’s NoteCritical Apparatusἐπιπέδῳ ὡρισμένον, οὐκ ἂν εἴη σῶμα ἄπειρον, οὔτε νοητὸν οὔτε
  • Editor’s NoteCritical Apparatus Link αἰσθητόν (ἀλλὰ μὴν οὐδ' ἀριθμὸς οὕτως ὡς κεχωρισμένος καὶ
  • Critical Apparatusἄπειρος· ἀριθμητὸν γὰρ ἀριθμὸς ἢ τὸ ἔχον ἀριθμόν· εἰ
  • Critical Apparatusοὖν τὸ ἀριθμητὸν ἐνδέχεται ἀριθμῆσαι, καὶ διεξελθεῖν ἂν
  • Editor’s Note10εἴη δυνατὸν τὸ ἄπειρον)· φυσικῶς δὲ μᾶλλον θεωροῦσιν ἐκ
  • Critical Apparatusτῶνδε. οὔτε γὰρ σύνθετον οἷόν τε εἶναι οὔτε ἁπλοῦν. σύν-
  • Editor’s NoteCritical Apparatusθετον μὲν οὖν οὐκ ἔσται τὸ ἄπειρον σῶμα, εἰ πεπερασμένα
  • Editor’s NoteCritical Apparatusτῷ πλήθει τὰ στοιχεῖα. ἀνάγκη γὰρ πλείω εἶναι, καὶ ἰσά-
  • ζειν ἀεὶ τἀναντία, καὶ μὴ εἶναι ἓν αὐτῶν ἄπειρον (εἰ γὰρ
  • Critical Apparatus15ὁποσῳοῦν λείπεται ἡ ἐν ἑνὶ σώματι δύναμις θατέρου, οἷον εἰ
  • Critical Apparatusτὸ πῦρ πεπέρανται, ὁ δ' ἀὴρ ἄπειρος, ἔστιν δὲ τὸ ἴσον πῦρ
  • Editor’s Noteτοῦ ἴσου ἀέρος τῇ δυνάμει ὁποσαπλασιονοῦν, μόνον δὲ ἀριθμόν
  • Critical Apparatusτινα ἔχον, ὅμως φανερὸν ὅτι τὸ ἄπειρον ὑπερβαλεῖ καὶ
  • Editor’s Noteφθερεῖ τὸ πεπερασμένον)· ἕκαστον δ' ἄπειρον εἶναι ἀδύνατον·
  • Critical Apparatus20σῶμα μὲν γάρ ἐστιν τὸ πάντῃ ἔχον διάστασιν, ἄπειρον δὲ τὸ
  • Critical Apparatusἀπεράντως διεστηκός, ὥστε τὸ ἄπειρον σῶμα πανταχῇ ἔσται
  • Editor’s NoteCritical Apparatus22διεστηκὸς εἰς ἄπειρον.
  • 22                                                ἀλλὰ μὴν οὐδὲ ἓν καὶ ἁπλοῦν εἶναι
  • Editor’s NoteCritical Apparatusσῶμα ἄπειρον ἐνδέχεται, οὔτε ὡς λέγουσί τινες τὸ παρὰ
  • Editor’s Noteτὰ στοιχεῖα, ἐξ οὗ ταῦτα γεννῶσιν, οὔθ' ἁπλῶς. εἰσὶν γάρ τι-
  • Critical Apparatus25νες οἳ τοῦτο ποιοῦσι τὸ ἄπειρον, ἀλλ' οὐκ ἀέρα ἢ ὕδωρ, ὅπως
  • μὴ τἆλλα φθείρηται ὑπὸ τοῦ ἀπείρου αὐτῶν· ἔχουσι γὰρ
  • pg 175Editor’s NoteCritical Apparatusπρὸς ἄλληλα ἐναντίωσιν, οἷον ὁ μὲν ἀὴρ ψυχρός, τὸ δ'
  • Critical Apparatusὕδωρ ὑγρόν, τὸ δὲ πῦρ θερμόν· ὧν εἰ ἦν ἓν ἄπειρον, ἔφθαρτο
  • Editor’s NoteCritical Apparatusἂν ἤδη τἆλλα· νῦν δ' ἕτερον εἶναί φασιν ἐξ οὗ ταῦτα. ἀδύ-
  • Critical Apparatus30νατον δ' εἶναι τοιοῦτον, οὐχ ὅτι ἄπειρον (περὶ τούτου μὲν γὰρ
  • κοινόν τι λεκτέον ἐπὶ παντὸς ὁμοίως, καὶ ἀέρος καὶ ὕδατος
  • καὶ ὁτουοῦν), ἀλλ' ὅτι οὐκ ἔστιν τοιοῦτον σῶμα αἰσθητὸν παρὰ
  • Critical Apparatusτὰ καλούμενα στοιχεῖα· ἅπαντα γὰρ ἐξ οὗ ἐστι, καὶ διαλύε-
  • ται εἰς τοῦτο, ὥστε ἦν ἂν ἐνταῦθα παρὰ ἀέρα καὶ πῦρ καὶ
  • Editor’s NoteCritical Apparatus35γῆν καὶ ὕδωρ· φαίνεται δ' οὐδέν. οὐδὲ δὴ πῦρ οὐδ' ἄλλο τι
  • Critical Apparatus205a Link τῶν στοιχείων οὐδὲν ἄπειρον ἐνδέχεται εἶναι. ὅλως γὰρ καὶ
  • Editor’s NoteCritical Apparatusχωρὶς τοῦ ἄπειρον εἶναί τι αὐτῶν, ἀδύνατον τὸ πᾶν, κἂν ᾖ
  • Editor’s Note Link πεπερασμένον, ἢ εἶναι ἢ γίγνεσθαι ἕν τι αὐτῶν, ὥσπερ Ἡρά-
  • Critical Apparatusκλειτός φησιν ἅπαντα γίγνεσθαί ποτε πῦρ (ὁ δ' αὐτὸς λόγος
  • Editor’s Note5καὶ ἐπὶ τοῦ ἑνός, οἷον ποιοῦσι παρὰ τὰ στοιχεῖα οἱ φυσικοί)·
  • Critical Apparatusπάντα γὰρ μεταβάλλει ἐξ ἐναντίου εἰς ἐναντίον, οἷον ἐκ θερμοῦ
  • Editor’s NoteCritical Apparatus7εἰς ψυχρόν.
  • 7                            δεῖ δὲ κατὰ παντὸς ἐκ τῶνδε σκοπεῖν, εἰ ἐνδέχε-
  • Critical Apparatus Link ται ἢ οὐκ ἐνδέχεται εἶναι [σῶμα ἄπειρον αἰσθητόν]. ὅτι δὲ ὅλως
  • Critical Apparatusἀδύνατον εἶναι σῶμα ἄπειρον αἰσθητόν, ἐκ τῶνδε δῆλον.
  • 10πέφυκε γὰρ πᾶν τὸ αἰσθητόν που εἶναι, καὶ ἔστιν τόπος τις
  • Editor’s Noteἑκάστου, καὶ ὁ αὐτὸς τοῦ μορίου καὶ παντός, οἷον ὅλης τε
  • Editor’s NoteCritical Apparatusτῆς γῆς καὶ βώλου μιᾶς, καὶ πυρὸς καὶ σπινθῆρος. ὥστε
  • εἰ μὲν ὁμοειδές, ἀκίνητον ἔσται ἢ ἀεὶ οἰσθήσεται· καίτοι
  • Critical Apparatusἀδύνατον (τί γὰρ μᾶλλον κάτω ἢ ἄνω ἢ ὁπουοῦν; λέγω δὲ
  • 15οἷον, εἰ βῶλος εἴη, ποῦ αὕτη κινηθήσεται ἢ ποῦ μενεῖ; ὁ γὰρ
  • Critical Apparatusτόπος ἄπειρος τοῦ συγγενοῦς αὐτῇ σώματος. πότερον οὖν κα-
  • Critical Apparatusθέξει τὸν ὅλον τόπον; καὶ πῶς; τίς οὖν ἢ ποῦ ἡ μονὴ καὶ
  • pg 176Critical Apparatusἡ κίνησις αὐτῆς; ἢ πανταχοῦ μενεῖ; οὐ κινηθήσεται ἄρα. ἢ
  • Editor’s NoteCritical Apparatusπανταχοῦ κινηθήσεται; οὐκ ἄρα στήσεται)· εἰ δ' ἀνόμοιον τὸ
  • Critical Apparatus20πᾶν, ἀνόμοιοι καὶ οἱ τόποι· καὶ πρῶτον μὲν οὐχ ἓν τὸ
  • Critical Apparatusσῶμα τοῦ παντὸς ἀλλ' ἢ τῷ ἅπτεσθαι· ἔπειτα ἤτοι πεπε-
  • Editor’s NoteCritical Apparatusρασμένα ταῦτ' ἔσται ἢ ἄπειρα τῷ εἴδει. πεπερασμένα μὲν
  • Editor’s NoteCritical Apparatusοὖν οὐχ οἷόν τε (ἔσται γὰρ τὰ μὲν ἄπειρα τὰ δ' οὔ, εἰ τὸ πᾶν
  • ἄπειρον, οἷον τὸ πῦρ ἢ τὸ ὕδωρ· φθορὰ δὲ τὸ τοιοῦτον τοῖς
  • Editor’s NoteCritical Apparatus25, 29ἐναντίοις [καθάπερ εἴρηται πρότερον])· [καὶ … κάτω.] εἰ δ' ἄπειρα
  • Editor’s NoteCritical Apparatus30καὶ ἁπλᾶ, καὶ οἱ τόποι ἄπειροι, καὶ ἔσται ἄπειρα τὰ στοιχεῖα· εἰ δὲ
  • Editor’s NoteCritical Apparatusτοῦτ' ἀδύνατον καὶ πεπερασμένοι οἱ τόποι, καὶ τὸ ὅλον [πε-
  • περάνθαι ἀναγκαῖον]· ἀδύνατον γὰρ μὴ ἀπαρτίζειν τὸν τό-
  • Editor’s Noteπον καὶ τὸ σῶμα· οὔτε γὰρ ὁ τόπος ὁ πᾶς μείζων ἢ ὅσον
  • Critical Apparatusἐνδέχεται τὸ σῶμα εἶναι (ἅμα δ' οὐδ' ἄπειρον ἔσται τὸ
  • Critical Apparatus35σῶμα ἔτι), οὔτε τὸ σῶμα μεῖζον ἢ ὁ τόπος· ἢ γὰρ κενὸν
  • Editor’s NoteCritical Apparatus205b 1,ἔσται τι ἢ σῶμα οὐδαμοῦ πεφυκὸς εἶναι. ⟨καὶ διὰ τοῦτ' οὐθεὶς
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  • Editor’s NoteCritical Apparatusἢ ὕδωρ ἢ ἀέρα ἢ τὸ μέσον αὐτῶν, ὅτι τόπος ἑκατέρου δῆλος ἦν
  • διωρισμένος, ταῦτα δ' ἐπαμφοτερίζει τῷ ἄνω καὶ κάτω.⟩
  • Critical Apparatus205bEditor’s NoteἈναξαγόρας δ'
  • 2ἀτόπως λέγει περὶ τῆς τοῦ ἀπείρου μονῆς· στηρίζειν γὰρ
  • Editor’s NoteCritical Apparatusαὐτὸ αὑτό φησιν τὸ ἄπειρον· τοῦτο δέ, ὅτι ἐν αὑτῷ (ἄλλο
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  • αὑτῷ στηριζόμενον καὶ ἐν αὑτῷ ὂν ἀκίνητον εἶναι ἀνάγκη),
  • ἀλλὰ διὰ τί οὐ πέφυκε κινεῖσθαι, λεκτέον. οὐ γὰρ ἱκανὸν τὸ
  • pg 177Editor’s NoteCritical Apparatus Link οὕτως εἰπόντα ἀπηλλάχθαι· εἴη γὰρ ἂν καὶ ὅτι οὐκ ἔχει ἀλλαχῆ
  • Editor’s Note10κινεῖσθαι οὐ κινούμενον, ἀλλὰ πεφυκέναι οὐδὲν κωλύει· ἐπεὶ καὶ
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  • Critical Apparatusσου· ἀλλ' οὐχ ὅτι οὐκ ἔστιν ἄλλο οὗ ἐνεχθήσεται, μείνειεν
  • Critical Apparatusἄν [ἐπὶ τοῦ μέσου], ἀλλ' ὅτι πέφυκεν οὕτω. καίτοι ἐξείη ἂν
  • Editor’s Noteλέγειν ὅτι στηρίζει αὑτήν. εἰ οὖν μηδ' ἐπὶ τῆς γῆς τοῦτο αἴ-
  • 15τιον ἀπείρου οὔσης, ἀλλ' ὅτι βάρος ἔχει, τὸ δὲ βαρὺ μένει
  • Critical Apparatusἐπὶ τοῦ μέσου, ἡ δὲ γῆ ἐπὶ τοῦ μέσου, ὁμοίως ἂν καὶ τὸ ἄπει-
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  • Editor’s NoteCritical Apparatusρον καὶ στηρίζει αὐτὸ ἑαυτό. ἅμα δὲ δῆλον ὅτι κἂν ὁτιοῦν
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  • Critical Apparatus Link 20ρίζον, οὕτως κἂν ὁτιοῦν ληφθῇ μέρος ἐν ἑαυτῷ μενεῖ· τοῦ
  • γὰρ ὅλου καὶ τοῦ μέρους ὁμοειδεῖς οἱ τόποι, οἷον ὅλης γῆς
  • καὶ βώλου κάτω καὶ παντὸς πυρὸς καὶ σπινθῆρος ἄνω. ὥστε
  • Critical Apparatusεἰ τοῦ ἀπείρου τόπος τὸ ἐν αὑτῷ, καὶ τοῦ μέρους ὁ αὐτός.
  • Editor’s NoteCritical Apparatus24μενεῖ ἄρα ἐν ἑαυτῷ.
  • 24                                        ὅλως δὲ φανερὸν ὅτι ἀδύνατον ἄπειρον
  • 25ἅμα λέγειν σῶμα καὶ τόπον τινὰ εἶναι τοῖς σώμασιν,
  • εἰ πᾶν σῶμα αἰσθητὸν ἢ βάρος ἔχει ἢ κουφότητα, καὶ εἰ
  • μὲν βαρύ, ἐπὶ τὸ μέσον ἔχει τὴν φορὰν φύσει, εἰ δὲ κοῦ-
  • Critical Apparatusφον, ἄνω· ἀνάγκη γὰρ καὶ τὸ ἄπειρον, ἀδύνατον δὲ ἢ
  • ἅπαν ὁποτερονοῦν ἢ τὸ ἥμισυ ἑκάτερον πεπονθέναι· πῶς γὰρ
  • Critical Apparatus30διελεῖς; ἢ πῶς τοῦ ἀπείρου ἔσται τὸ μὲν ἄνω τὸ δὲ κάτω,
  • Editor’s NoteCritical Apparatus Link ἢ ἔσχατον καὶ μέσον; ἔτι πᾶν σῶμα αἰσθητὸν ἐν τόπῳ, τόπου
  • Critical Apparatus Link δὲ εἴδη καὶ διαφοραὶ τἄνω καὶ κάτω καὶ ἔμπροσθεν καὶ
  • Editor’s Noteὄπισθεν καὶ δεξιὸν καὶ ἀριστερόν· καὶ ταῦτα οὐ μόνον πρὸς
  • Critical Apparatus Link ἡμᾶς καὶ θέσει, ἀλλὰ καὶ ἐν αὐτῷ τῷ ὅλῳ διώρισται.
  • pg 178Critical Apparatus35ἀδύνατον δ' ἐν τῷ ἀπείρῳ εἶναι ταῦτα. ἁπλῶς δ' εἰ ἀδύνατον
  • 206aCritical Apparatusτόπον ἄπειρον εἶναι, ἐν τόπῳ δὲ πᾶν σῶμα, ἀδύνατον ἄπει-
  • Editor’s NoteCritical Apparatus Link ρον [τι] εἶναι σῶμα. ἀλλὰ μὴν τό γε ποὺ ἐν τόπῳ, καὶ τὸ
  • Editor’s NoteCritical Apparatusἐν τόπῳ πού. εἰ οὖν μηδὲ ποσὸν οἷόν τ' εἶναι τὸ ἄπειρον—πο-
  • Critical Apparatusσὸν γὰρ τὶ ἔσται, οἷον δίπηχυ ἢ τρίπηχυ· ταῦτα γὰρ ση-
  • Critical Apparatus Link 5μαίνει τὸ ποσόν—οὕτω καὶ τὸ ἐν τόπῳ ὅτι πού, τοῦτο δὲ ἢ
  • Critical Apparatusἄνω ἢ κάτω ἢ ἐν ἄλλῃ τινὶ διαστάσει τῶν ἕξ, τούτων δ'
  • Editor’s NoteCritical Apparatusἕκαστον πέρας τί ἐστιν. ὅτι μὲν οὖν ἐνεργείᾳ οὐκ ἔστι σῶμα
  • Critical Apparatusἄπειρον, φανερὸν ἐκ τούτων.
  • 6 Editor’s NoteCritical Apparatus Link Ὅτι δ' εἰ μὴ ἔστιν ἄπειρον ἁπλῶς, πολλὰ ἀδύνατα
  • Link 10συμβαίνει, δῆλον. τοῦ τε γὰρ χρόνου ἔσται τις ἀρχὴ καὶ τε-
  • Editor’s NoteCritical Apparatus Link λευτή, καὶ τὰ μεγέθη οὐ διαιρετὰ εἰς μεγέθη, καὶ ἀριθμὸς
  • Critical Apparatus Link οὐκ ἔσται ἄπειρος. ὅταν δὲ διωρισμένων οὕτως μηδετέρως φαί-
  • Editor’s Noteνηται ἐνδέχεσθαι, διαιτητοῦ δεῖ, καὶ δῆλον ὅτι πὼς μὲν ἔστιν
  • Editor’s NoteCritical Apparatus Link πὼς δ' οὔ. λέγεται δὴ τὸ εἶναι τὸ μὲν δυνάμει τὸ δὲ ἐντε-
  • Editor’s NoteCritical Apparatus Link 15λεχείᾳ, καὶ τὸ ἄπειρον ἔστι μὲν προσθέσει ἔστι δὲ καὶ διαι-
  • Link ρέσει. τὸ δὲ μέγεθος ὅτι μὲν κατ' ἐνέργειαν οὐκ ἔστιν ἄπειρον,
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  • Critical Apparatus Link ὃ ἔσται ἐνεργείᾳ· ἀλλ' ἐπεὶ πολλαχῶς τὸ εἶναι, ὥσπερ ἡ
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  • Critical Apparatusοὕτω καὶ τὸ ἄπειρον (καὶ γὰρ ἐπὶ τούτων ἔστι καὶ δυνάμει
  • Link καὶ ἐνεργείᾳ· Ὀλύμπια γὰρ ἔστι καὶ τῷ δύνασθαι τὸν ἀγῶνα
  • Editor’s NoteCritical Apparatus Link 25γίγνεσθαι καὶ τῷ γίγνεσθαι)· ἄλλως δ' ἔν τε τῷ χρόνῳ δῆλον
  • Critical Apparatus Link [τὸ ἄπειρον] καὶ ἐπὶ τῶν ἀνθρώπων, καὶ ἐπὶ τῆς διαιρέσεως
  • pg 179 Link τῶν μεγεθῶν. ὅλως μὲν γὰρ οὕτως ἔστιν τὸ ἄπειρον, τῷ ἀεὶ
  • Critical Apparatusἄλλο καὶ ἄλλο λαμβάνεσθαι, καὶ τὸ λαμβανόμενον μὲν
  • ἀεὶ εἶναι πεπερασμένον, ἀλλ' ἀεί γε ἕτερον καὶ ἕτερον·
  • Critical Apparatus29a                                        [ἔτι τὸ εἶναι πλεοναχῶς λέγεται, ὥστε
  • Critical Apparatus30τὸ ἄπειρον οὐ δεῖ λαμβάνειν ὡς τόδε τι, οἷον ἄνθρωπον ἢ
  • Critical Apparatusοἰκίαν, ἀλλ' ὡς ἡ ἡμέρα λέγεται καὶ ὁ ἀγών, οἷς τὸ εἶναι
  • Critical Apparatusοὐχ ὡς οὐσία τις γέγονεν, ἀλλ' ἀεὶ ἐν γενέσει ἢ φθορᾷ,
  • Critical Apparatus Link πεπερασμένον, ἀλλ' ἀεί γε ἕτερον καὶ ἕτερον·] ἀλλ' ἐν
  • 206bCritical Apparatus Link τοῖς μεγέθεσιν ὑπομένοντος τοῦ ληφθέντος [τοῦτο συμβαί-
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  • Editor’s NoteCritical Apparatus3μὴ ἐπιλείπειν.
  • 3                                τὸ δὲ κατὰ πρόσθεσιν τὸ αὐτό ἐστί πως καὶ
  • Critical Apparatus Link τὸ κατὰ διαίρεσιν· ἐν γὰρ τῷ πεπερασμένῳ κατὰ πρόσθε-
  • Editor’s Note Link 5σιν γίγνεται ἀντεστραμμένως· ᾗ γὰρ διαιρούμενον ὁρᾶται εἰς
  • Critical Apparatus Link ἄπειρον, ταύτῃ προστιθέμενον φανεῖται πρὸς τὸ ὡρισμένον.
  • Critical Apparatus Link ἐν γὰρ τῷ πεπερασμένῳ μεγέθει ἂν λαβών τις ὡρισμένον
  • Editor’s NoteCritical Apparatusπροσλαμβάνῃ τῷ αὐτῷ λόγῷ, μὴ τὸ αὐτό τι τοῦ ὅλου μέγεθος
  • Critical Apparatusπεριλαμβάνων, οὐ διέξεισι τὸ πεπερασμένον· ἐὰν δ' οὕ-
  • Link 10τως αὔξῃ τὸν λόγον ὥστε ἀεί τι τὸ αὐτὸ περιλαμβάνειν μέ-
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  • Editor’s NoteCritical Apparatus Link ὁτῳοῦν ὡρισμένῳ. ἄλλως μὲν οὖν οὐκ ἔστιν, οὕτως δ' ἔστι τὸ
  • Editor’s NoteCritical Apparatus Link ἄπειρον, δυνάμει τε καὶ ἐπὶ καθαιρέσει (καὶ ἐντελεχείᾳ δὲ
  • Editor’s NoteCritical Apparatusἔστιν, ὡς τὴν ἡμέραν εἶναι λέγομεν καὶ τὸν ἀγῶνα)· καὶ δυ-
  • Critical Apparatus15νάμει οὕτως ὡς ἡ ὕλη, καὶ οὐ καθ' αὑτό, ὡς τὸ πεπερασμέ-
  • Editor’s Note Link νον. καὶ κατὰ πρόσθεσιν δὴ οὕτως ἄπειρον δυνάμει ἔστιν, ὃ
  • pg 180Critical Apparatus Link ταὐτὸ λέγομεν τρόπον τινὰ εἶναι τῷ κατὰ διαίρεσιν· ἀεὶ μὲν
  • Critical Apparatusγάρ τι ἔξω ἔσται λαμβάνειν, οὐ μέντοι ὑπερβαλεῖ
  • Critical Apparatus Link παντὸς μεγέθους, ὥσπερ ἐπὶ τὴν διαίρεσιν ὑπερ-
  • Critical Apparatus20βάλλει παντὸς ὡρισμένου καὶ ἀεὶ ἔσται ἔλαττον. ὥστε δὲ παν-
  • Critical Apparatusτὸς ὑπερβάλλειν κατὰ τὴν πρόσθεσιν, οὐδὲ δυνάμει οἷόν τε
  • Critical Apparatusεἶναι, εἴπερ μὴ ἔστι κατὰ συμβεβηκὸς ἐντελεχείᾳ ἄπειρον,
  • Editor’s NoteCritical Apparatusὥσπερ φασὶν οἱ φυσιολόγοι τὸ ἔξω σῶμα τοῦ κόσμου, οὗ ἡ
  • Editor’s NoteCritical Apparatus Link οὐσία ἢ ἀὴρ ἢ ἄλλο τι τοιοῦτον, ἄπειρον εἶναι. ἀλλ' εἰ μὴ
  • Critical Apparatus25οἷόν τε εἶναι ἄπειρον ἐντελεχείᾳ σῶμα αἰσθητὸν οὕτω, φανε-
  • ρὸν ὅτι οὐδὲ δυνάμει ἂν εἴη κατὰ πρόσθεσιν, ἀλλ' ἢ ὥσπερ
  • Editor’s Note Link εἴρηται ἀντεστραμμένως τῇ διαιρέσει, ἐπεὶ καὶ Πλάτων διὰ
  • Editor’s NoteCritical Apparatusτοῦτο δύο τὰ ἄπειρα ἐποίησεν, ὅτι καὶ ἐπὶ τὴν αὔξην δοκεῖ
  • Critical Apparatusὑπερβάλλειν καὶ εἰς ἄπειρον ἰέναι καὶ ἐπὶ τὴν καθαίρεσιν.
  • 30ποιήσας μέντοι δύο οὐ χρῆται· οὔτε γὰρ ἐν τοῖς ἀριθμοῖς τὸ
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  • Editor’s NoteCritical Apparatus33μόν).
  • 33              συμβαίνει δὲ τοὖναντίον εἶναι ἄπειρον ἢ ὡς λέγουσιν.
  • 207aEditor’s Noteοὐ γὰρ οὗ μηδὲν ἔξω, ἀλλ' οὗ ἀεί τι ἔξω ἐστί, τοῦτο ἄπειρόν
  • ἐστιν. σημεῖον δέ· καὶ γὰρ τοὺς δακτυλίους ἀπείρους λέγουσι
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  • 5γὰρ τοῦτό τε ὑπάρχειν καὶ μηδέ ποτε τὸ αὐτὸ λαμβά-
  • νεσθαι· ἐν δὲ τῷ κύκλῳ οὐ γίγνεται οὕτως, ἀλλ' αἰεὶ τὸ
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  • Critical Apparatusλαμβάνουσιν αἰεί τι λαμβάνειν ἔστιν ἔξω. οὗ δὲ μηδὲν ἔξω,
  • τοῦτ' ἔστι τέλειον καὶ ὅλον· οὕτω γὰρ ὁριζόμεθα τὸ ὅλον, οὗ
  • Editor’s NoteCritical Apparatus10μηδὲν ἄπεστιν, οἷον ἄνθρωπον ὅλον ἢ κιβώτιον. ὥσπερ δὲ
  • pg 181τὸ καθ' ἕκαστον, οὕτω καὶ τὸ κυρίως, οἷον τὸ ὅλον οὗ μηδέν
  • Critical Apparatusἐστιν ἔξω· οὗ δ' ἔστιν ἀπουσία ἔξω, οὐ πᾶν, ὅ τι ἂν ἀπῇ.
  • Critical Apparatus Link ὅλον δὲ καὶ τέλειον ἢ τὸ αὐτὸ πάμπαν ἢ σύνεγγυς τὴν
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  • Editor’s NoteCritical Apparatusθαι, "μεσσόθεν ἰσοπαλές". οὐ γὰρ λίνον λίνῳ συνάπτειν ἐστὶν
  • Critical Apparatusτῷ ἅπαντι καὶ ὅλῳ τὸ ἄπειρον, ἐπεὶ ἐντεῦθέν γε λαμβά-
  • Editor’s NoteCritical Apparatusνουσι τὴν σεμνότητα κατὰ τοῦ ἀπείρου, τὸ πάντα περιέχειν
  • Critical Apparatus20καὶ τὸ πᾶν ἐν ἑαυτῷ ἔχειν, διὰ τὸ ἔχειν τινὰ ὁμοιότητα
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  • Editor’s NoteCritical Apparatus Link ὕλη καὶ τὸ δυνάμει ὅλον, ἔντελεχείᾳ δ' οὔ, διαιρετὸν δ' ἐπί
  • Critical Apparatus Link τε τὴν καθαίρεσιν καὶ τὴν ἀντεστραμμένην πρόσθεσιν, ὅλον
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  • Editor’s NoteCritical Apparatus Link 25οὐ περιέχει ἀλλὰ περιέχεται, ᾗ ἄπειρον. διὸ καὶ ἄγνωστον
  • Critical Apparatusᾗ ἄπειρον· εἶδος γὰρ οὐκ ἔχει ἡ ὕλη. ὥστε φανερὸν ὅτι
  • Editor’s NoteCritical Apparatusμᾶλλον ἐν μορίου λόγῳ τὸ ἄπειρον ἢ ἐν ὅλου· μόριον γὰρ
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  • Editor’s NoteCritical Apparatusἐπεὶ εἴ γε περιέχει ἐν τοῖς αἰσθητοῖς, καὶ ἐν τοῖς νοητοῖς τὸ
  • 30μέγα καὶ τὸ μικρὸν ἔδει περιέχειν τὰ νοητά. ἄτοπον δὲ
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  • ὁρίζειν.
  • 7 Editor’s NoteCritical Apparatus Link Κατὰ λόγον δὲ συμβαίνει καὶ τὸ κατὰ πρόσθεσιν μὲν
  • Critical Apparatusμὴ εἶναι δοκεῖν ἄπειρον οὕτως ὥστε παντὸς ὑπερβάλλειν με-
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  • Critical Apparatus207bEditor’s NoteCritical Apparatusἐντὸς καὶ τὸ ἄπειρον, περιέχει δὲ τὸ εἶδος)· εὐλόγως δὲ καὶ
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  • pg 182Critical Apparatusτὸ πλεῖον ἀεὶ παντὸς ὑπερβάλλειν πλήθους, ἐπὶ δὲ τῶν
  • Critical Apparatusμεγεθῶν τοὖναντίον ἐπὶ μὲν τὸ ἔλαττον παντὸς ὑπερβάλλειν
  • 5μεγέθους ἐπὶ δὲ τὸ μεῖζον μὴ εἶναι μέγεθος ἄπειρον. αἴτιον
  • Critical Apparatusδ' ὅτι τὸ ἕν ἐστιν ἀδιαίρετον, ὅ τι περ ἂν ἓν ᾖ (οἷον ἄνθρωπος
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  • Critical Apparatus10ἀριθμῶν ἕκαστος), ἐπὶ δὲ τὸ πλεῖον ἀεὶ ἔστι νοῆσαι· ἄπειροι
  • Link γὰρ αἱ διχοτομίαι τοῦ μεγέθους. ὥστε δυνάμει μὲν ἔστιν,
  • Link ἐνεργείᾳ δ' οὔ· ἀλλ' ἀεὶ ὑπερβάλλει τὸ λαμβανόμενον παν-
  • Critical Apparatusτὸς ὡρισμένου πλήθους. ἀλλ' οὐ χωριστὸς ὁ ἀριθμὸς οὗτος
  • Editor’s NoteCritical Apparatus[τῆς διχοτομίας], οὐδὲ μένει ἡ ἀπειρία ἀλλὰ γίγνεται, ὥσπερ
  • Editor’s Note Link 15καὶ ὁ χρόνος καὶ ὁ ἀριθμὸς τοῦ χρόνου. ἐπὶ δὲ τῶν μεγε-
  • θῶν τοὖναντίον ἐστί· διαιρεῖται μὲν γὰρ εἰς ἄπειρα τὸ συνε-
  • χές, ἐπὶ δὲ τὸ μεῖζον οὐκ ἔστιν ἄπειρον. ὅσον γὰρ ἐνδέχε-
  • Critical Apparatusται δυνάμει εἶναι, καὶ ἐνεργείᾳ ἐνδέχεται τοσοῦτον εἶναι.
  • Editor’s Noteὥστε ἐπεὶ ἄπειρον οὐδέν ἐστι μέγεθος αἰσθητόν, οὐκ ἐνδέχεται
  • Critical Apparatus20παντὸς ὑπερβολὴν εἶναι ὡρισμένου μεγέθους· εἴη γὰρ ἄν τι
  • Editor’s NoteCritical Apparatusτοῦ οὐρανοῦ μεῖζον. τὸ δ' ἄπειρον οὐ ταὐτὸν ἐν μεγέθει καὶ
  • κινήσει καὶ χρόνῳ, ὡς μία τις φύσις, ἀλλὰ τὸ ὕστερον
  • Critical Apparatusλέγεται κατὰ τὸ πρότερον, οἷον κίνησις μὲν ὅτι τὸ μέγεθος
  • ἐφ' οὗ κινεῖται ἢ ἀλλοιοῦται ἢ αὐξάνεται, ὁ χρόνος δὲ διὰ
  • Editor’s Note25τὴν κίνησιν. νῦν μὲν οὖν χρώμεθα τούτοις, ὕστερον δὲ
  • Critical Apparatusἐροῦμεν καὶ τί ἐστιν ἕκαστον, καὶ διότι πᾶν μέγεθος
  • Editor’s Note27εἰς μεγέθη διαιρετόν.
  • 27                                                  οὐκ ἀφαιρεῖται δ' ὁ λόγος οὐδὲ τοὺς
  • Editor’s NoteCritical Apparatus Link μαθηματικοὺς τὴν θεωρίαν, ἀναιρῶν οὕτως εἶναι ἄπειρον
  • pg 183Critical Apparatus Link ὥστε ἐνεργείᾳ εἶναι ἐπὶ τὴν αὔξησιν ἀδιεξίτητον· οὐδὲ γὰρ
  • Critical Apparatus30νῦν δέονται τοῦ ἀπείρου (οὐ γὰρ χρῶνται), ἀλλὰ μόνον εἶναι ὅσην
  • Editor’s NoteCritical Apparatusἂν βούλωνται πεπερασμένην· τῷ δὲ μεγίστῳ μεγέθει
  • τὸν αὐτὸν ἔστι τετμῆσθαι λόγον ὁπηλικονοῦν μέγεθος ἕτερον.
  • Editor’s NoteCritical Apparatusὥστε πρὸς μὲν τὸ δεῖξαι ἐκείνοις οὐδὲν διοίσει τὸ [δ'] εἶναι ἐν
  • Editor’s NoteCritical Apparatus34τοῖς οὖσιν μεγέθεσιν.
  • 34                                            ἐπεὶ δὲ τὰ αἴτια διῄρηται τετρα-
  • Editor’s NoteCritical Apparatus35χῶς, φανερὸν ὅτι ὡς ὕλη τὸ ἄπειρον αἴτιόν ἐστι, καὶ ὅτι
  • 208aEditor’s NoteCritical Apparatusτὸ μὲν εἶναι αὐτῷ στέρησις, τὸ δὲ καθ' αὑτὸ ὑποκείμενον
  • Editor’s Noteτὸ συνεχὲς καὶ αἰσθητόν. φαίνονται δὲ πάντες καὶ οἱ ἄλ-
  • Editor’s NoteCritical Apparatusλοι ὡς ὕλῃ χρώμενοι τῷ ἀπείρῳ· διὸ καὶ ἄτοπον τὸ περι-
  • Critical Apparatusέχον ποιεῖν αὐτὸ ἀλλὰ μὴ περιεχόμενον.
  • 8 Editor’s NoteCritical Apparatus Link 5Λοιπὸν δ' ἐπελθεῖν καθ' οὓς λόγους τὸ ἄπειρον εἶναι δο-
  • Editor’s NoteCritical Apparatusκεῖ οὐ μόνον δυνάμει ἀλλ' ὡς ἀφωρισμένον· τὰ μὲν γάρ
  • Critical Apparatusἐστιν αὐτῶν οὐκ ἀναγκαῖα, τὰ δ' ἔχει τινὰς ἑτέρας ἀληθεῖς
  • Critical Apparatusἀπαντήσεις. οὔτε γὰρ ἵνα ἡ γένεσις μὴ ἐπιλείπῃ, ἀναγκαῖον
  • Editor’s Noteἐνεργείᾳ ἄπειρον εἶναι σῶμα αἰσθητόν· ἐνδέχεται γὰρ τὴν
  • Critical Apparatus10θατέρου φθορὰν θατέρου εἶναι γένεσιν, πεπερασμένου ὄντος τοῦ
  • παντός. ἔτι τὸ ἅπτεσθαι καὶ τὸ πεπεράνθαι ἕτερον. τὸ μὲν
  • Editor’s NoteCritical Apparatusγὰρ πρός τι καὶ τινός (ἅπτεται γὰρ πᾶν τινός), καὶ τῶν πε-
  • περασμένων τινὶ συμβέβηκεν, τὸ δὲ πεπερασμένον οὐ πρός τι·
  • Editor’s NoteCritical Apparatus Link οὐδ' ἅψασθαι τῷ τυχόντι τοῦ τυχόντος ἔστιν. τὸ δὲ τῇ νοήσει
  • Editor’s Note Link 15πιστεύειν ἄτοπον· οὐ γὰρ ἐπὶ τοῦ πράγματος ἡ ὑπεροχὴ καὶ ἡ
  • Critical Apparatusἔλλειψις, ἀλλ' ἐπὶ τῆς νοήσεως. ἕκαστον γὰρ ἡμῶν νοήσειέν
  • Critical Apparatusἄν τις πολλαπλάσιον ἑαυτοῦ αὔξων εἰς ἄπειρον· ἀλλ' οὐ
  • Editor’s NoteCritical Apparatusδιὰ τοῦτο ἔξω [τοῦ ἄστεός] τίς ἐστιν [ἢ] τοῦ τηλικούτου μεγέθους
  • pg 184ὃ ἔχομεν, ὅτι νοεῖ τις, ἀλλ' ὅτι ἔστι· τοῦτο δὲ συμβέβηκεν.
  • Editor’s Note Link 20ὁ δὲ χρόνος καὶ ἡ κίνησις ἄπειρά ἐστι καὶ ἡ νόησις οὐχ
  • Editor’s NoteCritical Apparatusὑπομένοντος τοῦ λαμβανομένου. μέγεθος δὲ οὔτε τῇ καθαιρέ-
  • Critical Apparatusσει οὔτε τῇ νοητικῇ αὐξήσει ἔστιν ἄπειρον. ἀλλὰ περὶ μὲν
  • Critical Apparatusτοῦ ἀπείρου, πῶς ἔστι καὶ πῶς οὐκ ἔστι καὶ τί ἐστιν, εἴρηται.

