§10.6ὁμοίως δὲ καὶ περὶ τοῦ ἑνὸς καὶ τῶν πολλῶν ἀπορήσειεν ἄν τις.
Similarly, one might puzzle about the one and the many.
εἰ γὰρ τὰ πολλὰ τῷ ἑνὶ ἁπλῶς ἀντίκειται, συμβαίνει ἔνια ἀδύνατα.
For if the many is simply opposed to the one, some impossible consequences follow.
τὸ γὰρ ἓν ὀλίγον ἢ ὀλίγα ἔσται· τὰ γὰρ πολλὰ καὶ τοῖς ὀλίγοις ἀντίκειται.
For the one will be few or a few; for the many is also opposed to the few.
ἔτι τὰ δύο πολλά, εἴπερ τὸ διπλάσιον πολλαπλάσιον λέγεται δὲ κατὰ τὰ δύο· ὥστε τὸ ἓν ὀλίγον· πρὸς τί γὰρ πολλὰ τὰ δύο εἰ μὴ πρὸς ἕν τε καὶ τὸ ὀλίγον;
Furthermore, two is many, if indeed the double is multiple, and this is spoken of on the basis of two; hence the one is few; for in relation to what is two many, if not to the one and the few?
οὐθὲν γάρ ἐστιν ἔλαττον.
For there is nothing less than two.
ἔτι εἰ ὡς ἐν μήκει τὸ μακρὸν καὶ βραχύ, οὕτως ἐν πλήθει τὸ πολὺ καὶ ὀλίγον, καὶ ὃ ἂν ᾖ πολὺ καὶ πολλά, καὶ τὰ πολλὰ πολύ (εἰ μή τι ἄρα διαφέρει ἐν συνεχεῖ εὐορίστῳ), τὸ ὀλίγον πλῆθός τι ἔσται.
Furthermore, if just as the long and the short are in length, so the much and the few are in multitude, and whatever is much is many, and the many is much (unless indeed there is some difference in a continuous thing that is easily bounded), the few will be a certain multitude.
ὥστε τὸ ἓν πλῆθός τι, εἴπερ καὶ ὀλίγον· τοῦτο δʼ ἀνάγκη, εἰ τὰ δύο πολλά.
Hence the one will be a certain multitude, if indeed it is also few; and this is necessary, if two is many.
ἀλλʼ ἴσως τὰ πολλὰ λέγεται μέν πως καὶ πολύ, ἀλλʼ ὡς διαφέρον, οἷον ὕδωρ πολύ, πολλὰ δʼ οὔ. ἀλλʼ ὅσα διαιρετά, ἐν τούτοις λέγεται, ἕνα μὲν τρόπον ἐὰν ᾖ πλῆθος ἔχον ὑπεροχὴν ἢ ἁπλῶς ἢ πρός τι (καὶ τὸ ὀλίγον ὡσαύτως πλῆθος ἔχον ἔλλειψιν), τὸ δὲ ὡς ἀριθμός, ὃ καὶ ἀντίκειται τῷ ἑνὶ μόνον.
But perhaps the many is spoken of in a way also as much, yet as differing, as for instance "much water," but not "many waters." Rather, in all things that are divisible, it is spoken of in this way: in one way, if there is a multitude having excess either simply or in relation to something (and the few likewise is a multitude having deficiency), and in another way as number, which is also opposed to the one alone.
οὕτως γὰρ λέγομεν ἓν ἢ πολλά, ὥσπερ εἴ τις εἴποι ἓν καὶ ἕνα ἢ λευκὸν καὶ λευκά, καὶ τὰ μεμετρημένα πρὸς τὸ μέτρον· οὕτως καὶ τὰ πολλαπλάσια λέγεται· πολλὰ γὰρ ἕκαστος ὁ ἀριθμὸς ὅτι ἕνα καὶ ὅτι μετρητὸς ἑνὶ ἕκαστος, καὶ ὡς τὸ ἀντικείμενον τῷ ἑνί, οὐ τῷ ὀλίγῳ.
For in this way we speak of one or many, just as if one were to say "one and ones" or "white and whites," and the things measured in relation to the measure; in this way too multiples are spoken of; for each number is many because it consists of ones and because each is measurable by the one, and as that which is opposed to the one, not to the few.
οὕτω μὲν οὖν ἐστὶ πολλὰ καὶ τὰ δύο, ὡς δὲ πλῆθος ἔχον ὑπεροχὴν ἢ πρός τι ἢ ἁπλῶς οὐκ ἔστιν, ἀλλὰ πρῶτον.
In this way, then, even two is many, but as a multitude having excess either in relation to something or simply it is not, but is the first.
