Authors/Ockham/Summa Logicae/Book III-1/Chapter 51

Latin	English
Cap. 51. De mixtione propositionum de necessario et de aliis modis ab istis quatuor in prima figura	Chapter 51. On the mixture of necessary propositions and of other modes from those four in the first figure.
Ultimo circa istam partem videndum est de mixtione propositionum de necessario et de aliis modis ab istis quatuor. Et est primo sciendum in prima figura, quod quando ambae praemissae sumuntur in sensu compositionis, raro vel numquam valet mixtio respectu conclusionis de alio modo quam de necessario. Sicut non sequitur, secundum principia Aristotelis, 'omne animal esse coloratum est necessarium; omnem ƿ hominem esse animal est per se; igitur omnem hominem esse coloratum est per se’. Verumtamen quando unus modus est inferior ad necessarium, tunc semper sequitur conclusio de necessario, sicut sequitur ‘omnem hominem esse coloratum est necessarium; Sortem esse hominem est per se; igitur Sortem esse coloraturum est necessarium’. Sed quando modus ille non est inferior ad necessarium, tunc non valet	Finally, regarding this part, we must see about the mixture of propositions of necessity and of other modes from these (previous) four. And it is first to be known in the first figure that when both premises are taken in the sense of composition, the mixture is rarely or never valid with respect to the conclusion of a mode other than of necessity. Just as it does not follow, according to Aristotle's principles, 'every animal being colored is necessary; that every man is an animal is per se; therefore that every man is colored is per se'. However, when one mode is inferior to necessity, then the conclusion of necessity always follows, as it follows 'every man being colored is necessary; that Socrates is a man is per se; therefore that Socrates is colored is necessary'. But when that mode is not inferior to necessity, then the mixture does not hold,
mixtio nec respectu conclusionis de necessario nec respectu conclusionis de illo modo. Sicut non sequitur 'omne album esse coloratum est necessarium; omnem hominem esse album est scitum a me; ergo omnem hominem esse coloratum est scitum a me', nec sequitur ista conclusio 'omnem hominem esse coloratum est necessarium’. Tamen aliquando sequitur conclusio de tali modo, sicut sequitur 'omnem triangulum habere tres est necessarium; isoscelem esse triangulum est scibile; ergo isoscelem habere tres est scibile. Unde quando aliquis modus non potest competere antecedenti nisi competat consequenti, tunc in tali mixtione sequitur conclusio de tali modo. Huiusmodi autem sunt tales modi 'scibile', large accipiendo scibile, 'credibile', ‘apprehensibile’, ‘cognoscibile', 'proferibile' et huiusmodi.	neither with respect to a conclusion of necessity nor with respect to a conclusion of that mode. Just as it does not follow that 'every white thing being colored is necessary; every man being white is known by me; therefore every man being colored is known by me', nor does the conclusion 'every man being colored is necessary' follow. However, sometimes a conclusion of such a mode follows, as it follows that 'every triangle having three (angles) is necessary; that an isosceles is a triangle is knowable; therefore that an isosceles has three (angles) is knowable. Hence when some mode cannot belong to the antecedent unless it belongs to the consequent, then in such a mixture a conclusion of such a mode follows. Now of this kind are such modes as 'knowable', knowable understood broadly, 'credible', 'apprehensible', 'cognizable', 'pronounceable' and the like.
Si autem utraque sumatur in sensu divisionis, semper valet syllogismus quando illa de modo infert suam de inesse, sicut in illis de inesse respectu conclusionis eiusdem modi de quo est maior, ita quod si maior sit de necessario, conclusio erit de necessario, si maior sit de alio modo, conclusio erit de alio modo. Et ideo tales syllogismi valent 'omnis homo per se est animal; Sortes de necessitate est homo; igitur Sortes per se est animal’; 'omne ens scitur a te esse in actu; persona divina de necessitate est ens; igitur persona divina scitur a te esse in actu ; 'omnis homo de necessitate est animal; Sortes scitur a te esse homo; igitur Sortes de necessitate est animal. Et ratio est, quia quandoque in talibus minor infert suam de inesse; nunc autem dictum est prius quod semper ex tali maiori de modo et minori de inesse sequitur conclusio de consimili ƿ modo. Et quidquid sequitur ad consequens, sequitur ad antecedens, igitur talis mixtio est bona.	But if both are taken in the sense of division, the syllogism is always valid when the latter infers its inherence from the mode, as in those of inherence with respect to the conclusion of the same mode as the major, so that if the major is of necessity, the conclusion will be of necessity, if the major is of another mode, the conclusion will be of another mode. And therefore such syllogisms are valid: 'every man is of himself (per se) an animal; Socrates is of necessity a man; therefore Socrates is of himself an animal'; 'every being is known by you to be actual; a divine person is of necessity a being; therefore a divine person is known by you to be actual; 'every man is of necessity an animal; Socrates is known by you to be a man; therefore Socrates is of necessity an animal. And the reason is that sometimes in such cases the minor infers its inherence; but now it has been said before that from such a major of a mode and a minor of inherence a conclusion of a similar mode always follows. And whatever follows the consequent, follows the antecedent, therefore such a mixture is good.
Si autem illa de modo non inferat suam de inesse, tunc non valet mixtio; sicut non sequitur ‘omne immortale de necessitate est Deus; intelligentia inferior Deo creditur esse immortalis; igitur intelligentia illa de necessitate est Deus’, nec etiam sequitur 'igitur creditur esse Deus'. Sicut non sequitur 'omnis Deus de necessitate est persona relativa; aliquod immortale creditur esse Deus; igitur aliquod immortale creditur esse persona relativa’. Et ita patet quod talis mixtio ex propositione de modo, quae non infert suam de inesse, non valet. Tales autem modi sunt huiusmodi 'credibile', 'opinabile', 'ponibile', 'apprehensibile', 'intelligibile' et huiusmodi.	But if a modal proposition does not infer its inherence, then the mixture is not valid; just as it does not follow that ‘every immortal thing is of necessity God; an intelligence inferior to God is believed to be immortal; therefore that intelligence is of necessity God’, nor does it follow that ‘therefore it is believed to be God’. Just as it does not follow that ‘every God is of necessity a relative person; something immortal is believed to be God; therefore something immortal is believed to be a relative person’. And so it is clear that such a mixture from a proposition of a mode, which does not infer its inherence, is not valid. Such modes are of the kind ‘credible’, ‘opinable’, ‘possible’, ‘apprehensible’, ‘intelligible’ and the like.