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Notes

Critical Apparatus
Tit. φυσικῆς ἀκροάσεως γ̄ περὶ ἀπείρου‎ E: φυσικῶν γ‎ I
Critical Apparatus
12 καὶ‎ EIJPST: καὶ στάσεως καὶ‎ FV
Editor’s Note
200b 12. Two reasons why the topics of books iii and iv must be studied by the physicist. (1) He must study change because nature is just a principle of change. He must study the infinite because change is continuous and it is in the continuous that infinity is most evident. He must study place, the void, and time because change is thought to involve these.
Critical Apparatus
13 ἐστι‎ om. E1V
δεῖ‎ … 14 κίνησις‎ om. EV
Critical Apparatus
14–16 ἀναγκαῖον … ἐφεξῆς] ἀναγκαῖον πρῶτον μὲν εἰπεῖν τί ἐστι κίνησις, ἔπειτα τοῦτο διορισαμένους περὶ τῶν ἐφεξῆς τὸν αὐτὸν ἐπελθεῖν τρόπον‎ V et in litura E
Editor’s Note
Books iii and iv form a continuous work in which Aristotle treats of the most general notions involved (or, in the case of the void, wrongly thought to be involved) in the notion of nature. These are motion (iii. 1–3), the infinite (iii. 4–8), place (iv. 1–5), the void (iv. 6–9), time (iv. 10–14). The reasons for the discussion of these subjects are given in iii. 1. 200b 12–25.
Editor’s Note
200b 16–17. δοκεῖ … συνεχῶν‎. This prima facie view is confirmed by argument in iv. 219 a10–13.
Editor’s Note
17–18. τὸ δʼ ἄπειρον … συνεχεῖ‎. Simplicius explains this as meaning that, though infinity belongs to both kinds of ποσόν‎, to the διωρισμένον‎ (discrete quantity, i.e. number) as well as to the συνεχές‎, it belongs primarily to the latter; it is the infinite divisibility of the continuous that gives rise to the infinity of the number series.
Critical Apparatus
18 συμβαίνει] ἀνάγκη‎ P: συμβαίνει ἀνάγκη‎ E
Editor’s Note
18–20. διὸ … ὄν‎. No definition of the continuous by any thinker earlier than Aristotle seems to be recorded. He himself frequently describes the continuous as infinitely divisible (Phys. 185b 10, 231a 24, 232a 24, 239a 22), but it is apparently only in De Caelo 268a 6 that this is put forward as its definition. He has other definitions of it as well—τὸ συνεχὲς ὧν τὰ ἔσχατα ἕν‎ (Phys. 228a 29, cf. 227a 11 = Met. 1069a 6, Cat. 5a 1), συνεχὲς οὗ κίνησις μία καθʼ αὑτό‎ (Met. 1016a 5), τὸ συνεχὲς ἕν τι ἐκ πλειόνων ἐνυπαρχόντων μάλιστα μὲν δυνάμει, εἰ δὲ μή, ἐνεργείᾳ‎ Met. 1023b 32).
Critical Apparatus
19 προσχρῆσθαι‎ IJ
ἀπείρου, ὡς τὸ εἰς‎ om. E
Editor’s Note
20–21. ἄνευ τόπου … κίνησιν ἀδύνατον εἶναι‎. This is obvious in the case of φορά‎, but according to Aristotle it is also true of the other kinds of change. Generation (Met. 1042b 1–5) and alteration (Phys. 260b 4) presuppose locomotion, and growth presupposes alteration (Phys. 260a 29).
Critical Apparatus
21 κίνησιν ἀδύνατον‎ FPS: ἀδύνατον κίνησιν‎ Λ‎
Editor’s Note
21. καὶ κενοῦ‎. It is not Aristotle's own opinion that motion implies a void; he does not believe in the existence of a void. The sentence is under the governance of φασί‎ 'understood from' δοκεῖ‎ (b 16). The implication of a void is one of the ἔνδοξα‎, since it was insisted on by the atomists.
Critical Apparatus
22 τε‎ E2Λ‎PS: om. E1
Editor’s Note
22. (2) Because of their universality these things must be studied before we come to more particular subjects of inquiry.
Critical Apparatus
23 ταῦτα‎ S: πᾶσι‎ E: ταῦτα πᾶσι‎ Λ‎P
Critical Apparatus
25 καὶ πρῶτον] πρῶτον δὲ‎ Λ‎
εἴπομεν‎ FI
Editor’s Note
25. We begin with change, and note that (a) the things in any category are divided into those that exist only actually and those that exist both potentially and actually;
Critical Apparatus
26 τι τὸ μὲν‎ Λ‎S et fecit E: τὸ μὲν‎ MP
μόνον‎ om. γρ‎. S
τὸ‎ Π‎M(Ab)APST Porphyrius: τὸ δὲ δυνάμει, τὸ‎ M(EJ), Spengel
Editor’s Note
26. ἔστι … καὶ ἐντελεχείᾳ‎. The text as printed is given in all the MSS. of the Physics and the best MS. of the Metaphysics (1065b 5) and was read by Alexander, Themistius, Porphyry (who, however, punctuated it, not to its improvement, with a comma before and not after καὶ ἐντελεχείᾳ‎), Philoponus, and Simplicius. Palaeographically, it is easy to explain the absence of the first τὸ δὲ δυνάμει‎ as due to haplography, or its presence as due to dittography or to deliberate correction by a copyist. Some support might be found for Spengel's reading by a comparison with De Int. 23a 23–6 καὶ τὰ μὲν ἄνευ‎ δυνάμεως ἐνέργειαί εἰσιν, οἷον αἱ πρῶται οὐσίαι, τὰ δὲ μετὰ δυνάμεως, ἃ τῇ μὲν φύσει πρότερα τῷ δὲ χρόνῳ ὕστερα, τὰ δὲ οὐδὲποτε ἐνέργειαί εἰσιν ἀλλὰ δυνάμεις μόνον‎. But the doctrine that there are δυνάμεις‎ that from the nature of the case cannot be realized is rather an excrescence on Aristotle's usual doctrine of δύναμις‎—a device which he adopts in order to deal with the difficult problems of the infinite and the void (Met. 1048b 9–17). The normal doctrine is that it is the nature of that which is potentially, to be realized. What is relevant here, where Aristotle is leading up to the definition of motion, is to oppose the changeable to the unchangeable, and this the reading of our text does. τὸ ἐντελεχείᾳ μόνον‎ is that which is always actually what it ever is, in respect of substance, size, quality, and the other categories (b 27–8); τὸ δυνάμει καὶ ἐντελεχείᾳ‎ is that which passes from a state of potentiality to one of actuality in any of these respects.
Critical Apparatus
27 τὸ δὲ‎ alt. om. F
Editor’s Note
27–8. καὶ … ὁμοίως‎. The antithesis of potentiality to actuality, and the possibility of a change from one to the other, exist in every category (e.g. a man who is actually sitting is potentially standing, so that there may be change in the category of κεῖσθαι‎). But in v. 1, 2 Aristotle gives reasons for holding that essentially there is μεταβολή‎ only in respect of the four categories substance, quality, quantity, place, and κίνησις‎ only in respect of the last three.
τῶν ἄλλων‎ is a loose partitive genitive, 'and so too in the case of things in the other categories'.
Critical Apparatus
28 τῶν‎ pr. E1J1S (cf. M): ἐπὶ τῶν‎ E2FIJ2
Editor’s Note
28. (b) of relative terms, some are related by way of excess and defect, others as respectively active and passive;
Editor’s Note
28–32. τοῦ δὲ πρός τι … κινητικοῦ‎. In the Categories τὸ πρός τι‎ is not divided into kinds. In Met. Δ‎. 15 it is divided into (1) τὰ ὡς … ὑπερέχον πρὸς ὑπερεχόμενον‎, (2) τὰ ὡς … τὸ ποιητικὸν πρὸς τὸ παθητικόν‎, (3) τὰ ὡς τὸ μετρητὸν πρὸς τὸ μέτρον καὶ ἐπιστητὸν πρὸς ἐπιστήμην καὶ αἰσθητὸν πρὸς αἴσθησιν‎. In Met. I. 1056b 35 it is divided into τὰ ὡς ἐναντία‎ and τὰ ὡς ἐπιστήμη πρὸς ἐπιστητόν‎. Met. Δ‎ thus contains the fullest classification; Phys. iii and Met. I both omit one of the three kinds. Top. 125a 33–b 4 classifies τὰ πρός τι‎ from a different point of view into (1) those that must be in or about their correlatives (e.g. διάθεσις‎, &c.), (2) those that may be in their correlatives (e.g. knowledge of a soul, which may be in the soul that is known), (3) those that cannot be in their correlatives (e.g. contraries, which cannot be in their contraries, and knowledge of anything but a soul).
The connexion of this section with what precedes is not very close, but seems to be as follows. Aristotle has just pointed out that the distinction of δύναμις‎ and ἐντελέχεια‎, and therefore the possibility of a transition from one to the other, which is κίνησις‎, exists in all the categories. The mention of the categories now leads him to point out that (while κίνησις‎ can occur in various categories) τὸ κινητικόν‎ and τὸ κινητόν‎ as such form one main part of the category of relation (or relata).
Critical Apparatus
b 29 λέγεται … ἔλλειψιν] καὶ ἔλλειψιν λέγεται‎ Λ‎: λέγεται καὶ ἔλλειψιν‎ P
Editor’s Note
29–31. τὸ δὲ … κινητόν. ποιητικὸν καὶ παθητικόν‎ is narrower than κινητικὸν καὶ κινητόν‎ because it refers only to change of quality (ἀλλοίωσις‎).
Critical Apparatus
30 τὸ‎ om. E: τό τε‎ F
κινητικόν τε καὶ κινητόν‎ Λ‎V: κινητόν τε καὶ κινητικόν‎ E
Critical Apparatus
31 τὸ μὲν γὰρ‎ F
Critical Apparatus
32 δὲ‎ EFJ Ammonius Stephanus: δέ τις‎ IS
Editor’s Note
32. (c) there is no such thing as change in the abstract; change is always in respect either of substance or of quantity or of quality or of place;
Editor’s Note
32. τὰ πράγματα‎ here means not the things that change but the various respects in which things may change (τὰ ἐν οἷς ἡ κίνησις‎). Aristotle's object is to state that, since there is no such thing as 'being' in the abstract, there is no such thing as change in the abstract; change is change either of substantial nature or of quantity or of quality or of place. Simplicius thinks that this is maintained in opposition to Plato (though he labours to show that the opposition is more apparent than real). But the passages he refers to—Parm. 138 b–139 b, 162 e–163 b, Soph. 248 e–249 b—do not show Plato to have differed from Aristotle on this point.
Critical Apparatus
33 ἀεὶ τὸ μεταβὰλλον‎ Λ‎Sc: τὸ μεταβάλλον ἀεὶ‎ E: τὸ μεταβάλλον‎ Sp
Critical Apparatus
34 ποσὸν ἢ κατὰ‎ S: ποσὸν ἢ‎ E: τὸ ποσὸν ἢ κατὰ τὸ‎ Λ‎
Critical Apparatus
35–201a 1 ἔστι … οὔτε‎ alt. Λ‎PS: om. E
Critical Apparatus
35 ἔφαμεν‎ I
Critical Apparatus
201a 27–202a 3 = 1065b 22–1066a 26
Critical Apparatus
201a 2 οὔτε‎ Λ‎
Critical Apparatus
3 εἰρημένα] εἰρημένα ὃ οὔτε τόδε οὔτε ποσὸν οὔτε ποιὸν ἔστι λαβεῖν ὡς φαμέν‎ (cf. 200b 35–201a 1) E
Editor’s Note
201a 3. (d) within each of these categories contraries are found—in substance form and privation, in quality (e.g.) white and black, in quantity complete and incomplete, in place (e.g.) above and below. Any such pair of contraries may form the termini of change.
Editor’s Note
201a 3–4. ἕκαστον … πᾶσιν‎, 'the character of each category is present in the various things that fall within the category, in either of two modes'. The expression is rather loose, but the meaning is that in respect of substance a thing may either have a certain substantial form (e.g. that of fire) or have the privation of this form; that in respect of quality it may have either whiteness or the absence of whiteness which is blackness; and so with the other categories.
Critical Apparatus
6 μὲν‎ FIM: μὲν γὰρ‎ EJ
Critical Apparatus
8 ὥστε‎ Π‎S: ὥστε καὶ‎ A
Editor’s Note
8–9. ὥστε … ὄντος‎. This might, as Alexander suggested, have followed directly after the last sentence but one. But the intervening sentence has supplied something towards the conclusion, since it has pointed out explicitly the existence of the termini between which change may take place in each of the four categories concerned.
The statement is not strictly true, since according to Aristotle there is μεταβολή‎ in respect of only four categories (substance, quality, quantity, place), and κίνησις‎ in respect of only three (quality, quantity, place): cf. 225b 7.
Editor’s Note
9. Change may now be defined as the actualization of the potential as such; alteration is the actualization of that which can be altered, growth and diminution of that which can grow or diminish, generation and destruction of that which can be generated or destroyed, locomotion of that which can be moved in space.
Editor’s Note
9–b 15. διῃρημένου … κινήσεων‎. An aggregate of bricks, stones, &c., may be regarded (1) as so many bricks, stones, &c., (2) as potentially a house, (3) as potentially being in course of being fashioned into a house. The movement of building is the realization not (1) of the materials as these materials (they are, previously to the movement of building, already actually these materials), nor (2) of their potentiality of being a house (the house is the realization of this), but (3) of their potentiality of being fashioned into a house. Similarly every movement is a realization-of-a-potentiality which is a stage on the way to a further realization of potentiality, and only exists while the further potentiality is not yet realized. Hence it is ἀτελής‎ (b 32), and, though in a sense an ἐνέργεια‎, is distinct from an ἐνέργεια‎ in the narrower sense in which ἐνέργεια‎ implies that no element of δύναμις‎ is present at all.
Critical Apparatus
10–11 ἡ … ἐντελέχεια‎ Π‎ γρ‎. S: τὴν … ἐνέργειαν‎ S (cf. M)
Editor’s Note
10–11. ἡ τοῦ δυνάμει ὄντος ἐντέλεχεια … ἐστιν‎. ἐντελέχεια‎ must here mean 'actualization', not 'actuality': it is the passage from potentiality to actuality that is κίνησις‎.
Critical Apparatus
11 τοιοῦτον‎ E γρ‎. S T: τοιοῦτόν ἐστι‎ IJMPS: τι τοιοῦτόν ἐστι‎ F
κίνησίς ἐστιν‎ Π‎ γρ‎. S: λέγω κίνησιν‎ MSp: λέγω κίνησιν εἶναι‎ Sl
Critical Apparatus
12 ᾗ‎ fecit E2
Critical Apparatus
14 γενητοῦ‎ EJS: γεννητοῦ‎ FI
γένεσις‎ fecit E
Critical Apparatus
15 τοῦ … ἔστιν] ὅτι δʼ ἐστὶ τοῦτο‎ F
Editor’s Note
15. The accuracy of our definition can be seen by studying typical changes such as being built, learning, healing, &c.
Critical Apparatus
16 αὐτὸν‎ E1
Editor’s Note
16–17. ᾗ … εἶναι‎, lit. 'in so far as we say it is such,' more strictly 'in that respect which we refer to when we call it "the buildable".' Building is the actualization of its buildability, not of its being brick or stone, which was actual before it began to be made into a house.
Critical Apparatus
a 18 ὁμοίως … μάθησις‎ in mg. E1
καὶ μάθησις‎ om. F: καὶ ἡ μάθησις‎ I
Critical Apparatus
19 ἅδρυνσις‎ (ἄνδρωσις‎ I1) καὶ γήρανσις‎ Π‎Sp: γήρανσις καὶ ἅδρυνσις‎ Sl (cf. M)
Critical Apparatus
19–27 ἐπεὶ … δὲ] συμβαίνει δὲ κινεῖσθαι ὅταν ᾖ ἐντελέχεια ἡ‎ [immo ἡ ἐντελέχεια ᾖ‎] αὐτή, καὶ οὔτε πρότερον οὐθʼ ὕστερον. ἡ δὴ‎ ex M ci. Diels
Editor’s Note
19. Since some self-identical things may be said to be both potentially and actually (only not to be potentially and actually the same thing at the same time), such things can act on, and be acted on by, each other. Thus that which moves in a physical way can be moved, and in fact moves by being moved. But we must not assume as some do that everything that moves moves thus; we shall find that there is an unmoved mover.
Editor’s Note
19–21. ἐπεὶ … αὐτό‎, 'since some self-identical things are both potentially so-and-so and actually so-and-so, only not at the same time or else not the same so-and-so'. Some things, not all, because pure forms (God and the intelligences that move the spheres) have no potentiality in them. Things that have both potentiality and actuality act by virtue of the latter and are acted on by virtue of the former; and thus if X which is actually A is potentially B, and Y which is actually B is potentially A, X by virtue of its actuality and Y's potentiality can make YB to be YA, and Y by virtue of its actuality and X's potentiality can make XA to be XB; while things that have only actuality act without being acted on.
Critical Apparatus
20 ταὐτὰ‎ Λ‎S: ταῦτα‎ E
Critical Apparatus
21–2 ἐντελεχείᾳ … δυνάμει‎ VST: δυνάμει … ἐντελεχείᾳ‎ Λ‎ et fecit E2
Editor’s Note
24. τὸ κινοῦν φυσικῶς‎. The πρῶτον κινοῦν ἀκίνητον‎ moves not φυσικῶς‎, but simply as being the object of desire or love (Met. 1072a 26, b 3).
Editor’s Note
25. δοκεῖ … κινοῦν‎. The reference may be, as Alexander thought, to Plato's view that soul, which is what moves other things, is itself self-moved. But the self-movement he ascribes to soul is not of any of the physical kinds recognized by Aristotle, and Simplicius is probably right in rejecting Alexander's interpretation and holding that the reference is to the early materialists.
Critical Apparatus
26 οὐκ οὖν ἀλλὰ‎ F
μὲν τούτου‎ F: μὲν τούτων‎ J: μὲν οὖν τούτων‎ I
Editor’s Note
26. ἐξ ἄλλων‎, viii. 5.
Critical Apparatus
27 ὅπως ἔχει‎ IP: πῶς ἔχει‎ FJ: om. E
κινοῦν‎ EV: τῶν κινούντων‎ Λ‎S
δὲ‎ Π‎P Aspasius: δὴ‎ MT Porphyrius
Editor’s Note
27. In our definition the words 'as such' are important. Change is not the actualization of anything in respect of its own specific character—e.g. of bronze as bronze—but of things qua changeable.
Critical Apparatus
28 ἐντελέχεια‎ Aldina: om. Π‎MAPS Aspasius Porphyrius
οὐχ‎ … 29 κινητόν γρ‎. I γρ‎. A Aspasius: ἢ‎ (ἤτοι‎ fort. A) αὐτὸ ἢ ἄλλο ᾗ κινητόν‎ EFJAP Porphyrius: ἢ αὐτὸ κινητόν‎ I: οὐχ ᾗ αὐτὸ ἀλλʼ ᾗ ἄλλο γρ‎. P, ut vid. T
Editor’s Note
28. ἐντελέχεια‎. It is necessary to insert either this or ἐνέργεια‎ after ἡ δὲ τοῦ δυνάμει ὄντος‎, and it is more likely that it is ἐντέλεχεια‎ that has been lost, by haplography. Diels points out that the words ἐπεὶ … ἀκίνητον‎ a 19–27 are represented in the summary in Met. K only by the words συμβαίνει δὲ κινεῖσθαι ὅταν ἡ ἐντελέχεια ᾖ αὐτή, καὶ οὔτε πρότερον οὔθʼ ὕστερον‎ (1065b 20–21), from which ἐντελέχεια‎ can easily be 'understood' after ὄντος‎; and he thinks that the passage a 19–27 belongs to a later amplified version which took the place of something answering more closely to what we have in Met. K. This is quite likely.
Editor’s Note
οὐχ ᾗ αὐτὸ ἀλλʼ ᾗ κινητόν‎, the reading of Aspasius (S. 422. 20), is the only one of all the variants here that gives a good sense (Simplicius sensibly describes it as 'safer' than that of Alexander, 423. 12): 'not in respect of being the thing that it is but in respect of being changeable'; cf. a 10–11.
Critical Apparatus
29 ᾗ‎ alt. … ὁ] ᾗ ἔστι γὰρ ὡδὶ ὁ‎ E
ὧδε‎ MS
Critical Apparatus
31 τῷ‎ E2
αὐτῶ τῶ‎ F: αὐτὸ‎ E1MST: αὐτῷ‎ E2
Critical Apparatus
32 κινητῷ‎ om. MS
ἦν] ἢ‎ E
Editor’s Note
32. κινητῷ‎, which is omitted in the Metaphysics (1065b 26) and by Simplicius, is pretty clearly a gloss on δυνάμει τινί‎. Themistius' δυνάμει ἀνδριάντι‎ (71. 11) is probably an interpretation of δυνάμει τινί‎; at any rate Themistius almost certainly did not read κινητῷ‎. Philoponus follows Themistius (352. 21).
Critical Apparatus
33 καὶ‎ Λ‎MV: ἢ‎ E
ἦν ἂν‎ E2Λ‎M: om. E1P
Critical Apparatus
34 κίνησις] κίνησις ἂν ἦν‎ E1P: κίνησίς τις‎ M
ὥσπερ‎ Λ‎
Editor’s Note
34. The presence of different capacities in the same thing may be seen in such a case as that of health and disease. The capacity of being well is different from that of being ill (if it were not, being well and being ill would be the same thing), yet they may be present in the same subject.
Editor’s Note
34–b 3. δῆλον … ἕν‎. The distinction between the substratum (e.g. bronze) and the capacity (e.g. the capacity for being shaped into a statue) is here brought out by pointing to the fact that a single substratum combines opposite capacities in itself. The capacity for health is obviously not the same as the capacity for disease, but the same body has both.
Critical Apparatus
201b 6–7 = 1065b 20–22
Editor’s Note
b 3. εἴθʼ ὑγρότης εἴθʼ αἷμα‎. The first view is that of Hippocrates, the founder of the humour-pathology, and of Plato (Tim. 81 e–86 a), the second probably that of Empedocles (cf. Diels3 i. 205. 9, 222. 38).
Editor’s Note
4. ὥσπερ … ὁρατόν‎. Colour is no doubt what is seen, but is defined by Aristotle as κινητικὸν τοῦ κατʼ ἐνέργειαν διαφανοῦς‎ (De An. 418a 31–b 2) or as τὸ τοῦ διαφανοῦς ἐν σώματι ὡρισμενῷ πέρας‎ (De Sensu 439b 11). It needs a further condition, viz. light, before it becomes visible (De An. 418b 2 διόπερ οὐχ ὁρατὸν ἄνευ φωτός, ἀλλὰ πᾶν τὸ ἑκάστου χρῶμα ἐν φωτὶ ὁρατόν‎). I.e., visibility is a συμβεβηκός‎ which under a certain condition the subject colour acquires.
Critical Apparatus
b 5 ὅτι] τὸ‎ E1
ἐστιν‎ Λ‎V: ἐστιν εἰ δὲ μὴ τὸ αὐτὸ ἀλλʼ ὡς χρῶμα τὸ αὐτὸ καὶ ὁρατόν, ἡ δυνάμει ἐστίν, τὴν τοῦ δυνατοῦ ᾗ δυνατὸν ἐντελέχειαν εἶναι λέγω κίνησιν‎ E (cf. b 3–5)
Critical Apparatus
5–15 ὅτι … κινήσεων‎ om. γρ‎. A