ὀλίγα δʼ ἁπλῶς τὰ δύο· πλῆθος γάρ ἐστιν ἔλλειψιν ἔχον πρῶτον (διὸ καὶ οὐκ ὀρθῶς ἀπέστη Ἀναξαγόρας εἰπὼν ὅτι ὁμοῦ πάντα χρήματα ἦν ἄπειρα καὶ πλήθει καὶ μικρότητι, ἔδει δʼ εἰπεῖν ἀντὶ τοῦ
"καὶ μικρότητι"
"καὶ ὀλιγότητι"
· οὐ γὰρ ἄπειρα), ἐπεὶ τὸ ὀλίγον οὐ διὰ τὸ ἕν, ὥσπερ τινές φασιν, ἀλλὰ διὰ τὰ δύο. —ἀντίκειται δὴ τὸ ἓν καὶ τὰ πολλὰ τὰ ἐν ἀριθμοῖς ὡς μέτρον μετρητῷ·
And two is simply few; for it is the first multitude having deficiency (which is why Anaxagoras did not step off correctly when he said that "all things were together, infinite both in multitude and in smallness," whereas he ought to have said instead of "and in smallness" "and in fewness"; for they are not infinite), since the few is not because of the one, as some say, but because of two. —Therefore, the one and the many in numbers are opposed as a measure to the measurable; and these are opposed as relative terms, such as are not relative in their own right.
ταῦτα δὲ ὡς τὰ πρός τι, ὅσα μὴ καθʼ αὑτὰ τῶν πρός τι. διῄρηται δʼ ἡμῖν ἐν ἄλλοις ὅτι διχῶς λέγεται τὰ πρός τι, τὰ μὲν ὡς ἐναντία, τὰ δʼ ὡς ἐπιστήμη πρὸς ἐπιστητόν, τῷ λέγεσθαί τι ἄλλο πρὸς αὐτό.
And it has been divided by us elsewhere that relative terms are spoken of in two ways, some as contraries, and others as knowledge to the knowable, by the fact that something else is spoken of in relation to it.
τὸ δὲ ἓν ἔλαττον εἶναι τινός, οἷον τοῖν δυοῖν, οὐδὲν κωλύει· οὐ γάρ, εἰ ἔλαττον, καὶ ὀλίγον.
But nothing prevents the one from being less than something, as for instance than the two; for it is not, if less, also few.
τὸ δὲ πλῆθος οἷον γένος ἐστὶ τοῦ ἀριθμοῦ· ἔστι γὰρ ἀριθμὸς πλῆθος ἑνὶ μετρητόν, καὶ ἀντίκειταί πως τὸ ἓν καὶ ἀριθμός, οὐχ ὡς ἐναντίον ἀλλʼ ὥσπερ εἴρηται τῶν πρός τι ἔνια· ᾗ γὰρ μέτρον τὸ δὲ μετρητόν, ταύτῃ ἀντίκειται, διὸ οὐ πᾶν ὃ ἂν ᾖ ἓν ἀριθμός ἐστιν, οἷον εἴ τι ἀδιαίρετόν ἐστιν.
And multitude is as it were the genus of number; for number is a multitude measurable by the one, and the one and number are opposed in a way, not as a contrary, but as has been said of some of the relative terms; for insofar as one is a measure and the other is measurable, in this way they are opposed, which is why not everything that is one is a number, as for instance if something is indivisible.
ὁμοίως δὲ λεγομένη ἡ ἐπιστήμη πρὸς τὸ ἐπιστητὸν οὐχ ὁμοίως ἀποδίδωσιν.
Similarly, though knowledge is spoken of in relation to the knowable, it does not render the relation in a similar way.
δόξειε μὲν γὰρ ἂν μέτρον ἡ ἐπιστήμη εἶναι τὸ δὲ ἐπιστητὸν τὸ μετρούμενον, συμβαίνει δὲ ἐπιστήμην μὲν πᾶσαν ἐπιστητὸν εἶναι τὸ δὲ ἐπιστητὸν μὴ πᾶν ἐπιστήμην, ὅτι τρόπον τινὰ ἡ ἐπιστήμη μετρεῖται τῷ ἐπιστητῷ.
For knowledge might seem to be the measure and the knowable the measured, but it turns out that while all knowledge is knowable, not all that is knowable is knowledge, because in a way knowledge is measured by the knowable.
τὸ δὲ πλῆθος οὔτε τῷ ὀλίγῳ ἐναντίον—ἀλλὰ τούτῳ μὲν τὸ πολὺ ὡς ὑπερέχον πλῆθος ὑπερεχομένῳ πλήθει—οὔτε τῷ ἑνὶ πάντως· ἀλλὰ τὸ μὲν ὥσπερ εἴρηται, ὅτι διαιρετὸν τὸ δʼ ἀδιαίρετον, τὸ δʼ ὡς πρός τι ὥσπερ ἡ ἐπιστήμη ἐπιστητῷ, ἐὰν ᾖ ἀριθμὸς τὸ δʼ ἓν μέτρον.
And multitude is neither contrary to the few—but to this, the much is contrary as an exceeding multitude to an exceeded multitude—nor is it in every way opposed to the one; but the one, as has been said, because the one is indivisible and the other divisible, and the other as a relative term, just as knowledge to the knowable, if there is number and the one is the measure.