Authors/Ockham/Summa Logicae/Book III-1/Chapter 31

Latin	English
Cap. 31. De mixtione necessarii et de inesse in prima figura	Chapter 31. On the mixture of necessary and assertoric (of inherence) propositions in the first figure.
Viso quomodo uniformis diversimode fit ex diversis propositionibus, de syllogismis mixtis est tractandum. Et primo de syllogismo mixto de inesse et modali, secundo de syllogismo mixto ex modalibus et modis diversis.	Having seen how a uniform proposition is formed in different ways from different propositions, we must treat of mixed syllogisms. And first of all of the mixed syllogism of essence and modal, and secondly of the mixed syllogism of different modals and modes.
Circa primum primo dicendum est de syllogismo mixto ex propositione de inesse et propositione modali de necessario. ƿ	Regarding the first, we must first speak of the mixed syllogism from a proposition about inherence and a modal proposition of the necessary . ƿ
Circa quod est primo sciendum quod ex maiore de necessario sumpta in sensu divisionis et minore de inesse semper sequitur conclusio de necessario in sensu divisionis non in sensu compositionis. Quod enim sequatur conclusio de necessario in sensu divisionis, patet, quia talis syllogismus regulatur per dici de omni vel de nullo. Unde sic arguendo ‘omnis homo de necessitate est animal; homo albus est homo; igitur homo albus de necessitate est animal’ arguitur per dici de omni, nam per istam propositionem ‘omnis homo de necessitate est animal’ non denotatur nisi quod quidquid est homo, de necessitate est animal. Cum igitur per minorem denotetur quod homo albus sit homo, sequitur per dici de omni quod homo albus de necessitate est animal.	Regarding this, it should first be known that from the major of the necessary taken in the sense of division and the minor of inherence, the conclusion of the necessary always follows in the sense of division, not in the sense of composition. For that the conclusion of the necessary follows in the sense of division is clear, because such a syllogism is regulated by to be said of all or none. Hence, in thus arguing ‘every man is of necessity an animal; a white man is a man; therefore a white man is of necessity an animal’, the argument is made by to be said of all, for by this proposition ‘every man is of necessity an animal’ nothing is denoted except that whatever is a man is of necessity an animal. Therefore, since by the minor it is denoted that a white man is a man, it follows by to be said of all that a white man is of necessity an animal.
Unde sciendum quod sicut per universalem affirmativam denotatur quod de quocumque dicitur subiectum quod de eodem dicitur praedicatum, et propter hoc sumendo minorem in qua praedicatur subiectum primae propositionis de aliquo, contingit inferre praedicatum primae propositionis de minore extremitate per dici de omni, ita, quia per propositionem de necessario in sensu divisionis et etiam aequivalentem tali denotatur quod de quocumque dicitur subiectum de eodem dicitur praedicatum cum modo necessitatis, et propter hoc sumendo minorem in qua subiectum primae praedicatur de aliquo, contingit inferre praedicatum idem vera praedicari de eadem minori extremitate per dici de omni.	Hence it should be known that just as by the universal affirmative it is denoted that of whatever the subject is said that of the same the predicate is said, and for this reason by taking the minor in which the subject of the first proposition is predicated of something, it is possible to infer the predicate of the first proposition from the lesser extreme by to be said of all, so because by the proposition of the necessary in the sense of division and also equivalent to such it is denoted that of whatever the subject is said that of the same the predicate is said with the mode of necessity, and for this reason by taking the minor in which the subject of the first is predicated of something, it is possible to infer the same true predicate to be predicated of the same lesser extreme by to be said of all.
