Authors/Ockham/Summa Logicae/Book III-1/Chapter 24

Latin	English
Cap. 24. De uniformi ex propositionibus de possibili in secunda figura	Chapter 24. On uniform syllogisms from de possibili propositions in the second figure.
In secunda figura si subiectum utriusque praemissae supponat pro his quae sunt, syllogismus non valet. Non enim sequitur ‘omnis persona divina potest non esse creans; Pater potest esse creans; igitur Pater potest non esse persona divina’. Nec sequitur ‘omnis persona divina potest non esse creans; omnis homo, qui est, potest esse creans; - ponatur quod nullus homo sit nisi Christus-; igitur omnis homo potest non esse persona divina’, nam illo casu posito praemissae sunt verae et conclusio falsa.	In the second figure, if the subject of both premises supposits for those things that are, the syllogism is not valid. For it does not follow that ‘every divine person can not be creative; the Father can be creative; therefore the Father can not be a divine person’. Nor does it follow that ‘every divine person can not be creative; every man who is can be creative; - let it be assumed that there is no man except Christ-; therefore every man can not be a divine person’, for in that case the premises are true and the conclusion false.
Si autem subiectum utriusque accipiatur pro his quae possunt esse, sic non tenet syllogismus. Nam non sequitur ‘omnis homo potest non esse albus; omne risibile potest esse album; igitur omne risibile potest non esse homo’; sicut non sequitur ‘omnis persona divina potest non esse creans; omnis persona producta potest esse creans; igitur omnis persona producta potest non esse persona divina’. Et ratio est quia negativa de possibili non convertitur in negativam de possibili. Non enim sequitur ‘quaelibet persona divina potest non esse creans, igitur omne quod est creans, vel potest esse creans, potest non esse persona divina’. Et ita talis syllogismus de possibili non potest reduci in primam figuram per conversionem, quia nullus syllogismus secundae figurae reducibilis ƿ per conversionem potest reduci nisi per conversionem universalis negativae.	But if the subject of both is taken for those things which can be, then the syllogism does not hold. For it does not follow that ‘every man can possibly not be white; everything that is able to laugh can be white; therefore everything that can laugh can possibly not be man’; just as it does not follow that ‘every divine person can be not creating; every produced person can be creating; therefore every produced person can possibly not be a divine person’. And the reason is that a negative of possibility is not converted into a negative of possibility. For it does not follow that ‘every divine person can not be creating, therefore everything which is creating, or can be creating, can possibly not be a divine person’. And thus such a syllogism of possibility cannot be reduced to the first figure by conversion, because no syllogism of the reducible second figure can be reduced by conversion except by conversion of the universal negative.
Quare autem non teneat talis syllogismus in quarto modo secundae figurae, ratio est quia non potest reduci nisi per impossibile. Sed hoc patebit inferius.	But the reason why such a syllogism does not hold in the fourth mode of the second figure is that it cannot be reduced except by an impossibility. But this will be clear below. .
Et si dicatur quod quamvis negativa de possibili non convertatur in illam de possibili, convertitur tamen in illam de inesse, sic ‘omnis persona divina potest non esse creans, igitur aliquid, quod potest non esse creans, est persona divina’; immo, in istam de possibili potest converti ‘aliquid, quod potest non esse creans, potest esse persona divina’; dicendum est igitur quod per talem conversionem potest reduci in primam figuram:	And if it is said that although the negative of possibility is not converted into that of possibility, it is nevertheless converted into that of inherence, thus ‘every divine person can possibly not be creative, therefore something that can possibly not be creative is a divine person’; indeed, it can be converted into that of possibility ‘something that can possibly not be creative can be a divine person’; it must therefore be said that by such a conversion it can be reduced to the first figure:
Dicendum est quod illud argumentum concludit oppositum, nam universalis negativa de possibili quamvis praedicto modo possit converti in illam de inesse vel de possibili, secundum quod subiectum aliter et aliter accipitur in antecedente, tamen numquam convertitur nisi in partictularem, quia bene sequitur ‘aliquid, quod est persona divina, potest non esse creans, igitur aliquid. quod potest non esse creans, est persona divina’. Similiter bene sequitur ‘quodlibet, quod potest esse persona divina, potest non esse creans, igitur aliquid, quod potest non esse creans, potest esse persona divina’; sed non sequitur ‘quodlibet, quod potest non esse creans, potest esse persona divina’. Et ita patet quod universalis negativa de possibili non convertitur nisi in particularem. Sed quando syllogismus secundae figurae reducitur per conversionem in primam figuram, semper conversa universalis negativae debet esse maior in prima figura, et per consequens si talis syllogismus reduceretur in primam figuram per conversionem, conversa negativae, quae est particularis, esset maior in prima figura; quod est impossibile, quia tunc non regularetur per dici de omni vel de nullo.	It must be said that that argument concludes the opposite, for although the universal negative of possibility can be converted in the aforementioned way into that of inherence or of possibility, according as the subject is taken differently in the antecedent, it is nevertheless never converted except into a particular, because it follows well that ‘something that is a divine person can be not creative, therefore something that can be not creative is a divine person’. Similarly, it follows well that ‘anything that can be a divine person can be not creative, therefore something that can be not creative can be a divine person’; but it does not follow that ‘anything that can be not creative can be a divine person’. And thus it is clear that the universal negative of the possible is not converted except into a particular. But when a syllogism of the second figure is reduced by conversion to the first figure, the converse of the universal negative must always be the major in the first figure, and consequently if such a syllogism were reduced to the first figure by conversion, the converse of the negative, which is particular, would be the major in the first figure; which is impossible, because then it would not be governed by saying of everything or of nothing.
Similiter, si altera praemissarum sumatur in sensu compositionis et ƿ altera in sensu divisionis, qualitercumque, non tenet syllogismus. Et ita patet quod qualitercumque propositiones de possibili combinentur, numquam valet uniformis de possibili in secunda figura. Et ratio est, quia idem potest ab eodem removeri et affirmari cum nota possibilitatis affirmativa, et ita ex tali affirmativa et negativa non sequitur negativa eiusdem a se, sicut patet in exemplis supra positis.	Similarly, if one of the premises is taken in the sense of composition and the other in the sense of division, in any way, the syllogism does not hold. And so it is clear that no matter how the propositions of possibility are combined, the uniform of possibility in the second figure is never valid. And the reason is that the same thing can be removed from the same thing and affirmed with the affirmative note of possibility, and so from such an affirmative and negative the negative of the same thing does not follow by itself, as is clear in the examples given above.