§2.2ἀλλὰ μὴν ὅτι γʼ ἔστιν ἀρχή τις καὶ οὐκ ἄπειρα τὰ αἴτια τῶν ὄντων οὔτʼ εἰς εὐθυωρίαν οὔτε κατʼ εἶδος, δῆλον.
But indeed, that there is a first principle and that the causes of things are not infinite, either in a straight line or in kind, is clear.
οὔτε γὰρ ὡς ἐξ ὕλης τόδʼ ἐκ τοῦδε δυνατὸν ἰέναι εἰς ἄπειρον (οἷον σάρκα μὲν ἐκ γῆς, γῆν δʼ ἐξ ἀέρος, ἀέρα δʼ ἐκ πυρός, καὶ τοῦτο μὴ ἵστασθαι), οὔτε ὅθεν ἡ ἀρχὴ τῆς κινήσεως (οἷον τὸν μὲν ἄνθρωπον ὑπὸ τοῦ ἀέρος κινηθῆναι, τοῦτον δʼ ὑπὸ τοῦ ἡλίου, τὸν δὲ ἥλιον ὑπὸ τοῦ νείκους, καὶ τούτου μηδὲν εἶναι πέρας)·
For neither can one thing proceed from another as from matter to infinity (e.g. flesh from earth, earth from air, air from fire, and this without stopping), nor can the source of movement do so (e.g. man be moved by air, air by the sun, the sun by strife, and of this there be no limit).
ὁμοίως δὲ οὐδὲ τὸ οὗ ἕνεκα εἰς ἄπειρον οἷόν τε ἰέναι, βάδισιν μὲν ὑγιείας ἕνεκα, ταύτην δʼ εὐδαιμονίας, τὴν δʼ εὐδαιμονίαν ἄλλου, καὶ οὕτως ἀεὶ ἄλλο ἄλλου ἕνεκεν εἶναι·
Similarly, neither can the final cause go on to infinity—walking for the sake of health, this for the sake of happiness, happiness for the sake of something else, and thus one thing always be for the sake of another.
καὶ ἐπὶ τοῦ τί ἦν εἶναι δʼ ὡσαύτως.
And the same holds of the essence.
τῶν γὰρ μέσων, ὧν ἐστί τι ἔσχατον καὶ πρότερον, ἀναγκαῖον εἶναι τὸ πρότερον αἴτιον τῶν μετʼ αὐτό.
For in the case of intermediates, which have a last and a prior term, the prior must be the cause of those following it.
εἰ γὰρ εἰπεῖν ἡμᾶς δέοι τί τῶν τριῶν αἴτιον, τὸ πρῶτον ἐροῦμεν· οὐ γὰρ δὴ τό γʼ ἔσχατον, οὐδενὸς γὰρ τὸ τελευταῖον· ἀλλὰ μὴν οὐδὲ τὸ μέσον, ἑνὸς γάρ (οὐθὲν δὲ διαφέρει ἓν ἢ πλείω εἶναι, οὐδʼ ἄπειρα ἢ πεπερασμένα).
For if we had to say which of the three is the cause, we should say the first; surely not the last, for the ultimate term is the cause of nothing; nor yet the intermediate, for it is the cause of only one (and it makes no difference whether there is one or more, or whether they are infinite or finite).
τῶν δʼ ἀπείρων τοῦτον τὸν τρόπον καὶ ὅλως τοῦ ἀπείρου πάντα τὰ μόρια μέσα ὁμοίως μέχρι τοῦ νῦν· ὥστʼ εἴπερ μηδέν ἐστι πρῶτον, ὅλως αἴτιον οὐδέν ἐστιν. —ἀλλὰ μὴν οὐδʼ ἐπὶ τὸ κάτω οἷόν τε εἰς ἄπειρον ἰέναι, τοῦ ἄνω ἔχοντος ἀρχήν, ὥστʼ ἐκ πυρὸς μὲν ὕδωρ, ἐκ δὲ τούτου γῆν, καὶ οὕτως ἀεὶ ἄλλο τι γίγνεσθαι γένος.
But of things which are infinite in this way, and of the infinite generally, all the parts are intermediates down to the present; so that if there is no first, there is no cause at all. — But indeed, neither can one proceed downwards to infinity, if the upwards has a beginning, so that from fire comes water, and from this earth, and thus some other kind of thing is always being produced.