Ex isto patet quod in tali mixtione nihil refert si minor sit de inesse simpliciter vel de inesse ut nunc. Unde iste syllogismus regulatur per dici de omni omne animal de necessitate est substantia; ‘omne album est animal; igitur omne album de necessitate est substantia’, sicut iste ‘omne animal de necessitate est substantia; omnis homo de necessitate est animal; igitur omnis homo de necessitate est substantia’. Sed si conclusio sumatur in sensu compositionis, discursus non valet, quia non sequitur ‘quaelibet persona divina de necessitate est Deus; creans est persona divina; igitur haec est necessaria: creans est Deus’, sed sequitur ‘igitur creans de necessitate est Deus’. Ex ista autem non sequitur haec ‘ista est necessaria: creans est Deus’, non plus quam ex ista ‘album potest ƿ esse nigrum’ sequitur ista ‘igitur haec est possibilis: album est nigrum’. Non enim sequitur ‘album potest esse nigrum, igitur haec est possibilis: album est nigrum’, ita non sequitur ‘creans de necessitate est Deus. igitur haec est necessaria: creans est Deus’.	From this it is clear that in such a mixture it does not matter whether the minor is of inherence simply or of inherence as of now. Hence this syllogism is regulated by to be said of all that every animal is of necessity a substance; ‘every white thing is an animal; therefore every white thing is of necessity a substance’, just as this ‘every animal is of necessity a substance; every man is of necessity an animal; therefore every man is of necessity a substance’. But if the conclusion is taken in the sense of composition, the discourse is not valid, because it does not follow ‘every divine person is of necessity God; the creator is a divine person; therefore this is necessary: ​​the creator is God’, but it follows ‘therefore the creator is of necessity God’. But from this does not follow this ‘this is necessary: ​​the creator is God’, any more than from this ‘a white thing can be black’ does this ‘therefore this is possible: a white thing is black’ follow. For it does not follow ‘a white thing can be black, therefore this is possible: a white thing is black’, so it does not follow ‘the creator is of necessity God. therefore this is necessary: ​​the creator is God’.
Ex isto sequitur quod conclusio indirecta de necessario non sequitur in tali mixtione. Unde non sequitur ‘quaelibet persona divina necessario est Deus; creans est persona divina; igitur Deus necessario est creans’. Et ratio est, quia ista ‘creans necessario est Deus’ non convertitur in istam ‘igitur Deus necessario est creans’ sed in istam ‘aliquid, quod necessario est Deus, est creans’. Et ista bene sequitur, nam sequitur 'quaelibet persona divina necessario est Deus; creans est persona divina; igitur quod est necessario Deus, est creans’, quia ista conclusio indirecta est convertibilis cum illa directa. Ex quo patet quod aliquando propositio de inesse convertitur in illam de necessario; sed tunc oportet in illa de inesse poni modum necessitatis, licet non faciat modum necessitatis, eo quod in illa non est determinatio compositionis principalis.	From this it follows that the indirect conclusion of necessity does not follow in such a mixture. Hence it does not follow that ‘every divine person is necessarily God; the Creator is a divine person; therefore God is necessarily the Creator’. And the reason is that this ‘The creator is necessarily God’ is not converted into this ‘therefore God is necessarily the Creator’ but into this ‘something that is necessarily God is the Creator’. And this follows well, for it follows that ‘every divine person is necessarily God; the Creator is a divine person; therefore what is necessarily God is the Creator’, because this indirect conclusion is convertible with the direct one. From which it is clear that sometimes the proposition of inherence is converted into that of necessity; but then it is necessary to put the mode of necessity in that of inherence, although it does not constitute the mode of necessity, because in it there is no determination of the principal composition.
Si autem maior in tali mixtione sumatur in sensu compositionis, non semper valet mixtio talis, sed oportet quod minor sumpta sub sit de inesse simpliciter non de inesse ut nunc. Si enim minor sit de inesse ut nunc, non valet mixtio.	But if the major in such a mixture is taken in the sense of composition, such a mixture is not always valid, but it is necessary that the minor taken under be of inherence simply, not of inherence as of now. For if the minor is of inherence as of now, the mixture is not valid.
Ad cuius evidentiam sciendum est quod illa minor est de inesse simpliciter in qua non potest praedicatum competere subiecto in uno tempore et negari in alio, sed semper uniformiter se habet, ita quod semper vere praedicatur vel numquam. Illa autem dicitur de inesse ut nunc in qua potest praedicatum uno tempore vere affirmari de subiecto et alio tempore vere negari. Et talis minor numquam debet sumi sub maiore de necessario. Unde non sequitur ‘omnem personam divinam esse Deum est necessarium; aliquis homo est persona divina, puta Christus; igitur aliquem hominem esse Deum est necessarium’. Nec sequitur ‘omnem hominem esse animal est necessarium; homo albus est homo; igitur hominem album esse animal est necessarium’. Sed talis mixtio tenet ‘omnem personam divinam esse Deum est necessarium; albedo est persona divina; igitur albedinem esse Deum est necessarium’. ƿ	To make this clear, it should be known that the minor is of inherence simply in which the predicate cannot belong to the subject at one time and be denied at another, but is always uniformly the case, so that it is always truly predicated or never. But that is said to be of inherence as now in which the predicate can be truly affirmed of the subject at one time and truly denied at another time. And such a minor should never be taken under the major of the necessary. Hence it does not follow that ‘it is necessary that every divine person be God; some man is a divine person, for example Christ; therefore it is necessary that some man be God’. Nor does it follow that ‘it is necessary that every man be an animal; a white man is a man; therefore it is necessary that a white man be an animal’. But such a mixture holds that ‘it is necessary that every divine person be God; whiteness is a divine person; therefore it is necessary that whiteness be God’.
