§14.1#1περὶ μὲν οὖν τῆς οὐσίας ταύτης εἰρήσθω τοσαῦτα, πάντες δὲ ποιοῦσι τὰς ἀρχὰς ἐναντίας, ὥσπερ ἐν τοῖς φυσικοῖς, καὶ περὶ τὰς ἀκινήτους οὐσίας ὁμοίως.
Let this much be said about this substance. On the other hand, everyone makes the principles contraries, just as in the case of physical things, and likewise in the case of immobile substances.
εἰ δὲ τῆς τῶν ἁπάντων ἀρχῆς μὴ ἐνδέχεται πρότερόν τι εἶναι, ἀδύνατον ἂν εἴη τὴν ἀρχὴν ἕτερόν τι οὖσαν εἶναι ἀρχήν, οἷον εἴ τις λέγοι τὸ λευκὸν ἀρχὴν εἶναι οὐχ ᾗ ἕτερον ἀλλʼ ᾗ λευκόν, εἶναι μέντοι καθʼ ὑποκειμένου καὶ ἕτερόν τι ὂν λευκὸν εἶναι· ἐκεῖνο γὰρ πρότερον ἔσται.
But if it is impossible for anything to be prior to the principle of all things, it would be impossible for the principle, being something else, to be a principle, as if one were to say that white is a principle, not in so far as it is something else, but in so far as it is white, yet that it exists of a subject and is white while being something else; for that subject will be prior to it.
ἀλλὰ μὴν γίγνεται πάντα ἐξ ἐναντίων ὡς ὑποκειμένου τινός· ἀνάγκη ἄρα μάλιστα τοῖς ἐναντίοις τοῦθʼ ὑπάρχειν.
But indeed all things come to be from contraries as from a certain subject; therefore, this must belong most of all to the contraries.
ἀεὶ ἄρα πάντα τὰ ἐναντία καθʼ ὑποκειμένου καὶ οὐθὲν χωριστόν, ἀλλʼ ὥσπερ καὶ φαίνεται οὐθὲν οὐσίᾳ ἐναντίον, καὶ ὁ λόγος μαρτυρεῖ.
Therefore, all contraries are always of a subject, and none is separate; and just as it also appears that nothing is contrary to substance, so too the argument testifies.
οὐθὲν ἄρα τῶν ἐναντίων κυρίως ἀρχὴ πάντων ἀλλʼ ἑτέρα.
Therefore, none of the contraries is properly the principle of all things, but the principle is something else.
—οἱ δὲ τὸ ἕτερον τῶν ἐναντίων ὕλην ποιοῦσιν, οἱ μὲν τῷ ἑνὶ τὸ ἄνισον, ὡς τοῦτο τὴν τοῦ πλήθους οὖσαν φύσιν, οἱ δὲ τῷ ἑνὶ τὸ πλῆθος (γεννῶνται γὰρ οἱ ἀριθμοὶ τοῖς μὲν ἐκ τῆς τοῦ ἀνίσου δυάδος, τοῦ μεγάλου καὶ μικροῦ, τῷ δʼ ἐκ τοῦ πλήθους, ὑπὸ τῆς τοῦ ἑνὸς δὲ οὐσίας ἀμφοῖν)·
But they make one of the contraries matter, some opposing the unequal to the one, as being the nature of multiplicity, and others opposing multiplicity to the one (for numbers are generated, for some from the dyad of the unequal, namely the great and the small, and for others from multiplicity, but in both cases by the substance of the one).
καὶ γὰρ ὁ τὸ ἄνισον καὶ ἓν λέγων τὰ στοιχεῖα, τὸ δʼ ἄνισον ἐκ μεγάλου καὶ μικροῦ δυάδα, ὡς ἓν ὄντα τὸ ἄνισον καὶ τὸ μέγα καὶ τὸ μικρὸν λέγει, καὶ οὐ διορίζει ὅτι λόγῳ ἀριθμῷ δʼ οὔ.
