Edward Ockham: Created page with "==Chapter 29== {| border=1 cellpadding=10 !valign = top width=33.33%|Greek !valign = top width=33.33%|Latin !valign = top width=33.33%|English |- valign = top | |(PL 64 0672C..."

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Created page with "==Chapter 29== {| border=1 cellpadding=10 !valign = top width=33.33%|Greek !valign = top width=33.33%|Latin !valign = top width=33.33%|English |- valign = top | |(PL 64 0672C..."

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==Chapter 29==
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|(PL 64 0672C) CAPUT XXX. De syllogismis assertoriis ad impossibile, et reliquis qui ex hypothesi.

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|{{a|bk45a23|45a23}} Τὸν αὐτὸν δὲ τρόπον ἔχουσι καὶ οἱ εἰς τὸ ἀδύνατον ἄγοντες συλλογισμοὶ τοῖς δεικτικοῖς· καὶ γὰρ οὗτοι γίνον ται διὰ τῶν ἑπομένων καὶ οἷς ἕπεται ἑκάτερον. καὶ ἡ αὐτὴ ἐπίσκεψις ἐν ἀμφοῖν· ὁ γὰρ δείκνυται δεικτικῶς, καὶ διὰ τοῦ ἀδυνάτου ἔστι συλλογίσασθαι διὰ τῶν αὐτῶν ὅρων, καὶ ὁ διὰ τοῦ ἀδυνάτου, καὶ δεικτικῶς, οἷον ὅτι τὸ Α οὐδενὶ τῶι Ε ὑπάρχει. κείσθω γὰρ τινὶ ὑπάρχειν· οὐκοῦν ἐπεὶ τὸ Β παντὶ τῶι Α, τὸ δὲ Α τινὶ τῶι Ε, τὸ Β τινὶ τῶν Ε ὑπάρξει· ἀλλ᾽ οὐδενὶ ὑπῆρχεν. πάλιν ὅτι τινὶ ὑπάρχει· εἰ γὰρ μηδενὶ τῶι Ε τὸ Α, τὸ δὲ Ε παντὶ τῶι Η, οὐδενὶ τῶν Η ὑπάρξει τὸ Α· ἀλλὰ παντὶ ὑπῆρχεν.

|(0672D) Eodem autem modo se habent et qui ad impossibile deducunt syllogismi, ostensivis, nam et ipsi fiunt per ea quae sequuntur, et quibus sequitur utrumque. Et eadem consideratio in utrisque, nam quod monstratur ostensive, et per impossibile est syllogizare, et per eosdem terminos, et quod per impossibile et ostensive. Ut quoniam A nulli E inest, ponatur enim alicui inesse, ergo quoniam B omni A, A autem alicui E, et B alicui E inerit, sed nulli inerat. Rursum quoniam alicui E inest A, si enim nulli E inest A, E autem omni G, nulli G inerit A, sed omni inerat.

|Syllogisms which lead to impossible conclusions are similar to ostensive syllogisms; they also are formed by means of the consequents and antecedents of the terms in question. In both cases the same inquiry is involved. For what is proved ostensively may also be concluded syllogistically per impossibile by means of the same terms; and what is proved per impossibile may also be proved ostensively, e.g. that A belongs to none of the Es. For suppose A to belong to some E: then since B belongs to all A and A to some of the Es, B will belong to some of the Es: but it was assumed that it belongs to none. Again we may prove that A belongs to some E: for if A belonged to none of the Es, and E belongs to all G, A will belong to none of the Gs: but it was assumed to belong to all.

