Authors/Aristotle/priora/Liber 2/C17

Chapter 17

Greek	Latin	English
	(PL 64 0704A) CAPUT XIX. De non propter hoc accidere falsum.	17
65a38 Τὸ δὲ μὴ παρὰ τοῦτο συμβαίνειν τὸ ψεῦδος, ὁ πολλάκις ἐν τοῖς λόγοις εἰώθαμεν λέγειν, πρῶτον μέν ἐστιν ἐν τοῖς εἰς τὸ ἀδύνατον συλλογισμοῖς, ὅταν πρὸς ἀντίφασιν ἦι ↵ τούτου ὁ ἐδείκνυτο τῆι εἰς τὸ ἀδύνατον. οὔτε γὰρ μὴ ἀντιφήσας ἐρεῖ τὸ οὐ παρὰ τοῦτο, ἀλλ᾽ ὅτι ψεῦδός τι ἐτέθη τῶν πρότερον, οὔτ᾽ ἐν τῆι δεικνυούσηι· οὐ γὰρ τίθησι ὁ ἀντίφησιν.	Non propter hoc autem accidere falsum (quod saepe in disputationibus solemus dicere) primum quidem est in iis qui ad impossibile syllogismis, quando ad contradictionem est huius quod monstratum est ea quae ad impossibile. (0704B) Nam neque qui non contradicit dicit non propter hoc, sed quoniam falsum est aliquid positum priorum, neque in ostensiva, non enim ponit quod contradicit.	The objection that ‘this is not the reason why the result is false’, which we frequently make in argument, is made primarily in the case of a reductio ad impossibile, to rebut the proposition which was being proved by the reduction. For unless a man has contradicted this proposition he will not say, ‘False cause’, but urge that something false has been assumed in the earlier parts of the argument; nor will he use the formula in the case of an ostensive proof; for here what one denies is not assumed as a premiss.
ἔτι δ᾽ ὅταν ἀναιρεθῆι τι δεικτικῶς διὰ τῶν Α Β Γ, οὐκ ἔστιν εἰπεῖν ὡς οὐ παρὰ τὸ κείμενον γεγένηται ὁ συλλογισμός. τὸ γὰρ μὴ παρὰ τοῦτο γίνεσθαι τότε λέγομεν, ὅταν ἀναιρεθέντος τούτου μηδὲν ἧττον περαίνηται ὁ συλλογισμός, ὅπερ οὐκ ἔστιν ἐν τοῖς δεικτικοῖς· ἀναιρεθείσης γὰρ τῆς θέσεως οὐδ᾽ ὁ πρὸς ταύτην ἔσται συλλογισμός. φανερὸν οὖν ὅτι ἐν τοῖς εἰς τὸ ἀδύνατον λέγεται τὸ μὴ παρὰ τοῦτο, καὶ ὅταν οὕτως ἔχηι πρὸς τὸ ἀδύνατον ἡ ἐξ ἀρχῆς ὑπόθεσις ὥστε καὶ οὔσης καὶ μὴ οὔσης ταύτης οὐδὲν ἧττον συμβαίνειν τὸ ἀδύνατον.	Amplius autem quando interimitur aliquid ostensive per A B C, non est dicere quoniam non propter quod positum est factus est syllogismus, nam non propter hoc fieri tunc dicimus, quando interempto hoc nihilominus perficitur syllogismus, quod non est in ostensivis, interempta enim propositione, nec qui ad hanc est erit syllogismus. Manifestum igitur quoniam in iis qui ad impossibile sunt dicitur non propter hoc, et quando sic se habet ad impossibile quae ex principio est hypothesis, ut cum sit, vel cum non sit haec, nihilominus accidit impossibile.	Further when anything is refuted ostensively by the terms ABC, it cannot be objected that the syllogism does not depend on the assumption laid down. For we use the expression ‘false cause’, when the syllogism is concluded in spite of the refutation of this position; but that is not possible in ostensive proofs: since if an assumption is refuted, a syllogism can no longer be drawn in reference to it. It is clear then that the expression ‘false cause’ can only be used in the case of a reductio ad impossibile, and when the original hypothesis is so related to the impossible conclusion, that the conclusion results indifferently whether the hypothesis is made or not.
