§2.1.3Ἐνίοις μὲν οὖν διὰ τὸ δεῖν τὰ πρῶτα ἐπίστασθαι οὐ δοκεῖ ἐπιστήμτη εἶναι, τοῖς δʼ εἶναι μέν, πάντων μέντοι ἀπόδειξις εἶναι·
For some, then, because of the necessity of knowing the first things, it does not seem that there is knowledge; while for others there is, but they think there is a demonstration of all things.
ὧν οὐδέτερον οὔτʼ ἀληθὲς οὔτʼ ἀναγκαῖον.
Neither of these views is either true or necessary.
οἱ μὲν γὰρ ὑποθέμενοι μὴ εἶναι ὅλως ἐπίστασθαι, οὗτοι εἰς ἄπειρον ἀξιοῦσιν ἀνάγεσθαι ὡς οὐκ ἂν ἐπισταμένους τὰ ὕστερα διὰ τὰ πρότερα, ὧν μὴ ἔστι πρῶτα, ὀρθῶς λέγοντες·
For those who assume that there is no knowing at all, these require a regress to infinity, on the ground that we would not know the subsequent things through the prior things unless there are first things—speaking correctly; for it is impossible to traverse infinite things.
ἀδύνατον γὰρ τὰ ἄπειρα διελθεῖν. εἴ τε ἵσταται καὶ εἰσὶν ἀρχαί, ταύτας ἀγνώστους εἶναι ἀποδείξεώς γε μὴ οὔσης αὐτῶν, ὅπερ φασὶν εἶναι τὸ ἐπίστασθαι μόνον·
And if the regress stops and there are starting-points, they say these are unknown, at least if there is no demonstration of them, which they say is the only way of knowing.
εἰ δὲ μὴ ἔστι τὰ πρῶτα εὐδέναι, οὐδὲ τὰ ἐκ τούτων εἶναι ἐπίστασθαι ἁπλῶς οὐδὲ κυρίως, ἀλλʼ ἐξ ὑποθέσεως, εἰ ἐκεῖνα ἔστιν.
But if it is not possible to know the first things, neither is it possible to know the things derived from them unqualifiedly or in the proper sense, but only on the hypothesis that those first things exist.
οἱ δὲ περὶ μὲν τοῦ ἐπίστασθαι ὁμολογοῦσι· διʼ ἀποδείξεως γὰρ εἶναι μόνον· ἀλλὰ πάντων εἶναι ἀπόδειξιν οὐδὲν κωλύειν· ἐνδέχεσθαι γὰρ κύκλῳ γίνεσθαι τὴν ἀπόδειξιν καὶ ἐξ ἀλλήλων.
The other group agrees about knowing; for they say it is only through demonstration; but they say that nothing prevents there being a demonstration of all things, since it is possible for demonstration to occur circularly and from one another.
Ἡμεῖς δέ φαμεν οὔτε πᾶσαν ἐπιστήμτην ἀποδεικτικὴν εἶναι, ἀλλὰ τὴν τῶν ἀμέσων ἀναπόδεικτον (καὶ τοῦθʼ ὅτι ἀναγκαῖον, φανερόν· εἰ γὰρ ἀνάγκη μὲν ἐπίστασθαι τὰ πρότερα καὶ ἐξ ὧν ἡ ἀπόδειξις, ἶσταται δέ ποτε τὰ ἄμεσα, ταῦτʼ ἀναπόδεικτα ἀνάγκη εἶναι)ταῦτά τʼ οὖν οὕτω λεγομεν, καὶ οὐ μόνον ἐπιστήμτην ἀλλὰ καὶ ἀρχὴν ἐπιστήμης εἶναί τινά φαμεν, τοὺς ὅρους γνωρίζομεν.
But we say that not all knowledge is demonstrative, but that the knowledge of immediate things is indemonstrable (and that this is necessary is clear; for if it is necessary to know the prior things and those from which the demonstration proceeds, and the immediate things must eventually stop, these immediate things must be indemonstrable). This, then, is what we say, and we say that there is not only knowledge but also a starting-point of knowledge, by which we recognize the terms.
κύκλῳ τε ὅτι ἀδύνατον ἀποδείκνυσθαι ἀπλῶς, δῇλον, εἴπερ ἐκ προτέρων δεῖ τὴν ἀπόδειξιν εἶναι καὶ γνωριμωτέρων·
And it is clear that it is impossible to demonstrate circularly in an unqualified sense, since a demonstration must proceed from prior and more known things.
ἀδύνατον γάρ ἐστι τὰ αὐτὰ τῶν αὐτῶν ἅμα πρότερα καὶ ὕστερα εἶναι, εἰ μὴ τὸν ἕτερον τρόπον, οἷον τὰ μὲν πρὸς ἡμᾶς τὰ δʼ ἁπλῶς, ὅνπερ τρόπον ἡ ἐπαγωγὴ ποιεῖ γνώριμον.
For it is impossible for the same things to be simultaneously prior and posterior to the same things, except in another manner, for instance, some to us and others unqualifiedly, which is the way induction makes things known.
εἰ δʼ οὕτως, οὐκ ἂν εἴη τὸ ἁπλῶς εἰδέναι καλῶς ὡρισμένον, ἀλλὰ διττόν· ἢ οὐχ ἀπλῶς ἡ ἑτέρα ἀπόδειξις, γινομένη γʼ ἐκ τῶν ἡμῖν· γνωριμωτέρων.