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|ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων προβλημάτων· ἀεὶ γὰρ ἔσται καὶ ἐν ἅπασιν ἡ διὰ τοῦ ἀδυνάτου δεῖξις ἐκ τῶν ἑπομένων καὶ οἷς ἕπεται ἑκάτερον. καὶ καθ᾽ ἕκαστον πρόβλημα ἡ αὐτὴ σκέψις δεικτικῶς τε βουλομένωι συλλογίσασθαι καὶ εἰς ἀδύνατον ἀγαγεῖν· ἐκ γὰρ τῶν αὐτῶν ὅρων ἀμφότεραι αἱ ἀποδείξεις, οἷον εἰ δέδεικται μηδενὶ ὑπάρχειν τῶι Ε τὸ Α, ὅτι συμβαίνει καὶ τὸ Β τινὶ τῶι Ε ὑπάρχειν, ὅπερ ἀδύνατον· ἐὰν ληφθῆι τῶι μὲν Ε μηδενὶ τῶι δὲ Α παντὶ ὑπάρχειν τὸ Β, φανερὸν {{ln|bk45b1}} ὅτι οὐδενὶ τῶι Ε τὸ Α ὑπάρξει.

|(0673A) Similiter autem est in aliis propositis, semper enim erit in omnibus per impossibile ostensio, ex sequentibus, et quibus sequitur utrumque. Et in uno quoque proposito, eadem consideratio et ostensive volenti syllogizare, et ad impossibile ducere, nam ex eisdem terminis utraeque demonstrationes. Ut si ostensum est nulli E inesse A, quoniam accidit et B alicui E inesse, quod est impossibile. Si sumptum sit E quidem nulli B, A autem omni B inesse, manifestum est enim quoniam nulli E inerit A.

|Similarly with the other propositions requiring proof. The proof per impossibile will always and in all cases be from the consequents and antecedents of the terms in question. Whatever the problem the same inquiry is necessary whether one wishes to use an ostensive syllogism or a reduction to impossibility. For both the demonstrations start from the same terms, e.g. suppose it has been proved that A belongs to no E, because it turns out that otherwise B belongs to some of the Es and this is impossible-if now it is assumed that B belongs to no E and to all A, it is clear that A will belong to no E.

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|πάλιν εἰ δεικτικῶς συλλελόγισται τὸ Α τῶι Ε μηδενὶ ὑπάρχειν, ὑποθεμένοις ὑπάρχειν τινὶ διὰ τοῦ ἀδυνάτου δειχθήσεται οὐδενὶ ὑπάρχον. ὁμοίως δὲ κἀπὶ τῶν ἄλλων· ἐν ἅπασι γὰρ ἀνάγκη κοινόν τινα λαβεῖν ὅρον ἄλλον τῶν ὑποκειμένων, πρὸς ὃν ἔσται τοῦ ψεύδους ὁ συλλογισμός, ὥστ᾽ ἀντιστραφείσης ταύτης τῆς προτάσεως, τῆς δ᾽ ἑτέρας ὁμοίως ἐχούσης, δεικτικὸς ἔσται ὁ συλλογισμὸς διὰ τῶν αὐτῶν ὅρων. διαφέρει γὰρ ὁ δεικτικὸς τοῦ εἰς τὸ ἀδύνατον, ὅτι ἐν μὲν τῶι δεικτικῶι κατ᾽ ἀλήθειαν ἀμφότεραι τίθενται αἱ προτάσεις, ἐν δὲ τῶι εἰς τὸ ἀδύνατον ψευδῶς ἡ μία.

|Rursum si ostensive syllogizatum sit A inesse nulli E, suppositis inesse per impossibile monstrabitur nulli inesse, similiter autem et in aliis. (0673B) In omnibus enim necesse est iis qui per impossibile communem aliquem sumere terminum alium A subiectis, ad quem erit mendacii syllogismus, quare conversa ea propositione, altera autem similiter se habente, ostensivus erit syllogismus per eosdem terminos. Differt autem ostensivus ab eo qui ad impossibile, quoniam in ostensivo secundum veritatem ambae propositiones ponuntur, in eo autem qui ad impossibile, falsa una.

|Again if it has been proved by an ostensive syllogism that A belongs to no E, assume that A belongs to some E and it will be proved per impossibile to belong to no E. Similarly with the rest. In all cases it is necessary to find some common term other than the subjects of inquiry, to which the syllogism establishing the false conclusion may relate, so that if this premiss is converted, and the other remains as it is, the syllogism will be ostensive by means of the same terms. For the ostensive syllogism differs from the reductio ad impossibile in this: in the ostensive syllogism both premisses are laid down in accordance with the truth, in the reductio ad impossibile one of the premisses is assumed falsely.

