Libro II, lezione IXDE NEGATIONE APPONENDA NON VERBO SED MODIS IN CONTRADICTIONIBUS PROPOSITIONUM MODALIUM
Il testo di Aristotele
Est ergo negatio eius quae est, possibile esse, ea quae est non possibile esse. Eadem quoque ratio est et in eo quod est contingens esse: etenim negatio eius est, non contingens esse; et in aliis quoque simili modo, ut in necessario et impossibili. Fiunt enim quemadmodum in illis, esse et non esse, appositiones, subiectae vero res, hoc quidem album, illud vero homo: eodem quoque modo hoc in loco, esse quidem et non esse, ut subiectum fit, posse vero et contingere appositiones sunt, determinantes (quemadmodum in illis esse et non esse) veritatem et falsitatem, similiter hae in eo quod est, esse possibile et esse non possibile. Eius vero, quae est, possibile non esse, negatio est non ea quae est, non esse, sed ea quae est, non possibile; et eius quae est, possibile esse, non ea quae est, possibile non esse, sed ea quae est, non possibile esse. Quare et sequi sese invicem videbuntur, possibile esse et possibile non esse. Idem enim possibile esse et non esse. Non enim contradictiones sunt sibi invicem huiusmodi, possibile esse et possibile non esse; sed possibile esse et non possibile esse, nunquam simul sunt in eodem verae sunt: opponuntur enim: neque ea quae est, possibile non esse et non possibile non esse, nunquam simul in eodem verae sunt. Similiter autem et eius quae est, necessarium est, negatio non est quae est, necessarium non esse, sed ea quae est, non necessarium esse; eius vero quae est, necessarium non esse, ea quae est, non necessarium non esse. Et eius quae est, impossibile esse, non ea quae est, impossibile non esse, sed haec, non impossibile esse; eius vero quae est, impossibile non esse, ea quae est, non impossibile non esse. Universaliter vero, quemadmodum dictum est, esse quidam et non esse oportet ponere quemadmodum subiecta, negationem vero et affirmationem haec facientem, ad esse et non esse apponere. Et has oportet putare esse oppositas dictiones: possibile non possibile; contingens non contingens; impossibile non impossibile; necessarium non necessarium; verum non verum.
La versione latina commentata da san Tommaso, nel testo dell'edizione leonina.
21b17But since it is impossible that contradictory propositions should both be true of the same subject, it follows that ‘may not be’ is not the contradictory of ‘it may be’. For it is a logical consequence of what we have said, either that the same predicate can be both applicable and inapplicable 21b20to one and the same subject at the same time, or that it is not by the addition of the verbs ‘be’ and ‘not be’, respectively, that positive and negative propositions are formed. If the former of these alternatives must be rejected, we must choose the latter.
21b23The contradictory, then, of ‘it may be’ is ‘it cannot be’. The same rule applies to the proposition ‘it is contingent that it should be’; the contradictory of this is ‘it is not 21b25contingent that it should be’. The similar propositions, such as ‘it is necessary’ and ‘it is impossible’, may be dealt with in the same manner. For it comes about that just as in the former instances the verbs ‘is’ and ‘is not’ were added to the subject-matter of the sentence ‘white’ and ‘man’, so here ‘that it should be’ and ‘that it should not be’ the other predicate must belong to any subject. Thus, since the proposition ‘a piece of wood is a white man’ is not true, the contradictory of this proposition must be true. 21b30are the subject-matter and ‘is possible’, ‘is contingent’, are added. These indicate that a certain thing is or is not possible, just as in the former instances ‘is’ and ‘is not’ indicated that certain things were or were not the case.2
21b33The contradictory, then, of ‘it may not be’ is not ‘it cannot be’, but ‘it cannot not be’, and the contradictory of ‘it may be’ is not ‘it may not be’, but ‘it cannot be’. 21b35Thus the propositions ‘it may be’ and ‘it may not be’ appear each to imply the other: for, since these two propositions are not contradictory ,the same thing both may and may not be. But the propositions ‘it may be’ and ‘it cannot be’ can never be true of the same subject at the same time, 22afor they are contradictory. Nor can the propositions ‘it may not be’ and ‘it cannot not be’ be at once true of the same subject.
22a3The propositions which have to do with necessity are governed by the same principle. The contradictory of ‘it is necessary that it should be’ is not ‘it is necessary that it should not be’, but ‘it is not necessary that it should be’, 22a5and the contradictory of ‘it is necessary that it should not be’ is ‘it is not necessary that it should not be’.
