§13.1περὶ μὲν οὖν τῆς τῶν αἰσθητῶν οὐσίας εἴρηται τίς ἐστιν, ἐν μὲν τῇ μεθόδῳ τῇ τῶν φυσικῶν περὶ τῆς ὕλης, ὕστερον δὲ περὶ τῆς κατʼ ἐνέργειαν·
So, concerning the substance of sensible things, it has been stated what it is: on the one hand, in the inquiry of physics concerning matter, and later concerning the substance in activity.
ἐπεὶ δʼ ἡ σκέψις ἐστὶ πότερον ἔστι τις παρὰ τὰς αἰσθητὰς οὐσίας ἀκίνητος καὶ ἀΐδιος ἢ οὐκ ἔστι, καὶ εἰ ἔστι τίς ἐστι, πρῶτον τὰ παρὰ τῶν ἄλλων λεγόμενα θεωρητέον, ὅπως εἴτε τι μὴ καλῶς λέγουσι, μὴ τοῖς αὐτοῖς ἔνοχοι ὦμεν, καὶ εἴ τι δόγμα κοινὸν ἡμῖν κἀκείνοις, τοῦτʼ ἰδίᾳ μὴ καθʼ ἡμῶν δυσχεραίνωμεν· ἀγαπητὸν γὰρ εἴ τις τὰ μὲν κάλλιον λέγοι τὰ δὲ μὴ χεῖρον.
But since our inquiry is whether there is some substance beside the sensible substances, which is motionless and eternal, or not, and if there is, what it is, first we must consider what is said by others, so that if they say anything not well, we may not be liable to the same charges, and if there is any doctrine common to us and them, we may not feel private unease about this as if it were directed against us; for it is a thing to be welcomed if someone should say some things better and others no worse.
δύο δʼ εἰσὶ δόξαι περὶ τούτων· τά τε γὰρ μαθηματικά φασιν οὐσίας εἶναί τινες, οἷον ἀριθμοὺς καὶ γραμμὰς καὶ τὰ συγγενῆ τούτοις, καὶ πάλιν τὰς ἰδέας.
And there are two opinions about these things: for some say that mathematical objects are substances, such as numbers and lines and things akin to these, and again, others say the Ideas are.
ἐπεὶ δὲ οἱ μὲν δύο ταῦτα γένη ποιοῦσι, τάς τε ἰδέας καὶ τοὺς μαθηματικοὺς ἀριθμούς, οἱ δὲ μίαν φύσιν ἀμφοτέρων, ἕτεροι δέ τινες τὰς μαθηματικὰς μόνον οὐσίας εἶναί φασι, σκεπτέον πρῶτον μὲν περὶ τῶν μαθηματικῶν, μηδεμίαν προστιθέντας φύσιν ἄλλην αὐτοῖς, οἷον πότερον ἰδέαι τυγχάνουσιν οὖσαι ἢ οὔ, καὶ πότερον ἀρχαὶ καὶ οὐσίαι τῶν ὄντων ἢ οὔ, ἀλλʼ ὡς περὶ μαθηματικῶν μόνον εἴτʼ εἰσὶν εἴτε μὴ εἰσί, καὶ εἰ εἰσὶ πῶς εἰσίν·
But since some make these two genera, namely the Ideas and mathematical numbers, and others make both a single nature, and still others say that only mathematical objects are substances, we must examine first concerning the mathematical objects, adding no other nature to them—for example, whether they happen to be Ideas or not, and whether they are principles and substances of existing things or not—but only as mathematical objects, whether they exist or do not exist, and if they exist, how they exist.
ἔπειτα μετὰ ταῦτα χωρὶς περὶ τῶν ἰδεῶν αὐτῶν ἁπλῶς καὶ ὅσον νόμου χάριν· τεθρύληται γὰρ τὰ πολλὰ καὶ ὑπὸ τῶν ἐξωτερικῶν λόγων, ἔτι δὲ πρὸς ἐκείνην δεῖ τὴν σκέψιν ἀπαντᾶν τὸν πλείω λόγον, ὅταν ἐπισκοπῶμεν εἰ αἱ οὐσίαι καὶ αἱ ἀρχαὶ τῶν ὄντων ἀριθμοὶ καὶ ἰδέαι εἰσίν·
Then, after this, we must examine separately about the Ideas themselves, simply and only as far as custom requires; for most points have already been made common talk even by the exoteric discourses.
μετὰ γὰρ τὰς ἰδέας αὕτη λείπεται τρίτη σκέψις.
And further, we must direct our longer discussion toward that other inquiry, when we examine whether the substances and principles of existing things are numbers and Ideas; for after the Ideas, this remains as a third inquiry.
—ἀνάγκη δʼ, εἴπερ ἔστι τὰ μαθηματικά, ἢ ἐν τοῖς αἰσθητοῖς εἶναι αὐτὰ καθάπερ λέγουσί τινες, ἢ κεχωρισμένα τῶν αἰσθητῶν (λέγουσι δὲ καὶ οὕτω τινές)· ἢ εἰ μηδετέρως, ἢ οὐκ εἰσὶν ἢ ἄλλον τρόπον εἰσίν·
And it is necessary, if mathematical objects exist, that they either exist in sensible things as some say, or separated from sensible things (and some say this also); or if in neither way, either they do not exist or they exist in another manner.
ὥσθʼ ἡ ἀμφισβήτησις ἡμῖν ἔσται οὐ περὶ τοῦ εἶναι ἀλλὰ περὶ τοῦ τρόπου.
So that our dispute will be not about their existence but about the manner of it.