Authors/Ockham/Summa Logicae/Book III-1/Chapter 33

Latin	English
Cap. 33. De mixtione necessarii et de inesse in tertia figura	Chapter 33. On the mixture of necessary and assertoric propositions in the third figure.
Quando autem debet fieri mixtio necessarii et inesse in tertia figura si illa de necessario sumatur in sensu compositionis vel aequivalens ei, mixtio non valet generaliter, sive minor fuerit de necessario sive maior. Si enim fuerit maior de necessario, patet instantia hic ‘omnem personam divinam esse Deum est necessarium; omnis persona divina est creans; igitur aliquem creantem esse Deum est necessarium’ quia praemissae sunt verae et conclusio falsa. Similiter, si minor sit de necessario, patet instantia, sicut hic ‘quaelibet persona divina est creans; omnem personam divinam esse Deum est necessarium; igitur aliquem Deum esse creantem est necessarium’.	But when a mixture of necessary and assertoric propositions must be made and be in the third figure if the premise de necessario is taken in the sense of composition or equivalent to it, the mixture is not valid in general, whether it is a minor de necessario or a major. For if it is a major de necessario, the instance here is clear: ‘It is necessary for every divine person to be God; every divine person is creating; therefore it is necessary for someone to be creating to be God’, because the premises are true and the conclusion false. Similarly, if the minor is of necessity, the instance is clear, as here: ‘Every divine person is creating; it is necessary for every divine person to be God; therefore it is necessary for someone to be creating to be God’.
Tamen sciendum quod si minor sit de inesse simpliciter, tenet mixtio, quia conversa minore sequitur conclusio de necessario in prima figura. Similiter, si maior sit universalis negativa et minor sit particularis et praedicetur inferius de superiori, est bonus discursus; sicut in prima figura quando maior est negativa de necessario et in minore praedicatur superius de suo inferiori, sive sit superius per se sive per accidens, semper est bonus discursus, sive minor sit de inesse simpliciter sive de inesse ut nunc. Non autem est sic de affirmativa: et ratio est, quia semper a superiori distributo ad quodcumque inferius tenet consequentia simplex negative non affirmative. Unde haec est consequentia simplex ‘nullum animal currit, igitur nullus homo currit’; sed haec consequentia non est consequentia simplex ‘omne animal currit, igitur omnis homo currit’. Sed si illa negativa sit particularis de necessario, valet mixtio si in universali affirmativa praedicetur superius de inferiori. Unde iste discursus est bonus ‘aliquem hominem non esse asinum est necessarium; omnis homo est homo albus; igitur aliquem hominem album non esse asinum est necessarium’. Et ratio est, quia quidquid negatur necessario particulariter ab aliquo superiori, negatur etiam particulariter a quolibet infeƿriori quod potest praedicari de superiori universaliter sumpto, quia non contingit reperire instantiam.	However, it should be known that if the minor is assertoric simply, the mixture holds, because when converted to the minor, the conclusion de necessario follows in the first figure. Similarly, if the major is a universal negative and the minor is particular and the inferior is predicated of the superior, it is a good discourse; just as in the first figure when the major is negative de necessario and in the minor the superior is predicated of its inferior, whether the superior is per se or accidentally, it is always a good discourse, whether the minor is assertoric simply or assertoric as of now. But it is not so of the affirmative: and the reason is that from the superior distributed to whatever is inferior the simple consequence always holds negatively, not affirmatively. Hence this is a simple consequence ‘no animal runs, therefore no man runs’; but this consequence is not a simple consequence ‘every animal runs, therefore every man runs’. But if that negative is particular de necessario, the mixture holds if the superior is predicated of the inferior in the universal affirmative. Hence this discourse is good ‘it is necessary that some man not be a donkey; every man is a white man; Therefore, it is necessary that some white man is not a donkey.’ And the reason is that whatever is necessarily denied in particular by something superior, is also denied in particular by any inferior which can be predicated of the superior taken universally, because it is not possible to find an instance.
Ex praedictis potest elici quomodo uniformiter est dicendum de omnibus in tertia figura, illa de necessario sumpta in sensu compositionis.	From the above it can be deduced how it is to be said uniformly about everything in the third figure, that de necessario taken in the sense of composition.