22a6Again, the contradictory of ‘it is impossible that it should be’ is not ‘it is impossible that it should not be’ but ‘it is not impossible that it should be’, and the contradictory of ‘it is impossible that it should not be’ is ‘it is not impossible that it should not be’.
22a9To generalize, we must, as has been stated, define the clauses ‘that it should be’ and ‘that it should not be’ as the subject-matter of the propositions, and in making these terms 22a10into affirmations and denials we must combine them with ‘that it should be’ and ‘that it should not be’ respectively.
22a11We must consider the following pairs as contradictory propositions:
22a12It may be. It cannot be.
22a12It is contingent. It is not contingent.
22a13It is impossible. It is not impossible.
22a14It is necessary. It is not necessary.
22a14It is true. It is not true.
I paragrafi del passo, nella traduzione di E. M. Edghill (The Works of Aristotle translated into English, ed. W. D. Ross, vol. I (Oxford: Clarendon Press, 1928)).
These things then being determined, let us consider how the affirmations, and negations of the possible and impossible to be, subsist with reference to each other, also of the contingent and the non-contingent, and of the impossible and necessary, since this has some doubtful points. For if among the complex, those contradictions are mutually opposed, which are arranged according to the verb “to be,” and “not to be,” (as for instance the negation “to be a man,” is “not to be man,” not this, “to be not a man,” and the negation of “to be a white man” is “not to be a white man,” and not this “to be not a white man,” since if affirmation or negation be true of every thing, it will be true to say “that wood is not a white man,”)—if this be so, in those things to which the verb “to be” is not added, that which is asserted instead of the verb “to be,” will produce the same thing. For example, the negation of “a man walks,” will not be “non-man walks,” but, “a man does not walk,” for there is no difference in saying that “a man walks,” or that “a man is walking,” so that if this is every where the case, the negation of “it is possible to be,” will be “it is possible not to be,” and not “it is not possible to be.” But it appears that it is possible for the same thing both to be, and not to be, for every thing which may possibly be cut, or may possibly walk, may also possibly not be cut, and not walk, and the reason is that every thing which is thus possible, does not always energize,2 so that negation will also belong to it, for that which is capable of walking, may not walk, and the visible may not be seen. Still however it is impossible that opposite affirmations and negations should be true of the same thing, wherefore the ne-of propositions and of syllogisms, comes from the Greek commentators, but is not Aristotelian. (Ammonius Schol. p. 130, a. 16.) The admission of modals into Logic, has been strongly advocated and opposed; the determination of the implied matter of a pure proposition is extralogical of course, but respecting the expressed matter of a modal, the reader will find some valuable remarks in Mansel’s Logic. The authorities are, on one side of the question Sir W. Hamilton, on the other Kant and St. Hilaire. A modal is reducible to a pure categorical, by uniting the modal word to the predicate, or to the subject when the mode only expresses the nature of the matter of the proposition, e. g. a fish necessarily lives in the water, i. e. all fish live in the water. Though the manner of connexion between the extremes is expressed in a modal, yet it does not thereby test the quantity of the proposition, as there are universals and particulars in each mode. On the distinction of propositional matter, see Sir. W. Hamilton, Ed. Rev. No. 115, p. 217. Also the commentary of Ammonius, de Int. 7, (Scholia, p. 115, a. 14). gation of “it is possible to be,” is not “it is possible not to be.” Now it results from this that we either at the same time affirm and deny the same thing of the same, or that the affirmations and negations are not made according to the additions, “to be” or “not to be;3” if therefore, that, be impossible, this, will be to be taken, wherefore the negation of “it is possible to be,” is “it is not possible to be,” (but4 not it is possible not to be). Now there is the same reasoning also about the being contingent, for the negation of this is, not to be contingent, and in like manner as to the rest, for example the necessary and impossible, since as in those it happens that, “to be,” and, “not to be,” are additions, but “whiteness” and “man” are subjects, so here “to be” and “not to be,” become as subjects, but “to be possible,” and “to be contingent,” are additions which determine the true and false in the (enunciations) “to be possible” and “to be not possible,” similarly as in those, “to be,” and “not to be.”5 But of “it is possible not to be,” the negation is not, “it is not possible to be,” but “it is not possible not to be,” and of “it is possible to be,” the negation is not, “it is possible not to be,” but, “it is not possible to be;” wherefore, “it is possible to be,” and, “it is possible not to be,” will appear to follow each other; for it is the same thing, “to be possible to be,” and “not to be,” since such things are not contradictories of each other, namely, “it is possible to be,” and, “it is possible not to be.” But “it is possible to be,” and “it is not possible to be,” are never true of the same thing at the same time, for they are opposed, neither at least are, “it is possible not to be,” and “it is not possible not to be,” ever true at the same time of the same thing. Likewise of, “it is necessary to be,” the negation is not, “it is necessary not to be,” but this, “it is not necessary to be,” and of, “it is necessary not to be,” (the negation) is this, “it is not necessary not to be.” Again, of, “it is impossible to be,” the negation is not “it is impossible not to be,” but “it is not impossible to be,” and of, “it is impossible not to be,” (the negation) is, “it is not impossible not to be.” In fact, universally, as we have said, “to be” and “not to be,” we must necessarily regard as subjects, but those things which produce affirmation and negation we must connect with “to be” and “not to be:” we ought also to consider these as opposite affirmations and negations; possible, impossible, contingent, non-contingent, impossible, not impossible, necessary, not necessary, true, not true.
