§13.9#2ὑπῆρχε γάρ, ὡς ἔοικε, καὶ πεπερασμένον πλῆθος, ἐξ οὗ αἱ πεπερασμέναι μονάδες καὶ τοῦ ἑνός· ἔστι τε ἕτερον αὐτὸ πλῆθος καὶ πλῆθος ἄπειρον·
For there was also, as it seems, a finite plurality, from which and from the One the finite units consist; and there is another plurality which is plurality itself and infinite plurality; which plurality, then, is the element along with the One?
ποῖον οὖν πλῆθος στοιχεῖόν ἐστι καὶ τὸ ἕν; ὁμοίως δὲ καὶ περὶ στιγμῆς ἄν τις ζητήσειε καὶ τοῦ στοιχείου ἐξ οὗ ποιοῦσι τὰ μεγέθη.
Similarly one might also inquire about the point and the element from which they make magnitudes.
οὐ γὰρ μία γε μόνον στιγμή ἐστιν αὕτη· τῶν γοῦν ἄλλων στιγμῶν ἑκάστη ἐκ τίνος;
For this point is surely not the only one; from what, then, does each of the other points consist?
οὐ γὰρ δὴ ἔκ γε διαστήματός τινος καὶ αὐτῆς στιγμῆς.
For surely it does not consist of some interval and the point itself.
ἀλλὰ μὴν οὐδὲ μόρια ἀδιαίρετα ἐνδέχεται τοῦ διαστήματος εἶναι, ὥσπερ τοῦ πλήθους ἐξ ὧν αἱ μονάδες· ὁ μὲν γὰρ ἀριθμὸς ἐξ ἀδιαιρέτων σύγκειται τὰ δὲ μεγέθη οὔ. —πάντα δὴ ταῦτα καὶ ἄλλα τοιαῦτα φανερὸν ποιεῖ ὅτι ἀδύνατον εἶναι τὸν ἀριθμὸν καὶ τὰ μεγέθη χωριστά, ἔτι δὲ τὸ διαφωνεῖν τοὺς τρόπους περὶ τῶν ἀριθμῶν σημεῖον ὅτι τὰ πράγματα αὐτὰ οὐκ ὄντα ἀληθῆ παρέχει τὴν ταραχὴν αὐτοῖς.
And yet, neither is it possible for there to be indivisible parts of an interval, as there are of the plurality from which the units consist; for number is composed of indivisibles, but magnitudes are not. —All these and other such things make it clear that it is impossible for number and magnitudes to exist separately, and further, the disagreement of the various ways of speaking about numbers is a sign that the facts themselves, not being true, cause this confusion for them.
οἱ μὲν γὰρ τὰ μαθηματικὰ μόνον ποιοῦντες παρὰ τὰ αἰσθητά, ὁρῶντες τὴν περὶ τὰ εἴδη δυσχέρειαν καὶ πλάσιν, ἀπέστησαν ἀπὸ τοῦ εἰδητικοῦ ἀριθμοῦ καὶ τὸν μαθηματικὸν ἐποίησαν· οἱ δὲ τὰ εἴδη βουλόμενοι ἅμα καὶ ἀριθμοὺς ποιεῖν, οὐχ ὁρῶντες δέ, εἰ τὰς ἀρχάς τις ταύτας θήσεται, πῶς ἔσται ὁ μαθηματικὸς ἀριθμὸς παρὰ τὸν εἰδητικόν, τὸν αὐτὸν εἰδητικὸν καὶ μαθηματικὸν ἐποίησαν ἀριθμὸν τῷ λόγῳ, ἐπεὶ ἔργῳ γε ἀνῄρηται ὁ μαθηματικός (ἰδίας γὰρ καὶ οὐ μαθηματικὰς ὑποθέσεις λέγουσιν)· ὁ δὲ πρῶτος θέμενος τὰ εἴδη εἶναι καὶ ἀριθμοὺς τὰ εἴδη καὶ τὰ μαθηματικὰ εἶναι εὐλόγως ἐχώρισεν·
For some, making only mathematical objects exist apart from sensible things, because they saw the difficulty and fictitious nature of the theory of Forms, abandoned Form-number and made mathematical number; while others, wishing to make the Forms and numbers exist at the same time, but not seeing how, if one posits these principles, mathematical number is to exist apart from Form-number, made Form-number and mathematical number the same in theory, since in fact mathematical number is done away with (for they state peculiar and non-mathematical hypotheses); and he who first posited that the Forms exist, and that the Forms are numbers, and that mathematical objects exist, naturally separated them.
ὥστε πάντας συμβαίνει κατὰ μέν τι λέγειν ὀρθῶς, ὅλως δʼ οὐκ ὀρθῶς.
So that it turns out that all say something that is correct, but as a whole not correct.
καὶ αὐτοὶ δὲ ὁμολογοῦσιν οὐ ταὐτὰ λέγοντες ἀλλὰ τὰ ἐναντία.
And they themselves admit this by not saying the same things but contrary things.
αἴτιον δʼ ὅτι αἱ ὑποθέσεις καὶ αἱ ἀρχαὶ ψευδεῖς.
The reason is that their hypotheses and principles are false.