Ὁ μὲν οὖν φανερώτατος τρόπος ἐστὶ τοῦ μὴ παρὰ τὴν θέσιν εἶναι τὸ ψεῦδος, ὅταν ἀπὸ τῆς ὑποθέσεως ἀσύναπτος ἦι ἀπὸ τῶν μέσων πρὸς τὸ ἀδύνατον ὁ συλλογισμός, ὅπερ εἴρηται καὶ ἐν τοῖς Τοπικοῖς. τὸ γὰρ τὸ ἀναίτιον ὡς αἴτιον τιθέναι τοῦτό ἐστιν, οἷον εἰ βουλόμενος δεῖξαι ὅτι ἀσύμμετρος ἡ διάμετρος, ἐπιχειροίη τὸν Ζήνωνος λόγον, ὡς οὐκ ἔστι κινεῖσθαι, καὶ εἰς τοῦτο ἀπάγοι τὸ ἀδύνατον· οὐδαμῶς γὰρ οὐδαμῆι συνεχές ἐστι τὸ ψεῦδος τῆι φάσει τῆι ἐξ ἀρχῆς.	(0704C) Ergo manifestissimus quidem modus est non propter suppositionem esse falsum, quando ab hypothesi inconiunctus est A mediis syllogismus ad impossibile, quod dictum est in Topicis; quod enim non est causa, ut causam ponere hoc est; ut si volens ostendere quoniam asymeter est diameter, conetur Zenonis ratione quoniam non est moveri, et ad hoc inducat impossibile, nullo enim modo continuum est falsum locutioni quae est ex principio.	The most obvious case of the irrelevance of an assumption to a conclusion which is false is when a syllogism drawn from middle terms to an impossible conclusion is independent of the hypothesis, as we have explained in the Topics. For to put that which is not the cause as the cause, is just this: e.g. if a man, wishing to prove that the diagonal of the square is incommensurate with the side, should try to prove Zeno’s theorem that motion is impossible, and so establish a reductio ad impossibile: for Zeno’s false theorem has no connexion at all with the original assumption.
ἄλλος δὲ τρόπος, εἰ συνεχὲς μὲν εἴη τὸ ἀδύνατον τῆι ὑποθέσει, μὴ μέντοι δι᾽ ἐκείνην συμβαίνοι. τοῦτο γὰρ ἐγχωρεῖ γενέσθαι καὶ ἐπὶ τὸ ἄνω καὶ ἐπὶ τὸ κάτω λαμβάνοντι τὸ συνεχές, οἷον εἰ τὸ Α τῶι Β κεῖται ὑπάρχον, τὸ δὲ Β τῶι Γ, τὸ δὲ Γ τῶι Δ, τοῦτο δ᾽ εἴη ψεῦδος, τὸ τὸ Β τῶι Δ ὑπάρχειν. εἰ γὰρ ἀφαιρεθέντος τοῦ Α μηδὲν ἧττον ὑπάρχοι τὸ Β τῶι Γ καὶ τὸ Γ τῶι Δ, οὐκ ἂν εἴη τὸ ψεῦδος διὰ τὴν ἐξ ἀρχῆς ὑπόθεσιν.	Alius autem modus, si continuum quidem sit impossibile hypothesi, non tamen propter illam accidat, hoc autem possibile est fieri, et in hoc quod superius, et in hoc quod inferius sumenti continuum, ut si A ponatur inesse B, B autem C, C vero D, hoc autem sit falsum B inesse D, nam (si ablato A, nihilominus B inest C, et C D ) non erit falsum propter eam quae ex principio est hypothesin.	Another case is where the impossible conclusion is connected with the hypothesis, but does not result from it. This may happen whether one traces the connexion upwards or downwards, e.g. if it is laid down that A belongs to B, B to C, and C to D, and it should be false that B belongs to D: for if we eliminated A and assumed all the same that B belongs to C and C to D, the false conclusion would not depend on the original hypothesis.
ἢ πάλιν εἴ τις ἐπὶ τὸ ἄνω λαμβάνοι τὸ συνεχές, οἷον εἰ τὸ μὲν Α τῶι Β, τῶι δὲ Α τὸ Ε καὶ τῶι Ε τὸ Ζ, ψεῦδος δ᾽ εἴη τὸ ὑπάρχειν τῶι Α τὸ Ζ· καὶ γὰρ οὕτως οὐδὲν ἂν ἧττον εἴη τὸ ἀδύνατον ἀναιρεθείσης τῆς ἐξ ἀρχῆς ὑποθέσεως. ἀλλὰ δεῖ πρὸς τοὺς ἐξ ἀρχῆς ὅρους συνάπτειν τὸ ἀδύνατον· οὕτω γὰρ ἔσται διὰ τὴν ὑπόθεσιν, οἷον ἐπὶ μὲν τὸ κάτω λαμβάνοντι τὸ συνεχὲς πρὸς τὸν κατηγορούμενον τῶν ὅρων (εἰ γὰρ ἀδύνατον τὸ Α τῶι Δ ὑπάρχειν, ἀφαιρεθέντος τοῦ Α οὐκέτι ἔσται τὸ ψεῦδοσ)·	(0704D) Aut rursum si quis in superiori sumat continuum, ut si A quidem B, E autem A, F vero E, falsum autem sit F inesse A, nam et sic nihilominus erit impossibile, interempta quae est ex principio hypothesi. Sed oportet ad eos qui ex principio terminos copulare impossibile, sic enim erit propter hypothesin, ut in inferiori quidem sumenti continuum ad praedicatum terminum; nam si impossibile est A inesse D, interempto A, non amplius erit falsum.	Or again trace the connexion upwards; e.g. suppose that A belongs to B, E to A and F to E, it being false that F belongs to A. In this way too the impossible conclusion would result, though the original hypothesis were eliminated. But the impossible conclusion ought to be connected with the original terms: in this way it will depend on the hypothesis, e.g. when one traces the connexion downwards, the impossible conclusion must be connected with that term which is predicate in the hypothesis: for if it is impossible that A should belong to D, the false conclusion will no longer result after A has been eliminated.