Editor’s Note
b 5. The truth of our definition may be seen, once more, by considering the case of that which is capable of being made into a house. The actualization of this must be either a house or the process of building. But the house cannot be the actualization of the buildable, since when the house exists the buildable has ceased to exist; therefore it must be the process of building that is the actualization of it qua buildable. Now building is a change. And generalizing we may say that the actualization of the potential as such is always a change.
Critical Apparatus
6 αὕτη‎ Λ‎MS: τοῦτο‎ P: αὕτη τοῦτο‎ E
ἡ‎ et 7 ᾖ‎ om. F
Critical Apparatus
7 αὕτη‎ FI
δῆλον‎ Λ‎MT: φανερόν‎ E
Critical Apparatus
8 γὰρ] μὲν γὰρ‎ F
τὸ‎ om. E
Critical Apparatus
9 καὶ] ᾗ οἰκοδομητὸν καὶ‎ M et fort. T
ἐνέργεια‎ Λ‎MS: ἐντελέχεια‎ E
Critical Apparatus
10 γὰρ‎ EV: γὰρ τοῦτό ἐστιν‎ FI: γὰρ τοῦτʼ ἐστιν ἡ‎ J
ἡ‎ IJT: om. EF
τοῦ οἰκοδομητοῦ‎ ET: om. Λ‎M
Editor’s Note
10–15. ἢ … κινήσεων‎. The fulfilment of the buildable must be either the act of building (or process of being built) or the resulting house. But when the house is there, the buildable is no longer there, so that the house cannot be the fulfilment of the buildable. Therefore the act of building is the fulfilment of the buildable. Now the act of building is a typical κίνησις‎, and a parallel account holds good of all κίνησις‎. Therefore κίνησις‎ is the fulfilment of potentiality.
Critical Apparatus
11 ἡ‎ om. FIJ1
ἔσται‎ Λ‎
Critical Apparatus
12 οὖν] ἄρα‎ IJM: ἄρα τὴν‎ F
Critical Apparatus
13 τις‎ Λ‎M: τίς ἐστιν‎ E
Editor’s Note
201b 16. The correctness of our definition of change is confirmed (1) by the failure of other attempts and (2) by the impossibility of finding any better definition.
Critical Apparatus
17–20 καὶ … ἔνιοι‎ Π‎ (cf. M): om. T
Editor’s Note
201b 17. περὶ αὐτῆς‎, i.e. about movement, referring back to b 5.
Critical Apparatus
18–19 οὔτε … τις‎ om. γρ‎. A
Critical Apparatus
18 καὶ τὴν μεταβολὴν‎ om. J: τὴν‎ om. S
Editor’s Note
18. (2) Change cannot be placed in any genus other than that in which we have placed it. (1) Change has been defined as otherness, inequality, or not-being. But what is other, unequal, or non-existent neither necessarily suffers change nor is a terminus of change, any more than its opposite does or is.
Editor’s Note
18–20. οὔτε … ἔνιοι. οὔτε …‎ 19 τις‎ answers to ἐκ τοῦ μὴ ῥᾴδιον εἶναι διορίσαι ἄλλως αὐτήν,‎ and δῆλόν τε σκοποῦσιν κτλ‎. to ἐξ ὧν οἱ ἄλλοι περὶ αὐτῆς λέγουσιν‎.
Critical Apparatus
19 θεῖναι‎ Π‎M: τιθέναι‎ S
δὲ‎ Λ‎MPS
Editor’s Note
19. δῆλόν τε‎. In the ordinary reading δῆλον δέ, δέ‎ has to be taken as answering loosely to οὔτε‎ b 18. But E seems to have preserved here the original reading.
Editor’s Note
19–21. ὡς … κίνησιν‎. According to the Greek commentators, the reference is to the Pythagoreans and to Plato τῆς ἑτέρας συστοιχίας‎ b 25 suggests a reference to the former, and in Met. 986a 25 κινούμενον‎ occurs in the συστοιχία‎ of the indefinite. But the reference to otherness, inequality, and not-being suggests rather Plato's view; cf. such passages as Soph. 256 d–e (τὸ μὴ ὄν‎ d 11, ἡ θατέρου φύσις‎ d 12), Tim. 57 e–58 c (ἀνωμαλότης‎ 57 e 7, ἀνισότης‎ 58 a 1).
Critical Apparatus
20 αὐτὴν ἔνιοι‎ EPS: ἔνιοι αὐτὴν‎ Λ‎
Editor’s Note
21–4. ὧν … ἀντικειμένων‎. To identify movement with otherness, inequality, or not-being can only (Aristotle argues) be a loose way of saying either that these are the subjects of movement or that they are the termini of movement. And to each of these statements there is an obvious objection.
Critical Apparatus
22 ᾖ] ᾖ οὔτʼ ἂν ἕτερα‎ E
ἂν‎ alt. om. FIP
Critical Apparatus
23 ἢ ἐκ‎ EJ2P: ἢ‎ FIJ1S
Editor’s Note
24. The popularity of such definitions is due to the facts that change is thought to be something indefinite and that otherness, inequality, and not-being have the indefiniteness that all privative terms have.
Critical Apparatus
25 τι‎ Π‎Pcp: om. PlT
Editor’s Note
25. τῆς … ἑτέρας συστοιχίας‎, the second of two columns of which the first contains positive terms, the second their opposites. The most famous of these pairs of columns is that set up by some Pythagoreans, Met. 986a 22–6; and in this ἠρεμοῦν‎ and κινούμενον‎ are placed under πέρας‎ and ἄπειρον‎ respectively.
Critical Apparatus
26 τοιόνδε‎ EFJM: τοσόνδε‎ IPT
Critical Apparatus
27 ἐστίν‎ om. Λ‎M
ὅτι‎ om. MVT, secl. Bonitz
Editor’s Note
27. The apparent indefiniteness of change is due to the fact that it cannot be identified either with potentiality or with actuality, since it is not true that either that which can be (e.g.) of a particular size or that which is actually of it necessarily changes to that size, and since change seems to be a sort of incomplete actualization.
Editor’s Note
28–9. οὔτε … ἐνέργειαν‎, 'neither on the δύναμις‎-side nor on the ἐνέργεια‎-side of reality'.
Critical Apparatus
b 29 οὐδὲ‎ F
αὐτήν‎ IJ1M: αὐτὴν ἁπλῶς‎ EFJ2
Critical Apparatus
30 ποσὸν εἶναι‎ EM: εἶναι ποσὸν‎ Λ‎
ἐνεργεῖν ἄποσον‎ E
Critical Apparatus
31 εἶναί τις δοκεῖ‎ S: εἶναι δοκεῖ τις‎ E1M: τις εἶναι δοκεῖ‎ Λ‎: εἶναι δοκεῖ‎ E2
Editor’s Note
31–2. ἥ τε κίνησις … ἀτελὴς δέ‎. The relation between κίνησις‎ and ἐνέργεια‎ is stated more fully in Met. 1048b 29–35 πᾶσα γὰρ κίνησις ἀτελής, ἰσχνασία μάθησις βάδισις οἰκαδόμησις· αὗται δὴ κινήσεις, καὶ ἀτελεῖς γε. οὐ γὰρ ἅμα βαδίζει καὶ βεβάδικεν, οὐδʼ οἰκοδομεῖ καὶ ᾠκοδόμηκεν, οὐδὲ γίγνεται καὶ γέγονεν ἢ κινεῖται καὶ κεκίνηται, ἀλλʼ ἕτερον, καὶ κινεῖ καὶ κεκίνηκεν· ἑώρακε δὲ καὶ ὅρᾳ ἅμα τὸ αὐτό, καὶ νοεῖ καὶ νενόηκεν. τὴν μὲν οὖν τοιαύτην ἐνέργειαν λέγω, ἐκείνην δὲ κίνησιν‎.
Critical Apparatus
32 ἐστιν‎ Λ‎M: ἐστιν ἡ‎ E
Editor’s Note
32. The 'incompleteness' of change is due to the fact that the potential, of which it is the actualization, is itself necessarily incomplete.
Critical Apparatus
33 αὐτὴ‎ E
ἢ‎ Λ‎P: εἰ‎ E
Editor’s Note
33. This is why change is difficult to define; it cannot be identified simply either with privation or with potentiality or with actuality, but only with the actualization of the potential.
Critical Apparatus
202a 13–21 = 1066a 26–34
Critical Apparatus
202a 1 τοίνυν] δὴ‎ E
Critical Apparatus
2 εἴπομεν‎ FIPT et fecit E
ἰδεῖν‎ fecit E
Editor’s Note
202a 2. οἵαν εἴπαμεν‎, 201a 10–11.
Critical Apparatus
3 εἶναι‎ Λ‎V: εἶναι ὅτι δὲ καλῶς εἴρηται δῆλον. οὐ γὰρ αὖ τὴν κίνησιν καὶ τὴν μεταβολὴν ἐν ἄλλῳ γένει θεῖναι δύναιτʼ ἄν τις, ἥ τε κίνησις ἐνέργεια μὲν εἶναι δοκεῖ τις, ἀτελὴς δέ. αἴτιον δὲ ὅτι ἀτελὲς τὸ δυνατόν‎ E (cf. 201b 16–19, 31–2)
πᾶν] εἰ πᾶν‎ Prantl
Editor’s Note
202a 3. A mover that is capable of being moved, whose previous lack of movement is not the mere negation of movement but is rest, i.e. the absence of movement in something that can be moved,—such a mover is always, in causing movement, itself moved. For it moves by contact, and in touching another it is touched, and therefore moved, by it.
Editor’s Note
3–4. κινεῖται … κινητόν‎. The sentence runs better with a comma after πᾶν‎ instead of commas before and after ὥσπερ εἴρηται. τὸ κινοῦν ὥσπερ εἴρηται = τὸ κινοῦν φυσικῶς‎ 201a 24.
Critical Apparatus
4 κινητόν‎ E1FIAS: κινητικόν‎ E2JV γρ‎. A Aspasius
Editor’s Note
4–5. ᾧ … ἠρεμία.‎ ἠρεμία‎, being the privative and not the bare negative of κίνησις‎, can be ascribed only to that which is susceptible of movement.
Critical Apparatus
5 τούτου‎ S: τούτῳ‎ Π‎
Editor’s Note
5–9. τὸ γὰρ πρὸς τοῦτο ἐνεργεῖν … πάσχει‎, 'for to act on a thing in respect of some characteristic it has, is identical with moving it; and this the agent does by contact, so that it is at the same time also acted on; thus movement is the actualization of the movable in respect of its movability, and this happens by the contact of that which has the capacity of moving it, which therefore is at the same time also acted on.' a 7–9 sums up the whole account of motion, with the corollary that for a thing which is capable of being moved to cause movement implies its also suffering movement.
Prantl bracketed a 8–9 συμβαίνει … πάσχει‎ as a doublet of a 6–7 τοῦτο … πάσχει‎. But the summing-up διὸ ἡ κίνησις ἐντελέχεια τοῦ κινητοῦ, ᾗ κινητόν‎ would be pointless here except as leading up to the corollary that this involves action of the patient on the agent. Simplicius has a 8–9 as well as a 6–7 (434. 32, 436. 16, 438. 5).
In De Gen. et Corr. 323a 25–33 it is pointed out that, though contact is usually mutual and action usually involves reaction, there are things (Aristotle means God and the beings that move the planets) which touch and act without being touched and acted on.
Critical Apparatus
8–9 συμβαίνει … πάσχει‎ secl. Prantl
Critical Apparatus
8 δὲ‎ om. F
ὥσθʼ …‎ 9 πάσχει‎ E2Λ‎S: om. E1V
Critical Apparatus
9 τι‎ Λ‎S: om. EVPT
Editor’s Note
9. A mover always has a definite characteristic, e.g. a substantial nature, a quality, or a size, by virtue of which it moves something else. Its moving of what it moves consists in imprinting on it in actuality this characteristic which the moved previously had only in potentiality.
Critical Apparatus
10 ἢ τοσόνδε‎ E2Λ‎VS: om. E1
Editor’s Note
10. ἢ τοσόνδε‎. There is something to be said for omitting these words (with E), since it is in γένεσις‎ and ἀλλοίωσις‎ that the transference of form is most apparent. But Simplicius has ἢ τοσόνδε‎, and the omission in E is probably due to haplography.
Critical Apparatus
11 κινῇ] μὴ ᾖ‎ in rasura E1
Editor’s Note
202a 13. Our definition of change enables us to answer the question what change is present in, by saying that it is in that which is changeable, since it is the actualization of this by the movent. Change is at the same time the actualization of the movent. For its potentiality is a potentiality of actualizing the potentiality of the moved. Thus the one change is the actualization of both movent and moved, as the same interval is the interval between one and two and between two and one. It is a case of there being one thing definable in two ways.
Editor’s Note
202a 13. τὸ ἀπορούμενον‎. This seems to refer not to any previous passage, but simply to a problem familiar to Aristotle's readers.
Editor’s Note
ἐν τῷ κινητῷ‎, sc. οὐκ ἐν τῷ κινητικῷ‎.
Critical Apparatus
14 ἐστι … κινητικοῦ‎ in rasura E
τούτου] τοῦ κινητοῦ‎ Andronicus
καὶ‎ om. MVPS: habent Π‎ Andronicus
τοῦ κινητικοῦ] τούτου‎ J Andronicus
Critical Apparatus
16 κινητὸν‎ I
Critical Apparatus
16 et 17 τῷ] τὸ‎ fecit E
Editor’s Note
18–21. ὁμοίως … ὥσπερ … ὁμοίως‎ is a good instance of Riddell's 'binary structure' (Apology of Plato, 198, § 209). Cf. Met. 983b 11–17 and Phys. 200a 34–b 3 n.
Critical Apparatus
a 19 πρὸς δύο‎ F
Editor’s Note
20. ἓν μέν ἐστιν‎, i.e. τῷ ὑποκειμένῳ‎, in respect of their substratum.
Editor’s Note
21. Yet, since there are two namable ἐνέργειαι‎, the activity of the agent and the passivity of the patient, we may ask what these are in. Are both in the patient, or is the activity in the agent and the passivity in the patient?
Editor’s Note
21. ἀπορίαν λογικήν‎. The meaning of λογικός‎ may be seen from such passages as Top. 162b 27 εἰ μὲν γὰρ ἐκ ψευδῶν ἐνδόξων δέ, λογικός‎ (sc. ὁ λόγος‎), G.A. 747b 28 λέγω λογικὴν‎ (sc. ἀπόδειξιν‎) σιὰ τοῦτο, ὅτι ὅσῳ καθόλου μᾶλλον, πορρωτέρω τῶν οἰκείων ἐστὶν ἀρχῶν‎ (cf. 748a 7–11). λογικὸς συλλογισμός‎ is opposed to ἀπόδειξις‎ (An. Post. 93a 15), λογικῶς θεωρεῖν, σκοπεῖσθαι (σκοπεῖν)‎ to ἐκ τῶν κειμένων‎ (An. Post. 88a 19, 30), or to φυσικῶς‎ (Phys. 204b 4, 10, De Gen. et Corr. 316a 11). What the present phrase intimates, then, is that the question is a superficial or dialectical one, turning on the verbal difference between ποίησις‎ and πάθησις‎ and failing to see that these are but two ways of describing the same event from two different points of view.
Critical Apparatus
22 τινα εἶναι‎ F
τοῦ‎ EJT: ἄλλην τοῦ‎ FIV
Critical Apparatus
23 καὶ ἄλλην τοῦ‎ I
δὴ] γὰρ‎ FI: γε‎ J
Critical Apparatus
25 ἔπει‎ IJ et fecit E: εἰ‎ FP
ἕτεραι‎ Λ‎PS: ἕτεραι εἰσιν‎ E
Editor’s Note
25–7. ἢ … πάσχοντι‎. The fuller form found in the Arabo-Latin translation and apparently in Themistius, and cited as a variant by Simplicius, would seem to be necessary to make the disjunction of possible views complete. But only the two alternatives found in our other authorities are taken up in the discussion, the second in a 28–31, the first in a 31–b 22. Aristotle evidently omits as patently impossible the view that both activity and passivity are embodied in the agent, and the fuller reading is the result of a later endeavour to make a formally complete disjunction without regard to the actual course of the discussion.
Critical Apparatus
26 ἐν … κινουμένῳ‎ in rasura E2
καὶ ποιουμένῳ‎ S
ἢ] ἢ ἐν τῷ ποιοῦντι καὶ διατιθέντι ἢ‎ V γρ‎. S et ut vid. T
Editor’s Note
28. (1) If the latter, movement must be in the mover, since the same account applies to mover and moved as to agent and patient. Thus either every mover will be moved or something that has movement in it will yet not be moved.
Editor’s Note
29–30. ὁ γὰρ αὐτὸς λόγος … κινουμένου‎. At first glance, one would suppose this to mean 'for the same account will apply to the mover as to the moved'. But then ἀλλὰ μὴν εἰ τοῦτο‎ would have to mean εἰ ἡ πάθησις ἐν τῷ πάσχοντι‎, whereas it must refer to the single indivisible view εἰ ἡ μὲν ποίησις ἐν τῷ ποιοῦντι, ἡ δὲ πάθησις ἐν τῷ πάσχοντι‎. We must therefore suppose ὁ γὰρ αὐτὸς λόγος … κινου‎. μένου‎ to mean 'for the same account will apply to mover and moved as to agent and patient'.
Editor’s Note
31. (2) If the former, the following difficulties apparently arise: (a) the actualization of each thing will not be in that thing.
Critical Apparatus
34 ἑκάστου] ἐν ἑκάστω‎ F δύο] τὸ δύο‎ FS: τὰς δύο‎ I
Editor’s Note
34. (b) It is absurd that the moved, in moving towards a single condition, should be undergoing two movements at once. The actualization of the mover and of the moved must, then, be a single actualization. But how can two specifically different things have the same actualization?
Critical Apparatus
35 τίνες … ἑνὸς‎ post 36 ἀδύνατον‎ transponenda vel τινὲς‎ legendum ci. A
Editor’s Note
35–6. τίνες … εἶδος‎; The patient is one thing and suffers change to one single condition (e.g. from ignorance to knowledge); how then can we suppose that it is suffering two alterations, as would be involved if the activity as well as the passivity takes place in it?
Critical Apparatus
b 2 ἡ … μάθησις‎ ES: ἡ μάθησις καὶ ἡ‎ (ἡ‎ om. I) δίδαξις‎ Λ‎P
Editor’s Note
b 2. (c) If the activity and the passivity are the same, the teacher must always be learning and the agent always being acted on.
Editor’s Note
5. These difficulties are not so serious as might appear. (a) It is not absurd that the actualization of one thing should be in another; teaching is the actualization of that which can teach, but the actualization of it in that which can learn.
Critical Apparatus
7 ἔν τινι] ἔστι γρ‎. S
καὶ‎ om. F
Critical Apparatus
8 ἀποτετμημένη‎ EFIS et fecit J1: ἀποτετμημένως γρ‎. S
κωλύει …‎ 9 εἶναι‎ pr. Λ‎S: τὴν αὐτὴν εἶναι κωλύει‎ E
Editor’s Note
8. (b) It is not absurd that the actualization of two things should be the same, provided this is taken to mean 'the same in substratum', not 'the same in essence'.
Critical Apparatus
b 9 τῷ‎ scripsi: τὸ Π‎
αὐτό, ὡς λώπιον καὶ ἱμάτιον, ἀλλʼ‎ I
Editor’s Note
b 9. μὴ … αὐτό‎, 'not as being the same thing in essence'. Grammar requires us to write τῷ εἶναι‎ for τὸ εἶναι‎; cf. 186a 31, 216b 5, &c.
Editor’s Note
9–10. ἀλλʼ … ἐνεργοῦν‎, i.e. the same in substratum though capable of being differently described. In the same way one and the same change may be described as activity from the point of view of the agent and as passivity from that of the patient.
Critical Apparatus
10 δυνάμει ὂν‎ Λ‎P: δυνάμενον‎ EV: δυνάμει‎ S
Editor’s Note
10. (c) Even if to act and to be acted on are the same, not in definition but in substratum, it does not follow that the teacher must always be learning. It is not things that are the same in any sense, but things whose essence is the same, that must have all their attributes the same.
Critical Apparatus
11 ποιεῖν καὶ πάσχειν‎ EVP: ποιεῖν καὶ τὸ πάσχειν‎ S: πάσχειν καὶ τὸ ποιεῖν‎ Λ‎
Critical Apparatus
12 ὥστε‎ scripsi: ὡς‎ Π‎
εἶναι ἕνα‎ IJV: om. EF
τὸν τὸ‎ Bonitz: τὸν‎ IJ: τὸ‎ E: om. F
Editor’s Note
12. μὴ … λὲγοντα‎. Grammar requires us to read ὥστε‎ for the ὡς‎ of the MSS.
Critical Apparatus
13 οἷον ὡς] οἷον‎ Λ‎: ὡς‎ Bekker
λώπιον καὶ ἱμάτιον‎ EV: τῷ λωπίῳ καὶ ἱματίῳ‎ Λ‎
Editor’s Note
14. ὥσπερ … πρότερον‎, a 18–20.
Critical Apparatus
15 ὑπάρχει‎ E2Λ‎P: ὑπάρξει‎ E1
Critical Apparatus
16 οὐ μὴν‎ erasit E, om. P
Editor’s Note
16. (d) Even if teaching is the same as learning, it does not follow that to teach is the same as to learn, just as, if the distance between two things is a single thing, it does not follow that to stretch from here to there and to stretch from there to here are the same.
Critical Apparatus
17 διδάσκειν‎ EP: διδάσκειν τὸ αὐτό‎ Λ‎
οὐδʼ εἰ] οὐδὲ‎ E2
Editor’s Note
19. (e) Strictly it is not true that activity is the same as passivity, but only that the movement which is describable as both is one and the same; to be the actualization of this in that and to be the actualization of that by this are things that have different definitions.
Critical Apparatus
20 et 21 ἡ] ὡς‎ I
Critical Apparatus
21 τοῦδε‎ E2FIVPS: τόδε‎ E1: τόδε τοῦδε‎ J
ἐν τῷδε καὶ‎ Λ‎VPS: om. E τὸ τοῦδε‎ Λ‎VP: τοῦδε‎ E: τόδε‎ S
Critical Apparatus
23 ἐστιν] ἡ‎ F
εἴρηται‎ hic EP: post 24 μέρος‎ Λ‎
Editor’s Note
23. We have now stated the general nature of change, and it is easy to apply this to the kinds of change; e.g. alteration will be the actualization of the alterable as such, or (more plainly) the actualization of that which is potentially active and of that which is potentially passive, as such.
Editor’s Note
23–4. τί … μέρος‎. This sums up the substance of chs. 1–3, especially of chs. 1 and 2.
Critical Apparatus
24 πῶς‎ IP: ὡς‎ EFJS
Critical Apparatus
27 ἢ] ὅτι‎ E (add. ἧ‎ sup. lin. E1): τι ἢ‎ J2
Critical Apparatus
28 δὲ‎ EFJ2S: om. IJ1
Critical Apparatus
30 μεγέθη τε καὶ‎ F
Editor’s Note
202b 30. Since the study of nature is concerned with magnitudes, change, and time, each of which must be either infinite or finite (even if there are other things that are neither), we must examine whether the infinite exists, and if so, what it is.
Editor’s Note
202b 33. οἷον πάθος ἢ στιγμή‎. A πάθος‎ is neither finite nor infinite because it is not in the category of quantity but in that of quality; a point is neither, because it is not a quantity but the limit of a certain quantum, viz. of a line.
Critical Apparatus
b 36 ταύτης‎ hic Λ‎ST, post 203a 1 θεωρία‎ E2 (expunctum), post ἐπιστήμης‎ P
Editor’s Note
36. The appropriateness of this discussion to physics is seen from the fact that all considerable physicists treat the infinite as a first principle.
Critical Apparatus
203a 1 ἡ … περὶ αὐτοῦ‎ IJS: ἡ περὶ αὐτὸ θεωρία‎ in litura E2: ἡ θεωρία περὶ αὐτοῦ‎ F: ἡ θεωρία‎ PT
οἱ δοκοῦντες‎ om. F
Critical Apparatus
2 ἧφθαι‎ fecit E: locus pluribus
Critical Apparatus
3 τοῦ‎ Λ‎S: om. ET
τινα …‎ 4 αὑτό‎ om. F
Critical Apparatus
3 ὄντων καὶ οἱ‎ I
Critical Apparatus
4 μὲν] μὲν οὖν‎ J
Editor’s Note