χαλεπὸν δʼ ἐκ μὴ καλῶς ἐχόντων λέγειν καλῶς, κατʼ Ἐπίχαρμον· ἀρτίως τε γὰρ λέλεκται, καὶ εὐθέως φαίνεται οὐ καλῶς ἔχον. —ἀλλὰ περὶ μὲν τῶν ἀριθμῶν ἱκανὰ τὰ διηπορημένα καὶ διωρισμένα (μᾶλλον γὰρ ἐκ πλειόνων ἂν ἔτι πεισθείη τις πεπεισμένος, πρὸς δὲ τὸ πεισθῆναι μὴ πεπεισμένος οὐθὲν μᾶλλον)·
And it is difficult to speak well from premises that are not well-founded, as Epicharmus says; for as soon as it is said, it is immediately seen to be not well-founded. —But regarding numbers, the difficulties raised and the definitions given are sufficient (for one who is already convinced would be still more convinced by more arguments, but for the purpose of convincing one who is not convinced, they would do nothing more).
περὶ δὲ τῶν πρώτων ἀρχῶν καὶ τῶν πρώτων αἰτίων καὶ στοιχείων ὅσα μὲν λέγουσιν οἱ περὶ μόνης τῆς αἰσθητῆς οὐσίας διορίζοντες, τὰ μὲν ἐν τοῖς περὶ φύσεως εἴρηται, τὰ δʼ οὐκ ἔστι τῆς μεθόδου τῆς νῦν· ὅσα δὲ οἱ φάσκοντες εἶναι παρὰ τὰς αἰσθητὰς ἑτέρας οὐσίας, ἐχόμενόν ἐστι θεωρῆσαι τῶν εἰρημένων.
But regarding the first principles and the first causes and elements, what those who define only sensible substance say has partly been discussed in our works on physics, and partly does not belong to our present inquiry; but what is said by those who assert that there are other substances besides sensible ones is the next thing to be considered after what has been said.
ἐπεὶ οὖν λέγουσί τινες τοιαύτας εἶναι τὰς ἰδέας καὶ τοὺς ἀριθμούς, καὶ τὰ τούτων στοιχεῖα τῶν ὄντων εἶναι στοιχεῖα καὶ ἀρχάς, σκεπτέον περὶ τούτων τί λέγουσι καὶ πῶς λέγουσιν.
Since, then, some say that the Ideas and numbers are of this nature, and that their elements are the elements and principles of existing things, we must examine what they say and in what way they say it.
οἱ μὲν οὖν ἀριθμοὺς ποιοῦντες μόνον καὶ τούτους μαθηματικοὺς ὕστερον ἐπισκεπτέοι· τῶν δὲ τὰς ἰδέας λεγόντων ἅμα τόν τε τρόπον θεάσαιτʼ ἄν τις καὶ τὴν ἀπορίαν τὴν περὶ αὐτῶν.
Those, then, who make only numbers and these mathematical, must be examined later; but of those who speak of Ideas, one might at the same time view their method and the difficulty concerning them.
ἅμα γὰρ καθόλου τε ποιοῦσι τὰς ἰδέας καὶ πάλιν ὡς χωριστὰς καὶ τῶν καθʼ ἕκαστον.
For they make the Ideas at once universal and again separate and of the class of particulars.
ταῦτα δʼ ὅτι οὐκ ἐνδέχεται διηπόρηται πρότερον.
And that this is not possible has been argued before.
αἴτιον δὲ τοῦ συνάψαι ταῦτα εἰς ταὐτὸν τοῖς λέγουσι τὰς οὐσίας καθόλου, ὅτι τοῖς αἰσθητοῖς οὐ τὰς αὐτὰς ἐποίουν· τὰ μὲν οὖν ἐν τοῖς αἰσθητοῖς καθʼ ἕκαστα ῥεῖν ἐνόμιζον καὶ μένειν οὐθὲν αὐτῶν, τὸ δὲ καθόλου παρὰ ταῦτα εἶναί τε καὶ ἕτερόν τι εἶναι.
The reason for combining these into the same thing for those who say that substances are universal is that they did not make them the same as sensible things; they thought that the particulars in the sensible world are in flux and none of them remains, but that the universal exists apart from these and is something else.
τοῦτο δʼ, ὥσπερ ἐν τοῖς ἔμπροσθεν ἐλέγομεν, ἐκίνησε μὲν Σωκράτης διὰ τοὺς ὁρισμούς, οὐ μὴν ἐχώρισέ γε τῶν καθʼ ἕκαστον· καὶ τοῦτο ὀρθῶς ἐνόησεν οὐ χωρίσας.
And this, as we said before, Socrates indeed started by means of definitions, yet he did not separate them from the particulars; and he was right in his thought in not separating them.
δηλοῖ δὲ ἐκ τῶν ἔργων· ἄνευ μὲν γὰρ τοῦ καθόλου οὐκ ἔστιν ἐπιστήμην λαβεῖν, τὸ δὲ χωρίζειν αἴτιον τῶν συμβαινόντων δυσχερῶν περὶ τὰς ἰδέας ἐστίν.
This is clear from the results; for without the universal it is not possible to acquire knowledge, but the separation is the cause of the difficulties that occur regarding the Ideas.
οἱ δʼ ὡς ἀναγκαῖον, εἴπερ ἔσονταί τινες οὐσίαι παρὰ τὰς αἰσθητὰς καὶ ῥεούσας, χωριστὰς εἶναι, ἄλλας μὲν οὐκ εἶχον ταύτας δὲ τὰς καθόλου λεγομένας ἐξέθεσαν, ὥστε συμβαίνειν σχεδὸν τὰς αὐτὰς φύσεις εἶναι τὰς καθόλου καὶ τὰς καθʼ ἕκαστον.
And others, thinking that if there are to be any substances besides the sensible and transient ones, they must be separate, having no other substances, set forth these that are called universal, so that it turns out that the universal and the particular natures are almost the same.
αὕτη μὲν οὖν αὐτὴ καθʼ αὑτὴν εἴη τις ἂν δυσχέρεια τῶν εἰρημένων.
This, then, would be in itself one difficulty among those mentioned.