§3.6#2ὥστε δὲ παντὸς ὑπερβάλλειν κατὰ τὴν πρόσθεσιν, οὐδὲ δυνάμει οἶόν τε εἶναι, εἴπερ μὴ ἔστι κατὰ συμβεβηκὸς ἐντελεχείᾳ ἄπειρον, ὥσπερ φασὶν οἱ φυσιολογοι τὸ ἔξω σῶμα τοῦ κόσμου, οὗ ἡ οὐσία ἢ ἀὴρ ἢ ἄλλο τι τοιοῦτον, ἄπειρον εἶναι.
So that to exceed every magnitude by addition is not possible even potentially, unless the infinite exists in actuality accidentally, as the physicists say that the body outside the cosmos, the essence of which is air or some other such thing, is infinite.
ἀλλʼ εἰ μὴ οἶόν τε εἶναι ἄπειρον ἐντελεχείᾳ σῶμα αἰσθητὸν οὕτω, φανερὸν ὅτι οὐδὲ δυνάμει ἂν εἴη κατὰ πρόσθεσιν, ἀλλʼ ἢ ὥσπερ εἴρηται ἀντεστραμμένως τῇ διαιρέσει, ἐπεὶ καὶ λάτων διά τοῦτο δύο τὰ ἄπειρα ἐποίησεν, ὅτι καὶ ἐπὶ τὴν αὔξην δοκεῖ ὑπερβάλλειν καὶ εἰς ἄπειρον ἰέναι καὶ ἐπὶ τὴν καθαίρεσιν.
But if it is not possible for a sensible body to be infinite in actuality in this way, it is clear that neither would it exist potentially by addition, except, as has been said, inversely to division. For Plato also for this reason made two infinites, because both in the direction of increase it seems to exceed and go to infinity, and in the direction of diminution.
ποιήσας μέντοι δύο οὐ χρῆται· οὔτε γὰρ ἐν τοῖς ἀριθμοῖς τὸ ἐπὶ τὴν καθαίρεσιν ἄπειρον ὑπάρχει (ἡ γὰρ μονὰς ἐλάχι· στον, οὔτε τὸ ἐπὶ τὴν αὔξην (μέχρι γὰρ δεκάδος ποιεῖ τὸν ἀριθμόν).
However, having made two, he does not use them; for neither in numbers does the infinite in the direction of diminution exist (for the monad is the smallest), nor that in the direction of increase (for he makes number only up to the decad).
συμβαίνει δὲ τοὐναντίον εἶναι ἄπειρον ἢ ὡς λέγουσιν.
But it turns out that the infinite is the contrary of what they say.
οὐ γὰρ οὗ μηδὲν ἔξω, ἀλλʼ οὗ ἀεί τι ἔξω ἐστί, τοῦτο ἄπειρόν ἐστιν.
For not that of which nothing is outside, but that of which some part is always outside, is the infinite.
σημεῖον δέ· καὶ γὰρ τοὺς δακτυλίους ἀπείρους λέγουσι τοὺς μὴ ἔχοντας σφενδόνην, ὅτι αἰεί τι ἔξω ἔστι λαμβάνειν, καθʼ ὁμοιότητα μέν τινα λέγοντες, οὐ μέντοι κυρίως· δεῖ γὰρ τοῦτό τε ὑπάρχειν καὶ μηδέ ποτε τὸ αὐτὸ λαμβάνεσθαι· ἐν δὲ τῷ κύκλῳ οὐ γίγνεται οὕτως, ἀλλʼ αἰεὶ τὸ ἐφεξῆς μόνον ἕτερον.
And here is a sign: for they call even rings without a bezel infinite, because it is always possible to take something outside, speaking indeed according to a certain similarity, but not strictly; for this must obtain and also that the same thing is never taken; but in the case of the circle this does not happen, but always only the successive part is different.
ἄπειρον μὲν οὖν ἐστιν οὗ κατὰ τὸ ποσὸν λαμβάνουσιν αἰεί τι λαμβάνειν ἔστιν ἔξω.
Therefore, the infinite is that of which, to those who take it according to quantity, it is always possible to take something outside.
οὗ δὲ μηδὲν ἔξω, τοῦτʼ ἔστι τέλειον καὶ ὅλον· οὕτω γὰρ ὁριζόμεθα τὸ ὅλον, οὗ μηδὲν ἄπεστιν, οἱον ἄνθρωπον ὅλον ἢ κιβώτιον.
