Authors/Ockham/Summa Logicae/Book III-1/Chapter 32

Latin	English
Cap. 32. De mixtione necessarii et de inesse in secunda figura	Chapter 32. On the mixture of necessary and assertoric propositions in the second figure.
In secunda figura, si illa de necessario sumatur in sensu compositionis, ad hoc quod mixtio sit bona requiritur quod illa de inesse sit de inesse simpliciter. Si enim sit de inesse ut nunc, quaecumque fuerit de necessario, non sequitur conclusio de necessario. Si enim affirmativa fuerit de necessario, non sequitur, sicut non sequitur ‘omnem Deum esse in actu est necessarium; nullus homo est in actu; igitur nullum hominem esse Deum est necessarium’. Nam si nullus homo esset in actu, praemissae essent verae et conclusio falsa. Similiter non sequitur ‘omnem hominem esse susceptibilem disciplinae est necessarium; nullus homo albus est susceptibilis disciplinae; igitur nullum hominem album esse hominem est necessarium’, nam si nullus homo esset albus, praemissae essent verae et conclusio falsa, secundum opinionem Aristotelis.	In the second figure, if the premise de necessario is taken in the sense of composition, for the mixture to be good it is required that the assertoric premise be assertoric simply. For if it is assertoric as of now, whatever is de necessario, the conclusion de necessario does not follow. For if the affirmative were de necessario, it does not follow, just as this does not follow: ‘it is necessary for every God to be actual; no man is actual; therefore it is necessary for no man to be God’. For if no man were actual, the premises would be true and the conclusion false. Similarly it does not follow ‘it is necessary for every man to be susceptible to discipline; no white man is susceptible to discipline; therefore it is necessary for no white man to be a man’, for if no man were white, the premises would be true and the conclusion false, according to Aristotle’s opinion.
Si autem negativa sit de necessario, non valet syllogismus. Non enim sequitur ‘nullum hominem esse asinum est necessarium; omne ƿ album est asinus; igitur nullum album esse hominem est necessarium’. Nec sequitur ‘nullum Deum esse humanitatem est necessarium; omnis homo est humanitas; igitur nullum hominem esse Deum est necessarium’.	But if a negative premise is de necessario, the syllogism is not valid. For it does not follow that ‘it is necessary that no man be a donkey; every white thing is a donkey; therefore it is necessary that no white thing be a man’. Nor does it follow that ‘it is necessary that no God be human; every man is human; therefore it is necessary that no man be God’.
Sciendum est tamen quod in secunda figura, quando negativa est de necessario et in affirmativa accipitur sub medio aliquid inferius ad medium terminum, sive sit per se inferius sive per accidens, semper discursus est bonus, tenens per istam regulam veram ‘quandocumque aliqua universalis negativa est necessaria, quaelibet universalis negativa, in qua removetur illud praedicatum ab aliquo inferiori ad subiectum, est necessaria’. Et sequitur ex ista regula quod semper a superiori ad inferius negative et cum distributione est bona consequentia. Voco autem hic ‘inferius’ omnem terminum qui non potest esse in plus, potest tamen esse in minus.	It should be noted, however, that in the second figure, when the negative is de necessario and in the affirmative something inferior to the middle term is taken as the middle, whether it is inferior per se or accidentally, the discourse is always good, holding by this true rule ‘whenever some universal negative is necessary, any universal negative in which that predicate is removed from something inferior to the subject is necessary’. And it follows from this rule that there is always a good consequence from the superior to the inferior negatively and with distribution. But here I call ‘inferior’ every term that cannot be in more, yet can be in less.