203a 4. (1) Some of these do not treat infinity as an attribute of something else but make the infinite itself a substance; but of these the Pythagoreans treat it as present in sensible things, and also describe what is outside the heavens as infinite, while Plato recognizes nothing outside the heavens, but makes the infinite a constituent both of sensible things and of Ideas;
Critical Apparatus
5 τινι ἑτέρῳ ἀλλʼ ὡς οὐσίαν … ἄπειρον‎ fecit E
Editor’s Note
203a 6. πλὴν … αἰσθητοῖς‎. Aristotle points out elsewhere (Met. 986a 23) that πέρας καὶ ἄπειρον‎ was one of the chief ways (περιττὸν καὶ ἄρτιον‎ being another) in which the Pythagoreans formulated the formal and the material principle constitutive of sensible realities. They did not suppose these to have any existence except as constituting sensible realities, while Plato assigned a double role to the formal and the material principle (a 9–10, cf. Met. 988a 8–14). The Ideas contained as formal principle the One and as material principle the great and small (or ἄπειρον‎); sensible realities contained as formal principle the Ideas and as material principle a different ἄπειρον‎ (spatial extension),
Editor’s Note
6–7. οὐ … ἀριθμόν‎. When Aristotle says (Met. 987b 27) that the Pythagoreans identified real things with numbers, it is not to be supposed that they reduced reality to an abstraction, but rather that they did not recognize the abstract nature of numbers. What they were doing was little more than to state that the characteristics of things depended, to a large extent, on the number and the numerical relations of their components.
Critical Apparatus
7 ποιοῦσιν‎ Λ‎Pp: εἶναι λέγουσιν‎ EPl
τὸ] δὲ‎ FP
οὐρανοῦ τὸ ἄπειρον‎ FS
Editor’s Note
7. καὶ … ἄπειρον‎. This may be illustrated by 213b 22–5. The Pythagoreans described the universe as 'breathing in' from the infinite πνεῦμα‎ or void which surrounded it. Cf. Stob. Ecl. i. 18, 6 (Dox. 316), where time also is described as breathed in from the infinite that surrounds the οὐρανός‎; and the problem ascribed to the Pythagorean Archytas by Simplicius (467. 26)—ἐν τῶ ἐσχάτῳ οἷον τῷ ἀπλανεῖ οὐρανῷ γενόμενος, πότερον ἐκτείναιμι ἂν τὴν χεῖρα ἢ τὴν ῥάβδον εἰς τὸ ἔξω, ἢ οὔ‎;
Thus Aristotle says that the Pythagoreans recognized τὸ ἄπειρον‎ (1) as an element in ordinary sensible things, and (2) as that which is outside the heavens.
Critical Apparatus
8 οὐδὲ‎ F
Critical Apparatus
9 εἶναι αὐτάς‎ Λ‎S: αὐτὰς εἶναι‎ E
Critical Apparatus
10 ἐκείναις‎ FJS: ἐκείνοις‎ EI
εἶναι‎ alt. om. F
Editor’s Note
10. and the Pythagoreans identify the infinite with the even (which, being a constituent in things and being limited by the odd, imparts to things their infinity), while Plato recognizes two infinites, the great and the small.
Editor’s Note
10–11. καὶ οἱ μὲν … ἄρτιον‎. For the reasons which led the Pythagoreans to identify the infinite with even number cf. my note on Met. 986a 18. Prof. Taylor has made a noteworthy further suggestion (C.R. xl (1926) 149 f.). He argues that on the Pythagorean assumption that the point is a μονὰς θέσιν ἔχουσα‎, every line consists of a finite number of finite but indivisible points separated by gaps, and that if this premiss be granted, a line containing an even number of points is capable of bisection ad infinitum (since every cut comes in a gap), while a line containing an odd number of points cannot be bisected at all (since the first cut would have to come at an indivisible point). This suggestion seems to me to offer a highly probable interpretation of the following passages. Stob. Ecl. i. 10 (Dox. 97) καὶ μὴν εἰς δύο διαιρουμένων ἴσα, τοῦ μὲν περισσοῦ μονὰς ἐν μέσῳ περίεστι, τοῦ δὲ ἀρτίου κενὴ λείπεται χώρα καὶ ἀδέσποτος καὶ ἀνάριθμος, ὡς ἂν ἐνδεοῦς καὶ ἀτελοῦς ὄντος‎. Plut. De Vita et Poesi Homeri 145 ὅθεν καὶ τῶν ἐφεξῆς ἀριθμῶν τὸν μὲν ἄρτιον ἐνδεᾶ καὶ ἀτελῆ, τὸν δὲ περισσὸν πλήρη τε καὶ τέλειον ἀπέφηνεν … γόνιμος γάρ ἐστι καὶ ἔχει δύναμιν ἀρχῆς καὶ διαίρεσιν οὐκ ἐπιδέχεται, ἀεὶ τῆς μονάδος ἐν αὐτῷ περιούσης. ὁ δʼ ἄρτιος οὔτε γεννᾷ ποτε τὸν περισσὸν συντιθέμενος ἑαυτῷ, οὔτε ἐστὶν ἀδιαίρετος‎. Plut. Mor. 388a ταῖς γὰρ εἰς ἴσα τομαῖς τῶν ἀριθμῶν, ὁ μὲν ἄρτιος πάντῃ διιστάμενος ὑπολείπει τινὰ δεκτικὴν ἀρχὴν οἷον ἐν ἑαυτῷ καὶ χώραν, ἐν δὲ τῷ περιττῷ ταὐτὸ παθόντι μέσον ἀεὶ περίεστι τῆς νεμήσεως γόνιμον‎. Ib. 288a καὶ διαιρουμένων εἰς τὰς μονάδας‎, ὁ μὲν ἄρτιος καθάπερ τὸ θῆλυ χῶραν μεταξὺ κενὴν ἐνδίδωσι, τοῦ δὲ περιττοῦ μόριον ἀεί τι πλῆρες ὑπολείπεται‎.
It may be noted that if Zeno's argument about the ὄγκοι‎ (239b 33–240a 18) was directed against Pythagoreans, it must have been against a different form of theory from that implied in Prof. Taylor's explanation; for the ὄγκοι‎ or indivisible units are represented as touching one another. So, too, are the points referred to in 227a 29.
Critical Apparatus
11 γὰρ‎ E2Λ‎S: γὰρ τὸ‎ E1
Critical Apparatus
12 παρέχει‎ EF
Editor’s Note
13–15. περιτιθεμένων … ἕν‎. There is no doubt what περιτιθεμένων τῶν γνωμόνων περὶ τὸ ἕν … ὁτὲ δὲ ἕν‎ refers to. It presupposes the Pythagorean method of representing numbers by dots arranged in a geometrical pattern, and expresses the fact that if you start with one dot and place gnomons successively round it, you get figures of constant shape, viz. squares
Fig. 1.
i.e. the fact that 1 + 3 + 5 + … (2 n–1) = n2. The question is, 'what is the other case that is opposed to this?'—in other words, 'how is καὶ χωρίς‎ to be interpreted?' Themistius says (80. 22–4) οἱ δὲ ἄρτιοι προστιθέμενοι τῇ μονάδι κατὰ τοὺς ἐφεξῆς ἀεὶ τι καινὸν εἶδος ποιοῦσι καὶ ἡ διαφορὰ πρόεισιν εἰς ἄπειρον, τρίγωνον, εἶτα ἑπτάγωνον, εἶθʼ ὅ τι καὶ τύχοι‎. In other words, he thinks the series 1, 1 + 2, 1 + 2 + 4 … is meant. Philoponus presents the same series, but also the series 2, 2 + 1, 2 + 3, 2 + 5 … and the series 3, 3 + 2, 3 + 4, 3 + 6 … (394. 11–13, 23–6).
Simplicius first interprets the passage as meaning περιτιθεμένων περὶ τὸν ἕνα ἀριθμὸν τὸν τετράγωνον ποτὲ μὲν χωρὶς τῶν γνωμόνων … ποτὲ δὲ χωρὶς τῶν ἀρτίων‎ (457. 8–11). Later, however, he mentions with approval Alexander's interpretation, that χωρίς‎ refers to ordinary arithmetical addition without the use of περίθεσις σχηματική‎ (ib. 12–25), and adds an interpretation of his own which is a variant upon this (ib. 25–458. 7).
Milhaud (Philosophes-Géomètres de la Grèce, 115–17), Burnet (E.G.P.3, § 48.), and Heath (Hist. of Gk. Math. i. 82–3) offer a different interpretation, viz. that καὶ χωρίς‎ refers to the figure
Fig. 2.
i.e. to the fact that 2 + 4 + 6 + … 2 n = n (n + 1), i.e. gives rise to a series of rectangular figures differing in the proportions of their adjacent sides, but gradually approaching to squareness. Prof. Taylor, in C.R. xl (1926). 150–1 has reverted to Themistius' interpretation, and supported it by citing Stob. i. 1. 10, p. 20 (Dox. 97) ἔτι δὲ τῇ μονάδι τῶν ἐφεξῆς περισσῶν γνωμόνων περιτιθεμένων, ὁ γινόμενος αἰεὶ πετράγωνός ἐστι· τῶν δὲ ἀρτίων ὁμοίως περιτιθεμένων, ἑτερομήκεις καὶ ἄνισοι πάντες ἀποβαίνουσιν, ἴσον δὲ ἰσάκις οὐδείς‎.
Simplicius' various interpretations may be dismissed as obviously inadequate, and so may that of Zeller (i6. 455, n. 3), that καὶ χωρίς‎ means καὶ περιτιθεμένων τῶν ἀριθμῶν χωρίς τῶν γνωμόνων‎ (i.e. περιτιθεμένων τῶν ἀρτίων‎). The question we are left with is whether τῶν γνωμόνων‎ is limited to odd numbers, and χωρίς‎ means 'in the other case' (i.e. in the case in which even numbers are placed round the one), or τῶν γνωμόνων‎ includes even numbers as well as odd, and χωρίς‎ means 'when gnomons are placed one round another, without the odd'. I doubt whether καὶ χωρίς‎ can have the meaning assigned to it in the first interpretation. The second interpretation involves taking χωρίς‎ as meaning 'separately' or 'apart from the one', which is a rendering much easier to accept. The matter seems to me to be settled by a long passage in Iamblichus' well-informed In Nicomachi Arithm. Introd. (73. 15 ff. Pistelli), which turns entirely on the unity of shape preserved in series (1) and the diversity of shape produced in series (2). That this is a genuine presentation of an early Pythagorean doctrine is confirmed by the fact that the antithesis τετράγωνον, ἑτερόμηκες‎ occurs in the list of Pythagorean contraries in Met. 986a 22–6, for an ἀριθμὸς ἑτερομήκης‎ is precisely a number of the form n (n + 1) (Nicom. Ar. ii. 17. 1, 18 2; Theon Sm. 26. 21 Hiller; Iamb. In Nic. 74. 19 Pistelli).
The question remains whether γνώμονες‎ can be used to include even numbers as well as odd. The stricter meaning of the word is 'the figure which remains of a square when a smaller square is cut out of it'; and in this sense each successive gnomon stands for an odd number, since the difference between two consecutive square numbers is always an odd number. But in a wider sense γνώμων‎ can stand for any number which when added to a figurate number gives the next number of the same figure (Iamb. In Nic. 58. 19 Pistelli; Hero Deff. 58). Now, though the successive rectangles produced in fig. (2) differ in their proportions, they agree in being of the form n (n + 1), and it was therefore a natural extension of the meaning of the word to call their complements γνώμονες‎.
Cornford suggests that 'possibly putting gnomons round without the unit means putting two minimum gnomons round one another, thus Book III. Each succeeding gnomon will then contain an even number (6, 8, 10, &c.). and we shall obtain the traditional series of oblongs'. This does not seem very likely, because the next step, that of putting six dots round the six, is so different in character from the putting of three dots round the first three.
Critical Apparatus
14 γιγνομένων‎ J1
Editor’s Note
15–6. Πλάτων … μικρόν‎. For the meaning of this cf. my note on Met. 987b 20. Prof. A. E. Taylor has put forward an ingenious and attractive theory of the meaning of the doctrine of the great and small (Mind, 1926, 419–40 and 1927, 12–33), but I have in my note on Theophr. Met. 6a 25 given reasons for doubting whether this can be accepted.
The reason given by Aristotle for Plato's describing the material principle in this way is ὅτι καὶ ἐπὶ τὴν αὐξὴν δοκεῖ ὑπερβάλλειν καὶ εἰς ἄπειρον ἰέναι καὶ ἐπὶ τὴν καθαίρεσιν‎ (206b 28), i.e. that plurality appears to be capable of indefinite extension both in the upward and in the downward direction.
Critical Apparatus
16 ἅπαντες ἀεὶ‎ Λ‎: ἀεὶ πάντες‎ E: πάντες‎ VPS
Editor’s Note
16. (2) The natural philosophers proper assign to the infinite element an underlying nature other than infinity (e.g. water, &c.). None of those who recognize a finite number of elements makes them infinite in extent; those who make them infinite in number, as Anaxagoras and Democritus do, describe the infinite as continuous by contact.
Editor’s Note
16. οἱ δὲ περὶ φύσεως‎. This, as in some other passages (e.g. Met. 1001a 12), excludes the Pythagoreans and Plato, who are thought of as being a priori theorists rather than genuine students of nature; it excludes also the Eleatics, who in denying the existence of movement denied the existence of φύσις‎, which is an ἀρχὴ κινήσεως‎; cf. 184b 17 n.
οἱ περὶ φύσεως πάντες‎ here means not all the physicists in the narrower sense but all of them who recognize the infinite; for some are said not to recognize it at all (a 18–19). Aristotle in effect divides οἱ περὶ φύσεως‎ (in the narrower sense) into three classes (though the first is not clearly marked off by him from the other two): (1) those who recognize one infinite body (a 16–18); (2) those who recognize a finite number of elements and do not think they make up an infinite whole (a 18–19); (3) those who recognize an infinite number of elements and treat them as making up an infinite whole (a 19–b 2).
Editor’s Note
17–18. ἑτέραν … στοιχείων‎, 'some other nature of the so-called elements', i.e. some underlying substance, viz. one of the so-called elements. For τῶν λεγομένων στοιχείων‎ cf. 187a 26 n.
Critical Apparatus
18 τὸ] τι‎ S
δὲ‎ om. E1
Editor’s Note
18. οἷον … ἀέρα‎. The reference is to Thales (ὕδωρ‎) and to Anaximenes and Diogenes of Apollonia (ἀέρα‎).
Editor’s Note
ἢ τὸ μεταξὺ τούτων‎. The reference (as in 205a 27, De Caelo 303b 12, De Gen. et Corr. 332a 20, Met. 989a 14) seems to be not to Anaximander (from whose doctrine the doctrine of the μεταξύ‎ is distinguished in 187a 14, 21) but to a member of the school of Anaximenes never named by Aristotle but identified (without much probability) by Diels with Idaeus; cf. 187a 14 n.
Editor’s Note
18–19. πεπερασμένα‎, finite in number; ἄπειρα‎, infinite in extent. The reference is to such thinkers as Empedocles.
Editor’s Note
21. τῶν ὁμοιομερῶν‎. Anaxagoras called these σπέρματα‎; Aristotle called them ὁμοιομερῆ‎ to bring out the fact that each portion of them has the same analysis as their whole mass (a 23–4).
Editor’s Note
τῆς πανσπερμίας τῶν σχημάτων‎, the differently shaped atoms which form the seed-bed, as it were, out of which all things grow.
Critical Apparatus
22 εἶναι τὸ ἄπειρον‎ F
Editor’s Note
22–3. τῇ ἁφῇ … φασίν‎. These thinkers recognize not one single infinite body (like the thinkers referred to in a 17), but an infinite number of bodies which make up an infinite whole only by continuity.
Critical Apparatus
23 ὁτιοῦν μόριον‎ E2IJPS
μῖγμα ὁμοίως‎ EP: ὁμοίως μῖγμα‎ Λ‎
Editor’s Note
23. Anaxagoras makes each part a mixture just as the whole is a mixture, because he sees everything coming out of everything. This is why he says all things were together. The separation of the various kinds of thing had a beginning, and this beginning was a single thing, such as what he calls reason, which must have had a beginning of its thinking and consequent action, so that before it began to act all things must have been together.
Critical Apparatus
24 γιγνόμενον‎ E2Λ‎P: γενόμενον‎ E1
Critical Apparatus
25 post καὶ‎ habent IJ et sup. lin. E τὸ‎
ἅπαντα‎ IJ et sup. lin. E: om. F
φάναι χρήματα‎ F: τὰ φάναι‎ E1
Editor’s Note
25. ὁμοῦ … εἶναι‎, fr. 1.
Critical Apparatus
a 26 ἄρα] κ̣α̣ὶ̣ ἄρα‎ E
Editor’s Note
27–8. καὶ … πὰντων‎. Since things existed ὁμοῦ‎, together in space, they existed ἅμα‎, simultaneously in time. For there was not only an originative source of the separation of each of them, but a single originative source of the separation of them all, and before this began to operate they must have existed simultaneously.
Critical Apparatus
28 τοῦ‎ om. I
Editor’s Note
28–33. ἐπεὶ … κινούμενα‎. The principal clause begins at καί τινα ἀρχήν‎ a 30.
Critical Apparatus
30 εἶναι δεῖ‎ Λ‎
Critical Apparatus
31 οἷον] ὃν‎ E2Λ‎
Editor’s Note
31–2. ὁ δὲ νοῦς … νοήσας‎, i.e. there must have been a moment of time at which the thought leading up to the separate activity of νοῦς‎ began; or perhaps the reference of ἀρχῆς τινος‎ may be to some principle the apprehension of which induced νοῦς‎ to begin its activity, or to some principle in its own nature which induced it to begin its work of separation.
Critical Apparatus
32 πάντα ποτὲ‎ I
Editor’s Note
33. Democritus describes none of his primary entities as coming into being out of another; but, for him, the universal bodily substance, whose parts differ only in size and shape, is the principle of all things.
Editor’s Note
33–b 2. Δημόκριτος … διαφέρον‎. While Anaxagoras says that out of every substance portions of all other substances may be separated, Democritus says there are atoms differing in size and shape (b 1–2) which cannot emerge out of each other. According to him all change is simply the regrouping of these unmodifiable elements. Still, since they differ in nothing but size and shape, they are themselves modifications of something that is common to them all, viz. σῶμα‎.
Critical Apparatus
34 φησίν] φύσεων‎ F
γε‎ EP: om. Λ‎
αὐτῷ‎ JP: αὐτῶν‎ E: αὐτὸ‎ FIV
Critical Apparatus
b 1 πάντων‎ EP: ἁπάντων‎ Λ‎
ἀρχή‎ om. E1
κατὰ τὰ μόρια‎ I
Editor’s Note
b 3. It is reasonable enough in these thinkers to describe the infinite as a principle. For (1) it cannot exist to no purpose, and it can have no function except as a principle. For everything is either a principle or derived from one, and the infinite cannot be derived from one, since then it would have a limit.
Critical Apparatus
5 γὰρ πάντες μάτην‎ E
οἷόν τε αὐτὸ‎ FI et fecit J1: αὐτὸ οἴονται‎ EV: αὐτὸ οἷόν τε‎ Bekker
αὐτῷ ὑπάρχειν‎ Λ‎
Critical Apparatus
7 ἂν‎ om. I
Editor’s Note
7. (2) Its being ungenerated and imperishable points to its being a principle; for there is a limit to all generation and destruction. This is why the infinite has no beginning but is itself thought to be the beginning of all other things and to contain and govern them, and to be what is divine.
Editor’s Note
b 7–9. ἔτι … φθορᾶς‎. The infinite is ingenerable and indestructible as being an ἀρχή‎, i.e. as it might be expected to be if it were an ἀρχή‎, so that its ingenerability and indestructibility confirm the view that it is an ἀρχή‎. Its ingenerability and indestructibility are themselves proved by the fact that if it were generated and destroyed its generation would come to an end when the whole of it had been generated, and its destruction when the whole of it had been destroyed; whereas that which is infinite has no last part to be generated or destroyed.
Critical Apparatus
8 ἀγένητον‎ EJS: ἀγέννητον‎ FI
Critical Apparatus
9 τέλος λαβεῖν‎ EP: λαβεῖν τέλος‎ Λ‎
Critical Apparatus
10 διόπερ καθὰ‎ I
Editor’s Note
11. πάντα κυβερνᾶν‎. Diels conjectures that this may be an expression of Anaximander's. The expression occurs also in Heraclitus fr. 41, Parmenides fr. 12. 3, but neither of these can be referred to here. The nearest extant parallel to the whole phrase περιέχειν ἅπαντα καὶ πάντα κυβερνᾶν‎ is Anaximenes fr. 2 οἷον ἡ ψυχὴ ἡ ἡμετέρα‎ ἀὴρ οὖσα συγκρατεῖ ἡμᾶς, καὶ ὅλον τὸν κόσμον πνεῦμα καὶ ἀὴρ‎ (Anaximenes' ἄπειρον‎) περιέχει‎.
Critical Apparatus
13 οἱονοῦν‎ E
Editor’s Note
13–14. ἀθάνατον … καὶ ἀνώλεθρον‎. Diels (Vors.3 17. 35) prints these words as a quotation from Anaximander, and so they may well be.
Critical Apparatus
14 ὥσπερ‎ Λ‎S: ὡς‎ E
φησὶν] φησὶν ὁ‎ F
Critical Apparatus
15 τι] τὸ‎ Sl
ἐκ πέντε‎ om. F
Editor’s Note
15. Belief in the infinite is derived from five sources: (1) from the infinity of time, (2) from the divisibility of magnitudes, (3) from the fact that the perpetuity of generation and destruction can be maintained only if there is an infinite source to draw upon, (4) from the fact that the limited is always limited by something else;
Critical Apparatus
16 συμβαίνει‎ E
Editor’s Note
17–18. χρῶνται … ἀπείρῳ‎, i.e. mathematicians assume that every line, plane, and solid is capable of being divided without limit.
Critical Apparatus
18 μαθητικοὶ‎ E
μόνῳ‎ J1
Editor’s Note
18–20. ἔτι … γιγνόμενον‎. This argument is ascribed to Anaximander (Plac. i. 3. 3). τὸ γιγνόμενον‎, sc. καὶ τὸ φθειρόμενον‎.
Critical Apparatus
19 ἐπιλείπειν‎ S
γένεσιν] τὴν γένεσιν‎ FST
εἰ …‎ 20 γιγνόμενον‎ om. E
Critical Apparatus
19 εἴη] ἦ‎ F
Critical Apparatus
b 20 τῷ‎ om. E
τὸ‎ om. F
Critical Apparatus
21 μηδὲν‎ Λ‎T: μηδὲ‎ E
Editor’s Note
22. but above all, the infinity of number, of magnitudes, and of what is outside the heavens is inferred (5) from the fact that there is no limit to our power of thinking of them; while the infinity of what is outside the heavens leads to belief in infinite body and in an infinite number of worlds. For why should there be body in one part of the void rather than in another? Further, if there is infinite void and place, there must be infinite body, since in eternal things there is no difference between being possible and existing.