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|Ταῦτα μὲν οὖν ἔσται μᾶλλον φανερὰ διὰ τῶν ἑπομένων, ὅταν περὶ τοῦ ἀδυνάτου λέγωμεν· νῦν δὲ τοσοῦτον ἡμῖν ἔστω δῆλον, ὅτι εἰς ταὐτὰ βλεπτέον δεικτικῶς τε βου λομένωι συλλογίζεσθαι καὶ εἰς τὸ ἀδύνατον ἄγειν. ἐν δὲ τοῖς ἄλλοις συλλογισμοῖς τοῖς ἐξ ὑποθέσεως, οἷον ὅσοι κατὰ μετάληψιν ἢ κατὰ ποιότητα, ἐν τοῖς ὑποκειμένοις, οὐκ ἐν τοῖς ἐξ ἀρχῆς ἀλλ᾽ ἐν τοῖς μεταλαμβανομένοις, ἔσται ἡ σκέψις, ὁ δὲ τρόπος ὁ αὐτὸς τῆς ἐπιβλέψεως. ἐπισκέ ψασθαι δὲ δεῖ καὶ διελεῖν ποσαχῶς οἱ ἐξ ὑποθέσεως.

|Haec vero erunt magis manifesta per sequentia quando de impossibili dicemus; nunc autem tantum nobis sit manifestus, quoniam ad haec perspiciendum, et ostensive volentibus syllogizare, et ad impossibile deducere. (0673C)In aliis autem syllogismis quicunque sunt ex hypothesi, ut quicunque secundum transsumptionem, aut secundum qualitatem in subiectis, non in prioribus, sed in transsumptis erit consideratio, modus autem inspectionis idem: considerare autem oportet, et dividere quot modis sunt ex hypothesi,

|These points will be made clearer by the sequel, when we discuss the reduction to impossibility: at present this much must be clear, that we must look to terms of the kinds mentioned whether we wish to use an ostensive syllogism or a reduction to impossibility. In the other hypothetical syllogisms, I mean those which proceed by substitution, or by positing a certain quality, the inquiry will be directed to the terms of the problem to be proved-not the terms of the original problem, but the new terms introduced; and the method of the inquiry will be the same as before. But we must consider and determine in how many ways hypothetical syllogisms are possible.

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|Δείκνυται μὲν οὖν ἕκαστον τῶν προβλημάτων οὕτως, ἔστι δὲ καὶ ἄλλον τρόπον ἔνια συλλογίσασθαι τούτων, οἷον τὰ καθόλου διὰ τῆς κατὰ μέρος ἐπιβλέψεως ἐξ ὑποθέσεως. εἰ γὰρ τὸ Γ καὶ τὸ Η ταὐτὰ εἴη, μόνοις δὲ ληφθείη τοῖς Η τὸ Ε ὑπάρχειν, παντὶ ἂν τῶι Ε τὸ Α ὑπάρχοι· καὶ πάλιν εἰ τὸ Δ καὶ Η ταὐτά, μόνων δὲ τῶν Η τὸ Ε κατηγοροῖτο, ὅτι οὐδενὶ τῶι Ε τὸ Α ὑπάρξει. φανερὸν οὖν ὅτι καὶ οὕτως ἐπιβλεπτέον. τὸν αὐτὸν δὲ τρόπον καὶ ἐπὶ τῶν ἀναγκαίων καὶ τῶν ἐνδεχομένων· ἡ γὰρ αὐτὴ σκέψις, καὶ διὰ τῶν αὐτῶν ὅρων ἔσται τῆι τάξει τοῦ τ᾽ ἐνδέχεσθαι καὶ τοῦ ὑπάρχειν ὁ συλλογισμός. ληπτέον δ᾽ ἐπὶ τῶν ἐνδεχομένων καὶ τὰ μὴ ὑπάρχοντα δυνατὰ δ᾽ ὑπάρχειν· δέ- δεικται γὰρ ὅτι καὶ διὰ τούτων γίνεται ὁ τοῦ ἐνδέχεσθαι συλλογισμός. ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων κατη γοριῶν.