Et propter hoc talis syllogismus est bonus ‘nullum hominem esse asinum est necessarium; omnis asinus albus est asinus; igitur nullum asinum album esse hominem est necessarium’. Et hoc quia iste terminus ‘asinus albus’ est inferior ad asinum, quamvis per accidens. Et debet talis discursus reduci in primam figuram per conversionem universalis negativae, quae semper convertitur in terminis in universalem negativam de necessario quando sumitur in sensu compositionis, sicut dictum est prius. Et ideo in prima figura in syllogismo negativo, maiore exsistente de necessario in sensu compositionis et sumpto sub aliquo inferiori ad subiectum, sive minor sit de inesse simpliciter sive de inesse ut nunc, semper est bona consequentia. Unde hic est bonus discursus ‘nullum hominem esse asinum est necessarium; homo albus est homo; igitur hominem album non esse asinum est necessarium’.	And for this reason, such a syllogism is good: ‘it is necessary that no man be a donkey; every white donkey is a donkey; therefore, it is necessary that no white donkey be a man’. And this because this term ‘white donkey’ is inferior to donkey, although accidentally. And such a discourse should be reduced to the first figure by the conversion of the universal negative, which is always converted in terms into a universal negative de necessario when taken in the sense of composition, as was said before. And therefore, in the first figure in a negative syllogism, the major existing de necessario in the sense of composition and taken under something inferior to the subject, whether the minor is assertoric simply or assertoric as of now, there is always a good consequence. Hence this is a good discourse ‘it is necessary that no man be a donkey; a white man is a man; therefore it is necessary that a white man not be a donkey’.
Sed si in secunda figura affirmativa sit de necessario in sensu compositionis et universalis negativa de inesse, non sequitur conclusio de necessario. Non enim sequitur ‘omne ens in actu esse ens est necessarium; nullus homo est ens; igitur nullum hominem esse in actu est necessarium. Nec sequitur, secundum opinionem Aristotelis ‘omnem hominem esse animal est necessarium; nullus homo albus est animal; igitur nullum hominem album esse hominem est necessarium’. Et tamen in affirmativa propositione accipitur aliquid inferius ad medium terminum, sicut de se patet. Et ratio est, quia aliquid potest cum modo necessitatis praedicari de aliquo et tamen non praedicatur de quolibet inferiori cum tali modo. Et hoc sequitur ex ista regula, quod ‘a superiori distributo ad inferius affirmative non semper est consequentia simplex’. Unde hic non est consequentia simplex secundum rei veritatem ‘omne animal est album, igitur omnis homo est albus’; et per consequens nec hic est consequentia simplex ‘omnis homo currit, igitur omnis homo albus currit’.	But if in the second figure the affirmative is de necessario in the sense of composition and the universal assertoric negative, the conclusion de necessario does not follow. For it does not follow that ‘every actual being is necessarily a being; no man is a being; therefore it is necessary for no man to be actual. Nor does it follow, according to Aristotle’s opinion, that ‘it is necessary that every man be an animal; no white man is an animal; therefore, it is necessary that no white man be a man’. And yet in an affirmative proposition something inferior is accepted for the middle term, as is self-evident. And the reason is that something can be predicated of something with the mode of necessity and yet it is not predicated of any inferior with such a mode. And this follows from the rule that ‘from the superior distributed to the inferior affirmatively there is not always a simple consequence’. Hence here there is not a simple consequence according to the truth of the matter ‘every animal is white, therefore every man is white’; and consequently, here there is not a simple consequence: ‘every man runs, therefore every white man runs’.
Ratio, quare prima consequentia non est simplex: nam si nullus homo esset in rerum natura, et omne animal aliud esset album, antecedens esset verum et consequens falsum. Et ratio quare talis consequentia non est consequentia simplex, est quia medium, per quod tenet, non est necessarium. Haec enim non est necessaria ‘omnis homo est animal’, sed contingens. Similiter, secundum opinionem Aristotelis, haec consequentia non est consequentia simplex ‘omne animal album est coloratum, igitur omnis homo albus est coloratus’. Et ideo sicut in prima figura ex affirmativa de necessario et affirmativa de inesse, quantumcumque minor extremitas sit inferior ad medium terminum, non sequitur conclusio de necessario, ita in secunda figura si affirmativa sit de necessario non sequitur conclusio de necessario.	The reason is, because the first consequence is not simple: for if there were no man in nature, and every other animal were white, the antecedent would be true and the consequent false. And the reason why such a consequence is not a simple consequence is that the middle, through which it holds, is not necessary. For this is not necessary ‘every man is an animal’, but contingent. Similarly, according to Aristotle’s opinion, this consequence is not a simple consequence ‘every white animal is colored, therefore every white man is colored’. And therefore, just as in the first figure from the affirmative de necessario and the assertoric affirmative, however much the inferior extreme is inferior to the middle term, the conclusion de necessario does not follow, so in the second figure if the affirmative is de necessario the conclusion de necessario does not follow.
