Leon Magentinos, Kommentar zu Anal. Post. I 03

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Leon Magentinos, Kommentar zu Anal. Post. I

Kapitel 3.

Anal. Post. I 03, 72b 05-07

Ἐνίοις | μὲν οὖν διὰ τὸ δεῖν τὰ πρῶτα ἐπίστασθαι·

ὁρισάμενος τί ἐστιν ἀπόδειξις, νῦν ἐπιχειρεῖ ζητῆσαι εἰ | ἔστιν ἀπόδειξις. ἀπορήσει δέ τις, εἰ τεσσάρων ὄντων τῶν ζητουμένων (εἰ ἔστι, τί ἐστιν, ὁποῖόν τι ἐστιν | καὶ διατί) καὶ τοῦ εἰ ἔστι προταττομένου | τῶν ἄλλων, τίνος χάριν πρῶτα μὲν ἀπέδωκε | τὸ τί ἐστιν ἀπόδειξις, εἶτα ζητεῖ εἰ ἔστιν | ἀπόδειξις. καί φαμεν ἐφ’ ὅσων | πραγμάτων ἀμυδρὰν γνῶσιν ἔχομεν τοῦ τί | ἐστι τὸ πρᾶγμα (καὶ εἰ μὴ τὸν ὁρισμὸν αὐτοῦ | γινώσκομεν, ἀλλ’ οὖν τὸ σημαινόμενον | αὐτοῦ οὐκ ἀγνοοῦμεν, οἷον ἐπὶ τοῦ | τραγελάφου γινώσκομεν τί σημαίνει | ἡ λέξις αὕτη), ἐπὶ τῶν τοιούτων γοῦν | ζητοῦμεν πρῶτον τὸ εἰ ἔστι, εἶτα τὸ τί ἐστιν. | ἐφ’ ὅσων δὲ παντελῶς ἀγνοοῦμεν καὶ τὴν | σημασίαν τοῦ προκειμένου, ἐπὶ τούτων ἀνάγκη ἐστὶ πρότερον γνωρίσαι τί ἐστι | τὸ ζητούμενον, εἶθ’ οὕτως ζητῆσαι καὶ τὸ | εἰ ἔστιν. ἐπεὶ δὲ ἡ ἀπόδειξις πάντῃ | ἦν ἀγνοουμένη ἡμῖν, διὰ τοῦτο πρῶ | τον εἰπὼν τί ἐστιν αὕτη, νῦν ζητεῖ τὸ | εἰ ἔστι καί φησιν ὅτι τινὲς εἶπον μὴ εἶναι ὅλως ἀπόδειξιν, μήτε μὴν ἀποδεικτόν τι συλλογιζόμενοι | ὑποθετικῶς, λαμβάνοντες ὅτι τὰ πράγματα ἄπειρά εἰσι καὶ διὰ τοῦτο ἄγνωστα. ἡ δὲ δεῖξις ἔστιν αὕτη· εἰ ἀπό | δειξίς ἐστιν, ἀνάγκη καὶ τὰ πρῶτα εἰδέναι δι’ ἀποδείξεως· ἀλλὰ μὴν ἀδύνατον εἰδέναι τὰ πρῶτα | ἤγουν τὰς προτάσεις δι’ ἀποδείξεως· οὐκ ἄρα ἀπόδειξίς ἐστι. δεικνύουσι δὲ ἀδύνατον εἶναι τὰ πρῶτα | εἰδέναι δι’ ἀποδείξεως οὕτως· εἰ πᾶσα ἀπόδειξις ἐκ προτάσεων γίνεται, τῶν δὲ προτάσεων ἔστι λαβεῖν | ἀρχοειδέστερον καὶ πρῶτον, καὶ τούτων ἕτερον ἀρχοειδέστερον καὶ πρὸ τούτων ἕτερα, καὶ ἀεὶ ἐπ’ ἄπειρον | προβαίνει ἡ πρόοδος τῶν ἀρχοειδεστέρων προτάσεων· τῶν δὲ ἀπείρων γνῶσις οὐκ ἔστι· λοιπὸν ἄρα | ἀδύνατόν ἐστι τὰς ληφθείσας εἰς ἀπόδειξιν προτάσεις γνῶναι. καὶ εἰ ταύτας ἀγνοοῦμεν, πῶς ἀποδείξομεν:–

