§3.6ὅλως δʼ ἀπορήσειεν ἄν τις διὰ τί καὶ δεῖ ζητεῖν ἄλλʼ ἄττα παρά τε τὰ αἰσθητὰ καὶ τὰ μεταξύ, οἷον ἃ τίθεμεν εἴδη.
On the whole, one might wonder why indeed it is necessary to seek other things besides sensible things and the intermediate things, such as the forms which we posit.
εἰ γὰρ διὰ τοῦτο, ὅτι τὰ μὲν μαθηματικὰ τῶν δεῦρο ἄλλῳ μέν τινι διαφέρει, τῷ δὲ πόλλʼ ἄττα ὁμοειδῆ εἶναι οὐθὲν διαφέρει, ὥστʼ οὐκ ἔσονται αὐτῶν αἱ ἀρχαὶ ἀριθμῷ ἀφωρισμέναι (ὥσπερ οὐδὲ τῶν ἐνταῦθα γραμμάτων ἀριθμῷ μὲν πάντων οὐκ εἰσὶν αἱ ἀρχαὶ ὡρισμέναι, εἴδει δέ, ἐὰν μὴ λαμβάνῃ τις τησδὶ τῆς συλλαβῆς ἢ τησδὶ τῆς φωνῆς· τούτων δʼ ἔσονται καὶ ἀριθμῷ ὡρισμέναι—ὁμοίως δὲ καὶ ἐπὶ τῶν μεταξύ· ἄπειρα γὰρ κἀκεῖ τὰ ὁμοειδῆ), ὥστʼ εἰ μὴ ἔστι παρὰ τὰ αἰσθητὰ καὶ τὰ μαθηματικὰ ἕτερʼ ἄττα οἷα λέγουσι τὰ εἴδη τινές, οὐκ ἔσται μία ἀριθμῷ ἀλλʼ εἴδει οὐσία, οὐδʼ αἱ ἀρχαὶ τῶν ὄντων ἀριθμῷ ἔσονται ποσαί τινες ἀλλὰ εἴδει· —εἰ οὖν τοῦτο ἀναγκαῖον, καὶ τὰ εἴδη ἀναγκαῖον διὰ τοῦτο εἶναι τιθέναι.
For if it is for this reason, because the mathematical things differ from the things here in some other respect, but in respect of being many of the same kind they do not differ at all, so that their principles will not be limited in number (just as indeed the principles of the letters here are not limited in number but in species, unless one takes this particular syllable or this particular sound—for of these they will also be limited in number—and likewise also in the case of the intermediate things, for there too the things of the same kind are infinite), so that if there are not other things besides sensible and mathematical things, such as some say the forms are, there will be no substance that is one in number but only in species, nor will the principles of existing things be some definite amount in number but only in species;—if, then, this is necessary, it is also necessary for this reason to posit the forms.
καὶ γὰρ εἰ μὴ καλῶς διαρθροῦσιν οἱ λέγοντες, ἀλλʼ ἔστι γε τοῦθʼ ὃ βούλονται, καὶ ἀνάγκη ταῦτα λέγειν αὐτοῖς, ὅτι τῶν εἰδῶν οὐσία τις ἕκαστόν ἐστι καὶ οὐθὲν κατὰ συμβεβηκός. — ἀλλὰ μὴν εἴ γε θήσομεν τά τε εἴδη εἶναι καὶ ἓν ἀριθμῷ τὰς ἀρχὰς ἀλλὰ μὴ εἴδει, εἰρήκαμεν ἃ συμβαίνειν ἀναγκαῖον ἀδύνατα. —σύνεγγυς δὲ τούτων ἐστὶ τὸ διαπορῆσαι πότερον δυνάμει ἔστι τὰ στοιχεῖα ἤ τινʼ ἕτερον τρόπον.
For even if those who say so do not articulate it well, still this is what they want, and they must say this, that each of the forms is a certain substance and none is by accident.— But indeed, if we are to posit that the forms exist and that the principles are one in number but not in species, we have already stated the impossible consequences that must follow.—And close to these is the difficulty of whether the elements exist potentially or in some other way.
εἰ μὲν γὰρ ἄλλως πως, πρότερόν τι ἔσται τῶν ἀρχῶν ἄλλο (πρότερον γὰρ ἡ δύναμις ἐκείνης τῆς αἰτίας, τὸ δὲ δυνατὸν οὐκ ἀναγκαῖον ἐκείνως πᾶν ἔχειν)· εἰ δʼ ἔστι δυνάμει τὰ στοιχεῖα, ἐνδέχεται μηθὲν εἶναι τῶν ὄντων· δυνατὸν γὰρ εἶναι καὶ τὸ μήπω ὄν· γίγνεται μὲν γὰρ τὸ μὴ ὄν, οὐθὲν δὲ γίγνεται τῶν εἶναι ἀδυνάτων. —ταύτας τε οὖν τὰς ἀπορίας ἀναγκαῖον ἀπορῆσαι περὶ τῶν ἀρχῶν, καὶ πότερον καθόλου εἰσὶν ἢ ὡς λέγομεν τὰ καθʼ ἕκαστα.
For if in some other way, there will be something else prior to the principles (for power is prior to that cause, and what is potential is not necessary for all of it to exist in that way); but if the elements exist potentially, it is possible for none of the existing things to exist; for it is possible for what is not yet existing to be; for what is not is generated, but nothing of what is impossible to exist is generated.—These difficulties, then, it is necessary to raise about the principles, and whether they are universal or as we say the particulars.
εἰ μὲν γὰρ καθόλου, οὐκ ἔσονται οὐσίαι (οὐθὲν γὰρ τῶν κοινῶν τόδε τι σημαίνει ἀλλὰ τοιόνδε, ἡ δʼ οὐσία τόδε τι· εἰ δʼ ἔσται τόδε τι καὶ ἓν θέσθαι τὸ κοινῇ κατηγορούμενον, πολλὰ ἔσται ζῷα ὁ Σωκράτης, αὐτός τε καὶ ὁ ἄνθρωπος καὶ τὸ ζῷον, εἴπερ σημαίνει ἕκαστον τόδε τι καὶ ἕν)· —εἰ μὲν οὖν καθόλου αἱ ἀρχαί, ταῦτα συμβαίνει· εἰ δὲ μὴ καθόλου ἀλλʼ ὡς τὰ καθʼ ἕκαστα, οὐκ ἔσονται ἐπιστηταί (καθόλου γὰρ ἡ ἐπιστήμη πάντων), ὥστʼ ἔσονται ἀρχαὶ ἕτεραι πρότεραι τῶν ἀρχῶν αἱ καθόλου κατηγορούμεναι, ἄνπερ μέλλῃ ἔσεσθαι αὐτῶν ἐπιστήμη.
For if they are universal, they will not be substances (for none of the common terms signifies a 'this' but a 'such', and substance is a 'this'; but if one is to posit the common predicate as a 'this' and one, Socrates will be many animals, namely himself, man, and animal, if indeed each signifies a 'this' and one);—if, then, the principles are universal, these things result; but if they are not universal but as particulars, they will not be knowable (for knowledge of all things is universal), so that there will be other principles prior to the principles, namely those predicated universally, if indeed there is to be knowledge of them.