Authors/Ockham/Summa Logicae/Book III-1/Chapter 44

Latin	English
Cap. 44. De mixtione necessarii et possibilis in prima figura	Chapter 44. On the mixture of necessary and possible propositions in the first figure.
Postquam dictum est de mixtionibus ex propositionibus de inesse et modalibus, dicendum est de mixtione ex propositionibus de necessario et ceteris modalibus. Et primo de mixtione necessarii et possibilis in prima figura; et primo quando utraque sumitur in sensu compositionis.	After having spoken of mixtures from propositions of inherence and modals, we must speak of mixtures from propositions of necessity and other modals. And first of the mixture of the necessary and the possible in the first figure; and first when both are taken in the sense of composition.
Et est primo sciendum quod in primo modo et tertio, si maior fuerit de necessario et minor de possibili, sequitur conclusio de possibili in eodem sensu. Sicut sequitur 'omnem hominem esse animal est necessarium; omne album esse hominem est possibile; igitur omne album esse animal est possibile'. Et similiter est de aliis modis. Et tenet talis modus arguendi per istam regulam 'si una praemissarum sit necessaria et alia possibilis, conclusio erit possibilis'. Et sequitur ex istis tribus: 'omne necessarium est possibile'; 'nullum possibile repugnat formaliter necessario'; 'si praemissae sunt possibiles et compossibiles, conclusio est possibilis'. Eodem modo, si maior fuerit de possibili et minor de necessario, sequitur conclusio de possibili per eandem regulam. Sed ex ƿ talibus praemissis non sequitur conclusio de inesse nec de necessario, sicut non sequitur 'nullum hominem esse asinum est necessarium; omne album esse hominem est possibile; igitur nullum album est asinus’. Et ita est de aliis.	And it should first be known that in the first and third modes, if the major is of necessity and the minor of possibility, a conclusion of possibility follows in the same sense. Just as it follows 'it is necessary for every man to be an animal; it is possible for every white man to be a man; therefore it is possible for every white man to be an animal'. And similarly it is with the other modes. And such a way of arguing holds by this rule 'if one of the premises is necessary and the other possible, the conclusion will be possible'. And it follows from these three: 'every necessary is possible'; 'no possible is formally inconsistent with necessity'; 'if the premises are possible and composable, the conclusion is possible'. In the same way, if the major is of possibility and the minor of necessity, a conclusion of possibility follows by the same rule. But from such premises neither a conclusion of inherence nor of necessity follows, just as it does not follow 'it is necessary for no man to be a donkey; it is possible for every white man to be a man; therefore nothing white is a donkey'. And so it is with the others.
Secundo videndum est de ista mixtione quando illa de necessario sumitur in sensu compositionis et illa de possibili in sensu divisionis. Circa quod sciendum est quod si maior sit de necessario et minor de possibili, sequitur conclusio de possibili, sumpta in sensu divisionis, ita tamen quod subiectum conclusionis habeat eandem acceptionem quam habet in minore. Unde iste syllogismus est bonus 'omnem hominem esse animal est necessarium; omne album potest esse homo; igitur omne album potest esse animal'. Similiter iste syllogismus est bonus 'nullum hominem esse asinum est necessarium; omne album potest esse homo; igitur omne album potest non esse asinus’. Sed conclusio de inesse et de necessario non sequitur.	Secondly, we must see about this mixture when the former is taken of necessity in the sense of composition and the latter of possibility in the sense of division. Regarding which it must be known that if the major is of necessity and the minor of possibility, the conclusion de possibility, taken in the sense of division, follows, so that the subject of the conclusion has the same meaning as it has in the minor. Hence this syllogism is good 'It is necessary for every man to be an animal; every white man can be a man; therefore, every white man can be an animal'. Similarly, this syllogism is good 'It is necessary for no man to be a donkey; every white man can be a man; therefore, it is possible for every white man not to be a donkey'. But conclusions of inherence and of necessity do not follow.