Sed si illa de necessario sumatur in sensu divisionis, quando maior est de necessario et universalis semper sequitur conclusio de necessario in sensu divisionis, quia tunc semper conversa minore, quae est de inesse, est syllogismus regulatus per dici de omni vel de nullo in prima figura respectu eiusdem conclusionis. Sicut sequitur ‘omnis homo de necessitate est animal; omnis homo, vel aliquis homo, est albus; igitur aliquod album de necessitate est animal’. Sicut sequitur ‘omnis homo de necessitate non est asinus; omnis homo, vel aliquis homo, est albus; igitur aliquod album de necessitate non est asinus’; quia in omnibus praedictis conversa minore, quae est de inesse, sequitur conclusio de necessario in prima figura.	But if that de necessario is taken in the sense of division, when the major is de necessario and universal, the conclusion de necessario in the sense of division always follows, because then it is always converted to the minor, which is assertoric, the syllogism is governed by 'dici de omni vel de nullo' in the first figure with respect to the same conclusion. As follows ‘every man is of necessity an animal; every man, or some man, is white; therefore something white is of necessity an animal’. As follows ‘every man is of necessity not a donkey; every man, or some man, is white; therefore something white is of necessity not a donkey’; because in all the above, converted to the minor, which is assertoric, the conclusion de necessario in the first figure follows.
Si autem maior sit particularis affirmativa, valet mixtio. Unde sequitur ‘aliquis homo de necessitate est animal; omnis homo est albus; igitur aliquod album de necessitate est animal’. Talis autem syllogismus reducitur in primam figuram per convexsionem maioris in unam de inesse et conversionem conclusionis in unam de inesse et per transpositionem propositionum, sic ‘omnis homo est albus; aliquid, quod de necessitate est animal, est homo; igitur aliquid, quod de necessitate est animal, est album’, qui est syllogismus regulatus per dici de omni.	But if the major is a particular affirmative, the mixture is valid. Hence it follows ‘some man is of necessity an animal; every man is white; therefore some white thing is of necessity an animal’. Such a syllogism is reduced to the first figure by the convergence of the major into one assertoric and the conversion of the conclusion into one assertoric and by the transposition of the propositions, thus ‘every man is white; something that is of necessity an animal is a man; therefore something that is of necessity an animal is white’, which is a syllogism regulated by 'dici de omni'.
Si autem maior sit particularis negativa, discursus valet, quia sequitur ‘aliquis producens de necessitate non est asinus; omnis producens est persona divina; igitur aliqua persona divina de necessitate non est asinus’. Probatur autem talis syllogismus per syllogismum expositorium. Si aliquis producens de necessitate non est asinus, sit ille a, tunc a de necessitate non est asinus; et a est persona divina, per minorem propositionem; igitur aliqua persona divina de necessitate non est asinus. Sic igitur patet quod semper mixtio est bona si maior sit de necessario in sensu divisionis vel acquivalens ei.	But if the major is a particular negative, the discourse is valid, because it follows that ‘some producer is of necessity not a donkey; every producer is a divine person; therefore, some divine person is of necessity not a donkey’. Such a syllogism is proved by an expository syllogism. If some producer is of necessity not a donkey, let that be ‘‘a’’, then ‘‘a’’ is of necessity not a donkey; and ‘‘a’’ is a divine person, by the minor proposition; therefore, some divine person is of necessity not a donkey. Thus, it is clear that a mixture is always good if the major is de necessario in the sense of division or equivalent to it.
Sed si minor sit de necessario, non valet mixtio. Non enim sequitur ƿ ‘omnis homo est albus; omnis homo de necessitate est animal; igitur aliquod animal de necessitate est album’, sicut non sequitur ‘omnis persona divina creat; omnis persona divina de necessitate est Deus; igitur Deus de necessitate creat’. Nec sequitur ‘nulla persona divina est incarnata; omnis persona divina de necessitate est Deus; igitur Deus de necessitate non est incarnatus’, nam ante incarnationem fuerunt praemissae verae et conclusio fuit simpliciter falsa.	But if the minor is de necessario, the mixture is not valid. For it does not follow that ‘every man is white; every man is of necessity an animal; therefore, some animal is of necessity white’, just as it does not follow that ‘every divine person creates; every divine person is of necessity God; therefore, God creates of necessity’. Nor does it follow that ‘no divine person is incarnate; every divine person is of necessity God; therefore, God is of necessity not incarnate’, for before the incarnation the premises were true, and the conclusion was simply false.