Critical Apparatus
25 μαθητικὰ‎ E
Editor’s Note
25. τὸ ἔξω τοῦ οὐρανοῦ‎, the space beyond the heavens; cf. a 7.
Editor’s Note
26. καὶ κόσμοι‎. The doctrine of an infinity of worlds is ascribed to many of the early thinkers—Anaximander, Anaximenes, Archelaus, Xenophanes, Diogenes, Metrodorus of Chios, Anaxarchus, Zeno. But the reference to the void makes it probable that it is the Atomists that are chiefly referred to.
Editor’s Note
28–30. ἅνα … ἀϊδίοις‎. The argument is an abbreviated form of one ascribed by Eudemus (fr. 30 Spengel) to Archytas (S. 467. 26–35). As abbreviated it runs: 'even if we waive the previous argument and suppose that there is ⟨not body but⟩ void and infinite place beyond the universe, still, since ⟨place is that in which there can be body, and since⟩ in the case of eternal things what can be is, if there is infinite place there must be infinite body too'.
Critical Apparatus
29 σῶμα‎ EP: σῶμα ἄπειρον‎ Λ‎VS
ἀναγκαῖον εἶναι‎ Λ‎P
Critical Apparatus
30 τὸ γὰρ ἐνδέχεσθαι‎ Λ‎ST
ἢ] τοῦ‎ Λ‎ST
εἶναι] εἶναι ἢ‎ fecit E
Editor’s Note
30. There are, however, difficulties both in denying and in asserting the existence of the infinite. Further, is (1) the infinite a substance, or is (2) infinity an essential attribute of something else, or is (3) something per accidens infinite in extent or number? The problem
Critical Apparatus
31 μὴ] καὶ μὴ‎ I
Critical Apparatus
33 ἢ‎ om. E1
ὡς‎ om. Bekker
Critical Apparatus
34 μηδετέρως‎ AS
ἢ‎ EJV: καὶ‎ FIS
Editor’s Note
34–204a 1. ἢ οὐδετέρως … πλήθει‎; The suggestion is that, though there is nothing whose nature it is just to be infinite, and nothing to which infinity belongs as an essential attribute, there may be something which by pure accident is infinite or forms an infinite plurality.
Critical Apparatus
204a 3–14 = 1066a 35–b 7
Critical Apparatus
204a 14–17 = 1066b 9–11
Critical Apparatus
17–19 = 1066b 7–9
Critical Apparatus
20–31 = 1066b 11–21
Critical Apparatus
34–b 8 = 1066b 21–6
Critical Apparatus
204a 1 φυσικῶ‎ J
ἐστιν σκέψασθαι‎ Π‎P: ἐπισκέψασθαι‎ ST
Editor’s Note
204a 1–2. εἰ … ἄπειρον‎, i.e. whether there is a body that is essentially infinite, the second alternative mentioned above (203b 33–4).
Critical Apparatus
2 οὖν‎ om. F
Editor’s Note
204a 2. We must first distinguish the senses of 'infinite': (1) that whose nature forbids its being traversed, (2) that which admits of incomplete or (3) difficult traversal, or (4) which, though of such a nature as to be traversable, yet does not admit of it. Again what is infinite is so in respect of addition, of division, or of both.
Editor’s Note
3–6. ἕνα … πέρας‎. On the various meanings of α‎- privative, cf. Met. 1022b 32.
Editor’s Note
3–4. ἕνα … ἀόρατος‎. This is the purely negative sense ('not limited') in which even something non-quantitative such as a πάθος‎ or στιγμή‎ might be said to be ἄπειρον‎ (202b 33), as opposed to the privative sense in which ἄπειρον‎ might be applied to that which, being a ποσόν‎, so far as its generic nature goes might be traversed, but in virtue of its specific or individual nature cannot be completely traversed, or can be traversed only with difficulty.
Critical Apparatus
4 ἡ] δʼ ἡ‎ E
Critical Apparatus
5 μόγις‎ Π‎S: μόλις‎ MPT
Editor’s Note
5. ἢ ὃ μόγις‎. This is the colloquial sense in which, as S. 470. 24 says, a maze or a pit might be called endless.
Editor’s Note
6–7. ἢ κατὰ πρόσθεσιν … διαίρεσιν‎, either capable of being added to, or capable of being divided, without limit. According to Aristotle, number is infinite κατὰ πρόσθεσιν‎, space κατὰ διαίρεσιν‎, and time ἀμφοτέρως‎.
Editor’s Note
204a 8. (1) The infinite cannot exist apart from sensible things as something that is infinite and nothing else. For if it is neither a magnitude nor a plurality nor an attribute of any kind, but its substantial nature is just to be infinite, it must be indivisible, but if it is indivisible it cannot be infinite except in the sense that it is not finite; which is not the sense we are interested in.
Editor’s Note
204a 8–9. αὐτό … ἄπειρον = τι ὂν αὐτὸ ἄπειπον‎ (cf. a 17–18), 'something that is itself just infinite and nothing more' (cf. ἀλλʼ οὐσία αὐτό ἐστι τὸ ἄπειρον‎ a 10). The reference is to the Pythagorean and Platonic view: cf. 203a 4–6.
Critical Apparatus
10 ἀλλʼ οὐσία] οὐσία δὲ‎ Λ‎M
Critical Apparatus
11–12 διαιρετὸν … πλῆθος‎ Λ‎T: μέγεθος καὶ τὸ πλῆθος διαιρετόν‎ E
Critical Apparatus
12 τοιοῦτον] ἀδιαίρετον‎ Λ‎MS
Editor’s Note
12–13. εἰ μὴ … ἀόρατος‎, cf. a 3–4.
Critical Apparatus
13 εἶναι‎ pr. om. I
Critical Apparatus
a 14 ἀδιεξίτητον‎ PST: ἀδιεζήτητον‎ E: ἀδιέξοδον‎ Λ‎M
εἰ δὲ‎ Λ‎PST: ἔτι εἰ‎ EM
Editor’s Note
(14. If on the other hand infinity is an attribute of something else, the infinite cannot be, as infinite, an ultimate element of reality.)
Critical Apparatus
15 τῶν ὄντων στοιχεῖον‎ I
Critical Apparatus
16 ᾗ] ᾗ δʼ‎ I
οὐδὲ‎ E2Λ‎MT: om. E1
Editor’s Note
16–17. ὥσπερ … ἀόρατος‎. It is not the unseen as such, but voice, which is per accidens unseen, that is the ἀρχή‎ of speech.
Critical Apparatus
17 εἶναί τι αὐτὸ‎ EP: αὐτὸ εἶναί τι‎ Λ‎
Editor’s Note
17. (2) There cannot be an infinite which is nothing else, unless there are similarly a number and a magnitude that are nothing else. For infinity is an attribute of number and magnitude, and an attribute of an attribute is even less capable of independent existence than an attribute.
Critical Apparatus
18 μὴ καὶ‎ Λ‎M: καὶ μὴ‎ E
Critical Apparatus
19 αὑτὰ‎ E
ἔτι …‎ 20 μέγεθος‎ om. E1
Editor’s Note
19–20. ἔτι … μέγεθος‎. Number and extension exist not as separate entities but as attributes of things. Still less, then, can infinity, which is (if anything) an attribute of number and extension, exist as a separate entity.
Critical Apparatus
20 εἶναι‎ Π‎T: οὐσίαν εἶναι‎ PS
Editor’s Note
20. (3) If the infinite existed as a substance, then if it were divisible every part of it would be infinite (since if it is a substance, not an attribute, it must be infinite through and through). Therefore it is either (i) indivisible or (ii) divisible into infinites.
Critical Apparatus
21 ἐνεργείᾳ ὂν‎ Λ‎S: ἐνέργειαν ὂν‎ E: ἐνέργειαν‎ T: ἐντελεχείᾳ ὂν‎ P
ἀρχήν‎ Λ‎MVS: ἀρχήν, ἀλλʼ ἧττον ἢ τὸν ἀριθμὸν καὶ μέγεθος. ἔτι ἀδύνατον οὐσίαν εἶναι τὸ ἄπειρον ἐντελεχείᾳ ὄντος τοῦ ἀπείρου‎ (cf. a 19–21) E
Editor’s Note
21. καὶ ἀρχήν‎. Only if there is an infinite whose essence is just to be infinite, i.e. only if the infinite as such is a substance, is the infinite as such a first principle or element of reality. If it is an attribute, it will be (at best) the subject of that attribute that will be an ἀρχή‎. Cf. a 14–17.
Critical Apparatus
25 ἄπειρα] ἄπειρα ἀδιαίρετα‎ E1
πολλὰ δʼ‎ Λ‎MS: ἔτι πολλὰ‎ E
ἄπειρα τὸ αὐτὸ εἶναι ἀδύνατον‎ E: εἶναι ἄπειρον τὸ αὐτὸ ἀδύνατον‎ S: εἶναι τὸ αὐτὸ ἀδύνατον ἄπειρον‎ M
Editor’s Note
25. But (ii) the same thing cannot be many infinites. Therefore (i) it must be indivisible. But what is actually infinite cannot be this, since it must be a quantum. Therefore infinity must be an attribute of something else, and then not it, but (if anything) that of which it is an attribute, will be a first principle.
Critical Apparatus
26 ἀλλὰ μὴν ὥσπερ] ὥσπερ γὰρ‎ MVP et ut vid. T ἀὴρ μέρος ἀέρος‎ F
Critical Apparatus
27 γε‎ E2Λ‎P: om. E1M
ἐστὶ‎ E2Λ‎MP: om. E1
Editor’s Note
28. ἀλλʼ … ἄπειρον‎, sc. ἀμέριστον καὶ ἀδιαίρετον εἶναι‎.
Critical Apparatus
30 αὐτὸ] τὸ αὐτὸ‎ F
Editor’s Note
30. εἴρηται‎, a 14–17.
Critical Apparatus
31 ᾧ] ἐκεῖνο ᾧ‎ Λ‎M et fecit E1
ἢ‎ om. E1
ἄρτιον‎ Λ‎MV: ἄρτιον ἂν λέγοιτο ἀρχή‎ E
Editor’s Note
31. τὸν ἀέρα‎, a reference to the view of Anaximenes and Diogenes of Apollonia.
Editor’s Note
ἢ τὸ ἄρτιον‎, a reference to the Pythagorean view. Cf. 203a 10–15.
Critical Apparatus
32 οὕτως ὥσπερ] ἐκεῖνο καθάπερ‎ Λ‎
Editor’s Note
32. Thus the Pythagoreans must be wrong in making it at the same time a substance and divisible.
Critical Apparatus
34 ἴσως‎ Λ‎PS: γὰρ‎ E
ἐστι‎ Λ‎S: ἂν εἴη‎ EP: om. M
ἡ‎ Λ‎MPS: om. E
ζήτησις‎ EMVS: ζήτησις μᾶλλον‎ Λ‎P
Editor’s Note
34. But this inquiry, whether infinity can exist among mathematical objects and among intelligible and non-extended things, is a more general inquiry than that on which we are bent, viz. whether there is among sensible things a body infinite in extension.
Editor’s Note
34. καὶ μερίζουσιν‎. The Pythagoreans used, as one of their reasons for identifying the infinite with τὸ ἄρτιον‎, the fact that an even number can be divided by two. Cf. my notes on 203a 10–11 and on Met. 986a 18.
Editor’s Note
34–b 4. ἀλλʼ … αὔξησιν‎. Aristotle presupposes here a division of entities into (1) αἰσθητά‎, (2) μαθηματικά‎, (3) νοητά‎ which have no magnitude either sensible or mathematical. The νοητά‎ are pure forms; the μαθηματικά‎ are forms combined with ὕλη νοητή‎ or extension (Met. 1036a 9; cf. 1059b 15); the αἰσθητά‎ are forms combined with both ὕλη νοητή‎ and ὕλη αἰσθητή‎. Cf. my note on Met. 1030a 9–10. For the threefold classification cf. ib. 1026a 13–16. It is derived from Plato's recognition of τὰ μαθηματικά‎ as a class μεταξύ‎, between Forms and sensible things (Met. 987b 14–18); but Aristotle modified Plato's doctrine by treating forms (apart from a few cases such as God and the beings that move the planetary spheres, which are pure disembodied forms) and mathematical objects as elements in sensible things, separable only by abstraction.
Critical Apparatus
35 ἄπειρον] τὸ ἄπειρον‎ E2Λ‎
Critical Apparatus
204b 10–24 = 1066b 26–36
Critical Apparatus
204b 32–205a 7 = 1066b 36–1067a 7
Critical Apparatus
b 1 καὶ‎ alt.] καὶ ἐν τοῖς‎ Λ‎
ἡμεῖς δʼ ἐπισκοποῦμεν‎ fecit E
Critical Apparatus
3 ἐν … ἔστι‎ Λ‎S: ἢ οὐκ ἔστιν ἐν αὐτοῖς‎ E
Critical Apparatus
4 ἐπὶ] περὶ‎ Moreliana
Critical Apparatus
4 τῶν τοιῶνδε] τῶνδε‎ F
Editor’s Note
b 4. (A) On the face of it such a thing would seem impossible, since body is defined as that which is limited by a surface. On this showing there cannot be an infinite body either intelligible or sensible; nor, for that matter, can there be an infinite number since number (or that which has number) is that which can be numbered.
Editor’s Note
b 4. ἐπὶ τὴν αὔξησιν‎ = κατὰ πρόσθεσιν‎ a 6, infinitely extended, as opposed to infinitely divisible.
Editor’s Note
λογικῶς‎. Cf. 202a 21 n. The abstract argument (b 4–10) is one that applies to mathematical as well as to physical objects (οὔτε νοητὸν‎ (see b 6 n.) οὔτε αἰσθητόν‎ b 6); the concrete argument (b 10 ff.) applies only to physical objects and turns on the division of these into ἁπλᾶ‎ and σύνθετα‎ (b 11).
Critical Apparatus
5 λόγος τὸ‎ fecit E2
Critical Apparatus
6 ἐπιπέδῳ‎ Π‎T: ἐπιπέδοις‎ MS
Editor’s Note
6. νοητόν‎ here corresponds not to ἐν τοῖς νοητοῖς‎ (b 1) but to ἐν τοῖς μαθηματικοῖς‎ (a 35). The νοητά‎ of b 1 do not include σώματα‎ at all, for σώματα‎ must have μέγεθος‎. But τὰ μαθηματικά‎, which are combinations of form with ὕλη νοητή‎, may in a looser sense be called νοητά‎. Cf. Met. 1036a 2–5.
Critical Apparatus
7 οὐδʼ‎ EFP: οὔτε‎ IJ
Editor’s Note
7. ὡς κεχωρισμένος‎, sc. from numbered things.
Critical Apparatus
8 γὰρ‎ EFIJ1P: γὰρ ὁ‎ J2MS
Critical Apparatus
9 διεξελθεῖν‎ EIJPS: διελθεῖν‎ FT
Editor’s Note
10. (B) Passing to more concrete arguments, (1) the supposed infinite body must be either complex or simple. Now (a) it cannot be complex, if the elements are finite in number; for there must be more than one element, and (i) one element cannot be infinite and another finite; for even if the finite element exceeds the other in power, still, if it exceeds it by a limited amount, the infinite element will by its size destroy the other.
Editor’s Note
10. τὸ ἄπειρον‎, the supposed infinite number.
Critical Apparatus
11 τῶνδε δῆλον. οὔτε‎ MV
τε εἶναι‎ Λ‎M: εἶναι τὸ ἄπειρον σῶμα‎ EV
Critical Apparatus
12 ἔστι‎ FP
Editor’s Note
12–13. εἰ … στοιχεῖα‎. Aristotle does not in this proof (b 11–205a 7) consider the other alternative, that there is an infinite number of elements. Alexander complained that he overlooked it (S. 478. 18); but he has already disproved it in Phys. i. 6, and he takes account of it in a later argument (205a 29).
Critical Apparatus
13 στοιχεῖα εἴη. ἀνάγκη‎ FP
Editor’s Note
13. ἀνάγκη … εἶναι‎. If the elements are finite in number, it is in the abstract possible that there should be only one. But Aristotle has already refuted this possibility in i. 4, 5.
Critical Apparatus
15 ὁποσῳοῦν‎ EJV: ὁπωσοῦν‎ FI
Critical Apparatus
16 πεπέρασται‎ FI
Editor’s Note
17–18. μόνον … ἔχον‎, i.e. provided that the δύναμις‎ of a portion of fire exceeds that of an equal portion of air in a finite ratio.
Critical Apparatus
18 ὑπερβάλλει καὶ φθείρει‎ IJ et fecit E
Editor’s Note
19. And (ii) each element cannot be infinite, since what is infinite is infinite in all directions.
Critical Apparatus
20 μὲν‎ om. FIM
Critical Apparatus
21 πανταχοῦ‎ F: παντῇ‎ MP
ἔσται‎ IJMS: ἐστιν‎ E: om. F
Critical Apparatus
22 εἰς‎ Λ‎S: καὶ εἰς‎ E
εἶναι‎ om. F
Editor’s Note
22. (b) Nor can the infinite body be simple, either (i) as something other than the elements, out of which they are derived, or (ii) in general. (i) This view was adopted because it was thought that if one of the elements were infinite, it would destroy its contrary.
Critical Apparatus
23 ἐνδέχεται τὸ ἄπειρον σῶμα‎ Λ‎: τὸ ἄπειρον σῶμα ἐνδέχεται‎ P
Editor’s Note
23–4. οὔτε … γεννῶσιν‎. This may be a reference either to the ἄπειρον‎ of Anaximander (so Simplicius) or to an element intermediate between the four commonly recognized elements. The two views are distinguished in 187a 14, 21; the present reasoning would apply to both. But see next note.
Editor’s Note
24–9. εἰσὶν … ταῦτα‎. This appears to refer to one of Anaximander's arguments for the existence of an ἄπειρον‎ distinct from all the things of our world. He assumed a strife between the opposites that make up the world—warm and cold, dry and wet. If any one of these had been the fundamental reality, nothing else could ever have existed. Cf. Burnet, E.G.P., § 14, and the passages quoted by him.
Critical Apparatus
25 ποιοῦσι‎ Λ‎P: ποιοῦντες‎ E
ὅπως‎ IJP: ὡς‎ EF
Critical Apparatus
b 27–8 ψυχρός‎ (ψυχροῦς‎ E) … ὑγρόν‎ Π‎PST: ὑγρός … ψυχρόν‎ ci. S
Editor’s Note
27–8. οἷον … ὑγρόν‎. Aristotle holds that, strictly speaking, air is characterized primarily by being ὑγρός‎ and water by being ψυχρόν‎ (De Gen. et Corr. 331a 4–5); and he holds that air is not ψυχρός‎ but θερμός‎, in addition to being ὑγρός‎ (ib. 330b 4 et passim). Simplicius therefore suggests (481. 33) that there may be a scribal error, i.e. that the original reading may have been ὁ μὲν ἀὴρ ὑγρός, τὸ δʼ ὕδωρ ψυχρόν‎. But his other suggestion is more probable, that Aristotle in a purely illustrative reference to the four elements may not have aimed at strict accuracy. It may even be that when he wrote this he had not worked out the doctrine expounded in the De Gen. et Corr.
Critical Apparatus
28 ὧν] ὡς‎ T
Critical Apparatus
29 ἂν‎ om. F
φασιν εἶναι τὸ ἐξ‎ Λ‎
Editor’s Note
29. It is refuted by the fact that no such body other than air, fire, earth, and water is ever observed.
Critical Apparatus
30 μὲν‎ om. F
Critical Apparatus
33 καλούμενα στοιχεῖα‎ Λ‎T: στοιχεῖα καλούμενα‎ E
ἅπαν‎ IT: ἅπαν μὲν‎ F
Critical Apparatus
35 τι‎ EP: om. F, post 205a 1 εἶναι‎ ponunt IJ
Editor’s Note
35. (ii) Nor can the infinite be fire or any other element; for it is impossible for the universe, even if it be finite, to be or become identical with one of the elements; as it is impossible for it to be or become identical with the One apart from the elements which is posited by the physicists; in fact everything comes out of its contrary.
Critical Apparatus
205a 10–26 = 1067a 7–20
Critical Apparatus
205a 29–32 = 1067a 20–23
Critical Apparatus
205a 2 τὸ‎ Λ‎M: om. E
κἂν ᾖ‎ Λ‎M: ἠ καὶ‎ E
Editor’s Note
205a 2–7. ἀδύνατον … ψυχρόν‎. The reason why the universe can never have been, and can never come to be, identical with (a) one of the elements (a 2–3) or with (b) something more ultimate than the elements (a 4–5) is that everything comes out of its contrary (a 6–7). This premiss (which has itself been argued in i. 4, 5) proves the point, for Aristotle takes it as self-evident that (a) none of the four elements can be contrary to the other three, and that (b) something more ultimate than the four elements cannot be contrary to them all. The argument is made clearer by putting ὁ δʼ αὐτὸς λόγος … φυσικοί‎ a 4–5 in brackets.
Editor’s Note
3–4. ὥσπερ Ἡράκλειτος … πῦρ‎, frr. 30, 31, 63–6, 90. What Aristotle ascribes to Heraclitus is not the belief in a future simulaneous conflagration of all things (so Zeller i6. 867), but the view that all things at one stage in their cyclical process of change become fire. The evidence for a Heraclitean doctrine of a general conflagration is late and untrustworthy; cf. Burnet, E.G.P., §§ 77–8.
Critical Apparatus
4 φησι δὲ ἅπαντα‎ E
Editor’s Note
5. τοῦ ἑνὸς … φυσικοί‎, cf. 204b 23–6.
Critical Apparatus
6 πᾶν‎ MP
ἐναντίον‎ Λ‎P: ἐναντία‎ E
Critical Apparatus
7 κατὰ] περὶ‎ E2FIPS
ἐκ] καὶ ἐκ‎ Λ‎VPS
Editor’s Note
205a 7. (2) The impossibility of an infinite sensible body may be seen also from the following considerations: Every kind of sensible body has a place where it tends to be, and this is the same for a part as for the whole. Thus (a) if the infinite body is homogeneous, every part will be either immovable or always in movement, yet both are impossible; for in the infinite place proper to the infinite body why should it move or rest in any direction rather than in another?
Editor’s Note
7. κατὰ παντός‎, i.e. the following argument is one which is equally applicable whether the infinite body is supposed to be one of the commonly recognized elements (204b 35–205a 4) or something apart from these (205a 4–5).
Critical Apparatus
8 ἢ οὐκ ἐνδέχεται‎ om. F
εἶναι … αἰσθητόν‎ F: σῶμα εἶναι ἄπειρον αἰσθητόν‎ IJ: εἶναι ἄπειρον‎ S: εἶναι‎ E
Critical Apparatus
9 εἶναι … αἰσθητόν‎ Π‎P: secl. Prantl
Editor’s Note
11. καὶ … παντός‎. Aristotle does not mean that the place (i.e. τὸ τοῦ περιέχοντος πέρας‎, the inner limit of that which contains the thing, 212a 20) of a whole is identically the same as that of any of its parts, but that the region of the universe proper to a whole is also the region proper to each of its parts. A clod of earth tends to fall towards the region proper to the earth, i.e. the part of the universe next the centre.
Critical Apparatus
12 βώλου μιᾶς‎ ES: μιᾶς βώλου‎ Λ‎T
Editor’s Note
12–b 1. ὥστε … εἶναι‎. The argument against an infinite body based on difficulties about its place discusses it under two alternative hypotheses, (a) that it is homogeneous throughout (a 12–19), (b) that it contains parts of different nature (a 19–b 1).
Editor’s Note
12–19. ὥστε … στήσεται‎. The argument to show that there cannot be a homogeneous infinite body is difficult. Aristotle first states the general position and then (a 14–19) illustrates it by taking a particular case. The general argument is:
  • (A) If the infinite body is homogeneous, it will be immovable or else always in motion.

