§7.11#1ἀπορεῖται δὲ εἰκότως καὶ ποῖα τοῦ εἴδους μέρη καὶ ποῖα οὔ, ἀλλὰ τοῦ συνειλημμένου.
It is with good reason also that people are puzzled as to which parts are parts of the form and which are not, but rather parts of the concrete whole.
καίτοι τούτου μὴ δήλου ὄντος οὐκ ἔστιν ὁρίσασθαι ἕκαστον· τοῦ γὰρ καθόλου καὶ τοῦ εἴδους ὁ ὁρισμός·
And yet, if this is not clear, it is not possible to define each thing; for definition is of the universal and of the form.
ποῖα οὖν ἐστὶ τῶν μερῶν ὡς ὕλη καὶ ποῖα οὔ, ἐὰν μὴ ᾖ φανερά, οὐδὲ ὁ λόγος ἔσται φανερὸς ὁ τοῦ πράγματος.
Therefore, what sort of parts are as matter and what sort are not, if they are not clear, the formula of the thing will not be clear either.
ὅσα μὲν οὖν φαίνεται ἐπιγιγνόμενα ἐφʼ ἑτέρων τῷ εἴδει, οἷον κύκλος ἐν χαλκῷ καὶ λίθῳ καὶ ξύλῳ, ταῦτα μὲν δῆλα εἶναι δοκεῖ ὅτι οὐδὲν τῆς τοῦ κύκλου οὐσίας ὁ χαλκὸς οὐδʼ ὁ λίθος διὰ τὸ χωρίζεσθαι αὐτῶν· ὅσα δὲ μὴ ὁρᾶται χωριζόμενα, οὐδὲν μὲν κωλύει ὁμοίως ἔχειν τούτοις, ὥσπερ κἂν εἰ οἱ κύκλοι πάντες ἑωρῶντο χαλκοῖ· οὐδὲν γὰρ ἂν ἧττον ἦν ὁ χαλκὸς οὐδὲν τοῦ εἴδους· χαλεπὸν δὲ ἀφελεῖν τοῦτον τῇ διανοίᾳ.
Now, as for those things which appear to supervene upon things different in form, such as a circle in bronze, in stone, and in wood, these seem to make it clear that the bronze or the stone is no part of the substance of the circle, because of their being separated from them; but as for those things which are not seen to be separated, there is nothing to prevent them from being in the same case as these, just as if all circles were seen to be of bronze; for the bronze would none the less be no part of the form; yet it would be difficult to abstract this in thought.
οἷον τὸ τοῦ ἀνθρώπου εἶδος ἀεὶ ἐν σαρξὶ φαίνεται καὶ ὀστοῖς καὶ τοῖς τοιούτοις μέρεσιν· ἆρʼ οὖν καὶ ἐστὶ ταῦτα μέρη τοῦ εἴδους καὶ τοῦ λόγου;
For example, the form of man always appears in flesh and bones and parts of this kind; are these then also parts of the form and of the formula?
ἢ οὔ, ἀλλʼ ὕλη, ἀλλὰ διὰ τὸ μὴ καὶ ἐπʼ ἄλλων ἐπιγίγνεσθαι ἀδυνατοῦμεν χωρίσαι;
Or are they not, but rather matter, and is it only because it does not supervene upon other things as well that we are unable to separate them?
ἐπεὶ δὲ τοῦτο δοκεῖ μὲν ἐνδέχεσθαι ἄδηλον δὲ πότε, ἀποροῦσί τινες ἤδη καὶ ἐπὶ τοῦ κύκλου καὶ τοῦ τριγώνου ὡς οὐ προσῆκον γραμμαῖς ὁρίζεσθαι καὶ τῷ συνεχεῖ, ἀλλὰ πάντα καὶ ταῦτα ὁμοίως λέγεσθαι ὡσανεὶ σάρκες καὶ ὀστᾶ τοῦ ἀνθρώπου καὶ χαλκὸς καὶ λίθος τοῦ ἀνδριάντος· καὶ ἀνάγουσι πάντα εἰς τοὺς ἀριθμούς, καὶ γραμμῆς τὸν λόγον τὸν τῶν δύο εἶναί φασιν.
