Authors/Ockham/Summa Logicae/Book III-1/Chapter 22

Latin	English
Cap. 22. De uniformi de necessario in tertia figura	Chapter 22. On uniform syllogisms from de necessario propositions in the third figure.
In tertia figura quando omnes praemissae sumuntur in sensu compositionis tenet syllogismus sicut ex suis de inesse, quia arguitur per istam regulam ‘si praemissae fuerint necessariae, conclusio erit necessaria’. Si autem omnes sumantur in sensu divisionis, omnis discursus valet. Unde in primis duobus modis valet talis syllogismus, quia quamvis ista deƿ necessario non convertatur in illam de necessario, semper tamen convertitur in illam de inesse. Nunc autem in prima figura, maiore exsistente de necessario in sensu divisionis et minore de inesse, sequitur conclusio de necessario in sensu divisionis, sicut posterius ostendetur. Et quidquid sequitur ad consequens, sequitur ad antecedens; igitur ex eadem maiore et minore de necessario, quae convertitur in illam de inesse, sequitur conclusio eadem in tertia figura.	In the third figure, when all the premises are taken in the sense of composition, the syllogism holds in the assertoric sense, because it is argued by this rule ‘if the premises are necessary, the conclusion will be necessary’. But if all are taken in the sense of division, the whole discourse is valid. Hence in the first two ways such a syllogism is valid, because although one de necessario proposition is not converted into another de necessario proposition, it is always converted into the assertoric. Now, however, in the first figure, with the major existing de necessario in the sense of division and the assertoric minor, the conclusion follows de necessario in the sense of division, as will be shown later. And whatever follows to the consequent, follows to the antecedent; therefore from the same major and minor de necessario, which are converted into the assertoric, the same conclusion follows in the third figure.
Per idem patet quod quartus et sextus modus valent ex talibus propositionibus; sicut bene sequitur ‘quaelibet persona divina de necessitate est Deus; aliqua persona divina de necessitate est Pater; igitur Pater de necessitate est Deus’. Et sic potest probari tertius modus. Vel potest probari per expositionem, sic ‘si aliquod creans de necessitate est Deus et omne creans de necessitate est persona divina, igitur aliqua persona divina de necessitate est Deus’. Quia si aliquod creans de necessitate est Deus, sit illud a: tunc a de necessitate est Deus et similiter a de necessitate est persona divina, ex quibus sequitur quod persona divina de necessitate est Deus.	By the same token, it is clear that the fourth and sixth modes are valid from such propositions; as it follows well that ‘every divine person is of necessity God; some divine person is of necessity the Father; therefore the Father is of necessity God’. And thus the third mode can be proved. Or it can be proved by exposition, thus ‘if some creator is of necessity God and every creator is of necessity a divine person, therefore some divine person is of necessity God’. For if some creator is of necessity God, let that be ‘a’: then ‘a’ is of necessity God and similarly ‘a’ is of necessity a divine person, from which it follows that a divine person is of necessity God.
Et per istum modum probatur quintus modus. Nam iste syllogismus est bonus ‘aliquis homo de necessitate non est Deus; omnis homo de necessitate est natura intellectualis; igitur aliqua natura intellectualis de necessitate non est Deus. Quia si haec sit vera ‘aliquis homo de necessitate non est Deus’, sit ille a: tunc a de necessitate non est Deus et a de necessitate est natura intellectualis, quia omnis homo de necessitate est natura intellectualis, per minorem; nunc autem sequitur ‘ade necessitate non est Deus; a de necessitate est natura intellectualis; igitur aliqua natura intellectualis de necessitate non est Deus’.	And in this way the fifth mode is proven. For this syllogism is good: ‘some man is not necessarily God; every man is necessarily an intellectual nature; therefore some intellectual nature is not necessarily God'. For if this is true ‘some man is not necessarily God’, let that be ‘a’: then ‘a’ is not necessarily God and ‘a’ is necessarily an intellectual nature, because every man is necessarily an intellectual nature, by the minor; but now it follows ‘a’ is not necessarily God; ‘a’ is necessarily an intellectual nature; therefore some intellectual nature is not necessarily God’.
Si autem maior sumatur in sensu compositionis et minor in sensu divisionis, non sequitur conclusio in sensu divisionis nec in sensu compositionis. Non enim sequitur ‘omne falsum esse falsum est necessarium; aliquod falsum de necessitate est ista propositio: tu sedes; igitur ista propositio de necessitate est falsa’; nec etiam sequitur ‘igitur istam propositionem esse falsam est necessarium’.	But if the major is taken in the sense of composition and the minor in the sense of division, the conclusion does not follow in the sense of division or in the sense of composition. For it does not follow that ‘every false thing is necessarily false; something false is necessarily this proposition: you are sitting; therefore this proposition is necessarily false’; nor does it follow that ‘therefore this proposition is necessarily false’.
ƿ Si autem maior sumatur in sensu divisionis et minor in sensu compositionis, semper sequitur conclusio in sensu divisionis, non in sensu compositionis Quod enim illa in sensu divisionis sequatur, patet quia minor convertitur in illam de inesse, ex qua et maiore sequitur conclusio de necessario in sensu divisionis, non in sensu compositionis, sicut inferius ostendetur.	But if the major is taken in the sense of division and the minor in the sense of composition, the conclusion always follows in the sense of division, not in the sense of composition. For that the latter follows in the sense of division, is clear because the minor is converted into the former assertoric, from which the conclusion follows from the major de necessario in the sense of division, not in the sense of composition, as will be shown below.
Haec dicta sunt quantum ad illos modos qui reducuntur per conversionem, et ex istis potest faciliter sciri quid dicendum est de aliis modis qui non reducuntur sic.	These things have been said with regard to those modes that are reduced by conversion, and from these it can be easily known what is to be said about other modes that are not reduced in this way.