  • (B) Both are impossible, for

  • (C) why should it rest, or move, down or up, or anywhere in particular, rather than anywhere else?

(Therefore (D) there cannot be a homogeneous infinite body.)
The justification for (A) is as follows: Since the whole is homogeneous, there is no part of its place which is more appropriate to one part of the whole than to another. The natural conclusion is that each part, and therefore the whole, should remain where it is. But if the whole should move, then since no part of its place is a more appropriate resting-place for any part of the whole than any other, it will never cease moving.
(B) καίτοι ἀδύνατον‎ must be taken to set aside both these alternatives. This it will do if τί … ὁπουοῦν‎; be taken to mean 'why should any part of the whole be resting unmoved, or be moving, in the downward or the upward or any particular region?' The question is grounded on the fact that, the whole being homogeneous, every part of its region is equally proper to every part of the whole. κάτω, ἄνω, ὁπουοῦν‎ must refer to the places of rest, or motion, of the parts of the infinite whole; as applied to the place of the whole itself they would be unmeaning. Accordingly Aristotle proceeds to illustrate his argument by the case of a clod of earth.
He considers and rejects various alternatives that present themselves. (1) Will the single clod occupy the whole region of earth? Obviously not. (2) How else can it rest, or move? (a) Suppose it to rest somewhere, it will equally well rest everywhere (all parts of the region of earth being alike to it), and so will never move. (b) Suppose it to move in one place, it will equally move everywhere, and so will never rest. That it should never move, and that it should never rest, Aristotle treats as alike absurd, in view of his experience of the fact that earth sometimes moves, viz. when it is not as near the centre of the universe as it can get, and sometimes rests, viz. when it is as near as it can get.
Critical Apparatus
14 ὁπουοῦν‎ MV Bonitz: ποῦ‎ EIJ: ὁποιονοῦν‎ F
Critical Apparatus
16 αὐτῆς‎ EM
Critical Apparatus
17 ἢ‎ EFP: καὶ‎ IJ
ἡ‎ om. F
Critical Apparatus
a 18 αὐτῆ‎ E1
οὐ …‎ 19 στήσεται‎ Λ‎MP: om. E
Critical Apparatus
19 ἀνόμοιον‎ Π‎M: ἀνομοειδὲς‎ S
Editor’s Note
19. (b) If the whole is not homogeneous, the proper places of its parts will be unlike. Then (i) the body of the whole will be one only by contact. (ii) The parts will be either finite or infinite in variety of kind. (a) Finite they cannot be, for then if the whole is to be infinite some parts must be infinite and others not, and the infinite will be death to the finite.
Editor’s Note
19. τὸ πᾶν‎, the whole infinite body.
Critical Apparatus
20 πᾶν‎ Λ‎MP: ἅπαν‎ E
Critical Apparatus
21 τῷ‎ Λ‎M: τοῦ‎ E
Critical Apparatus
22 ἔσται‎ Λ‎M: ἐστιν‎ E
πεπερασμένα μὲν οὖν‎ EFMP: καὶ πεπερασμένα μὲν‎ IJ
Editor’s Note
22. ταῦτʼ‎, the unlike parts of the infinite body.
Critical Apparatus
23 εἰ] ἢ‎ J
Editor’s Note
23–4. ἔσται … ἄπειρον‎. Since finite amounts of each of a finite number of kinds of body cannot make up an infinite whole, there would have to be infinite amounts of some of these kinds, and finite amounts of others. Aristotle silently rejects the possibility of there being infinite amounts of each of the kinds, because they would be limited by each other and therefore not be infinite.
Critical Apparatus
25 καθάπερ … πρότερον‎ om. EM
καὶ …‎ 29 κάτω‎ hic Π‎PST: post b 1 εἶναι‎ ponenda ci. Pacius: ante καὶ‎ lacunam statuit Hayduck
Editor’s Note
29. (β‎) If they are infinite and simple, their places will be infinite in number, and so will the elements be. But the possible places are limited in number, and so must the whole be. For a body and its place must fit each other; the place must not be greater than what will hold the body, nor the body greater than the place; for then there would be either a void, or a body with no proper place.
Editor’s Note
25. This is why the physicists identify the one infinite body not with fire or earth, but with water or air or their intermediate; that is because the place of the latter is indeterminate in respect of up and down.
Critical Apparatus
30 ἁπλᾶ‎ Λ‎MPS: τὰ ἁπλᾶ‎ E
ἔσται‎ post στοιχεῖα‎ F
Editor’s Note
30. καὶ ἔσται … στοιχεῖα‎. This consequence of the hypothesis is not used in the refutation, which directs itself to the other consequence οἱ τόποι ἄπειροι‎. But Aristotle has proved elsewhere that there cannot be an infinite number of elements (i. 6).
Editor’s Note
30–1. εἰ … τόποι‎. Aristotle assumes that space has just three dimensions, each of which extends in two directions (b 31–3).
Critical Apparatus
31 καὶ‎ alt. Λ‎M: ὥστε καὶ‎ EV
ἀναγκαῖον πεπεράνθαι‎ M: om. E
Editor’s Note
31. καὶ τὸ ὅλον‎, i.e. the universe must contain a finite number of kinds of part, and therefore (in view of the argument in a 22–5) be itself finite.
Editor’s Note
33–4. οὔτε … εἶναι‎. If Aristotle had been speaking of the place actually occupied by a body, he would have said ἢ ὅσον τὸ σῶμά ἐστι‎.
Since he is speaking of the proper place, to which a body tends, he says ἢ ὅσον ἐνδέχεται τὸ σῶμα εἶναι‎, 'than what the body is capable of filling'.
Critical Apparatus
34 σῶμα‎ EPT: σῶμα ἅμα‎ Λ‎
οὐδʼ‎ Λ‎PST: om. E
Critical Apparatus
35 ἔτι‎ EP: om. Λ‎
Critical Apparatus
25 τοῦτο θεὶς‎ E1
Editor’s Note
25–8. καὶ … κάτω‎. This section is quite out of place where it occurs in the MSS. and Greek commentators, viz. before εἰ δʼ ἄπειρα‎ in a 29; for it does not turn on the destruction of one element by an infinite contrary element (a 24–5), and in fact contemplates not a plurality of elements at all but a single infinite element (a 26). The words fit in better where I have, on Pacius' suggestion, placed them. They do not occur at all in Met. K, where 1067a 18–23 answers exactly to 205a 22–32 without this section. Their absence from K is less surprising if we suppose them to have occurred in the Physics where I have placed them; for the whole of Phys. 205 a32–b 24 is omitted in K.
The section fits in well after a 29–b 1, for it turns on the point raised there, of the necessity for each element and its proper region fitting one another. Fire has a determinate τόπος‎, viz. the circumference of the universe, and earth has a determinate τόπος‎, viz. the centre of the universe; therefore neither fire nor earth can be supposed to be itself infinite, but (if anything) only air or water (since these tend to occupy the interspace between circumference and centre, and thus 'share the properties of upness and downness', have both an upward and a downward tendency), or a supposed intermediate between them.
Alternatively we might suppose with Hayduck that there is a lacuna after πρότερον‎ in a 25, where there stood something answering to Themistius' words (88. 27–9) προσέτι δὲ οὐδὲ οἷόν τε ἓ τῶν στοιχείων ἄπειρον εἶναι ἐν τῇ συνθέσει ὂν πῦρ ἢ γῆ. ὥρισται γὰρ ἑκάστου τούτων ὁ τόπος, καὶ οὐ πᾶς οἰκεῖος ἅπαντι, ἀλλὰ τῷ μὲν ἄνω τῷ δὲ κάτω‎.
Editor’s Note
25–6. καὶ … φυσιολόγων‎. Aristotle says in Met. 989a 5–8 that each of the four elements except earth has found an advocate among the physicists. But it is true that fire does not play the same part in Heraclitus' system that air or water does in some others. Fire is in his system only one of the phases through which everything passes (cf. 205a 3–4 n.), and is, apart from this, simply a symbol of the change and destruction which is the law of the universe. The reason given in the Metaphysics for earth not having been treated as the element is different from that here mentioned. In 189b 5–8 yet another reason is given for the preferability of air and water as elements. Aristotle is in each case simply guessing.
Critical Apparatus
26 ἓν καὶ ἄπειρον‎ EIJP: ἄπειρον καὶ ἓν‎ F: ἄπειρον‎ T
Critical Apparatus
27 ἢ‎ pr. om. E2T
Editor’s Note
27. ἢ ὕδωρ‎ probably refers to Thales, though he does not seem to have characterized water as infinite.
Editor’s Note
ἢ ἀέρα‎ refers to Anaximenes.
Editor’s Note
ἢ τὸ μέσον αὐτῶν‎. Cf. 203a 18 n.
Critical Apparatus
205b 24–206a 7 = 1067a 23–33
Editor’s Note
b 1. Anaxagoras has an absurd argument about the stationariness of the infinite body. He says it steadies itself because it is in itself (since there is nothing else surrounding it), on the ground that where a thing is, there it is its nature to be.
Critical Apparatus
b 3 αὑτό] αὑτῷ‎ E2 et ut vid. T
Editor’s Note
b 3–4. τοῦτο … εἶναι‎. Anaxagoras' argument as stated by Aristotle (we have no other evidence for it) is: the infinite is in itself (since there is nothing bigger than it for it to be in); now where a thing is, there it is its nature to be; therefore it is the nature of the infinite to be in itself; therefore it supports itself in its existing position. Aristotle criticizes by saying that the fact that a thing is where it is does not prove that it is not its nature to move elsewhere; it might be kept where it is by βία‎. Thus even if we admit for the sake of argument that the infinite is at rest, being self-supported, it has still to be shown why it must be at rest.
Critical Apparatus
4 οὐδὲ‎ E
περιέχειν‎ T et ut vid. PS, Bonitz: περιέχει‎ Π‎
εἶναι‎ Λ‎PS: ὂν‎ E
Editor’s Note
5. But (1) a thing may be where it is, under compulsion. (2) However much the whole is stationary (since that which is steadied by itself must be stationary), it is still a question why it is not its nature to be moved. It is not enough to leave the matter as Anaxagoras has left it; the infinite might be stationary because it has nowhere to move to, and yet its nature might be to move.
Critical Apparatus
6 κινῆται‎ J
γὰρ] γὰρ ἐν‎ Λ‎PS
Critical Apparatus
b 9–10 ὅτι … κινεῖσθαι‎ EPST: ὁτιοῦν ἄλλο‎ Λ‎
Editor’s Note
9–10. εἴη … κινούμενον‎. It is clear that Themistius (89. 25), Philoponus (449. 13–14, 451. 16), and Simplicius (486. 1–2) had before them E's reading εἴη γὰρ ἂν καὶ ὅτι οὐκ ἔχει ἀλλαχῆ κινεῖσθαι οὐ κινούμενον‎, 'for it might be at rest because it has nowhere else to move to', and yet it might be its nature to move.
Editor’s Note
10. The earth does not move, and would not do so if it were infinite, provided it were prevented by the centre of the universe; but it would rest, not because there is nowhere for it to move to but because it is its nature to rest at the centre. Yet it might be said to steady itself.
Editor’s Note
10–18. ἐπεὶ … ἑαυτό‎. The earth also might be described as supporting itself (b 13–14). But that explains nothing. In the case of the earth we can reject the explanation of immobility suggested above, that it has nowhere else to move to. Its immobility is produced by the attraction exercised on it by the centre of the universe (b 11), or in other words by the nature of earth (b 13), which is to move to the centre and rest there, or in other words by its having weight (b 15). So, too, a definite reason should be given for the immobility of the infinite body.
Critical Apparatus
11 εἰργμένη‎ Λ‎P: ἠργμένη‎ fecit E
ὑπὸ‎ S: ἀπὸ‎ Π‎
Critical Apparatus
12 μείνη‎ F: μένειεν‎ IJ
Critical Apparatus
13 ἐπὶ τοῦ μέσου‎ om. E et fort. S
ὅτι‎ E1VT: ὅτι οὐ‎ E2Λ‎
λέγειν ἂν‎ I
Editor’s Note
14. If, then, the earth (if supposed infinite) would rest where it does, not for the alleged reason, but because it has weight and what is heavy rests at the centre, similarly the infinite body will rest in itself not because it is infinite and steadies itself, but for some other reason.
Critical Apparatus
16 ἡ … μέσου‎ om. I
Critical Apparatus
17 ἐν‎ EFS: ἂν ἐν‎ IJ
τινα‎ fecit E2
Critical Apparatus
18 ἑαυτό‎ E1FPS: αὐτό‎ J2: αὑτῷ‎ E2J1 et ut vid. T: αὐτῶ‎ I
Editor’s Note
18. (3) On that showing every part should be stationary; for the places of the whole and of its parts are similar.
Editor’s Note
18–24. ἅμα … ἑαυτῷ‎. Aristotle now confirms his refutation of Anaxagoras' explanation of the immobility of his infinite body (a 1–18), by showing that on that basis every part of the infinite body, i.e. every sensible body, ought to be always at rest.
Critical Apparatus
20 μένει‎ EFS
Critical Apparatus
23 τὸ ἐν αὑτῷ‎ Λ‎S: om. E
Critical Apparatus
24 μένει‎ E
ἄπειρον ἅμα‎ ES: ἅμα ἄπειρον‎ IJM: ἅμα‎ F: τὸ ἄπειρον ἅμα‎ P
Editor’s Note
24. In general, there cannot be an infinite body and at the same time proper places for bodies, if any sensible body has either weight or lightness and therefore tends either to or from the centre; for then the infinite must do so too, but neither can the whole of it do either nor can each half of it do one of the two; for how can you divide the infinite into up and down, or extreme and middle?
Editor’s Note
24–31. ὅλως … μέσον‎; Aristotle now passes to a further attack on the belief in an infinite body, by showing that it is incompatible with the assigning of a proper place to bodies. The argument is that if you assign a proper place to bodies, and say that every sensible body tends to move either to or from the centre of the universe, you ought to say the same of the infinite body; but neither can it as a whole have one of the two movements nor can each half of it have one of the two; for how can you divide an infinite into halves, or how can part of it be up and part down, or part circumference and part centre?
Critical Apparatus
28 ἄπειρον σῶμα, ἀδύνατον‎ IJ
ἢ ἅπαν] εἶναι πᾶν‎ corr. E: ἢ πᾶν‎ MS
Critical Apparatus
30 διέλης‎ fecit E
τὸ μὲν ἄνω ἔσται‎ I
Critical Apparatus
31 καὶ‎ MVPS: ἢ‎ Π‎
Editor’s Note
31. Again, every sensible body is in a place, and the varieties of place are up and down, before and behind, right and left; and these exist not merely in relation to us, but absolutely. But these varieties cannot exist in what is infinite. In general, if there cannot be an infinite place, and if every body is in place, there cannot be an infinite body.
Critical Apparatus
32 τἄνω καὶ κάτω‎ om. J1
καὶ‎ alt.] τὸ‎ IJ2: καὶ τὸ‎ F
καὶ ἔμπροσθεν‎ ET: καὶ τὸ ἔμπροσθεν‎ F: τὸ πρόσθεν‎ IJ
Editor’s Note
33–4. καὶ ταῦτα … διώρισται‎. Cf. 208b 8–22. Aristotle discusses in De Caelo iv. 1 the view that there is no absolute up or down in the universe (308a 17), and declares that there is an absolute up, the circumference of the universe, and an absolute down, its centre (ib. 21, 30). (Elsewhere he lays it down that the south pole is absolutely the ἄνω πόλος‎ and the north pole the κάτω‎ (De Caelo 285b 14), but that is not his usual way of defining the ἄνω‎ and κάτω‎.) Again, the right side of the universe is stated to be that in which the stars arise, and the left that in which they set (De Caelo 285b 16). In De Caelo ii. 5 Aristotle says that the movement of the heavens must be supposed to proceed forwards and not backwards; but that does not give us a definite ἔμπροσθεν‎ and ὄπισθεν‎ in the universe, since the movement is circular.
Critical Apparatus
34 θέσει ἐστὶν ἀλλὰ‎ E2IJ
Critical Apparatus
b 35 ἀπείρῳ σώματι εἶναι‎ EMVPS
εἰ‎ om. E
Critical Apparatus
206a 1 τὸ τόπον‎ I
ἄπειρον εἶναι‎ EMS: εἶναι ἄπειρον‎ Λ‎P
πᾶν‎ Λ‎PS: πᾶν τὸ‎ E
Critical Apparatus
2 τι εἶναι‎ EF: εἶναί τι‎ IP: εἶναι‎ ST
Editor’s Note
206a 2. But what is somewhere is in place, and what is in place is somewhere. Just as what is infinite cannot have size since it would have to have a particular size, that being what having size means, so being in place means being somewhere—up or down or in some other of the six directions, each of which has a limit.
Critical Apparatus
3 πόσον γὰρ‎ Λ‎
Editor’s Note
206a 3–5. εἰ … πού‎. The construction of this sentence is difficult, and Bonitz thought it necessary to read in a 5 οὕτω οὐδὲ ἐν τόπῳ, ὅτι ποῦ‎ (sc. ἔσται‎), where οὐδὲ ἐν τόπῳ‎ is parallel to μηδὲ ποσόν‎ in a 3, ποσὸν γὰρ … ποσόν‎ a 3–5 being parenthetical. Bonitz thinks that the Greek commentators all support his reading. It is impossible to be certain what Themistius (91. 4–5) and Philoponus (464. 1–5) read. Simplicius read καὶ τὸ ἐν τόπῳ‎ (490. 27) (τῷ‎ before τόπῳ‎ in the MSS. of S. is plainly corrupt), and his οὐδὲ ἐν τόπῳ‎ (ib. 22) is merely paraphrase.
The reading of the MSS. and Simplicius may be justified if we treat ποσὸν γὰρ … ποσόν‎ a 3–5 as parenthetical, and suppose that the apodosis takes a form conforming not to the protasis but to the end of the parenthesis. 'If, then, the infinite cannot be a quantum—for it would have to be a particular quantum, e.g. two or three cubits long; for that is the sort of thing that "a quantum" means—so, too, "in place" means' (understand σημαίνει‎) 'that a thing is in a particular place' (sc. and therefore the infinite cannot be in place any more than it can be a quantum). Cf. Met. 1067a 31 (the parallel passage) τὸ γὰρ ἐν τόπῳ πού, τοῦτο δὲ σημαίνει ἢ ἄνω κτλ‎.
Critical Apparatus
4 δίπηχυ ἢ τρίπηχυ‎ Λ‎VPST: τρίπηχυ ἢ δίπηχυ‎ E
Critical Apparatus
5 καὶ τὸ‎ Λ‎S: καὶ‎ E: οὐδὲ‎ Bonitz
ἐν‎ Λ‎ST: om. E
ἢ‎ om. F
Critical Apparatus
6 ἄνω ἢ κάτω‎ Λ‎MVST: κάτω ἢ ἄνω‎ E
τοῦ‎ E
Critical Apparatus
7 οὐκ ἔστι σῶμα‎ EFS: σῶμα οὐκ ἔστιν‎ IJ
Editor’s Note
7. Clearly then there is no actually existent infinite body.
Critical Apparatus
8 τούτων] τῶν εἰρημένων‎ F
Critical Apparatus
9 ἁπλῶς] μηδὲ ἄλλως‎ Pl: μηδαμῶς‎ Pp
Editor’s Note
206a 9. On the other hand the complete denial of an infinite involves many difficulties. Time will have a beginning and end, there will be magnitudes not divisible into magnitudes, and number will not be unlimited. Clearly then we need an arbitrator between the opposing views; each view must be in some sense true.
Critical Apparatus
11 εἰς μέγεθος‎ Λ‎
Editor’s Note
206a 11. καὶ … εἰς μεγέθη‎, 'and magnitudes will not be invariably divisible into magnitudes.' If infinite divisibility be denied, there are indivisible magnitudes; which are proved in vi. 1 to be impossible.
Critical Apparatus
12 διωρισμένων οὕτως‎ E2Λ‎P: ὡρίσωμεν οὕτως καὶ‎ E1
φαίνεται‎ F
Editor’s Note
13. διαιτητοῦ δεῖ‎. Cf. De Caelo 279b 11.
Critical Apparatus
14 δὴ] δὲ‎ F
τὸ‎ pr. om. S
Editor’s Note
14. 'To be' means (1) to exist potentially, (2) to exist actually; what is infinite is infinite by addition or by division. Spatial extension is not infinite in actuality, but is so (a) by division (the belief in indivisible lines is easily refuted); therefore the spatially infinite must exist potentially.
Critical Apparatus
15 καὶ‎ alt. om. F
διαιρέσει‎ E1FJ2PST: ἀφαιρέσει‎ E2IJ1V
Editor’s Note
15. καὶ … διαιρέσει‎. Aristotle takes up at once (a 16–b 3) the ἄπειρον διαιρέσει‎, and explains in b 3–12 the ἄπειρον προσθέσει‎.
Editor’s Note
διαιρέσει‎. This is the reading of T. 91. 22, P. 464. 21, 24, and S. 491. 28, and διαίρεσις‎ occurs elsewhere in the context (a 17, b 4, 17, 19, 27, cf. 203b 17, 204a 7). καθαίρεσις‎ also occurs, b 13, 29, 31, 207a 23, 208a 21. The reading ἀφαιρέσει‎ may owe its origin to the fact that ἀφαίρεσις‎ is the obvious opposite of πρόσθεσις‎. But the process Aristotle has in mind is essentially one of division.
Critical Apparatus
17 αὐτομάτους‎ F
Editor’s Note
17. εἴρηται‎, ch. 5.
Editor’s Note
τὰς ἀτόμους γραμμάς‎. This doctrine is ascribed to Plato in Met. 992a 20–22, and to Xenocrates by later writers (Proclus, in Tim. 36b, ii. 246 Diehl, in Encl. 279. 5 Friedlein; Al. in Met. 120. 6, 766. 33; T. in Phys. 12. 6; P. in Phys. 83. 20, 84. 20; S. in Phys. 138. 14, 140. 12, 142. 16, in De Caelo 563. 22, 665. 7; Syr. in Met. 124. 2). The pseudo-Aristotelian treatise De Lineis Insecabilibus is apparently directed against Xenocrates' view. In my note on Met. 992a 20 I have discussed the reasons which may have led Plato and Xenocrates to this strange belief. Aristotle discusses this view in Phys. vi. 1.
Editor’s Note
18. We need not suppose that this involves that it will sometime exist actually. 'To be' has more than one meaning; the being of the infinite is analogous to that of a contest, whose being consists in one thing happening after another. Even in such a case the contrast of 'potentially' and 'actually' is found; there 'are' Olympic games both in the sense that the contest may take place and in the sense that it is taking place.
Editor’s Note
18. δυνάμει‎, i.e. by virtue of the potentiality which spatial extension has of being divided without limit.
Editor’s Note
18–25. οὐ … τῷ γίγνεσθαι‎. Aristotle here in effect divides τὰ δυνάμει ὄντα‎ into two kinds—one whose potentiality can be completely realized once for all (as the bronze which is potentially a statue becomes actually a statue), and one whose potentiality admits of progressive realization but is never completely realized at any one time. Thus when it is night, or before the Olympic games have begun, we may say 'there is (sc. potentially) such a thing as day' or there are Olympic games', and later we may say 'it is (actually) day' or 'it is (actually) the Olympic games to-day' (a 24–5), but the actualization is not such that the whole day or the whole of the games exists at any one time. Their actualization is essentially a process, a fieri. The infinite admits only of such an actualization as this; we can say of it 'it is being actualized', but never 'it has been actualized.'
Critical Apparatus
19 τουτὶ‎ S
Critical Apparatus
20 τοῦτʼ‎ Λ‎S: om. E καὶ ἄπειρον‎ EP: καὶ ἄπειρόν τι‎ F: τι καὶ ἄπειρον‎ IJS
Critical Apparatus
21 ἡ‎ om. EIJ
Critical Apparatus
22 ἔστι‎ om. S
Critical Apparatus
23–5 καὶ γὰρ … τῷ γίγνεσθαι‎ Λ‎P: om. E
Critical Apparatus
23 καὶ‎ ult. om. F
Critical Apparatus
25 ἄλλως δʼ‎ Λ‎S: καὶ ἄλλως δὲ‎ P: καὶ ἄλλως τε‎ E
τε‎ EIS: om. FJ
Editor’s Note
25. The infinite exhibits itself (i) in one way in time and in the generations of mankind, (ii) in another in the division of spatial magnitudes. In general the infinite exists by one thing being taken after another, each being limited but a new one always being available; but in case (ii) what was previously taken persists, while in case (i) each member of the series perishes, but so that the series does not fail.
Editor’s Note
25–b 3. ἄλλως … ἐπιλείπειν‎. Having compared the progressive but never complete realization of the infinite to that of a day or a contest, Aristotle now points out that nevertheless the actualization of infinity admits of two kinds. The realization of both alike consists in the emergence of a series of parts each of which is itself limited but has successors which follow upon it without limit; but in the realization of infinity in a spatial magnitude by successive divisions of it each part persists after it has been called into being by an act of division; while in the progressive realization of time or of a natural kind such as mankind each member perishes, yet so that the succession never fails.
It will be seen that a 27–9 ὅλως … καὶ ἕτερον‎, a 33–b 3 ἀλλʼ … ἐπιλείπειν‎ form a single sentence such as is required to justify the general statement in a 25–7 ἄλλως … μεγεθῶν‎; a sentence which would be seriously interrupted by the section a 29 a–33 ἔτι … καὶ ἕτερον‎. It is plain too that ἔτι … καὶ ἕτερον‎ is an alternative version of a 18–29. Themistius seems, as his editor Schenkl observes (note on 92. 22) to have had a conflation of both versions before him (cf. 92. 20 with a 19, 92. 25 with a 31). Philoponus says (468. 9) that the second version was omitted in the more accurate MSS. Simplicius says (495. 8) that it was omitted in many of the MSS. and that Alexander was aware of this. It was probably an alternative version which occurred in the margin of the original and was at an early date incorporated into the text in most of the MSS.
Editor’s Note
25–7. ἄλλως … μεγεθῶν‎. Aristotle means to distinguish not three but two modes of realization of the infinite; χρόνος‎ and ἄνθρωποι‎ are contrasted with ἡ διαίρεσις τῶν μεγεθῶν‎, as is evident from a 33–b 3.
Critical Apparatus
26 τὸ ἄπειρον‎ Λ‎P: om. E
Critical Apparatus
a 28 καὶ … τὸ‎ E2Λ‎PS: ἄλλο‎ E1
μὲν ἀεὶ πεπερασμένον εἶναι‎ Λ‎Sp: μὲν ἀεὶ πεπερασμένον‎ Sc: εἶναι μὲν ἀεὶ πεπερασμένον‎ P
Critical Apparatus
29a ἔτι‎ (ὅτι‎ E2) … λέγεται‎ EVPS: om. Λ‎ γρ‎. A γρ‎. P γρ‎. S
ὥστε‎ … 33 ἕτερον‎ Π‎PS: om. γρ‎. A γρ‎. P γρ‎. S
Critical Apparatus
30 τὸ] τὸ ἐπʼ‎ S
οὐδεὶς λαμβάνει‎ E
Critical Apparatus
31 ἡ‎ IJST: om. EF
οἷς] ἃ‎ fecit E
Critical Apparatus
32 τις‎ om.
ἢ‎ F2IJS: καὶ‎ EF1
Critical Apparatus
33 πεπερασμένον‎ IJS: εἰ πεπερασμένον‎ fecit E: εἰ καὶ πεπερασμένον‎ F
γε‎ EIJSp: om. FSc ἐν‎ EIP: ἐν μὲν‎ FJ
Critical Apparatus
b 1 τοῦτο συμβαίνει‎ Λ‎P: om. E
Critical Apparatus
2 τοῦ … ἀνθρώπων‎ EP: τῶν ἀνθρώπων καὶ τοῦ χρόνου‎ Λ‎
οὕτως‎ E2Λ‎S: om. E1
Critical Apparatus
3 ἐπιλείπειν‎ E1S: ὑπολείπειν‎ E2Λ‎
ἐστί πως‎ EP: πώς ἐστι‎ S: πῶς ἐστι‎ Λ‎
Editor’s Note
b 3. (b) The infinite in respect of addition is in a sense the same thing as the infinite in respect of division; for where division is going on indefinitely, the part first marked off is being indefinitely added to. For if in a finite magnitude you take a determinate part and add to it in a constant ratio less than 1:1, you will never exhaust the finite whole (though if you increase the ratio to 1:1 you will exhaust the whole).
Editor’s Note