Ista dicta sint quantum ad veritatem. Tamen secundum intentionem Philosophi ad hoc quod mixtio esset bona, sufficeret sumere sub aliquid per se in genere, importans rem distinctam absolute, ita quod non esset nomen connotativum nec relativum. Unde secundum intentionem Philosophi iste syllogismus est bonus ‘omne animal esse coloratum, est necessarium; omnis homo est animal; igitur omnem hominem esse coloratum est necessarium’. Ita quod, secundum eum, quandocumque sumitur sub subiecto aliquod absolutum quod non est relativum nec connotativum, semper est mixtio bona.	These things are said in terms of truth. However, according to the Philosopher's intention, for a mixture to be good, it would be sufficient to take under something per se in the genus, implying a distinct thing absolutely, so that it would not be a connotative or relative name. Hence, according to the Philosopher's intention, this syllogism is good: 'It is necessary for every animal to be colored; every man is an animal; therefore it is necessary for every man to be colored'. So that, according to him, whenever something absolute is taken under the subject that is neither relative nor connotative, the mixture is always good.
Sed istud secundum veritatem non est verum, nam ista mixtio non valet ‘omne ens esse in actu est necessarium; omnis homo est ens; igitur omnem hominem esse in actu est necessarium’, nam praemissae sunt verae et conclusio falsa. Quod enim maior sit vera, patet, nam haec est as necessaria ‘omne ens est in actu’; igitur maior est necessaria. Minor etiam est manifesto, et tamen conclusio est falsa, sive sumatur in sensu compositionis sive in sensu divisionis. Nullus enim homo necessario est. Haec etiam non est necessaria ‘omnis homo est ens’.	But this is not true according to the truth, for this mixture is not valid ‘every being is necessary to be in an act; every man is a being; therefore every man is necessary to be in an act’, for the premises are true and the conclusion false. For that the major is true is clear, for this is necessary as ‘every being is in an act’; therefore the major is necessary. The minor is also clear, and yet the conclusion is false, whether taken in the sense of composition or in the sense of division. For no man is necessary. This is also not necessary ‘every man is a being’.
Si autem maior sit de inesse et minor de necessario in sensu divisionis vel aequivalens ei, discursus non valet. Non enim sequitur ‘quaelibet persona divina est creans; Pater de necessitate est persona divina; igitur Pater de necessitate est creans, quia praemissae sunt verae et conclusio falsa. Haec enim est vera ‘omnis persona divina est creans’, certum est; et haec est vera ‘Pater de necessitate est persona divina’; et tamen haec est falsa ‘Pater de necessitate est creans’.	But if the major is of inherence and the minor of the necessary in the sense of division or equivalent to it, the discourse is not valid. For it does not follow that ‘every divine person is creative; the Father is of necessity a divine person; therefore the Father is of necessity creative, because the premises are true and the conclusion false. For this is true ‘every divine person is creative’, it is certain; and this is true ‘the Father is of necessity a divine person’; and yet this is false ‘the Father is of necessity a creative person’.
Si autem minor sumatur in sensu compositionis, non valet. Nam non sequitur ‘omnis Deus est creans; quamlibet personam divinam esse Deum est necessarium; igitur quamlibet personam divinam esse creantem est necessarium’, nam praemissae sunt verae et conclusio falsa. Et ratio est quia aliquid potest contingenter praedicari tam de superiori quam de inferiori, non obstante quod praedicatio superioris de inferiori esset necessaria. Et ita est de aliis.	But if the minor is taken in the sense of composition, it is not valid. For it does not follow that ‘every God is a creator; it is necessary for any divine person to be God; therefore it is necessary for any divine person to be a creator’, for the premises are true and the conclusion false. And the reason is that something can be contingently predicated of both the superior and the inferior, notwithstanding that the predication of the superior of the inferior would be necessary. And so it is with the others.
