Authors/Ockham/Summa Logicae/Book III-1/Chapter 34

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Latin English
Cap. 34. De mixtione de inesse et possibilis in prima figura Chapter 34. On the mixture of assertoric and possible propositions in the first figure.
Post mixtionem de inesse et necessarii dicendum est de mixtione de inesse et possibilis, et primo de prima figura. After the mixture of the assertoric and the necessary, we must speak of the mixture of the assertoric and the possible, and first of the first figure.
Unde primo sciendum est quod si illa de possibili sumatur in sensu compositionis vel aequivalens ei, sive maior fuerit de possibili sive minor, non valet mixtio talis universaliter, quia contingit praemissas esse veras conclusione exsistente falsa. Patet hoc per instantiam in terminis, sic ‘omnem hominem esse album est possibile; omne nigrum est homo; igitur omne nigrum esse album est possibile’; ‘nullum hominem esse Deum est possibile; omnis Filius Dei est homo; igitur nullum Filium Dei esse Deum est possibile’; ‘nullus creans est Deus; omnem personam divinam esse creantem est possibile; igitur omnem personam divinam non esse Deum est possibile’. In omnibus praedictis exemplis patet quod praemissae possunt esse verae conclusione exsistente falsa. Hence, first of all, it should be known that if the proposition de possibili is taken in the sense of composition or equivalent to it, whether the major is de possibili or the minor, such a mixture is not valid universally, because it happens that the premises are true while the conclusion is false. This is clear by the instance in the terms, thus ‘it is possible for every man to be white; every black man is a man; therefore it is possible for every black man to be white’; ‘it is possible for no man to be God; every Son of God is a man; therefore it is possible for no Son of God to be God’; ‘no creating thing is God; it is possible for every divine person to be creating; therefore it is possible for every divine person not to be God’. In all the above examples, it is clear that the premises can be true while the conclusion is false.
Sciendum est tamen quod si minor sit de inesse simpliciter sive maior, valet mixtio. It should be noted, however, that if the minor is assertoric simply or the major, the mixture is valid.
Similiter sciendum quod si in syllogismo negativo sumatur sub aliquod inferius ad medium terminum, sive minor sit de inesse simpliciter sive de inesse ut nunc, mixtio valet. Unde bene sequitur ‘nullum hominem esse Deum est possibile; omnis homo albus est homo; igitur nullum hominem album esse Deum est possibile’. Sed in syllogismo affirmativo non sufficit accipere sub aliquod inferius ad medium terƿminum. Et ratio est, quia a superiori distributo ad quodcumque inferius est consequentia simplex negative non affirmative, sicut dictum est prius[1]. Similarly, it should be noted that if in a negative syllogism some inferior term is taken as the middle term, whether the minor is assertoric simply or assertoric as of now, the mixture is valid. Whence it follows well that ‘it is possible for no man to be God; every white man is a man; therefore it is possible for no white man to be God’. But in an affirmative syllogism it is not enough to take something inferior as the middle term. And the reason is that from the superior distributed to whatever is inferior, the consequence is simple negative, not affirmative, as was said before[2].
Si autem illa de possibili sumatur in sensu divisionis vel aequivalens ei, aut maior est de possibili aut minor: si maior, aut subiectum stat pro his quae sunt vel pro his quae possunt esse. Si primo modo, semper est mixtio bona, quia semper discursus talis regulatur per dici de omni vel de nullo. Sicut sequitur ‘omne album potest esse homo; Sortes est albus; igitur Sortes potest esse homo’, quia per maiorem denotatur quod omne illud quod est album potest esse homo et per minorem denotatur quod Sortes est albus, ex quo sequitur quod Sortes potest esse homo. Si autem subiectum supponat pro his quae possunt esse[3] adhuc mixtio valet, nam semper illa de possibili, quando sumitur pro his quae possunt esse, infert illam de possibili quando subiectum sumitur pro his quae sunt; et ex secunda et illa de inesse sequitur talis conclusio de possibili, igitur ex alia, quia quidquid sequitur ad consequens, sequitur ad antecedens. But if the proposition de possibili is taken in the sense of division or equivalent to it, either the major is de possibili or the minor: if the major, either the subject stands for things that are or for things that can be. If in the first way, there is always a good mixture, because such a discourse is always governed by 'dici de omni vel de nullo'. As follows ‘every white thing can be a man; Socrates is white; therefore Socrates can be a man’, because by the major it is denoted that everything that is white can be a man and by the minor it is denoted that Socrates is white, from which it follows that Socrates can be a man. But if the subject supposits for things that can be[4] the mixture is still valid, for the proposition de possibili, when taken for things that can be, always infers that de possibili when the subject is taken for things that are; and from the second and that assertoric such a conclusion de possibili follows, therefore from the other, because whatever follows from the consequent, follows from the antecedent.
Si autem minor sit de possibili et maior de inesse, non valet mixtio, quia non sequitur ‘omne album est homo; omnis asinus potest esse albus; igitur omnis asinus potest esse homo’; et hoc qualitercumque sumatur subiectum in illa de possibili. But if the minor is de possibili and the major is assertoric, the mixture is not valid, because it does not follow that ‘every white thing is a man; every donkey can be white; therefore every donkey can be a man’; and this no matter how the subject is taken in that de possibili.
Sciendum est etiam quod quamvis quando est mixtio bona semper sequatur conclusio directa, non tamen semper sequitur conclusio de possibili indirecta, et hoc, quia, sicut dictum est prius[5], illa de possibili non semper convertitur in illam de possibili, sed aliquando convertitur in illam de inesse. It should also be known that although when there is a good mixture a direct conclusion always follows, an indirect conclusion de possibili does not always follow, and this because, as was said before, the proposition de possibili is not always converted into that de possibili, but sometimes it is converted into the assertoric.
Est autem sciendum quod in conclusione subiectum non debet stare nisi pro his quae sunt, ex quo minor est de inesse in tali mixtione. ƿ But it should be known that in a conclusion the subject should not stand except for those things that are, from which the minor is assertoric in such a mixture.

Notes

  1. ↑ Supra, cap. 33, lin. 20-22.
  2. ↑ Supra, cap. 33, lin. 20-22.
  3. ↑ Nota bene quae dixit supra, Parte II. c. 25, lin. 22-43, simul sum lectionibus variantibus.
  4. ↑ Note well what he said above, Part II. c. 25, lin. 22-43, together with variant readings.
  5. ↑ Ibidem.
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