Authors/Aristotle/priora/Liber 2/C16

Chapter 16

Greek	Latin	English
	(PL 64 0703A) CAPUT XVIII. De petitione principii.	16
64b28 Τὸ δ᾽ ἐν ἀρχῆι αἰτεῖσθαι καὶ λαμβάνειν ἐστὶ μέν, ὡς ἐν γένει λαβεῖν, ἐν τῶι μὴ ἀποδεικνύναι τὸ προκείμενον, τοῦτο δὲ συμβαίνει πολλαχῶς· καὶ γὰρ εἰ ὅλως μὴ συλλογίζεται, καὶ εἰ δι᾽ ἀγνωστοτέρων ἢ ὁμοίως ἀγνώστων, καὶ εἰ διὰ τῶν ὑστέρων τὸ πρότερον· ἡ γὰρ ἀπόδειξις ἐκ πιστοτέρων τε καὶ προτέρων ἐστίν. τούτων μὲν οὖν οὐδέν ἐστι τὸ αἰτεῖσθαι τὸ ἐξ ἀρχῆς· ἀλλ᾽ ἐπεὶ τὰ μὲν δι᾽ αὑτῶν πέφυκε γνωρίζεσθαι τὰ δὲ δι᾽ ἄλλων (αἱ μὲν γὰρ ἀρχαὶ δι᾽ αὑτῶν, τὰ δ᾽ ὑπὸ τὰς ἀρχὰς δι᾽ ἄλλων), ὅταν μὴ τὸ δι᾽ αὑτοῦ γνωστὸν δι᾽ αὑτοῦ τις ἐπιχειρῆι δεικνύναι, τότ᾽ αἰτεῖται τὸ ἐξ ἀρχῆς.	In principio autem petere et accipere est quidem, ut in genere, sumere in eo quod non est demonstrare propositum. Hoc autem accidit multipliciter, nam et si omnino non syllogizatur, et si per ignotiora aut similiter ignota, et si per posteriora quod prius est, demonstratio enim ex prioribus et notioribus est. (0703B) Horum ergo nullum est petere quod ex principio est, sed quia haec quidem nata sunt per se cognosci, illa vero per alia (nam principia quidem per se, quae autem sub principiis, per alia), quando quod non per se notum est, per se aliquis conatur ostendere, tunc petit quod ex principio est.	To beg and assume the original question is a species of failure to demonstrate the problem proposed; but this happens in many ways. A man may not reason syllogistically at all, or he may argue from premisses which are less known or equally unknown, or he may establish the antecedent by means of its consequents; for demonstration proceeds from what is more certain and is prior. Now begging the question is none of these: but since we get to know some things naturally through themselves, and other things by means of something else (the first principles through themselves, what is subordinate to them through something else), whenever a man tries to prove what is not self-evident by means of itself, then he begs the original question.
τοῦτο δ᾽ ἔστι μὲν οὕτω ποιεῖν ὥστ᾽ εὐθὺς ἀξιῶσαι τὸ προκείμενον, ἐνδέχεται δὲ καὶ μεταβάντας ἐπ᾽ ἄλλα ἄττα τῶν πεφυκότων δι᾽ ἐκείνου δείκνυσθαι διὰ τούτων ↵ ἀποδεικνύναι τὸ ἐξ ἀρχῆς, οἷον εἰ τὸ Α δεικνύοιτο διὰ τοῦ Β, τὸ δὲ Β διὰ τοῦ Γ, τὸ δὲ Γ πεφυκὸς εἴη δείκνυσθαι διὰ τοῦ Α· συμβαίνει γὰρ αὐτὸ δι᾽ αὑτοῦ τὸ Α δεικνύναι τοὺς οὕτω συλλογιζομένους. ὅπερ ποιοῦσιν οἱ τὰς παραλλήλους οἰόμενοι γράφειν· λανθάνουσι γὰρ αὐτοὶ ἑαυτοὺς τοιαῦτα λαμβάνοντες ἃ οὐχ οἷόν τε ἀποδεῖξαι μὴ οὐσῶν τῶν παραλλήλων. ὥστε συμβαίνει τοῖς οὕτω συλλογιζομένοις ἕκαστον εἶναι λέγειν, εἰ ἔστιν ἕκαστον· οὕτω δ᾽ ἅπαν ἔσται δι᾽ αὑτοῦ γνωστόν· ὅπερ ἀδύνατον.	Hoc autem est sic facere quidem ut statim postulet id quod propositum est: contingit autem et transgredientes et ad alia eorum quae nata sunt per illa ostendi per haec monstrare quod ex principio est, ut si A ostendatur per B, et B per C, C autem natum sit ostendi per A, accidit enim idem A per se demonstrare eos qui sic syllogizant, quod faciunt qui parallelas arbitrantur scribere, latent enim ipsi seipsos talia sumentes quae non valent demonstrare, cum non sint parallelae. (0703C) Quare accidit sic syllogizantibus unumquodque esse dicere si est unumquodque, sic autem omne erit per se notum, quod est impossibile.	This may be done by assuming what is in question at once; it is also possible to make a transition to other things which would naturally be proved through the thesis proposed, and demonstrate it through them, e.g. if A should be proved through B, and B through C, though it was natural that C should be proved through A: for it turns out that those who reason thus are proving A by means of itself. This is what those persons do who suppose that they are constructing parallel straight lines: for they fail to see that they are assuming facts which it is impossible to demonstrate unless the parallels exist. So it turns out that those who reason thus merely say a particular thing is, if it is: in this way everything will be self-evident. But that is impossible.