b 3–12. τὸ δὲ κατὰ πρόσθεσιν … ὡρισμένῳ‎. Aristotle now explains the sense in which there is an ἄπειρον προσθέσει‎. If you divide a whole μέγεθος‎ AA′ into AB and BA′, BA′ into BC and CA′, CA′ into CD and DA′, &c., and add BC, CD, &c. to AB, then just as AA′ can be divided without limit, AB can be added to without limit. But, as he points out, the process of addition is limitless only if the fractions added to the ὡρισμένον‎ (AB) diminish in a constant ratio. If the fractions added are equal, the whole will be exhausted in a finite number of additions.
This last statement is equivalent to the famous Axiom of Archimedes, which had already been used by Eudoxus, and possibly by Hippocrates of Chios (Heath, Greek Math. i. 326–8).
Critical Apparatus
4 κατὰ‎ alt.] τὸ κατὰ‎ Laas
Editor’s Note
5. ἀντεστραμμένως‎, since, as the parts taken diminish, the μέγεθος‎ produced by adding them to one of the original parts increases.
Critical Apparatus
6 αὕτη‎ E1
Critical Apparatus
7 ἐν γὰρ‎ Λ‎VPST: ἐὰν ἐν‎ E
ἂν‎ Λ‎P: om. E
τις‎ Λ‎P: τί‎ E
Critical Apparatus
8 τι‎ sup. lin. E1
τοῦ ὅλου μέγεθος‎ FS: μέγεθος τῷ ὅλῳ‎ E1: μέγεθος τῷ λόγῳ‎ E2IJP: τοῦ λόγου μέρος γρ‎. S
Editor’s Note
8. τοῦ ὅλου μέγεθος‎. The MS. variants arose, as Diels points out,
from an original written thus: τοῦ ὅλου‎ μέγεθος‎.τοῦ λόγου μέγεθος‎
Critical Apparatus
9 διέξεισι‎ fecit E τὸ‎ om. F
Critical Apparatus
11 πᾶν] πᾶν τὸ‎ IJ
Critical Apparatus
12 ἄλλως … ἔστιν‎ Λ‎P: om. E
Editor’s Note
12. The infinite exists in no other way, but does exist (1) in the way described, potentially and by way of exhaustion, though it also exists actually, in the sense in which we say a day exists actually; and its potential existence is akin to that of matter; it has no independent existence as the finite has.
Editor’s Note
12–15. ἄλλως … πεπερασμένον‎. The punctuation I have adopted seems on the whole most likely to represent the course of Aristotle's thought. He first makes a statement which reproduces what he has said in a 16–18, that the infinite exists potentially, and by way of division (i.e. as the infinitely divisible, not as the infinitely extended). He then remarks parenthetically that (while it does not exist at any time as a given entity), it does exist actually in the special sense that, when division of a line is going on, a process which is in principle endless is being progressively actualized, as a day or a contest is progressively actualized (cf. a 21–5). Finally, he elucidates its potential existence by a comparison of it with matter.
It would also be possible to omit δὲ ἔστιν‎, with E, and take δυνάμει … ἐντέλεχείᾳ‎ as meaning (1) 'both potentially-and-by-way-of-exhaustion and actually', or (2) 'both potentially and, by way of exhaustion, also actually'; and some readers may prefer one of these interpretations.
Critical Apparatus
13 καὶ ἐπὶ καθαιρέσει‎ secl. Stölzle
δὲ ἔστιν‎ Λ‎S: ἐντελεχείᾳ δὲ ἐστίν‎ Prantl
Editor’s Note
13. ἐπὶ καθαιρέσει‎, 'along the way of diminution', refers to the same process that has hitherto been called διαίρεσις‎, but refers to it in a slightly different aspect. In the one the whole is regarded as divided into parts; in the other as diminished by the removal of parts.
Critical Apparatus
14 λέγομεν εἶναι‎ F
Editor’s Note
14–15. καὶ δυνάμει … πεπερασμένον‎. The explanation of ἐντελεχείᾳ‎ by the words ὡς … ἀγῶνα‎ leads Aristotle to revert to the existence of the ἄπειρον δυνάμει‎ and offer a corresponding explanation of that. Just as ὕλη‎ exists δυνάμει‎ in the sense that it is capable of taking on successively a number of different forms, in each of which it is partially, and in none completely, realized, so too the ἄπειρον‎ exists δυνάμει‎ in the sense that it is capable of being partially realized by successive divisions of a whole. It never exists as a self-subsistent entity as the finite does.
The reading of E, Philoponus, and Simplicius καὶ οὐ καθʼ αὑτὸ πεπερασμένον‎ derives some support from 207a 24, but gives a less suitable meaning here than the fuller reading.
Critical Apparatus
15 ὡς τὸ‎ om. EPS
Editor’s Note
16. There is also (2) potentially an additive infinite, in the way which we describe as being in some sense identical with the way of division; you may always take something beyond what you have taken, but not so as to exceed any and every magnitude, as in division you can get something smaller than any assigned magnitude. You cannot even potentially get beyond every assigned magnitude by way of addition, unless there is a body which is actually infinite, as the physicists suppose there is. If there cannot be such a sensible body, an additive infinite exists only in the way we have stated.
Editor’s Note
16–17. ὃ … διαίρεσιν‎, cf. b 3–12. But Aristotle adds now that the κατὰ πρόσθεσιν ἄπειρον‎ is only τρόπον τινά‎ parallel to the κατὰ διαίρεσιν ἄπειρον‎. You can always find, within a μέγεθος‎ A, something beyond what you have taken before. If you have taken A 2 , you can get A 2 + A 4 , A 2 + A 4 + A 8 , &c., just as, if you have taken A 2 , you can get A 4 , A 8 , &c. But while by the latter method you can get something smaller than any assigned magnitude, you cannot by the former get something greater than any assigned magnitude, but only something greater than what you have already got by the application of the method; for A is the limit of what you can get by adding A 4 , A 8 , &c. to A 2 . And in fact the universe is of a finite size which frustrates any attempt to find an infinite magnitude (b 20–7); for the proof of the finitude of the universe cf. De Caelo i. 5.
Critical Apparatus
b 17 εἶναι τρόπον τινὰ‎ F
Critical Apparatus
18 τι‎ EPS: τι αὐτοῦ‎ Λ‎
ἐστὶ‎ F
ὑπερβάλλει‎ Λ‎P
Critical Apparatus
19 παντὸς‎ EPST: παντὸς ὡρισμένου‎ Λ‎V an ὑπερβαλεῖ‎?
Critical Apparatus
20 ἀεὶ‎ EV: om. Λ‎
Critical Apparatus
21 τὴν‎ om. F
Critical Apparatus
22 ἔσται‎ E
Critical Apparatus
23 ὥς‎ J1
ἔξωθεν‎ E
Editor’s Note
23–4. ὥσπερ … εἶναι‎, cf. 203a 7, b 25–6.
Critical Apparatus
24 ἢ‎ pr. et εἶναι‎ om. FI
Editor’s Note
24–5. εἰ … οὕτω‎. Aristotle considers himself to have proved this in ch. 5.
Critical Apparatus
25 εἶναι ἄπειρον‎ om. E
Editor’s Note
27. Plato said there were two infinites for this reason, viz. that it is possible to proceed without limit both by way of increase and by way of diminution. But though he posits two infinites he does not use them; for in numbers there is for him no infinitesimal (for the unit is a minimum), and no infinite (for he makes ten the maximum).
Critical Apparatus
28 δύο τὰ ἄπειρα‎ EPT: ἄπειρα δύο‎ Λ‎
καὶ‎ om. F
Editor’s Note
28. δύο τὰ ἄπειρα‎, sc. τὸ μέγα καὶ τὸ μικρόν‎. Cf. 203a 15–16 n.
Critical Apparatus
29 καὶ‎ alt. om. F
Critical Apparatus
32 τὸ‎ PST, Bywater: om. Π‎ ἐπὶ] περὶ‎ E
γὰρ‎ om. F
Editor’s Note
32. μέχρι … ἀριθμόν‎. This doctrine was held by the Pythagoreans (Theon Smyrn. pp. 99. 17 Hiller; Theolog. Arithm. pp. 59 Ast; Photius, Bibl. p. 439a 5 Bekker). Aristotle ascribes the view to some of the Platonists in Met. 1073a 20, 1084a 12, 31. Plato may have thought that the numbers higher than 10 could be treated as mere combinations of the numbers up to 10; though this involves treating the higher numbers, contrary to his own principle, as συμβλητοί‎. But it is quite possible that Aristotle is taking seriously some mere obiter dictum of his master. It may have been simply that he pointed out that both the Greek names for the numbers and the Greek symbols for them (jumping from ιʹ‎ = 10 to κʹ‎ = 20) were based on a decimal system. This is the line of explanation suggested by S. 499. 16–20, 32–500. 2.
Critical Apparatus
33 ἄπειρον εἶναι‎ ST
ἢ‎ Λ‎PST: om. E
Editor’s Note
33. The characteristic of the infinite is the opposite of that usually assigned to it. It is not that which there is nothing beyond, but that of which some part is always beyond. This is illustrated by the bezel-less rings which people call endless; but these are not strictly infinite, because though you can always find some part beyond what you have got to, the same part does duty over and over again.
Editor’s Note
207a 1–2. οὐ … ἐστιν‎. It seems that there is a slight play upon words in this aphorism. The οὗ‎ in οὗ μηδὲν ἔξω‎ seems to depend on ἔξω‎. The ἄπειρον ἔξω τοῦ οὐρανοῦ‎ was that which unlike the οὐρανός‎ has nothing beyond it. The οὗ‎ in οὗ ἀεί τι ἔξω ἐστί‎ seems to be a partitive genitive depending on τι‎, for the infinite as conceived by Aristotle is that of which there is always some part beyond the point you have reached in dividing it or in building it up by addition. When, on the other hand, Aristotle identifies that οὗ μηδὲν ἔξω‎ with the complete (a 8–9), here too οὗ‎ is a partitive genitive, and ἔξω‎ is used in a different sense, viz. = 'lacking' (ἄπεστιν‎ a 10). This strange use of ἔξω‎, adopted for the sake of epigram, leads to the still stranger and really indefensible phrase οὗ ἔστιν ἀπουσία ἔξω‎ (a 12).
Critical Apparatus
207a 3 τι‎ FIPS: τι ἄλλο‎ ET: om. J
ἔξω λαμβάνειν ἐστι‎ E: ἔστιν ἔξω λαμβάνειν‎ IJ
Critical Apparatus
7 οὖν τοῦτʼ ἐστιν‎ Λ‎P
τὸ‎ E2IJS: om. EIFPT
Editor’s Note
207a 7. The infinite is that of which some part is always beyond; that of which there is nothing beyond is complete and whole. 'Complete' and 'whole' mean very much the same thing; they involve the presence of a limit.
Critical Apparatus
8 λαβεῖν‎ E2Λ‎T: om. S
οὗ πρὸς τὰ μέρη μηθὲν ἄπεστιν ἔξω‎ I
Critical Apparatus
10 ὅλον‎ post κιβώτιον‎ F
κιβώτιον‎ Λ‎ST: κιβωτόν‎ E
δὲ‎ om. F: δὲ καὶ‎ E
Editor’s Note
10–12. ὥσπερ … ἐστιν ἔξω‎, 'as we say of individual things "that is whole of which no part is outside or lacking", so we say of that which is strictly the whole (i.e. the universe) that it is that which nothing is outside, or from which nothing is lacking'.
Critical Apparatus
a 12 ὧ τι‎ E
Critical Apparatus
13 τὸ ὅλον‎ Λ‎ST
ἢ‎ alt.] ἢ τὸ‎ E
Critical Apparatus
14 φύσιν‎] φύσιν ἐστίν‎ Λ‎
Editor’s Note
15. Hence Parmenides spoke more correctly than Melissus; the former says the whole is limited, while the latter calls the infinite 'whole', thus joining incompatibles; for the dignity ascribed to the infinite, its containing everything, is ascribed to it just by virtue of its partial similarity to a whole.
Critical Apparatus
16 τὸ ἄπειρον‎ Π‎S: ἄπειρον τὸ‎ Bonitz et fort. PT
Editor’s Note
16. ὁ μὲν γὰρ … φησίν‎. Bonitz emended this to ὁ μὲν γὰρ ἄπειρον τὸ ὅλον φησίν‎, thus getting a more precise antithesis to ὁ δὲ τὸ ὅλον πεπεράνθαι‎. But Aristotle is simply saying that Melissus applied the word ὅλον‎ to his ἄπειρον‎, while Parmenides applied the word πεπερασμένον‎ to his ὅλον‎ or universe, and he thus gets at any rate a verbal antithesis which suits his purpose. Bonitz gets some support from T. 95. 10 and P. 475. 2, but Simplicius clearly had the MS. reading (502. 5, 20). Bonitz points out rightly that Aristotle's usual way of referring to Melissus' doctrine is to say that he describes τὸ ὄν‎ or ὁ οὐρανός‎ as infinite (185a 32, b 17, 254a 25, Met. 986b 20, Soph. El. 167b 13, 181a 29). But Simplicius affords a perfectly simple explanation of the form of words used here when he says (502. 5) Μέλισσος μὲν γάρ, ἄπειρον εἰπὼν τὸ ὄν, καὶ ὅλον αὐτό φησιν εἶναι‎. It may be added that the repetition of τὸ ὅλον‎ produced by Bonitz's reading is unnecessary and uncharacteristic of Aristotle.
Critical Apparatus
17 συνάπτειν ἐστὶ‎ EPS: ἐστι συνάπτειν‎ Λ‎
Editor’s Note
17. μεσσόθεν ἰσοπαλές‎. Fr. 8. 44 μεσσόθεν ἰσοπαλὲς πάντῃ‎, 'equal in all directions from the middle.'
Editor’s Note
λίνον λίνῳ συνάπτειν‎, a proverb for putting like things together. Cf. Pl. Euthyd. 298 c, Strattis Potam. fr. 38.
Critical Apparatus
18 γε‎] δὴ‎ I
Critical Apparatus
19 σεμνότητα‎ fecit E
πᾶν‎ E2
περιέχειν‎ ET: περιέχον‎ Λ‎
Editor’s Note
19–20. περιέχειν … ἔχειν‎. Bonitz's emendation of Bekker's περιέχον … ἔχον‎ is sufficiently supported by T. 95, 15; E also has περιέχειν‎, and its omission of the words following περιέχειν‎ is easier to explain if its original had ἔχειν‎, not ἔχον‎. For the view in question cf. 203b 11.
Critical Apparatus
20 καὶ‎ … ἑαυτῷ‎ Λ‎T: om. EV
ἔχειν‎ T, Bonitz: ἔχον‎ Λ‎: om. EV
Critical Apparatus
21 τοῦ‎ sup. lin. E1
Editor’s Note
21. The infinite element in the completeness of magnitude is matter, that which is potentially though not actually a whole; divisible indefinitely (which involves an inverse indefinite addition), and a whole and finite not per se but per aliud; and qua infinite it does not contain but is contained.
Editor’s Note
21–2. ἔστι … οὔ‎, 'the infinite element in the complete constitu-tion of a magnitude is matter'; i.e. in any actual extended thing that which is infinite in the sense in which Aristotle has admitted the infinite, viz. that which is infinitely divisible, or in other words spatial extension, is the material element, which needs to be supplemented by the formal element, i.e. definite shape. It is only when thus supplemented that it becomes actually a ὅλον‎; apart from such supplementation it is only potentially a ὅλον‎.
The order of the words is in favour of taking τῆς … τελειότητος‎ as depending on τὸ ἄπειρον‎, not on ὕλη‎.
Critical Apparatus
22 ὕλη‎ Π‎PT: ἡ ὕλη‎ S
διαιρετὸν‎ … 24 ἄλλο‎ Π‎PST: secl. Stölzle
Editor’s Note
22–3. διαιρετὸν … πρόσθεσιν‎. The wording is very loose, and the phrase is excised by Stölzle; but it is sufficiently supported by P. 479. 15–18, S. 502. 31–2, T. 95. 22–4. For the meaning of τὴν ἀντεστραμμένην πρόσθεσιν‎ cf. 206b 3–12.
Critical Apparatus
23 ἀνεστραμμένην‎ E1
Editor’s Note
24. κατʼ ἄλλο‎, in virtue of the element of form or definite shape.
Critical Apparatus
25 οὐ‎ … περιέχεται‎ FJ2VPST: οὐχ ὑπερέχει ἀλλὰ ὑπερέχεται‎ EIJ1
Editor’s Note
25. Hence qua infinite it is unknowable; for matter is formless. Thus the infinite is of the nature of a part rather than a whole; for matter is only a part of the whole thing; for if it contained in the sensible realm, in the intelligible realm the great and small should contain the intelligibles. It is absurd to make the unknowable and infinite that which contains and limits.
Critical Apparatus
26 ᾗ ἄπειρον‎ EIJP: om. FT
Critical Apparatus
27 ὅλω‎ EF1
Editor’s Note
27. ἐν μορίου λόγῳ‎, a fairly common idiom in Aristotle (cf. H.A. 559b 20, E.N. 1131b 20), as well as elsewhere (e.g. Hdt. 3. 120 ἐν ἀνδρῶν λόγῳ‎, 'to be reckoned as a man).'
Critical Apparatus
29 περιέχει‎ Λ‎PpT: περιέχοι‎ E
ἐν‎ alt. om. I
Editor’s Note
29–30. ἐπεὶ … νοητά‎. Bonitz's punctuation restores sense to a passage which as printed by Bekker, with a comma after μικρόν‎ and none after αἰσθητοῖς‎, was unintelligible. If the ἄπειρον‎ is what contains or bounds in the case of sensible things, then the μέγα καὶ μικρόν‎, which is Plato's ἄπειρον‎ (203a 15), should be what contains in the case of intelligible things. But Plato actually makes it the material or bounded element in the Ideas (as well as in sensible things), Met. 987b 20.
Critical Apparatus
31 τὸ‎ om. E
καὶ‎ alt. EP: καὶ τὸ‎ Λ‎S
Critical Apparatus
33 μὲν‎] ὡς‎ F
Editor’s Note
207a 33. The fact that there is not a spatial extension greater than any that can be assigned, while there is one less than any that can be assigned, follows naturally from the fact that it is the nature of the infinite to be bounded by the formal element.
Critical Apparatus
34 οὕτως ἄπειρον‎ F
Critical Apparatus
35 ἡ‎ ES: ὡς ἡ‎ Λ‎
Critical Apparatus
207b 21–5 = 1067a 33–7
Critical Apparatus
b 1 καὶ‎ pr. Λ‎V: om. E
Editor’s Note
b 1. The contrast between number, which has a minimum but no maximum, and extension, which has a maximum but no minimum, is only natural. Number is number of units and finds its minimum in the unit, whose nature is to be indivisible; while the possibility of an indefinite series of subdivisions of extension involves that there is no maximum of number. The infinity of number, being thus secured by the possibility of division without limit, exists itself only in potentiality; it lies in the fact that a number can be found greater than any assigned number. Infinite number has no separate existence; the infinity of number is something that is always coming into being but never persists, any more than time does.
Critical Apparatus
2 ἓν‎ EI
μὲν‎ Λ‎PST: om. E μὲν‎ om. Λ‎PlT
Critical Apparatus
b 3 τὸ πλεῖον‎ EFT: τὸ πλείω‎ J: τὰ πλείω‎ I
πάντως‎ J
δὲ‎ om. F
Critical Apparatus
4 ἐλάχιστον‎ F
Critical Apparatus
6 περ‎ Λ‎P: om. E
ἓν‎ fecit E1
Critical Apparatus
7 εἷς ἄνθρωπος‎ om. I
ἕνα‎ E1FS: ἑνὸς‎ IJP et fecit E
Critical Apparatus
8 τὸ‎ alt. ET: τὰ‎ Λ‎PS
τρία καὶ δύο‎ EPS: δύο καὶ τρία‎ Λ‎VT
Editor’s Note
207b 8–10. τὸ γὰρ τρία … ἕκαστος‎, i.e. the nouns representing the numbers (as when we say 'two is an even number') are related παρωνύμως‎ to the corresponding adjectives; 'two' means 'the number containing two units', and the nominal use arises from the adjectival use. Aristotle's doctrine of παρώνυμα‎ is not very satisfactory, since in it metaphysical and linguistic considerations are blended. In general, he holds that adjectives expressing the presence of some quality are παρώνυμα‎ as compared with the corresponding abstract nouns (Cat. 1a 14, 10a 30, b 9, E.E. 1228a 35), as also adjectives of material as compared with the nouns of material (Phys. 245b 11). He can hardly mean by this that they are etymologically derived from them; for he can hardly have thought that λευκός‎ was derived from λευκότης‎ (Cat. 10a 30) or ἐστάναι‎ from στάσις‎ (ib. 6b 13). A word is called a παρώνυμον‎ of another when (1) there is a linguistic connexion between the words (Cat. 10a 32–b 9) and (2) the latter stands for something metaphysically simpler and more fundamental than what the former stands for. λευκός‎ is παρώνυμον‎ from λευκότης‎ because it means 'characterized by λευκότης‎'. Similarly the noun 'two' is derived from the adjective 'two' because it means 'the number composed of two units'.
For the order τὸ τρία καὶ δύα‎ cf. Phys. 227a 32 οὐδὲ γὰρ μεταξὺ δυάδος καὶ μονάδος‎.
Critical Apparatus
9 παρώνυμα‎ E2Λ‎PS: om. E1
Critical Apparatus
10 ἐπὶ‎ Λ‎P: ἐπεὶ‎ E
Critical Apparatus
13 πληθους] μεγέθους‎ I οὗτος ὁ ἀριθμὸς‎ IJPS
Critical Apparatus
14 τῆς διχοτομίας‎ seclusi, om. PS: τοῦ τῆς διχοτομίας‎ E: ταύτης διχοτομίας‎ V
ἀλλὰ] ἀλλʼ ἀεὶ‎ VPS
Editor’s Note
14. τῆς διχοτομίας‎ is probably a (correct) gloss on χωριστός‎. 'This number has no existence apart from the bisection which gives rise to it'. Simplicius interprets χωριστός‎ rather differently; he thinks the meaning is that the number thus produced is not an abstract number, ἐν ἐπινοίᾳ κείμενος‎, but a σωματικὸς ἀριθμός‎ (so too Philoponus).
Editor’s Note
14–15. οὐδὲ … χρόνου‎, cf. 206a 21–b 3.
Editor’s Note
15. With spatial extension it is otherwise; what is continuous can be divided without limit, but there is no infinite in the direction of increase. For there cannot be a potential extension greater than the greatest possible actual extension, so that if there were a potential spatial infinite, there would have to be actually something greater than the sensible universe, which there is not.
Critical Apparatus
18 εἶναι τοσοῦτον‎ F
Editor’s Note
19. ἐπεὶ … αἰσθητόν‎. This Aristotle considers himself to have established in ch. 5.
Critical Apparatus
20 τις‎ J
Critical Apparatus
21 τὸ δʼ‎ E2Λ‎MPS: δὲ τὸ‎ E1
κινήσει καὶ μεγέθει‎ F
Editor’s Note
21. The infinite in extension, movement, and time is not one single thing; movement is infinite because the extension it covers is infinite; and time is so because the movement that occupies it is so. We use these conceptions of infinity of movement and time meanwhile, but will explain them later, as well as why every extension is divisible into extensions.
Editor’s Note
21–5. τὸ δʼ ἄπειρον … κίνησιν‎. The infinity which Aristotle believes to exist in μέγεθος‎ is not infinite extent but infinite divisibility (with what follows from it, the possibility of indefinite addition of diminishing fractions to an original fraction of the whole) (206a 16–18, b 3–12). It is a therefore a corresponding infinity that he here ascribes to movement and to time. Since there is no μέγεθος‎ infinite in extent, there can be no movement over an infinite μέγεθος‎. But there may be infinite movement in another sense. Time is infinite in extent (251b 13, 26), and circular movement lasting throughout infinite time will itself be infinite (241b 19, 261b 27–265a 12).
Critical Apparatus
23 τὸ‎ om. J1
τὸ‎ E1VS: πρότερον‎ E2Λ‎
Editor’s Note
25–7. νῦν … διαιρετόν‎, i.e. we use for the present the phrases 'infinite magnitude', 'infinite movement', 'infinite time', but we shall show later what each of them stands for, and why every magnitude is divisible into magnitudes. The reference is to vi. 1, 2, 4.
Critical Apparatus
26 ἐροῦμεν‎ EV et ut vid. T: πειρασόμεθα λέγειν‎ Λ‎
τί ἐστιν‎ Λ‎S: ὅτι‎ E
Editor’s Note
27. Our account does not rob mathematicians of their science, by denying an actual inexhaustible infinite; they do not need this nor use it, but only demand that there may be a finite line as large as they wish. Now any magnitude may be divided in the same ratio as the largest magnitude. Thus for the purpose of proof it will make no difference to them whether an infinite exists among existing magnitudes.
Critical Apparatus
28 μαθητικοὺς‎ E
an ⟨τὸ⟩ οὕτως‎?
οὕτως εἶναι‎ FIP: μὴ εἶναι οὕτως‎ EV: οὕτω μὴ εἶναι‎ J
ἄπειρον] τὸ ἄπειρον‎ FIT: τι ἄπειρον‎ P
Editor’s Note
28. ἀναιρῶν … ἄπειρον‎. I can find no other instance of this use of ἀναιρεῖν‎ with an accusative and infinitive. ἀναιρεῖν τὸ διαλέγεσθαι‎ (Met. 1062b 11, 1063b 11) and ἀναιρεῖν τὸ ἐπίστασθαι‎ (ib. 994b 20) are found, and possibly we should insert τό‎ here.
Critical Apparatus
b 29 αὔξησιν‎ EPT: αὔξην‎ Λ‎
ἀδιεξίτητον‎ EF2JT: ὡς ἀδιεξίτητον‎ F1IVP
Critical Apparatus
30 οὐ γὰρ‎ EV et fort. ST: οὐδὲ‎ F: οὐδὲ γὰρ‎ IJ
Critical Apparatus
31 βούλονται‎ J
πεπερασμένην‎ Λ‎P: τὴν πεπερασμένην‎ E
Editor’s Note
31–2. τῷ δὲ μεγίστῳ μεγέθει … ἕτερον‎. Any straight line, however short, can be divided in the same ratio as any other however long (Eucl. El. vi. 10), and therefore any property that could be proved by the use of a great magnitude can equally be proved by the use of a small one. Thus mathematics does not need very great magnitudes, let alone infinite ones.
Critical Apparatus
33 ἐκείνοις‎ EV: ἐκείνως‎ Λ‎P
δʼ‎ seclusi: habent Π‎PS
Editor’s Note
33–4. ὥστε … μεγέθεσιν‎. Reading τὸ δὲ εἶναι ἐν τοῖς οὖσιν ἔσται μεγέθεσιν‎, S. 511. 26 interprets κἂν τὴν ἀπόδειξιν δυνατὸν ὁμοίως καὶ ἐπὶ τῶν μὴ ὄντων ἀλλʼ ἐπινοουμένων μεγεθῶν ποιεῖσθαι, ἀλλὰ τά γε ὑφεστῶτα σχήματα οὐκ ἐν πᾶσι μεγέθεσιν· οὐ γὰρ δὴ καὶ ἐν τοῖς ἐπινοου-‎μένοις ἀλλʼ ἐν τοῖς οὖσίν ἐστι‎. This is not very satisfactory. It would be more natural to take the words as meaning 'thus a small line will serve as well for proof as an infinite one, but its being will be (while that of an infinite line cannot be) in the realm of actually existing entities'. But even this is not very naturally expressed E's reading gives an easy enough meaning, but the absence of οὐδέν ἐστιν ἀναγκαῖον‎ in Philoponus and Simplicius puts these words under serious suspicion of being a gloss. Both readings seem to me to have originated from that which I have adopted, through an attempt to balance the μέν‎ clause with a δέ‎ clause; this is unnecessary, as will be seen from De Int. 23b 30, De Part. An. 690b 21 and from L. and S. s.v. μέν‎, A. i. 2.
Critical Apparatus
34 οὖσιν‎ E, litteris tribus deletis sequentibus: οὖσιν ἐστι‎ FP: οὖσιν ἔσται‎ IJS μεγέθεσιν‎ Λ‎PS: μεγέθεσιν οὐδέν ἐστιν ἀναγκαῖον‎ EV, ἐστιν‎ quidem corr. in E
Editor’s Note
34. In the fourfold scheme of causes, the infinite is evidently a material cause; its being is a privation, and its substratum is what is continuous and sensible. All other thinkers as well use it as matter; hence it is absurd of them to make it what contains, not what is contained.
Editor’s Note
34. ἐπεὶ … τετραχῶς‎, ii. 3.
Critical Apparatus
35 ὅτι‎] τι‎ E
ἐστιν αἴτιον‎ Bekker
Editor’s Note
35. ὡς … ἐστι‎, cf. 206b 15, 207a 21.
Critical Apparatus
208a 1 αὐτῶν‎ E
στέρησίς ἐστι τὸ‎ Λ‎P
Editor’s Note
208a 1. τὸ μὲν εἶναι αὐτῷ στέρησις‎, sc. the mere absence of limit.
Editor’s Note
2–3. φαίνονται … ἀπείρῳ‎. This is true both of the physicists who believed in infinite water or air, or an infinite intermediate element (205a 27), or an infinite ὁμοῦ πάντα‎ (203a 25), or a πανσπερμία τῶν σχημάτων‎ (ib. 21), as the matter out of which existing things were formed; and of the Pythagoreans and Plato, who posited a pure ἄπειρον‎ as the material element in existing things (ib. 4).
Critical Apparatus
3 καὶ‎ om. E
Editor’s Note
3–4. διὸ … περιεχόμενον‎, cf. 203b 11, 207a 18–32.
Critical Apparatus
4 μὴ] μὴ τὸ‎ Λ‎S
Critical Apparatus
5 δʼ] δεῖ‎ VP
Editor’s Note
208a 5. Of the arguments for an actual infinite, some have no demonstrative force; others can be met by valid counter-arguments. (1) An actual infinite sensible body is not needed to provide for the continuance of coming to be; for the destruction of one thing may be the generation of another.
Critical Apparatus
6 ἀφωρισμένον‎ Λ‎VPT: ἀφωρισμένον ἐπελθεῖν‎ E
Editor’s Note
The arguments for an actual infinite reviewed in this chapter correspond to those mentioned in ch. 4:

208a 8–11 answers to

203b 18–20,

11–14

20–22,

14–19

22–30,

20–21

16–17,

21–22

17–18.

Editor’s Note
208a 6–8. τὰ μὲν γὰρ … ἀπαντήσεις‎. The distinction meant to be conveyed is not very clear. It may be that Aristotle means that some of the arguments (presumably those answered in a 8–19) have no convincing power, while the others, though they have this, can be met by counter-arguments which prevent us from drawing the full conclusion which believers in an actual infinite wish us to draw.
Critical Apparatus
7 ἑτέρας ἀληθεῖς‎ EP: ἀληθεῖς ἑτέρας‎ Λ‎: ἀληθεῖς‎ T
Critical Apparatus
8 ἡ‎ Λ‎PT: fecit E
ἐπιλείποι ἀνάγκη‎ E
Editor’s Note
9–10. ἐνδέχεται … γένεσιν‎. It is Aristotle's actual opinion that there is no absolute γένεσις‎ and no absolute φθορά‎; the γένεσις‎ of one thing is always the φθορά‎ of another and vice versa (De Gen. et Corr. 319a 20).
Critical Apparatus
10 γένεσιν θατέρου εἶναι‎ Λ‎
τοῦ‎ om. F
Critical Apparatus
12 τινός‎ pr. Λ‎P: τινὸς ἅπτεται‎ E
κἂν τῶν‎ F
Editor’s Note
12. ἅπτεται γὰρ πᾶν τινός‎, 'for everything that is in contact is in contact with something'.
Critical Apparatus
14 δὲ‎ Λ‎PS: δὲ ἐπὶ‎ E
Editor’s Note
14. (3) The reliance placed on our thinking is absurd; the excess and defect in question depend on our thinking, not on the object. For any one might suppose any of us to be many times his own size, exaggerating his size indefinitely; but if some one is bigger than we are, it is not because some one thinks so but because it is so, and that some one thinks so is an accident.
Editor’s Note
14. οὐδʼ … ἔστιν‎, a second argument against this argument. Everything that exists is limited, but not any and every thing can be in contact with any and every other. Simplicius illustrates by saying that an utterance and a line cannot be in contact though both are limited. Contact can only exist either between two material things or between two mathematical objects, and is thus clearly distinct from limitation.
Editor’s Note
15–16. οὐ … νοήσεως‎, the infinitely great and infinitely small quantities that we get exist not in reality but in our thought. ἐπί‎ = 'on the side of'.
Critical Apparatus
16 ἂν ἡμῶν νοήσειε‎ Λ‎
Critical Apparatus
17 ἑαυτοῦ‎ om. E
Critical Apparatus
18 τοῦ ἄστεος‎ Π‎PST: τοῦ ἀστέρος γρ‎. Eudemus: om. γρ‎. P, Diels
τί‎ JS
ἢ‎ Π‎PST: om. γρ‎. P, Diels
τηλικούτου‎ E1PS: τηλικοῦδε‎ E2Λ‎
Editor’s Note
18. ἔξω … μεγέθους‎. Alexander took ἔξω τοῦ ἄστεος‎ to mean 'outside the city' (so too Themistius and Philoponus); but Simplicius objects that this would not be directly relevant to the discussion of the infinite, and prefers (after Eudemus) to take the words as meaning 'bigger than the city'. This has the advantage of avoiding the zeugma in the use of ἔξω‎ implied in Alexander's interpretation. But it gives a most unnatural meaning to ἔξω τοῦ ἄστεος‎. Diels seems to be right in following the 'more accurate manuscripts' reported by P. 495. 6 as having omitted τοῦ ἄστεος‎ and ἤ‎. Diels is very likely right in thinking the interpolation arises from some words in Eudemus' commentary such as οὐ διὰ τοῦτο Διάρης χιλίων σταδίων ἐστὶν ἢ τοῦ ἄστεος μείζων‎ (cf. S. 517. 13–17).
Editor’s Note
20. (4) Time, movement, and thought are infinite without implying the permanence of the successive phases;
Editor’s Note
20–1. ὁ δὲ χρόνος … λαμβανομένου‎. Here Aristotle allows some importance to the first of the arguments for an infinite put forward in ch. 4. Time, movement, and thought must be admitted to be limitless, but their being is a constant coming into being and passing away; they never exist as given infinite wholes. Cf. 206a 25–b 3.
Critical Apparatus
a 21 ὑπολαμβανομένου‎ J
Editor’s Note
21. and (5) magnitude is not infinite either by virtue of its infinite divisibility or by virtue of our magnification of it in thought.
Editor’s Note
21–2. μέγεθος … ἄπειρον‎. Aristotle here denies the force of the second argument put forward in ch. 4. An actual infinite is not proved to exist either by our power of actually whittling away a given magnitude without limit, or by our power of imaginatively supposing it increased without limit. νοητικῇ‎ is advisedly added to αὐξήσει‎ and not to καθαιρέσει‎; for Aristotle thinks there is a maximum, though no minimum, of really existing magnitude; cf. 207b 3–5.
Critical Apparatus
22 νοητῇ‎ F
ἄπειρον‎ Λ‎P: om. E
Critical Apparatus
23 τοῦ‎ om. E
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