ἐπὶ δὲ τὸ ἄνω, καθ᾽ οὗ κατηγορεῖται (εἰ γὰρ τῶι Β μὴ ἐγχωρεῖ τὸ Ζ ὑπάρχειν, ἀφαιρεθέντος τοῦ Β οὐκέτι ἔσται τὸ ἀδύνατον). ὁμοίως δὲ καὶ στερητικῶν τῶν συλλογισμῶν ὄντων.	In superiori autem de quo praedicatur; nam si F non possibile est inesse B, interempto B non amplius erit impossibile; similiter autem et cum privativi sint syllogismi.	If one traces the connexion upwards, the impossible conclusion must be connected with that term which is subject in the hypothesis: for if it is impossible that F should belong to B, the impossible conclusion will disappear if B is eliminated. Similarly when the syllogisms are negative.
↵ Φανερὸν οὖν ὅτι τοῦ ἀδυνάτου μὴ πρὸς τοὺς ἐξ ἀρχῆς ὅρους ὄντος οὐ παρὰ τὴν θέσιν συμβαίνει τὸ ψεῦδος. ἢ οὐδ᾽ οὕτως ἀεὶ διὰ τὴν ὑπόθεσιν ἔσται τὸ ψεῦδος; καὶ γὰρ εἰ μὴ τῶι Β ἀλλὰ τῶι Κ ἐτέθη τὸ Α ὑπάρχειν, τὸ δὲ Κ τῶι Γ καὶ τοῦτο τῶι Δ, καὶ οὕτω μένει τὸ ἀδύνατον	Manifestum ergo quoniam cum impossibile non ad priores terminos, non propter positionem accidit falsum; an nec sic semper propter hypothes in erit falsum? (0705A) nam si non ei quod est B, sed ei quod est k positum est inesse A, k autem C, et hoc D, et sic manet impossibile;	It is clear then that when the impossibility is not related to the original terms, the false conclusion does not result on account of the assumption. Or perhaps even so it may sometimes be independent. For if it were laid down that A belongs not to B but to K, and that K belongs to C and C to D, the impossible conclusion would still stand.
(ὁμοίως δὲ καὶ ἐπὶ τὸ ἄνω λαμβάνοντι τοὺς ὅρουσ), ὥστ᾽ ἐπεὶ καὶ ὄντος καὶ μὴ ὄντος τούτου συμβαίνει τὸ ἀδύνατον, οὐκ ἂν εἴη παρὰ τὴν θέσιν. ἢ τὸ μὴ ὄντος τούτου μηδὲν ἧττον γίνεσθαι τὸ ψεῦδος οὐχ οὕτω ληπτέον ὥστ᾽ ἄλλου τιθεμένου συμβαίνειν τὸ ἀδύνατον, ἀλλ᾽ ὅταν ἀφαιρεθέντος τούτου διὰ τῶν λοιπῶν προτάσεων ταὐτὸ περαίνηται ἀδύνατον, ἐπεὶ ταὐτό γε ψεῦδος συμβαίνειν διὰ πλειόνων ὑποθέσεων οὐδὲν ἴσως ἄτοπον, οἷον τὰς παραλλήλους συμπίπτειν καὶ εἰ μείζων ἐστὶν ἡ ἐντὸς τῆς ἐκτὸς καὶ εἰ τὸ τρίγωνον ἔχει πλείους ὀρθὰς δυεῖν;	similiter autem et in sursum sumenti terminos, quare (quoniam cum est, et cum non est, hoc accidit impossibile) non erit propter positionem, aut cum non est hoc, nihilominus fieri falsum. Nec sic sumendum ut alio posito accidat impossibile, sed quando ablato hoc idem per reliquas propositiones concluditur impossibile, eo quod idem falsum accidere per plures hypotheses nihil fortasse inconveniens est, ut parallelas, contingere, et si maior est qui interius est, eo qui exterius, et si triangulus habet plures rectos duobus.	Similarly if one takes the terms in an ascending series. Consequently since the impossibility results whether the first assumption is suppressed or not, it would appear to be independent of that assumption. Or perhaps we ought not to understand the statement that the false conclusion results independently of the assumption, in the sense that if something else were supposed the impossibility would result; but rather we mean that when the first assumption is eliminated, the same impossibility results through the remaining premisses; since it is not perhaps absurd that the same false result should follow from several hypotheses, e.g. that parallels meet, both on the assumption that the interior angle is greater than the exterior and on the assumption that a triangle contains more than two right angles.