| “ ἐνίοις μὲν οὖν οὐ δοκεῖ εἶναι ἐπιστήμη” καὶ “ἀπόδειξις διὰ τὸ” λέγειν “δεῖν ἐπίστασθαι” δι’ ἀποδείξεως “τὰ πρῶτα” ἤγουν | τὰς προτάσεις. τισὶ δὲ τῶν φιλοσόφων δοκεῖ εἶναι ἀπόδειξις πάντων τῶν πραγμάτων καὶ πάντα εἶναι ἀπο | δεικτά, ὧν οὐδέτερον ἀληθές· ψεύδονται γὰρ καὶ οἱ λέγοντες πάντα εἶναι ἀναπόδεικτα καὶ οἱ ἀποδεικτά, | ἀλλ’ οὐδ’ ἀναγκαῖόν ἐστι δι’ ἀποδείξεως εἰδέναι τὰς ληφθείσας προτάσεις ἐν τῇ ἀποδείξει· | οἱ μὲν γὰρ ὑποθέμενοι μὴ εἶναι ὅλως ἐπίστασθαι ἤγουν ἀπόδειξιν, οὗτοι ἀξιοῦσιν εἶναι τὰ πράγματα | ἄπειρα καὶ ἀεὶ τῶν ληφθεισῶν προτάσεων ἔστι λαβεῖν ἀρχοειδέστερον ἕτερον:–

a. “Some people think that because you must understand the primitives”: after having defined what demonstration is, [Aristotle] now attempts to investigate if there is demonstration. Since there are four kinds of things that can be investigated (‘if something is’, ‘what it is’, ‘of what kind something is’ and ‘why something is’) and since the investigation on ‘if something is’ is put before the others, one will question the reason why he first accounts for the investigation of ‘what a demonstration is’, than he investigates ‘if there is demonstration’. And we say: in case of so many things in relation to which we have a vague knowledge of ‘what a thing is’ (and if we are not aware of its definition, we still do not ignore its meaning, such as in the case of goat-stag, we are aware of what this word means), in relation to such things, at any rate, we first investigate the ‘if it is’, than the ‘what it is’. In all the cases in which we completely ignore even the meaning of the matter at hand, it is necessary first to become familiar with what the subject of investigation is and then to investigate also the ‘if it is’ this way. Since we were completely unaware of the demonstration, for this reason he first said what this is, now he investigates the ‘if it is’. He also affirms that some said that there is no demonstration at all nor anything demonstrable by using a hypothetical syllogism and assuming that the things are infinite and therefore unknown. The proof is this: if there is a demonstration, it is necessary to know also the primitives through demonstration. However, it is impossible to know the primitives – i.e. the premises – through demonstration, hence there is no demonstration. They demonstrate that it is impossible to know the primitives through demonstration this way: if every demonstration comes about from premises, and if it is possible to assume something more basic and first than the premises, and something else more basic than these, and yet other ones prior to these, and if the progression of more basic premises always proceeds to the infinite, but there is no knowledge of infinite things, it is impossible to know the premises that are assumed for the demonstration. And if we ignore these, how will we be able to make a demonstration?

b. “Some people think that there is no understanding and demonstration” because they say that “one must understand the primitives” – i.e. the premises – “through demonstration”. Some philosophers think that there is demonstration of all the things and that everything is demonstrable, but neither of the two opinions is true, since those who say that everything is indemonstrable and those who say that everything is demonstrable are equally mistaken. However, it is not even necessary to know the premises assumed in a demonstration through demonstration. In fact, those who suppose that there is no understanding at all, i.e. no demonstration, think that things are infinite and that it is always possible to assume something else more basic than the premises that have been assumed.

Anal. Post. I 03, 72b 18–22

〈Ἡμεῖς δέ φαμεν οὔτε πᾶσαν ἐπιστήμην ἀποδεικτικὴν εἶναι, ἀλλὰ τὴν τῶν ἀμέσων ἀναπόδεικτον (καὶ τοῦθ’ ὅτι ἀναγκαῖον, φανερόν· εἰ γὰρ ἀνάγκη μὲν ἐπίστασθαι τὰ πρότερα καὶ ἐξ ὧν ἡ ἀπόδειξις, ἵσταται δέ ποτε τὰ ἄμεσα, ταῦτ’ ἀναπόδεικτα ἀνάγκη εἶναι)〉