Εἰ οὖν τις ἀδήλου ὄντος ὅτι τὸ Α ὑπάρχει τῶι Γ, ὁμοίως δὲ καὶ ὅτι τῶι Β, αἰτοῖτο τῶι Β ὑπάρχειν τὸ Α, οὔπω δῆλον εἰ τὸ ἐν ἀρχῆι αἰτεῖται, ἀλλ᾽ ὅτι οὐκ ἀποδείκνυσι, δῆλον· οὐ γὰρ ἀρχὴ ἀποδείξεως τὸ ὁμοίως ἄδηλον. εἰ μέντοι τὸ Β πρὸς τὸ Γ οὕτως ἔχει ὥστε ταὐτὸν εἶναι, ἢ δῆλον ὅτι ἀντιστρέφουσιν, ἢ ἐνυπάρχει θάτερον θατέρωι, τὸ ἐν ἀρχῆι αἰτεῖται. καὶ γὰρ ἂν ὅτι τῶι Β τὸ Α ὑπάρχει δι᾽ ἐκείνων δεικνύοι, εἰ ἀντιστρέφοι (νῦν δὲ τοῦτο κωλύει, ἀλλ᾽ οὐχ ὁ τρόποσ). εἰ δὲ τοῦτο ποιοῖ, τὸ εἰρημένον ἂν ποιοῖ καὶ ἀντιστρέφοι διὰ τριῶν.	Si ergo aliquis dubitat assumpto dubio quoniam A inest C, similiter et quoniam B, petat autem i inesse B, nondum manifestum si quod in principio est petat, sed quoniam non demonstravit manifestum, non enim est principium demonstrationis, quod similiter est incertum. Si autem B ad C sic se habet ut idem sit, aut manifestum quod convertuntur, aut inest alterum alteri, quod in principio est petit, nam et quoniam A inest B, per illa monstrabit si convertantur, nunc autem hoc prohibet, sed non modus. (0703D) Si autem hoc faciat, quod dictum est faciet, et convertet per tria,	If then it is uncertain whether A belongs to C, and also whether A belongs to B, and if one should assume that A does belong to B, it is not yet clear whether he begs the original question, but it is evident that he is not demonstrating: for what is as uncertain as the question to be answered cannot be a principle of a demonstration. If however B is so related to C that they are identical, or if they are plainly convertible, or the one belongs to the other, the original question is begged. For one might equally well prove that A belongs to B through those terms if they are convertible. But if they are not convertible, it is the fact that they are not that prevents such a demonstration, not the method of demonstrating. But if one were to make the conversion, then he would be doing what we have described and effecting a reciprocal proof with three propositions.
