Authors/Ockham/Summa Logicae/Book III-3/Chapter 13

Latin	English
CAP 13. DE COMPARATIONE MODORUM AD INVICEM.	Chapter 13. On the comparison of the modes for conversion.
Quia circa propositionum modalium aequipollentias et repugnantias sunt variae difficultates, ideo ad istius negotii completionem est de eis breviter tractandum.	Since there are various difficulties concerning the equivalence and incompatibility of modal propositions, therefore for the completion of this business it is necessary to treat of them briefly.
Oportet autem scire quod modorum quidam sunt repugnantes, quidam sunt secundum superius et inferius se habentes, quidam sunt disparati.	It is necessary to know that some of the methods are contradictory, some are according to the superior and inferior, and some are disparate.
Repugnantes sunt sicut necessarium et impossibile, possibile et impossibile, necessarium et contingens ad utrumlibet, contingens ad utrumlibet et impossibile, necessarium et inopinabile, demonstrabile et indemonstrabile, et tales multi.	Contradictory are those such as necessary and impossible, possible and impossible, necessary and contingent to either, contingent to either and impossible, necessary and unexpected, demonstrable and indemonstrable, and many such.
Secundum superius et inferius se habentes sunt sicut necessarium et possibile; nam omne necessarium est possibile, et non e converso. Similiter contingens et possibile; nam omne contingens est possibile, et ƿ non e converso. Similiter se habent necessarium et scibile, et necessarium et demonstrabile.	According to superior and inferior, there are pairs such as necessary and possible; for everything necessary is possible, and not vice versa. Similarly contingent and possible; for every contingency is possible, and not the other way around. Necessary and knowable, and necessary and demonstrable, have the same relation.
Disparati sunt sicut possibile et dubitabile et huiusmodi.	Those are disparate such as possible and doubtful and the like.
Secundo notandum est quod modorum repugnantium quidam sunt immediati, ita quod de qualibet propositione verificatur alter eorum; sicut se habent possibile et impossibile, quia omnis propositio est possibilis vel impossibilis.	Secondly, it must be noted that some of the contradictory modes are immediate, so that one of them is verified for every proposition; as the possible and the impossible are related, because every proposition is either possible or impossible.
Quidam sunt mediati, sicut necessarium et impossibile; nam impossibile est quod aliqua propositio, saltem non multiplex, simul et semel sit necessaria et impossibilis, et tamen aliqua propositio nec est necessaria nec impossibilis.	Some are intermediate, as the necessary and the impossible; for it is impossible for any proposition, at least not a multiple one, to be both necessary and impossible at the same time, and yet some proposition is neither necessary nor impossible.
Tertio oportet scire quod quandoque unus modus repugnat pluribus modis; sicut contingens repugnat tam necessario quam impossibili, quia propositio contingens ad utrumlibet nec est necessaria nec impossibilis. Similiter necessarium repugnat tam contingenti quam impossibili.	Thirdly, it is necessary to know that sometimes one method conflicts with several methods; just as the contingent contradicts both necessity and impossibility, because a proposition contingent on either is neither necessary nor impossible. Similarly, the necessary is opposed both to the contingent and to the impossible.
Quarto oportet scire quod modorum quidam sunt simpliciter affirmativi, sicut necessarium, possibile, scibile, demonstrabile et huiusmodi. Quidam sunt simpliciter negativi, sicut impossibile, quia impossibile idem est quod non possibile. Similiter est de inopinabili et indemonstrabili et huiusmodi.	Fourthly, we must know that some of the modes are simply affirmative, such as necessary, possible, knowable, demonstrable, and the like. Some are simply negative, such as impossible, because impossible is the same as not possible. The same is true of the unthinkable and the undemonstrable, and the like.
Quidam nec sunt simpliciter affirmativi nec simpliciter negativi, sed quasi aequivalenter sunt affirmativi et negativi, pro quanto simpliciter negant unum modum affirmativum et alium simpliciter inferunt; sicut est de contingenti, nam contingens repugnat necessario et absolute infert possibile. Unde `contingens' aequivalet isti `propositio possibilis non necessaria'.	Some are neither simply affirmative nor simply negative, but are, as it were, equivalently affirmative and negative, inasmuch as they simply negate one affirmative mode and simply infer another; just as it is about the contingent, for the contingent contradicts the necessary and absolutely entails the possible. Hence the `contingent' is equivalent to this `possible proposition not necessary'.
Quinto sciendum est quod in modalibus quaedam sunt propositiones simpliciter primae, quarum aequipollentiae non sunt quaerendae; et sunt omnes propositiones in quibus ponuntur modi simpliciter affirmativi vel non simpliciter affirmativi, tamen non negativi, et de quarum praeiacentibus non est quaerenda aequipollentia.	Fifthly, it must be known that in the modals there are certain propositions that are simply first, the equivalences of which are not to be sought; and such are all propositions in which modes are posited that are simply affirmative or not simply affirmative, yet not negative, and of whose predicates it is not necessary to seek equivalence.
Cuiusmodi sunt tales `possibile est omnem hominem currere'; `possibile est nullum hominem currere': `possibile est aliquem hominem currere'; ƿ `possibile est aliquem hominem non currere'. 'Necesse est omne ens esse in actu'; `necesse est nullum ens esse in actu'; `necesse est aliquod ens esse in actu'; `necesse est aliquod ens non esse in actu'. `Non contingit omnem hominem currere'; `contingit nullum hominem currere'; `contingit aliquem', `contingit aliquem non', et sic de aliis.	They are of such a kind as `it is possible for every man to run'; `it is possible for no man to run': `it is possible for any man to run'; `it is possible for some man not to run'. 'It is necessary for every being to be in action'; `it is necessary that there be no being in action'; `It is necessary for some being to exist in an act'; `It is necessary that some being not be in act.' `It is not possible for every man to run'; `It happens that no man runs'; `it happens to someone', `it happens to noone', and so on about others.
De aliis autem propositionibus modalibus quaerendae sunt earum aequipollentiae. Unde de omni propositione in qua ponitur iste modus `impossibile' quaerendum est cui aequipollet.	As for other modal propositions, their equivalence must be sought. Therefore, in every proposition in which this mode of `impossible' is used, it is necessary to seek which is equivalent to it.
Sexto oportet scire quod in propositione cuius quaeritur aequipollentia quandoque modus affirmatur et quandoque negatur; sicut patet in istis `necesse est nullum hominem non currere'; `non necesse est nullum hominem currere'.	Sixth, we must know that in the proposition whose equivalence is sought, the mode is sometimes affirmed and sometimes denied; as it is clear in these, `it is necessary for no man not to run'; `it is not necessary for any man to run'.