Notandum est quod si maior sit de inesse simpliciter, talis mixtio ƿ tenet, quia quando aliquid non potest praedicari de aliquo in uno tempore et negari in alio, sed vel semper praedicatur vel numquam, non potest subiectum de aliquo praedicari cum modo necessitatis nisi praedicatum praedicetur de eodem cum eodem modo.	It should be noted that if the major is of inherence simply, such a mixture holds, because when something cannot be predicated of something in one time and denied in another, but is either always predicated or never, the subject cannot be predicated of something with the mode of necessity unless the predicate is predicated of the same with the same mode.
Et si dicatur quod Philosophus negat unam et concedit aliam, igitur falsum est quod hic dicitur quod ita valet una sicut alia, dicendum est quod Philosophus loquitur de illa de necessario in sensu divisionis; et tunc pater evidenter quod maiore existente de necessario et minore de inesse sequitur conclusio de necessario, et hoc sive minor sit de inesse simpliciter sive de inesse ut nunc. Non sic autem valet talis discursus si maior sit de inesse, et ideo negat unam mixtionem et concedit aliam.	And if it is said that the Philosopher denies one and concedes another, then it is false that it is said here that one is as valid as the other, it must be said that the Philosopher speaks of the necessary in the sense of division; and then the father clearly follows since with the major being of the necessary and the minor of inherence, the conclusion of the necessary follows, and this whether the minor is of inherence simply or of inherence as of now. But such a discourse is not valid if the major is of inherence , and therefore he denies one mixture and concedes another.
Et si dicatur quod Philosophus dicit uniformem de necessario esse bonum in omni figura, sed dictum est prius quod uniformis de necessario in sensu divisionis in secunda figura non valet, igitur Philosophus non loquitur de illis de necessario in sensu divisionis sed in sensu compositionis tantum; igitur Philosophus loquitur de illis in sensu compositionis:	And if it is said that the Philosopher says that the uniform of the necessary is good in every figure , but it was said before that the uniform of the necessary in the sense of division is not valid in the second figure, therefore the Philosopher does not speak of those of the necessary in the sense of division but only in the sense of composition; therefore the Philosopher speaks of them in the sense of composition:
Dicendum est quod Philosophus loquitur aliquando de illis de modo in sensu compositionis et aliquando in sensu divisionis. Et ideo ubi docet uniformem ex illis de necessario, loquitur de eis in sensu compositionis et de eis aequivalentibus; quando autem docet mixtionem in prima figura, loquitur de illis in sensu divisionis et de ei aequivalente. Et hoc facit ut sciatur quomodo arguendum est ex talibus modalibus sive in uno sensu sive in alio. Unde ex dictis suis ubi loquitur de propositionibus modalibus in sensu compositionis et ex illis locis in quibus loquitur de eis in sensu divisionis potest studiosus elicere quomodo semper arguendum est ex talibus qualitercumque sumantur in quacumque materia, secundum quamcumque combinationem. ƿ	It must be said that the Philosopher sometimes speaks of them in the sense of composition and sometimes in the sense of division. And therefore where he teaches a uniform syllogism of them of necessity, he speaks of them in the sense of composition and of their equivalents; but when he teaches a mixture in the first figure, he speaks of them in the sense of division and of its equivalent. And this makes it known how one must argue from such modals whether in one sense or another. Hence from his sayings where he speaks of modal propositions in the sense of composition and from those places in which he speaks of them in the sense of division, the student can elicit how one must always argue from such things, no matter how they are taken in any matter, according to any combination.
Sciendum est igitur quod si maior sit de inesse simpliciter, mixtio tenet sive minor sumatur in sensu divisionis sive in sensu compositionis. Nec hoc negat Philosophus; sed negat quod universaliter ex maiore de inesse et minore de necessario sequitur conclusio de necessario; sed non negat quando maior est de inesse simpliciter, quia praemissae non possunt esse verae conclusione exsistente falsa. Si enim sit de inesse simpliciter et sit vera, ipsa erit necessaria; et si hoc, sequitur conclusio de necessario.	It should be known, therefore, that if the major is of inherence simply, the mixture holds whether the minor is taken in the sense of division or in the sense of composition. Nor does the Philosopher deny this; but he denies that universally from the major of inherence and the minor of necessity the conclusion of necessity follows; but he does not deny when the major is of inherence simply, because the premises cannot be true while the conclusion is false. For if it is of inherence simply and is true, it will be necessary; and if this, the conclusion of necessity follows.