For even he who says that the unequal and the one are elements, and that the unequal is a dyad consisting of the great and the small, speaks of the unequal, the great, and the small as being one, and does not distinguish that they are one in definition, but not in number.
ἀλλὰ μὴν καὶ τὰς ἀρχὰς ἃς στοιχεῖα καλοῦσιν οὐ καλῶς ἀποδιδόασιν, οἱ μὲν τὸ μέγα καὶ τὸ μικρὸν λέγοντες μετὰ τοῦ ἑνός, τρία ταῦτα στοιχεῖα τῶν ἀριθμῶν, τὰ μὲν δύο ὕλην τὸ δʼ ἓν τὴν μορφήν, οἱ δὲ τὸ πολὺ καὶ ὀλίγον, ὅτι τὸ μέγα καὶ τὸ μικρὸν μεγέθους οἰκειότερα τὴν φύσιν, οἱ δὲ τὸ καθόλου μᾶλλον ἐπὶ τούτων, τὸ ὑπερέχον καὶ τὸ ὑπερεχόμενον.
But indeed they do not correctly render the principles which they call elements, some speaking of the great and the small along with the one, making these three elements of numbers, two as matter and the one as form, others speaking of the much and the few, because the great and the small are by nature more proper to magnitude, and others speaking of what is more universal in these cases, the exceeding and the exceeded.
διαφέρει δὲ τούτων οὐθὲν ὡς εἰπεῖν πρὸς ἔνια τῶν συμβαινόντων, ἀλλὰ πρὸς τὰς λογικὰς μόνον δυσχερείας, ἃς φυλάττονται διὰ τὸ καὶ αὐτοὶ λογικὰς φέρειν τὰς ἀποδείξεις.
And this makes virtually no difference with respect to some of the consequences, but only with respect to the logical difficulties, which they guard against because they themselves bring forward logical demonstrations.
πλὴν τοῦ αὐτοῦ γε λόγου ἐστὶ τὸ ὑπερέχον καὶ ὑπερεχόμενον εἶναι ἀρχὰς ἀλλὰ μὴ τὸ μέγα καὶ τὸ μικρόν, καὶ τὸν ἀριθμὸν πρότερον τῆς δυάδος ἐκ τῶν στοιχείων· καθόλου γὰρ ἀμφότερα μᾶλλόν ἐστιν.
Except that it belongs to the same argument to claim that the exceeding and the exceeded are principles rather than the great and the small, and that number is prior to the dyad from the elements; for both are more universal.
νῦν δὲ τὸ μὲν λέγουσι τὸ δʼ οὐ λέγουσιν.
But now they assert the one but do not assert the other.
οἱ δὲ τὸ ἕτερον καὶ τὸ ἄλλο πρὸς τὸ ἓν ἀντιτιθέασιν, οἱ δὲ πλῆθος καὶ τὸ ἕν.
Others oppose the other and the different to the one, and others multiplicity and the one.
εἰ δέ ἐστιν, ὥσπερ βούλονται, τὰ ὄντα ἐξ ἐναντίων, τῷ δὲ ἑνὶ ἢ οὐθὲν ἐναντίον ἢ εἴπερ ἄρα μέλλει, τὸ πλῆθος, τὸ δʼ ἄνισον τῷ ἴσῳ καὶ τὸ ἕτερον τῷ ταὐτῷ καὶ τὸ ἄλλο αὐτῷ, μάλιστα μὲν οἱ τὸ ἓν τῷ πλήθει ἀντιτιθέντες ἔχονταί τινος δόξης, οὐ μὴν οὐδʼ οὗτοι ἱκανῶς· ἔσται γὰρ τὸ ἓν ὀλίγον· πλῆθος μὲν γὰρ ὀλιγότητι τὸ δὲ πολὺ τῷ ὀλίγῳ ἀντίκειται.