Sciendum est etiam quod in quarto modo secundae figurae, sive propositio affirmativa fuerit de necessario sive negativa, non sequitur conclusio de necessario etiam quantumcumque in affirmativa praedicetur superius de inferiori. Nam non sequitur ‘aliquod ens non esse animal est necessarium; omnis homo est animal; igitur aliquem hominem non esse ens est necessarium’, nam praemissae sunt verae et conclusio falsa. Vel arguitur sic aliquod ens non esse animalitatem est necessarium; omnis humanitas est animalitas; igitur aliquam humanitatem non esse ens est necessarium. Nec etiam sequitur ‘omnem personam divinam esse Deum est necessarium; aliquod ens non est Deus; igitur aliquod ens non esse personam divinam est necessarium’. Sic igitur patet quomodo valet mixtio necessarii et de inesse in secunda figura quando illa de necessario ƿ sumitur in sensu compositionis. Et secundum istum modum debet exponi Aristoteles de ista materia in libro Priorum.	It should also be noted that in the fourth mode of the second figure, whether the affirmative proposition is de necessario or negative, the conclusion de necessario does not follow, even though in the affirmative the superior is predicated of the inferior. For it does not follow that ‘it is necessary that some being is not an animal; every man is an animal; therefore, it is necessary that some man is not a being’, for the premises are true and the conclusion false. Or it is argued thus: 'that some being is not animality is necessary; all humanity is animality; therefore it is necessary that some humanity is not a being'. Nor does it follow that ‘it is necessary that every divine person is God; some being is not God; therefore, it is necessary that some being is not a divine person’. Thus, therefore, it is clear how the mixture of the necessary and the assertoric is valid in the second figure when that de necessario is taken in the sense of composition. And according to this method, Aristotle should be expounded on this matter in the book 'Prior Analytics'.
Si autem illa de necessario sumatur in sensu divisionis, non valet mixtio, sive affirmativa sive negativa fuerit de necessario. Quod enim non valeat si affirmativa fuerit de necessario, patet, nam non sequitur ‘omnis homo de necessitate est Deus; nulla humanitas est Deus; igitur omnis humanitas de necessitate non est homo’, quia si nullus homo esset nisi Christus, praemissae essent verae et conclusio falsa. Haec enim esset vera ‘omnis homo de necessitate est Deus’ nam praedicatum necessario inert cuilibet pro quo subiectum supponit, illo casu posito. Nam illo casu posito ‘homo’ non supponeret nisi pro Filio Dei, quia tantum Filius Dei esset homo, et manifestum est quod Filius Dei de necessitate est Deus. Igitur tunc esset haec vera ‘omnis homo de necessitate est Deus’, quia quaelibet singularis esset vera. Similiter minor esset vera, immo esset necessaria, nam haec est necessaria ‘nulla humanitas est Deus’, quia quamvis de facto homo sit Deus, tamen haec est falsa ‘humanitas est Deus’. Immo, nec aliqua humanitas potest esse Deus, sicut nec humanitas potest esse immortalis vel aeterna. Quod autem conclusio esset falsa, isto casu posito, patet, nam humanitas Christi, quamvis non sit homo, potest tamen esse homo; quia si deponeretur a Filio Dei, statim eo ipso esset homo.	But if that (premise) de necessario is taken in the sense of division, the mixture is not valid, whether affirmative or negative de necessario. For that it is not valid if the affirmative is de necessario is clear, for it does not follow that ‘every man is of necessity God; no humanity is God; therefore, all humanity is of necessity not man’, because if there were no man except Christ, the premises would be true and the conclusion false. For this would be true ‘every man is of necessity God’, for the predicate is necessarily inert to anyone for whom the subject supposits, in that case. For in that case ‘man’ would not supposit except for the Son of God, because only the Son of God would be man, and it is clear that the Son of God is of necessity God. Therefore, then this would be true ‘every man is of necessity God’, because any singular would be true. Similarly, the inferior would be true, indeed it would be necessary, for this is necessary ‘no humanity is God’, because although man is de facto God, nevertheless this is false ‘humanity is God’. Indeed, neither can any humanity be God, just as neither can humanity be immortal or eternal. But that the conclusion would be false, in this case, is clear, for the humanity of Christ, although not man, can nevertheless be man, because if it were taken from the Son of God, it would immediately by that very fact be man.