Since, then, this seems to be possible but it is unclear when, some are already puzzled even in the case of the circle and the triangle, on the ground that it is not fitting to define them by lines and by the continuous, but that all these too should be spoken of in the same way, just as flesh and bones of man, and bronze and stone of the statue; and they reduce all things to numbers, and say that the formula of a line is that of the number two.
καὶ τῶν τὰς ἰδέας λεγόντων οἱ μὲν αὐτογραμμὴν τὴν δυάδα, οἱ δὲ τὸ εἶδος τῆς γραμμῆς, ἔνια μὲν γὰρ εἶναι τὸ αὐτὸ τὸ εἶδος καὶ οὗ τὸ εἶδος (οἷον δυάδα καὶ τὸ εἶδος δυάδος), ἐπὶ γραμμῆς δὲ οὐκέτι.
And of those who assert the ideas, some make the dyad the line-itself, and others the form of the line; for they say that in some cases the form and that of which it is the form are the same (such as the dyad and the form of the dyad), but in the case of the line this is no longer so.
συμβαίνει δὴ ἕν τε πολλῶν εἶδος εἶναι ὧν τὸ εἶδος φαίνεται ἕτερον (ὅπερ καὶ τοῖς Πυθαγορείοις συνέβαινεν), καὶ ἐνδέχεται ἓν πάντων ποιεῖν αὐτὸ εἶδος, τὰ δʼ ἄλλα μὴ εἴδη· καίτοι οὕτως ἓν πάντα ἔσται.
It turns out, then, that there is one form of many things whose form appears to be different (which also happened to the Pythagoreans), and it is possible to make one self-substantial form for all things, and to say that the others are not forms; and yet in this way all things will be one.
ὅτι μὲν οὖν ἔχει τινὰ ἀπορίαν τὰ περὶ τοὺς ὁρισμούς, καὶ διὰ τίνʼ αἰτίαν, εἴρηται· διὸ καὶ τὸ πάντα ἀνάγειν οὕτω καὶ ἀφαιρεῖν τὴν ὕλην περίεργον· ἔνια γὰρ ἴσως τόδʼ ἐν τῷδʼ ἐστὶν ἢ ὡδὶ ταδὶ ἔχοντα.
That the matters concerning definitions, therefore, involve some puzzle, and for what reason, has been stated; and for this reason, to reduce all things in this way and to abstract the matter is superfluous; for some things are perhaps this in this, or these things in such-and-such a state.
καὶ ἡ παραβολὴ ἡ ἐπὶ τοῦ ζῴου, ἣν εἰώθει λέγειν Σωκράτης ὁ νεώτερος, οὐ καλῶς ἔχει· ἀπάγει γὰρ ἀπὸ τοῦ ἀληθοῦς, καὶ ποιεῖ ὑπολαμβάνειν ὡς ἐνδεχόμενον εἶναι τὸν ἄνθρωπον ἄνευ τῶν μερῶν, ὥσπερ ἄνευ τοῦ χαλκοῦ τὸν κύκλον.
And the comparison in the case of the animal, which the younger Socrates was accustomed to state, is not well; for it leads away from the truth, and makes one suppose that it is possible for man to exist without his parts, just as the circle can exist without the bronze.
τὸ δʼ οὐχ ὅμοιον· αἰσθητὸν γάρ τι τὸ ζῷον, καὶ ἄνευ κινήσεως οὐκ ἔστιν ὁρίσασθαι, διὸ οὐδʼ ἄνευ τῶν μερῶν ἐχόντων πώς.
But the cases are not similar; for the animal is something sensible, and it is not possible to define it without motion, and therefore not without its parts being in a certain state.
οὐ γὰρ πάντως τοῦ ἀνθρώπου μέρος ἡ χείρ, ἀλλʼ ἢ δυναμένη τὸ ἔργον ἀποτελεῖν, ὥστε ἔμψυχος οὖσα· μὴ ἔμψυχος δὲ οὐ μέρος.
For it is not in any state whatsoever that a hand is a part of man, but only when it is able to fulfill its function, so that it is animate; but when not animate, it is not a part.
περὶ δὲ τὰ μαθηματικὰ διὰ τί οὐκ εἰσὶ μέρη οἱ λόγοι τῶν λόγων, οἷον τοῦ κύκλου τὰ ἡμικύκλια;
But in the case of mathematical objects, why are the formulae not parts of the formulae, for example, the semicircles of the circle?