διχῶς γὰρ γίγνεται τόδε ἐκ τοῦδε—μὴ ὡς τόδε λέγεται μετὰ τόδε, οἷον ἐξ Ἰσθμίων Ὀλύμπια, ἀλλʼ ἢ ὡς ἐκ παιδὸς ἀνὴρ μεταβάλλοντος ἢ ὡς ἐξ ὕδατος ἀήρ.
For one thing comes from another in two ways—not as one event is said to follow another, as the Olympic games follow the Isthmian, but either as a man comes from a boy through change, or as air comes from water.
ὡς μὲν οὖν ἐκ παιδὸς ἄνδρα γίγνεσθαί φαμεν, ὡς ἐκ τοῦ γιγνομένου τὸ γεγονὸς ἢ ἐκ τοῦ ἐπιτελουμένου τὸ τετελεσμένον (ἀεὶ γάρ ἐστι μεταξύ, ὥσπερ τοῦ εἶναι καὶ μὴ εἶναι γένεσις, οὕτω καὶ τὸ γιγνόμενον τοῦ ὄντος καὶ μὴ ὄντος· ἔστι γὰρ ὁ μανθάνων γιγνόμενος ἐπιστήμων, καὶ τοῦτʼ ἐστὶν ὃ λέγεται, ὅτι γίγνεται ἐκ μανθάνοντος ἐπιστήμων)· τὸ δʼ ὡς ἐξ ἀέρος ὕδωρ, φθειρομένου θατέρου.
Now, we say that a man comes from a boy in the sense that that which has become comes from that which is becoming, or the finished from the being finished (for there is always an intermediate, and just as becoming is between being and non-being, so that which is becoming is between what is and what is not; for the learner is becoming a man of science, and this is what is meant when we say that from a learner comes a man of science); but the other way, as water from air, involves the destruction of one of them.
διὸ ἐκεῖνα μὲν οὐκ ἀνακάμπτει εἰς ἄλληλα, οὐδὲ γίγνεται ἐξ ἀνδρὸς παῖς (οὐ γὰρ γίγνεται ἐκ τῆς γενέσεως τὸ γιγνόμενον ἀλλʼ ὃ ἔστι μετὰ τὴν γένεσιν· οὕτω γὰρ καὶ ἡμέρα ἐκ τοῦ πρωΐ, ὅτι μετὰ τοῦτο· διὸ οὐδὲ τὸ πρωῒ ἐξ ἡμέρας)· θάτερα δὲ ἀνακάμπτει.
Therefore, the former do not cycle back into one another, nor does a boy come from a man (for that which is becoming does not come from the process of becoming, but that which exists after the process of becoming; for thus also day comes from dawn, because it is after it, and therefore dawn does not come from day); but the other class of things do cycle back.
ἀμφοτέρως δὲ ἀδύνατον εἰς ἄπειρον ἰέναι·
But in both cases it is impossible to proceed to infinity.
τῶν μὲν γὰρ ὄντων μεταξὺ ἀνάγκη τέλος εἶναι, τὰ δʼ εἰς ἄλληλα ἀνακάμπτει· ἡ γὰρ θατέρου φθορὰ θατέρου ἐστὶ γένεσις. —ἅμα δὲ καὶ ἀδύνατον τὸ πρῶτον ἀΐδιον ὂν φθαρῆναι·
For of those things which are intermediate there must be an end, and the others cycle back into one another; for the destruction of one is the generation of the other. — At the same time, it is also impossible for the first, being eternal, to be destroyed.
ἐπεὶ γὰρ οὐκ ἄπειρος ἡ γένεσις ἐπὶ τὸ ἄνω, ἀνάγκη ἐξ οὗ φθαρέντος πρώτου τι ἐγένετο μὴ ἀΐδιον εἶναι.
For since the generation upwards is not infinite, that first thing, by the destruction of which something else came to be, must not be eternal.