But if existing things are, as they wish, from contraries, and to the one either nothing is contrary, or if it must be so, multiplicity is, and the unequal is contrary to the equal, and the other to the same, and the different to it, then those who oppose the one to multiplicity hold a certain opinion most of all, yet not even these do so adequately; for the one will be few, since multiplicity is opposed to fewness, and much to few.
—τὸ δʼ ἓν ὅτι μέτρον σημαίνει, φανερόν.
But that the "one" signifies a measure is clear.
καὶ ἐν παντὶ ἔστι τι ἕτερον ὑποκείμενον, οἷον ἐν ἁρμονίᾳ δίεσις, ἐν δὲ μεγέθει δάκτυλος ἢ ποὺς ἤ τι τοιοῦτον, ἐν δὲ ῥυθμοῖς βάσις ἢ συλλαβή· ὁμοίως δὲ καὶ ἐν βάρει σταθμός τις ὡρισμένος ἐστίν·
And in everything there is some other subject, as in harmony a quarter-tone, and in magnitude a finger or a foot or something of the sort, and in rhythms a beat or a syllable; and likewise in weight there is some definite weight.
καὶ κατὰ πάντων δὲ τὸν αὐτὸν τρόπον, ἐν μὲν τοῖς ποιοῖς ποιόν τι, ἐν δὲ τοῖς ποσοῖς ποσόν τι, καὶ ἀδιαίρετον τὸ μέτρον, τὸ μὲν κατὰ τὸ εἶδος τὸ δὲ πρὸς τὴν αἴσθησιν, ὡς οὐκ ὄντος τινὸς τοῦ ἑνὸς καθʼ αὑτὸ οὐσίας.
And in all cases it is in the same manner, in qualities a certain quality, in quantities a certain quantity, and the measure is indivisible, either in form or to perception, since the one is not some substance in itself.
καὶ τοῦτο κατὰ λόγον· σημαίνει γὰρ τὸ ἓν ὅτι μέτρον πλήθους τινός, καὶ ὁ ἀριθμὸς ὅτι πλῆθος μεμετρημένον καὶ πλῆθος μέτρων (διὸ καὶ εὐλόγως οὐκ ἔστι τὸ ἓν ἀριθμός· οὐδὲ γὰρ τὸ μέτρον μέτρα, ἀλλʼ ἀρχὴ καὶ τὸ μέτρον καὶ τὸ ἕν).
And this is reasonable; for the "one" signifies that it is a measure of some multiplicity, and number that it is a measured multiplicity and a multiplicity of measures (wherefore also reasonably the "one" is not a number; for the measure is not measures, but both the measure and the "one" are principles).
δεῖ δὲ ἀεὶ τὸ αὐτό τι ὑπάρχειν πᾶσι τὸ μέτρον, οἷον εἰ ἵπποι, τὸ μέτρον ἵππος, καὶ εἰ ἄνθρωποι, ἄνθρωπος.
But the measure must always belong as some same thing to all; for instance, if they are horses, the measure is a horse, and if they are men, a man.
εἰ δʼ ἄνθρωπος καὶ ἵππος καὶ θεός, ζῷον ἴσως, καὶ ὁ ἀριθμὸς αὐτῶν ἔσται ζῷα.
And if they are a man, a horse, and a god, the measure is perhaps an animal, and their number will be animals.
εἰ δʼ ἄνθρωπος καὶ λευκὸν καὶ βαδίζον, ἥκιστα μὲν ἀριθμὸς τούτων διὰ τὸ ταὐτῷ πάντα ὑπάρχειν καὶ ἑνὶ κατὰ ἀριθμόν, ὅμως δὲ γενῶν ἔσται ὁ ἀριθμὸς ὁ τούτων, ἤ τινος ἄλλης τοιαύτης προσηγορίας.
But if they are a man, white, and walking, their number is least of all, because they all belong to the same thing which is one in number; nevertheless, their number will be a number of genera, or of some other such designation.