But if so, knowing unqualifiedly would not be well defined, but would be twofold; or the other demonstration, which proceeds from things more known to us, is not unqualified.
συμβαίνει δὲ τοῖς λέγουσι κύκλῳ τὴν ἀπόδειξιν εἶναι οὐ μόνον τὸ νῦν εἰρημένον, ἀλλ᾿ οὐδὲν ἄλλο λέγειν ἢ ὅτι τοῦτʼ ἔστιν εἰ τοῦτʼ ἔστιν·
And there happens to those who say that demonstration is circular not only what has just been said, but also that they say nothing other than "this exists if this exists"; and in this way it is easy to show everything.
οὕτω δὲ πάντα ῥάδιον δεῖξαι. δῆλον δʼ ὅτι τοῦτο συμβαίνει τριῶν ὅρων τεθέντων.
And it is clear that this happens when three terms are posited.
τὸ μὲν γὰρ διὰ πολλῶν ἢ διʼ ὀλίγων ἀνακάμπτειν φάναι οὐδὲν διαφέρει, διʼ ὀλίγων δʼ ἢ δυοῖν.
For to say that the regression bends back through many or through few terms makes no difference, nor does it make a difference whether through few or through two.
ὅταν γὰρ τοῦ Α ὄντος ἐξ ἀνάγκης ᾖ τὸ Β, τούτου δὲ τὸ Γ, τοῦ Α ὄντος ἔσται τὸ Γ. εἰ δὴ τοῦ Α ὄντος ἀνάγκη τὸ Β εἶναι, τούτου δʼ ὄντος τὸ (τοῦτο γὰρ ἦν τὸ κύκλῳ), κείσθω τὸ ἐφʼ οὗ τὸ Γ. τὸ οὖν τοῦ Β ὄντος τὸ Α εἶναι λέγειν ἐστὶ τὸ Γ εἶναι λέγειν, τοῦτο δʼ ὅτι τοῦ Α ὄντος τὸ Γ ἔστι· τὸ δὲ Γ τῷ Α τὸ αὐτό.
For when, A existing, B must exist of necessity, and of this, C, then, A existing, C will exist. If then, A existing, B must exist, and when this exists, that exists (for this was the circular), let C be placed where C is. Therefore, to say that A exists when B exists is to say that C exists, and this is that C exists when A exists; but C is the same as A.
ὥστε συμβαίνει λέγειν τοὺς κύκλῳ φάσκοντας εἶναι τὴν ἀπόδειξιν οὐδὲν ἕτερον πλὴν ὅτι τοῦ Α ὄντος τὸ Α ἔστιν.
So it happens that those who assert that demonstration is circular say nothing other than that A exists when A exists.
οὕτω δὲ πάντα δεῖξαι ῥᾴδιον.
And in this way it is easy to show everything.
Οὐ μὴν ἀλλʼ οὐδὲ τοῦτο δυνατόν, πλὴν ἐπὶ τούτων ὅσα ἀλλήλοις ἕπεται, ὥσπερ τὰ ἴδια.
Nevertheless, not even this is possible except in the case of those things which follow from one another, such as properties.
ἑνὸς μὲν οὖν κειμένου δέδεικται ὅτι οὐδέποτʼ ἀνάγκη τι εἶναι ἕτερον (λέγω δʼ ἑνός, ὅτι οὔτε ὅρου ἑνὸς οὔτε θέσεως μιᾶς τεθείσης), ἐκ δύο δὲ θέσεων πρώτων καὶ ἐλαχίστων ἐνδέχεται, εἴπερ καὶ συλλογίσασθαι.
Now, when one thing is posited, it has been shown that nothing else is ever of necessity (by "one" I mean that neither one term nor one thesis being posited makes it so), but from two first and minimal theses it is possible, if indeed it is possible to deduce at all.
ἐὰν μὲν οὖν τό τε Α τῷ Β καὶ τῷ Γ ἕπηται, καὶ ταῦτʼ ἀλλήλοις καὶ τῷ Α, οὕτω μὲν ἐνδέχεται ἐξ ἀλλήλων δεικνύναι πάντα τὰ αἰτηθέντα ἐν τῷ πρώτῳ σχήματι, ὡς δέδεικται ἐν τοῖς περὶ συλλογισμοῦ, δέδεικται δὲ καὶ ὅτι ἐν τοῖς ἄλλοις σχήμασιν ἢ οὐ γίνεται συλλογισμὸς ἢ οὐ περὶ τῶν ληφθέντων.
If, then, A follows both B and C, and these follow each other and A, in this way it is possible to show from one another all the things asked in the first figure, as has been shown in the treatise *On Deduction*. And it has also been shown that in the other figures either no deduction occurs or it is not concerning the assumed premises.
τὰ δὲ μὴ ἀντικατηγορούμενα οὐδαμῶς ἔστι δεῖξαι κύκλῳ, ὥστʼ ἐπειδὴ ὀλίγα τοιαῦτα ἐν ταῖς ἀποδείξεσι, φανερὸν ὅτι κενόν τε καὶ ἀδύνατὸν τὸ λέγειν ἐξ ἀλλήλων εἶναι τὴν ἀπόδειξιν καὶ διὰ τοῦτο πάντων ἐνδέχεσθαι εἶναι ἀπόδειξιν.
But things that are not reciprocally predicated can in no way be shown circularly; so that since there are few such things in demonstrations, it is clear that it is empty and impossible to say that demonstration is from one another, and that because of this there can be a demonstration of all things.