But that of which nothing is outside is complete and whole; for thus we define the whole, as that from which nothing is absent, like a whole man or a box.
ὥσπερ δὲ τὸ καθʼ ἕκαστον, οὕτω καὶ τὸ κυρίως, οἷον τὸ ὅλον οὗ μηδέν ἐστιν ἔξω· οὗ δʼ ἔστιν ἀπουσία ἔξω, οὐ πᾶν, ὅ τι ἂν ἀπῇ.
And just as it is in particular cases, so it is also in the strict sense, as the whole is that of which nothing is outside; but that from which there is an absence outside is not a whole, whatever it is that is absent.
ὅλον δὲ καὶ τέλειον ἢ τὸ αὐτὸ πάμπαν ἢ σύνεγγυς τὴν φύσιν.
And whole and complete are either entirely the same or very close in nature.
τέλειον δʼ οὐδὲν μὴ ἔχον τέλος· τὸ δὲ τέλος πέρας.
And nothing is complete that does not have an end; and the end is a limit.
διὸ βέλτιον οἰητέον Παρμενίδην Μελίσσου εἰρηκέναι· ὁ μὲν γὰρ τὸ ἄπειρον ὅλον φησίν, ὁ δὲ τὸ ὅλον πεπεράν· θαι, “μεσσόθεν ἰσοπαλές”.
Therefore, we must think that Parmenides spoke better than Melissus; for the latter says that the infinite is the whole, while the former says that the whole is limited, "equally balanced from the middle".
οὐ γὰρ λίνον λίνῳ συνάπτειν ἐστὶν τῷ ἅπαντι καὶ ὅλῳ τὸ ἄπειρον, ἐπεὶ ἐντεῦθέν γε λαμβάνουσι τὴν σεμνότητα κατὰ τοῦ ἀπείρου, τὸ πάντα περιέχειν καὶ τὸ πᾶν ἐν ἑαυτῷ ἔχειν, διὰ τὸ ἔχειν τινὰ ὁμοιότητα τῷ ὅλῳ.
For to couple the infinite with the all and the whole is not "to join thread to thread", since it is from this that they derive the majesty attributed to the infinite, namely that it contains all things and has the all in itself, because of its having some similarity to the whole.
ἔστι γὰρ τὸ ἄπειρον τῆς τοῦ μεγέθους τελειότητος ὕλη καὶ τὸ δυνάμει ὅλον, ἔντελεχείᾳ δʼ οὔ, διαιρετὸν δʼ ἐπί τε τὴν καθαίρεσιν καὶ τὴν ἀντεστραμμένην πρόσθεσιν, ὅλον δὲ καὶ πεπερασμένον οὐ καθʼ αὐτὸ ἀλλὰ κατʼ ἄλλο· καὶ οὐ περιέχει ἀλλὰ περιέχεται, ᾗ ἄπειρον.
For the infinite is the matter of the completeness of magnitude, and is the whole potentially, but not in actuality, and is divisible both in the direction of diminution and in the inverse addition, and is whole and limited not by itself but by another; and it does not contain but is contained, in so far as it is infinite.
διὸ καὶ ἄγνωστον ᾗ ἄπειρον· εἶδος γὰρ οὐκ ἔχει ἡ ὕλη.
Therefore also it is unknown in so far as it is infinite; for matter does not have form.
ὥστε φανερὸν ὅτι μᾶλλον ἐν μορίου λόγῳ τὸ ἄπειρον ἢ ἐν ὅλου μόριον γὰρ ἡ ὕλη τοῦ ὅλου ὥσπερ ὁ χαλκὸς τοῦ χαλκοῦ ἀνδριάντος, ἐπεὶ εἴ γε περιέχει ἐν τοῖς αἰσθητοῖς, καὶ ἐν τοῖς νοητοῖς τὸ μέγα καὶ τὸ μικρὸν ἔδει περιέχειν τὰ νοητά.
So that it is clear that the infinite is rather in the account of a part than in that of a whole; for matter is a part of the whole, just as bronze is of the bronze statue, since if indeed it contains in the case of sensible things, in the case of intelligible things also the great and the small ought to contain the intelligible things.
ἄτοπον δὲ καὶ ἀδύνατον τὸ ἄγνωστον καὶ ἀόριστον περιέχειν καὶ ὁρίζειν.
But it is absurd and impossible for the unknown and indefinite to contain and limit.