I capitoli interi, nella traduzione di Octavius Freire Owen (London: George Bell & Sons, 1889 (Bohn's Classical Library), vol. I, from the plates of the first edition (London: H. G. Bohn, 1853), same pagination).
Il commento del Gaetano
1. Determinat ubi ponenda sit negatio ad assumendam modalium contradictionem. Et circa hoc quatuor facit: primo, determinat veritatem summarie; secundo, assignat determinatae veritatis rationem, quae dicitur rationi ad oppositum inductae; ibi: Fiunt enim etc.; tertio, explanat eamdem veritatem in omnibus modalibus; ibi: Eius vero etc.; quarto, universalem regulam concludit; ibi: Universaliter vero etc. Quia igitur negatio aut verbo aut modo apponenda est, et quod verbo non addenda est, declaratum est per locum a divisione; concludendo determinat: Est ergo negatio eius quae est possibile esse, ea quae est non possibile esse, in qua negatur modus. Et eadem est ratio in enunciationibus de contingenti. Huius enim, quae est, contingens esse, negatio est, non contingens esse. Et in aliis, scilicet de necesse et impossibile idem est iudicium.
2. Deinde cum dicit: Fiunt enim in illis appositiones etc., subdit huius veritatis rationem talem. Ad sumendam contradictionem inter aliquas enunciationes oportet ponere negationem super appositione, idest coniunctione praedicati cum subiecto; sed in modalibus appositiones sunt modi; ergo in modalibus negatio apponenda est modo, ut fiat contradictio. Huius rationis, maiore subintellecta, minor ponitur in littera per secundam similitudinem ad illas de inesse. Et dicitur quod quemadmodum in illis enunciationibus de inesse appositiones, idest praedicationes, sunt esse et non esse, idest verba significativa esse vel non esse (verbum enim semper est nota eorum quae de altero praedicantur), subiective vero appositionibus res sunt, quibus esse vel non esse apponitur, ut album, cum dicitur, album est, vel homo, cum dicitur, homo est; eodem modo hoc in loco in modalibus accidit: esse quidem subiectum fit, idest dictum significans esse vel non esse subiecti locum tenet; contingere vero et posse oppositiones, idest modi, praedicationes sunt. Et quemadmodum in illis de inesse penes esse et non esse veritatem vel falsitatem determinavimus, ita in istis modalibus penes modos. Hoc est enim quod subdit, determinantes, scilicet, fiunt ipsi modi veritatem, quemadmodum in illis esse et non esse, eam determinat.
3. Et sic patet responsio ad argumentum in oppositum primo adductum, concludens quod negatio verbo apponenda sit, sicut illis de inesse. Dicitur enim quod cum modalis enunciet modum de dicto sicut enunciatio de inesse, esse vel esse tale, puta esse album de subiecto, eumdem locum tenet modus hic, quem ibi verbum; et consequenter super idem proportionaliter cadit negatio hic et ibi. Eadem enim, ut dictum est, proportio est modi ad dictum, quae est verbi ad subiectum. - Rursus cum veritas et falsitas affirmationem et negationem sequantur, penes idem attendenda est affirmatio vel negatio enunciationis, et veritas vel falsitas eiusdem. Sicut autem in enunciationibus de inesse veritas vel falsitas esse vel non esse consequitur, ita in modalibus modum. Illa namque modalis est vera quae sic modificat dictum sicut dicti compositio patitur, sicut illa de inesse est vera, quae sic significat esse sicut est. Est ergo negatio modo hic apponenda, sicut ibi verbo, cum sit eadem utriusque vis quoad veritatem et falsitatem enunciationis. Adverte quod modos, appositiones, idest, praedicationes vocavit, sicut esse in illis de inesse, intelligens per modum totum praedicatum enunciationis modalis, puta, est possibile. In cuius signum modos ipsos verbaliter protulit dicens: Contingere vero et posse appositiones sunt. Contingit enim et potest, totum praedicatum modalis continent.