Similiter, si illa de necessario sit minor et maior de possibili, sequitur conclusio de possibili non de inesse nec de necessario, subiecto conclusionis habente eandem suppositionem quam habet subiectum maioris. Sicut sequitur 'omne animal potest esse album; omnem hominem esse animal est necessarium; igitur omnis homo potest esse albus’. Sed si subiectum maioris accipiatur pro his quae sunt praecise et subiectum conclusionis pro his quae possunt esse, non valet. Non enim sequitur 'omne coloratum potest esse musicum; omne album esse coloratum est necessarium; igitur omne, quod potest esse album, potest esse musicum’. Nec sequitur 'omne producens potest esse Deus; omne generans esse producens est necessarium; igitur omne, quod potest esse generans, potest esse Deus', quia posito quod nihil producat aliquid nisi Deus, praemissae sunt verae, si subiectum maioris accipiatur pro eo quod est, et conclusio falsa.	Similarly, if the proposition of necessity is minor and the major is of possibility, the conclusion follows of possibility, not of inherence nor of necessity, the subject of the conclusion having the same supposition as the subject of the major. As follows: 'every animal can be white; it is necessary for every man to be an animal; therefore every man can be white'. But if the subject of the major is taken for those things that are precisely and the subject of the conclusion for those things that can be, it is not valid. For it does not follow 'every colored thing can be musical; it is necessary for every white thing to be colored; therefore everything that can be white can be musical'. Nor does it follow 'every producing thing can be God; it is necessary that every generating thing be producing; therefore everything that can be generating can be God', because, assuming that nothing produces anything except God, the premises are true if the subject of the major is taken for that which is, and the conclusion false.
Tertio videndum est de ista mixtione quando illa de necessario sumitur in sensu divisionis et illa de possibili in sensu compositionis. Et est sciendum quod si maior sit de possibili et minor de necessario, non sequitur conclusio nec de necessario nec de inesse, sed de possibili, sumpta ƿ conclusione in sensu compositionis. Sequitur enim 'omnem hominem esse album est possibile; Sortes de necessitate est homo; igitur Sortem esse album est possibile’. Et consimiliter est in alias modis.	Thirdly, we must see about this mixture when the former is taken of necessity in the sense of division and the latter of possibility in the sense of composition. And it must be known that if the major is of possibility and the minor of necessity, the conclusion does not follow either of necessity or of inherence, but of possibility, taken from the conclusion in the sense of composition. For it follows that 'it is possible for every man to be white; Socrates is of necessity a man; therefore it is possible for Socrates to be white'. And similarly it is in the other modes.
Sed si maior sit de necessario et minor de possibili, non valet. Non enim sequitur 'omnis producens de necessitate est Deus; ignem esse producentem est possibile; igitur ignem esse Deum est possibile'. Nec sequitur 'omnis homo de necessitate non est Deus; personam divinam esse hominem est possibile; igitur personam divinam non esse Deum est possibile', nam ante incarnationem fuerunt praemissae verae et conciusio falsa.	But if the major is of necessity and the minor of possibility, it is not valid. For it does not follow that 'every producing thing is of necessity God; it is possible for fire to be producing; therefore it is possible for fire to be God'. Nor does it follow that 'every man of necessity is not God; it is possible for a divine person to be a man; therefore it is possible for a divine person not to be God', for before the incarnation the premises were true and the conclusion false.
Quarto videndum est de ista mixtione utraque praemissa sumpta in sensu divisionis. Circa quod sciendum quod si maior sit de necessario et minor de possibili, non valet, sicut non sequitur omne sciens de necessitate est Deus; omnis homo potest esse sciens; igitur omnis homo potest esse Deus'. Nec sequitur ‘omnis homo de necessitate non est Deus; Filius Dei potest esse homo; igitur Filius Dei potest non esse Deus’. Sed si maior fuerit de possibili et minor de necessario, semper valet et regulatur per dici de omni vel de nullo. Quod patet, quia semper illa de necessario infert illam de inesse. Sed dictum est prius quod maiore exsistente de possibili et minore de inesse, sequitur conclusio de possibili, quamcumque acceptionem habeat subiectum maioris. Oportet tamen quod subiectum conclusionis non accipiatur pro his quae possunt esse, si subiectum maioris accipiatur praecise pro his quae sunt.	Fourthly, we must see about this mixture of both premises taken in the sense of division. Regarding which it should be known that if the major is of necessity and the minor of possibility, it is not valid, just as it does not follow that every knowing thing is of necessity God; every man can be knowing; therefore every man can be God'. Nor does it follow that 'every man of necessity is not God; the Son of God can be man; therefore it is possible for the Son of God not to be God'. But if the major is of possibility and the minor of necessity, it is always valid and is governed by 'to be said of all or of none'. Which is clear, because a proposition of necessity always infers a proposition of inherence. But it was said before that if the major exists of possibility and the minor of inherence, the conclusion of possibility follows, whatever the subject of the major may be. However, it is necessary that the subject of the conclusion is not taken for things that can be, if the subject of the major is taken precisely for things that are.