ὡσαύτως δὲ κἂν εἰ τὸ Β τῶι Γ λαμβάνοι ὑπάρχειν, ὁμοίως ἄδηλον ὂν καὶ εἰ τὸ Α, οὔπω τὸ ἐξ ἀρχῆς, ἀλλ᾽ οὐκ ἀποδείκνυσιν. ἐὰν δὲ ταὐτὸν ἦι τὸ Α καὶ Β ἢ τῶι ἀντιστρέφειν ἢ τῶι ἕπεσθαι τῶι Β τὸ Α, τὸ ἐξ ἀρχῆς αἰτεῖται διὰ τὴν αὐτὴν αἰτίαν· τὸ γὰρ ἐξ ἀρχῆς τί δύναται, εἴρηται ἡμῖν, ὅτι τὸ δι᾽ αὑτοῦ δεικνύναι τὸ μὴ δι᾽ αὑτοῦ δῆλον.	similiter autem et si B sumat inesse C, quod similiter incertum sit, ut et si A inest C, nondum quod ex principio petit, sed neque demonstrat. Si autem idem sit A et B, aut eo quod convertuntur, aut eo quod A sequitur ei quod est B, quod ex principio est petit propter eamdem causam, nam ex principio quod valet, prius dictum est A nobis, quoniam per se monstrabitur quod non est per se manifestum.	Similarly if he should assume that B belongs to C, this being as uncertain as the question whether A belongs to C, the question is not yet begged, but no demonstration is made. If however A and B are identical either because they are convertible or because A follows B, then the question is begged for the same reason as before. For we have explained the meaning of begging the question, viz. proving that which is not self-evident by means of itself.
Εἰ οὖν ἐστι τὸ ἐν ἀρχῆι αἰτεῖσθαι τὸ δι᾽ αὑτοῦ δεικνύναι τὸ μὴ δι᾽ αὑτοῦ δῆλον, τοῦτο δ᾽ ἐστὶ τὸ μὴ δεικνύναι, ὅταν ὁμοίως ἀδήλων ὄντων τοῦ δεικνυμένου καὶ δι᾽ οὗ δείκνυσιν ἢ τῶι ταὐτὰ τῶι αὐτῶι ἢ τῶι ταὐτὸν τοῖς αὐτοῖς ὑπάρχειν, ἐν μὲν τῶι μέσωι σχήματι καὶ τρίτωι ἀμφοτέρως ἂν ἐνδέχοιτο τὸ ἐν ἀρχῆι αἰτεῖσθαι, ἐν δὲ κατηγορικῶι συλλογισμῶι ἔν τε τῶι τρίτωι καὶ τῶι πρώτωι.	(0704A) Si ergo est in principio petere per se monstrare quod non per se est manifestum, hoc autem est non ostendere quando similiter dubitantur quod monstratur et per quod monstratur, vel eo quod eadem eidem, vel eo quod idem eisdem inesse sumitur, in media quidem figura et tertia utrorumque continget similiter quod est in principio petere, in praedicativo quidem syllogismo et in tertia figura, et in prima,	If then begging the question is proving what is not self-evident by means of itself, in other words failing to prove when the failure is due to the thesis to be proved and the premiss through which it is proved being equally uncertain, either because predicates which are identical belong to the same subject, or because the same predicate belongs to subjects which are identical, the question may be begged in the middle and third figures in both ways, though, if the syllogism is affirmative, only in the third and first figures.
ὅταν δ᾽ ἀποφατικῶς, ὅταν τὰ αὐτὰ ἀπὸ τοῦ αὐτοῦ· καὶ οὐχ ὁμοίως ἀμφότεραι αἱ προτάσεις (ὡσαύτως δὲ καὶ ἐν τῶι μέσωι), διὰ τὸ μὴ ἀντιστρέφειν τοὺς ὅρους κατὰ τοὺς ἀποφατικοὺς συλλογισμούς.	negative autem quando eadem ab eodem, et non similiter utraeque propositiones, similiter autem et in media, eo quod non convertuntur termini secundum negativos syllogismos.	If the syllogism is negative, the question is begged when identical predicates are denied of the same subject; and both premisses do not beg the question indifferently (in a similar way the question may be begged in the middle figure), because the terms in negative syllogisms are not convertible.
ἔστι δὲ τὸ ἐν ἀρχῆι αἰτεῖσθαι ἐν μὲν ταῖς ἀποδείξεσι τὰ κατ᾽ ἀλήθειαν οὕτως ἔχοντα, ἐν δὲ τοῖς διαλεκτικοῖς τὰ κατὰ δόξαν.	Est autem in principio petere in demonstrationibus quidem quae secundum veritatem sic se habent, in dialecticis autem, quae secundum opinionem.	In scientific demonstrations the question is begged when the terms are really related in the manner described, in dialectical arguments when they are according to common opinion so related.