Authors/Ockham/Summa Logicae/Book III-1/Chapter 21

Latin	English
[Cap. 21. De uniformi de necessario in secunda figura]	[Chapter 21. On uniform syllogisms from de necessario propositions in the second figure.
Quando omnes propositiones de necessario in secunda figura sumuntur in sensu compositionis vel aequivalentes eis, semper sequitur conclusio de necessario sumpta in sensu compositionis vel aequivalens ei; quando scilicet syllogismus ex illis de inesse tenet, quia talis syllogismus tenet per istam regulam ‘si praemissae sint necessariae, conclusio erit necessaria’, quae semper vera est. Et ideo bene sequitur ‘nullum hominem esse asinum est necessarium; omne rudibile esse asinum est necessarium; igitur nullum rudibile esse hominem est necessarium’.	When all the de necessario propositions in the second figure,or something equivalent to them,  are taken in the sense of composition, a de necessario conclusion,or something equivalent to it, always follows, taken in the sense of composition: namely when the syllogism holds from them de inesse (assertoric), for such a syllogism holds through the rule "if the premisses are necessary, the conclusion will be necessary", which is always true.  And therefore "it is necessary that no man is a donkey, it is necessary that everything tame is a donkey, therefore it is necessary that nothing tame is a man".
Probatur etiam talis syllogismus aliter, scilicet per reductionem talis syllogismi in syllogismum primae figurae per conversionem, quia dicƿtum est prius quod illa de necessario in sensu compositionis vel aequivalens ei convertitur sicut sua de inesse.	Such a syllogism is proved in another way, namely by reduction of such a syllogism into a syllogism of the first figure by conversion, for it was said before that a de necessario syllogism in the sense of composition, or something equivalent to it, is converted just as its assertoric.
Si autem omnes praemissae sumantur in sensu divisionis vel aequivalentes eis, non semper valet syllogismus. Unde Philosophus negaret istum syllogismum esse bonum ‘omne lucidum de necessitate est corpus caeleste vel elementum; corpus mixtum de necessitate non est corpus caeleste nec elementum; igitur corpus mixtum de necessitate non est lucidum’. Nam si nihil esset lucidum nisi corpus caeleste vel elementum, praemissae essent verae, secundum opinionem Aristotelis, et conclusio falsa, sicut manifeste patet. Quod enim maior esset vera, patet, quia quaelibet singularis est vera, per casum, igitur universalis est vera.	But if all the premises are taken in the sense of division or equivalent to them, the syllogism is not always valid. Hence the Philosopher would deny that this syllogism is good: ‘every luminous thing is of necessity a celestial body or an element; a mixed body is of necessity neither a celestial body nor an element; therefore a mixed body is of necessity not luminous’. For if nothing were luminous except a celestial body or an element, the premises would be true, according to Aristotle’s opinion, and the conclusion false, as is clearly evident. For that the major would be true is evident, because every singular is true, by chance, therefore the universal is true.
Similiter, ponatur quod Deus suspendat actionem cuiuscumque agentis creati, ita quod nullum activum creatum aliquid producat, tunc sunt istae praemissae verae ‘omnis producens de necessitate est Deus; omnis natura creata de necessitate non est Deus’ et tamen haec est falsa ‘omnis natura creata de necessitate non est producens’. Quod enim maior sit vera, patet, quia quaelibet singularis est vera, per casum; et ita patet quod talis conclusio de necessario non sequitur. Tamen sequitur alia conclusio de inesse, talis ‘igitur aliquid, quod de necessitate non est Deus, non est producens’.	Similarly, suppose that God suspends the action of any created agent, so that no created agent produces anything, then these premises are true: ‘every producing thing is of necessity God; every created nature is of necessity not God’, and yet this is false: ‘every created nature is of necessity not producing’. For it is clear that the major is true, because every singular is true, by chance; and so it is clear that such a conclusion de necessario does not follow. Yet another assertoric conclusion follows, such as ‘therefore something that is not of necessity God is not producing’.
Similiter, si maior sit universalis negativa, non valet syllogismus; nam ante incarnationem fuerunt istae praemissae verae ‘omnis homo de necessitate non est Deus; omnis persona divina de necessitate est Deus’ et tamen ista conclusio est falsa ‘omnis persona divina de necessitate non est homo’, et ita talis syllogismus non valet.	Similarly, if the major is a universal negative, the syllogism is not valid; for before the incarnation these premises were true, ‘every man is not of necessity God; every divine person is of necessity God’, and yet this conclusion is false, ‘every divine person is not of necessity man’, and so such a syllogism is not valid.
Nec potest talis syllogismus perfici et reduci in primam figuram per conversionem, quia dictum est prius, quod illa de necessario non convertitur in illam de necessario quando sumitur in sensu divisionis vel aequivalens ei. Sicut non sequiƿtur ‘aliquis creans de necessitate est Deus, igitur Deus de necessitate est creans’, sed sic ‘igitur aliquid, quod de necessitate est Deus, est creans’. Et ideo quamvis iste syllogismus sit bonus in prima figura ‘omnis Deus de necessitate non est homo; quaelibet persona divina de necessitate est Deus; igitur quaelibet persona divina de necessitate non est homo’, tamen iste discursus non valet ‘omnis homo de necessitate non est Deus; quaelibet persona divina de necessitate est Deus; igitur quaelibet persona divina de necessitate non est homo’, et hoc quia ista maior in secunda figura ‘omnis homo de necessitate non est Deus’, non convertitur in istam ‘omnis Deus de necessitate non est homo’.	Nor can such a syllogism be completed and reduced to the first figure by conversion, because it was said before, that a de necessario is not converted into a de necessario when it is taken in the sense of division or equivalent to it. Just as it does not follow ‘someone creating is of necessity God, therefore God is of necessity creating’, but rather ‘therefore something that is of necessity God is creating’. And therefore although this syllogism is good in the first figure ‘every God is of necessity not man; every divine person is of necessity God; therefore every divine person is of necessity not man’, yet this discourse is not valid ‘every man is of necessity not God; every divine person is of necessity God; therefore every divine person is of necessity not man’, and this because the major in the second figure ‘every man is of necessity not God’, is not converted into that ‘every God is of necessity not man’.
Sic igitur patet, quod quamvis omnes propositiones sumantur in sensu divisionis vel sint aequivalentes eis, quod discursus non valet in secunda figura. Si autem maior sumatur in sensu compositionis et minor in sensu divisionis, valet discursus respectu conclusionis sumptae in sensu divisionis, et hoc quia conversa maiore tenet in prima figura, sicut dictum est prius. Si autem maior sumatur in sensu divisionis et minor in sensu compositionis, non sequitur conclusio in sensu compositionis. Nam non sequitur ‘nullam creaturam esse Deum est necessarium; omne producens de necessitate est Deus; igitur nullum producens esse creaturam est necessarium’, quia praemissae sunt possibles et conclusio impossibilis. Sed conclusio in sensu divisionis bene sequitur, quia conversa maiore sequitur in prima figura.	Thus it is clear that although all propositions are taken in the sense of division or are equivalent to them, the discourse is not valid in the second figure. But if the major is taken in the sense of composition and the minor in the sense of division, the discourse is valid with respect to the conclusion taken in the sense of division, and this because the converse of the major holds in the first figure, as was said before. But if the major is taken in the sense of division and the minor in the sense of composition, the conclusion in the sense of composition does not follow. For it does not follow that ‘it is necessary for no creature to be God; every producer is of necessity God; therefore it is necessary for no producer to be a creature’, because the premises are possible and the conclusion impossible. But the conclusion in the sense of division follows well, because the converse of the major follows in the first figure.