|monstratur ergo unumquodque propositorum sic. Est autem et alio modo quaedam syllogizare horum, ut universalia per particularem inspectionem ex hypothesi. Si enim C et G eadem sint, solum G autem sumatur E inesse, omni E inerit A, et rursum si G et D eadem, solum autem de G praedicetur E, quoniam nulli E inerit A, manifestum ergo quoniam sic inspiciendum. Eodem autem modo et in necessariis, et in contingentibus, nam eadem consideratio, et per eosdem terminos erit, eodemque ordine et contingentis, et inesse syllogismus. Sumendum autem et in contingentibus et quae non insunt, possibilia autem inesse. (0673D) Ostensum est enim quoniam et per haec fit contingentis syllogismus, similiter autem se habebit et in aliis praedicationibus.

|Each of the problems then can be proved in the manner described; but it is possible to establish some of them syllogistically in another way, e.g. universal problems by the inquiry which leads up to a particular conclusion, with the addition of an hypothesis. For if the Cs and the Gs should be identical, but E should be assumed to belong to the Gs only, then A would belong to every E: and again if the Ds and the Gs should be identical, but E should be predicated of the Gs only, it follows that A will belong to none of the Es. Clearly then we must consider the matter in this way also. The method is the same whether the relation is necessary or possible. For the inquiry will be the same, and the syllogism will proceed through terms arranged in the same order whether a possible or a pure proposition is proved. We must find in the case of possible relations, as well as terms that belong, terms which can belong though they actually do not: for we have proved that the syllogism which establishes a possible relation proceeds through these terms as well. Similarly also with the other modes of predication.

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|(PL 64 0673D) CAPUT XXXI. Quod omnium scientiarum syllogismi superioribus praeceptis efficiantur.

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|Φανερὸν οὖν ἐκ τῶν εἰρημένων οὐ μόνον ὅτι ἐγχωρεῖ διὰ ταύτης τῆς ὁδοῦ γίνεσθαι πάντας τοὺς συλλογισμούς, ἀλλὰ καὶ ὅτι δι᾽ ἄλλης ἀδύνατον. ἅπας μὲν γὰρ συλλογισμὸς δέδεικται διά τινος τῶν προειρημένων σχημάτων γινόμενος, ταῦτα δ᾽ οὐκ ἐγχωρεῖ δι᾽ ἄλλων συσταθῆναι πλὴν διὰ τῶν ἑπομένων καὶ οἷς ἕπεται ἕκαστον· ἐκ τούτων γὰρ {{ln|bk46a1}} αἱ προτάσεις καὶ ἡ τοῦ μέσου λῆψις, ὥστ᾽ οὐδὲ συλλογισμὸν ἐγχωρεῖ γίνεσθαι δι᾽ ἄλλων.

|Manifestum ergo ex praedictis quoniam non solum possibile est per hanc viam fieri omnes syllogismos, sed etiam quoniam per aliam impossibile. Omnis enim syllogismus ostensus est quoniam per aliquam praedictarum figurarum fit, has autem non contingit per alia constitui quam per sequentia et quae sequitur unumquodque, ex his enim propositiones, et medii sumptio, quare nec syllogismum possibile est fieri per alia.

|It is clear then from what has been said not only that all syllogisms can be formed in this way, but also that they cannot be formed in any other. For every syllogism has been proved to be formed through one of the aforementioned figures, and these cannot be composed through other terms than the consequents and antecedents of the terms in question: for from these we obtain the premisses and find the middle term. Consequently a syllogism cannot be formed by means of other terms.

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==Notes==
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Authors/Aristotle/priora/Liber 1/C29 - Revision history

Edward Ockham: Created page with "==Chapter 29== {| border=1 cellpadding=10 !valign = top width=33.33%|Greek !valign = top width=33.33%|Latin !valign = top width=33.33%|English |- valign = top | |(PL 64 0672C..."