4. Deinde cum dicit: Eius vero quod est possibile est non esse etc., explanat determinatam veritatem in omnibus modalibus, scilicet de possibili, et necessario, et impossibili. Contingens convertitur cum possibili. Et quiaquilibet modus facit duas modales affirmativas, alteram habentem dictum affirmatum, et alteram habentem dictum negatum; ideo explanat in singulis modis quae cuiusque affirmationis negatio sit. Et primo in illis de possibili. Et quia primae affirmativae de possibili (quae scilicet habet dictum affirmatum) scilicet possibile esse, negatio assignata fuit, non possibile esse; ideo ad reliquam affirmativam de possibili transiens ait: Eius vero, quae est possibile non esse (ubi dictum negatur) negatio est non possibile non esse. Et hoc consequenter probat per hoc quod contradictoria huius, possibile non esse, aut est, possibile esse, aut illa, quam diximus, scilicet, non possibile non esse. Sed illa, scilicet, possibile esse, non est eius contradictoria. Non enim sunt sibi invicem contradicentes, possibile esse, et, possibile non esse, quia possunt simul esse verae. Unde et sequi sese invicem putabuntur: quoniam, ut supra dictum fuit, idem est - possibile esse, et - non esse, et consequenter sicut ad, posse esse, sequitur, posse non esse, ita e contra ad, posse non esse, sequitur, posse esse. Sed contradictoria illius, possibile esse, quae non potest simul esse vera est, non possibile esse: hae enim, ut dictum est, opponuntur. Remanet ergo quod huius negatio, possibile non esse, sit illa, non possibile non esse: hae namque simul nunquam sunt verae vel falsae. Dixit quod possibile esse et non esse sequi se invicem putabantur, et non dixit quod se invicem consequuntur: quia secundum veritatem universaliter non sequuntur se, sed particulariter tantum, ut infra dicetur; propter quod putabitur quod simpliciter se invicem sequantur. Deinde declarat hoc idem in illis de necessario. Et primo, in affirmativa habente dictum affirmatum, dicens: Similiter eius quae est, necessarium esse, negatio non est ea, quae dicit necessarium non esse, ubi modus non negatur, sed ea quae est, non necessarium esse. Deinde subdit de affirmativa de necessario habente dictum negatum, et ait: Eius vero, quae est, necessarium non esse, negatio est ea, quae dicit, non necessarium non esse. Deinde transit ad illas de impossibili, eumdem ordinem servans, et inquit: Et eius, quae dicit, impossibile esse, negatio non est ea quae dicit, impossibile non esse, sed, non impossibile esse: ubi iam modus negatur. Alterius vero affirmativae, quae est, impossibile non esse, negatio est ea quae dicit, non impossibile non esse. Et sic semper modo negatio addenda est.
5. Deinde cum dicit: Universaliter vero etc., concludit regulam universalem dicens quod, quemadmodum dictum est, dicta importantia esse et non esse oportet ponere in modalibus ut subiecta, negationem vero et affirmationem hoc, idest contradictionis oppositionem, facientem, oportet apponere tantummodo ad suum eumdem modum, non ad diversos modos. Debet namque illemet modus negari, qui prius affirmabatur, si contradictio esse debet. Et exemplariter explanans quomodo hoc fiat, subdit: Et oportet putare has esse oppositas dictiones, idest affirmationes et negationes in modalibus, possibile et non possibile, contingens et non contingens. Item cum dixit negationem alio tantum modo ad modum apponi debere, non exclusit modi copulam, sed dictum. Hoc enim est singulare in modalibus quod eamdem oppositionem facit, negatio modo addita, et eius verbo. Contradictorie enim opponitur huic, possibile est esse, non solum illa, non possibile est esse, sed ista, possibile non est esse. Meminit autem modi potius, et propter hoc quod nunc diximus, ut scilicet insinuaret quod negatio verbo modi postposita, modo autem praeposita, idem facit ac si modali verbo praeponeretur, et quia, cum modo numquam caret modalis enunciatio, semper negatio supra modum poni potest. Non autem sic de eius verbo: verbo enim modi carere contingit modalem, ut cum dicitur, Socrates currit necessario; et ideo semper verbo negatio aptari potest. - Quod autem in fine addidit, verum et non verum, insinuat, praeter quatuor praedictos modos, alios inveniri, qui etiam compositionem enunciationis determinant, puta, verum et non verum, falsum et non falsum: quos tamen inter modos supra non posuit, quia, ut declaratum fuit, non proprie modificant.
Di questo commento non esiste una traduzione inglese di pubblico dominio: qui si dà il latino.