“ ἡμεῖς δὲ” λέγομεν ὅτι “οὐ πᾶσα ἐπιστήμη ἐστὶν ἀποδεικτική”, ἤγουν δι’ ἀποδείξεως γινώσκουσα τὰ | πράγματα, ἀλλ’ ἔστι καὶ ἑτέρα ἐπιστήμη ἡ γινώσκουσα τὰ πράγματα κρειττόνως ἢ κατὰ ἀπόδειξιν. γρά | φεται δὲ καὶ “ οὕτω πᾶσαν ἐπιστήμην ἀποδεικτὴν εἶναι” καὶ νοεῖται οὕτως· ὅτι οὐ πᾶσα γνῶσις | δι’ ἀποδείξεως ἡμῖν ἐπιγίνεται· ἡ γὰρ ἐπιστήμη “τῶν ἀμέσων” προτάσεων “ἀναπόδεικτός” ἐστιν, ἀλλ’ ἐπι | δείκνυται δι’ ἐπιστήμης ἣ κρείττων ἢ κατὰ ἀπόδειξιν· ὥστε τινὰ μέν εἰσιν ἀποδεικτά, ὡς αἱ ἔμ | μεσοι προτάσεις, τινὰ δὲ ἀναπόδεικτα, ὡς αἱ ἄμεσοι. καὶ τοῦτο, ὅτι αἱ ἄμεσοι προτάσεις εἰσὶν | ἀναπόδεικτοι, φανερόν:–

‘We’ affirm that ‘not all understanding is demonstrative’, that is to say that it gains knowledge of the things through demonstration. But there is also another understanding which gains knowledge of the things in a more effective way than according to a demonstration. It is also written that ‘not all understanding is demonstrable’, and this is meant in this sense: that not every knowledge comes about for us through demonstration, since the understanding ‘of immediate’ premises is ‘indemonstrable’, but it is shown through (a form of) understanding which is more effective than the one gained according to a demonstration. Thus, some (propositions) are demonstrable, such as the intermediate premises, while others are indemonstrable, such as the immediate ones. And it is clear that the immediate propositions are indemonstrable.

Anal. Post. I 3, 73b 18–22

〈Ἡμεῖς δέ φαμεν οὔτε πᾶσαν ἐπιστήμην ἀποδεικτικὴν εἶναι, ἀλλὰ τὴν τῶν ἀμέσων ἀναπόδεικτον (καὶ τοῦθ’ ὅτι ἀναγκαῖον, φανερόν· εἰ γὰρ ἀνάγκη μὲν ἐπίστασθαι τὰ πρότερα καὶ ἐξ ὧν ἡ ἀπόδειξις, ἵσταται δέ ποτε τὰ ἄμεσα, ταῦτ’ ἀναπόδεικτα ἀνάγκη εἶναι)〉

“ ἵσταται δέ ποτε” εἰς “τὰ | ἄμεσα, καὶ ἀνάγκη ταῦτα” τὰ | ἄμεσα “ἀναπόδεικτα εἶναι”· καὶ | οὐ μόνον λέγομεν εἶναι ἐπιστήμην ἑτέραν | τῆς ἀποδεικτικῆς κρείττονα ταύτης, ἀλ | λὰ καὶ ἀρχὴν τῆς τοιαύτης ἐπιστήμης λέ | γομεν εἶναι, ἐν ᾗ τοὺς ὅρους γινώσκομεν. | ἀρχὴν δὲ νόει τὸν ἡμέτερον νοῦν, ὅρους δὲ | τὸν ὑποκείμενον καὶ κατηγορούμενον τῶν κοι | νῶν ἀξιωμάτων. ὁ γοῦν νοῦς ὁ ἡμέτερος | ἁπλαῖς ἐπιβολαῖς καὶ ἄνευ ἀποδείξεως | γινώσκει τοὺς ὅρους τῶν ἀμέσων | προτάσεων ἤγουν τῶν κοινῶν ἀξιωμάτων. καὶ | αὕτη μὲν ἡ ἐξήγησίς ἐστιν ἀρίστη.:–

‘Things come to a stop at some point’ in ‘the immediate things’, and ‘these’ immediate things ‘must be indemonstrable’. And we affirm not only that another understanding is more effective than this demonstrative one, but we also call principle of such understanding that one in which we gain knowledge of the definitions. Think of our intellect as principle, the subject and the predicate of common propositions as limits. Thus, our intellect knows the limits of immediate premi¬ses, that is, of common propositions, by means of simple intuition and without demonstration. And this is the best explanation. It is also explained this way: since there were some people, as we have said, who affirmed that things are infinite and do not end at any principle or limits, Aristotle confutes them and says that limits are also boundaries of things, the celestial bodies of the perceptible things, since they mark the boundaries and surround these things, the intelligible substances are limits of the celestial bodies. Principle of these things is the divine intelligence, and our human intelligence, illuminated by this divine intelligence, gains knowledge of these limits – i.e. the celestial bodies and the intelligible substances – by means of simple intuition.