ἔτι δὲ τὸ οὗ ἕνεκα τέλος, τοιοῦτον δὲ ὃ μὴ ἄλλου ἕνεκα ἀλλὰ τἆλλα ἐκείνου, ὥστʼ εἰ μὲν ἔσται τοιοῦτόν τι ἔσχατον, οὐκ ἔσται ἄπειρον, εἰ δὲ μηθὲν τοιοῦτον, οὐκ ἔσται τὸ οὗ ἕνεκα, ἀλλʼ οἱ τὸ ἄπειρον ποιοῦντες λανθάνουσιν ἐξαιροῦντες τὴν τοῦ ἀγαθοῦ φύσιν (καίτοι οὐθεὶς ἂν ἐγχειρήσειεν οὐδὲν πράττειν μὴ μέλλων ἐπὶ πέρας ἥξειν)· οὐδʼ ἂν εἴη νοῦς ἐν τοῖς οὖσιν·
Moreover, the final cause is an end, and such that it is not for the sake of anything else, but other things are for its sake; so that if there is to be such an ultimate term, it will not be infinite, but if there is no such term, there will be no final cause. But those who introduce the infinite do not realize that they are doing away with the nature of the Good (although no one would try to do anything if he were not going to reach a limit); nor would there be intellect in things.
ἕνεκα γάρ τινος ἀεὶ πράττει ὅ γε νοῦν ἔχων, τοῦτο δέ ἐστι πέρας· τὸ γὰρ τέλος πέρας ἐστίν.
For he who has intellect always acts for the sake of something, and this is a limit; for the end is a limit.
ἀλλὰ μὴν οὐδὲ τὸ τί ἦν εἶναι ἐνδέχεται ἀνάγεσθαι εἰς ἄλλον ὁρισμὸν πλεονάζοντα τῷ λόγῳ· ἀεί τε γὰρ ἔστιν ὁ ἔμπροσθεν μᾶλλον, ὁ δʼ ὕστερος οὐκ ἔστιν, οὗ δὲ τὸ πρῶτον μὴ ἔστιν, οὐδὲ τὸ ἐχόμενον·
But indeed, neither can the essence be reduced to another definition which is more extensive in its formula; for the prior definition is always more of a definition, and the later is not, and where the first does not exist, neither does the next.
ἔτι τὸ ἐπίστασθαι ἀναιροῦσιν οἱ οὕτως λέγοντες, οὐ γὰρ οἷόν τε εἰδέναι πρὶν εἰς τὰ ἄτομα ἐλθεῖν·
Further, those who speak thus destroy knowledge; for it is impossible to know anything until one comes to the indivisibles.
καὶ τὸ γιγνώσκειν οὐκ ἔστιν, τὰ γὰρ οὕτως ἄπειρα πῶς ἐνδέχεται νοεῖν;
And there is no understanding; for how can one think things that are infinite in this way?
οὐ γὰρ ὅμοιον ἐπὶ τῆς γραμμῆς, ἣ κατὰ τὰς διαιρέσεις μὲν οὐχ ἵσταται, νοῆσαι δʼ οὐκ ἔστι μὴ στήσαντα (διόπερ οὐκ ἀριθμήσει τὰς τομὰς ὁ τὴν ἄπειρον διεξιών), ἀλλὰ καὶ τὴν ὅλην οὐ κινουμένῳ νοεῖν ἀνάγκη.
For it is not like the line, which indeed does not stop in its divisions, but which cannot be thought unless one stops (wherefore he who goes through the infinite will not count the segments), but it is necessary to think the whole line too without moving.
καὶ ἀπείρῳ οὐδενὶ ἔστιν εἶναι· εἰ δὲ μή, οὐκ ἄπειρόν γʼ ἐστὶ τὸ ἀπείρῳ εἶναι. —ἀλλὰ μὴν καὶ εἰ ἄπειρά γʼ ἦσαν πλήθει τὰ εἴδη τῶν αἰτίων, οὐκ ἂν ἦν οὐδʼ οὕτω τὸ γιγνώσκειν· τότε γὰρ εἰδέναι οἰόμεθα ὅταν τὰ αἴτια γνωρίσωμεν· τὸ δʼ ἄπειρον κατὰ τὴν πρόσθεσιν οὐκ ἔστιν ἐν πεπερασμένῳ διεξελθεῖν.
And nothing can exist for an infinite; otherwise, at least the essence of being infinite is not infinite. — But indeed, even if the kinds of causes were infinite in number, knowledge would still be impossible; for we think we know only when we have recognized the causes; but the infinite by addition cannot be gone through in a finite time.