Similiter, iste discursus non valet ‘omnis persona de necessitate est Deus; nulla humanitas seu natura intellectualis creata est Deus; igitur omnis humanitas seu omnis natura intellectualis creata de necessitate non est persona’. Si enim nullus homo esset nisi Christus, nec aliquis angelus, haec esset vera ‘omnis persona de necessitate est Deus’, nam quaelibet singularis est vera. Et minor esset vera, certum est, et tamen conclusio est falsa, nam adhuc aliqua natura intellectualis, scilicet illa assumpta a Verbo, posset esse persona, quia si deponeretur a Verbo, esset persona. Similiter, isto casu posito istae praemissae essent verae ‘omnis persona de necessitate est non assumpta a Verbo; nulla natura intellectualis creata est non assumpta a Verbo’ et tamen haec conclusio esset falsa ƿ ‘omnis nature intellectualis creata de necessitate non est persona’, et per consequens talis discursus non valet.	Similarly, this argument is not valid: ‘Every person is of necessity God; no humanity or created intellectual nature is God; therefore, every humanity or created intellectual nature is not of necessity a person.’ For if there were no man except Christ, nor any angel, this would be true: ‘Every person is of necessity God’, for every singular is true. And the lesser would be true, it is certain, and yet the conclusion is false, for still some intellectual nature, namely that assumed by the Word, could be a person, because if it were removed from the Word, it would be a person. Similarly, in this case, these premises would be true: ‘Every person is of necessity not assumed by the Word; no created intellectual nature is not assumed by the Word’, and yet this conclusion would be false: ‘Every created intellectual nature is of necessity not a person’, and consequently such an argument is not valid.
Similiter, secundum opmionem Aristotelis, talis discursus non valet ‘omne album de necessitate est cygnus; nullus asinus est cygnus; igitur omnis asinus de necessitate non est albus’, quia si nihil sit album nisi cygnus, praemissae sunt verae et conclusio falsa. Haec enim esset vera ‘omne album de necessitate est cygnus’, quia quaelibet singularis esset vera, igitur ipsa est vera. Et certum est quod minor est vera, et manifestum est quod conclusio est falsa. Igitur talis discursus non valet. Verumtamen quod dictum est de isto exemplo, non est dictum nisi gratia exempli.	Similarly, according to Aristotle's opinion, such a discourse is not valid 'every white thing is necessarily a swan; no donkey is a swan; therefore every donkey is necessarily not white', because if nothing is white except a swan, the premises are true and the conclusion false. For this would be true 'every white thing is necessarily a swan', because any singular would be true, therefore it is true. And it is certain that the minor is true, and it is clear that the conclusion is false. Therefore such a discourse is not valid. However, what was said about this example was not said except for the sake of the example.
Si autem negativa sit de necessario, adhuc discursus non valet, quia non sequitur ‘omne album de necessitate non est asinus; omne rudibile est asinus; igitur rudibile de necessitate non est album’. Nam si nullus asinus sit albus, praemissae sunt verae et conclusio falsa. Tunc enim maior est vera, ista scilicet ‘omne album de necessitate non est asinus’, nam quaelibet singularis est vera. Quocumque enim albo demonstrate haec est vera ‘hoc de necessitate non est asinus’ quia ex quo, per casum, nullum album est asinus, omne album est aliud ab asino et per consequens non potest esse asinus, et ita de necessitate non est asinus. Et ratio veritatis talium propositionum est ista: quia, sicut frequenter est tactum, per istam ‘omne album de necessitate non est asinus’ non denotatur quod illa propositio sit necessaria in qua praedicatum removetur ab illo subiecto, puta ab hoc subiecto ‘album’, sicut non denotatur quod haec sit necessaria ‘nullum album est asinus’; sicut nec per istam ‘album potest esse nigrum’ denotatur quod haec sit possibilis ‘album est nigrum’. Sed per istam ‘omne album de necessitate non est asinus’ denotatur quod quaelibet propositio in qua hoc praedicatum ‘asinus’ per verbum de praesenti removetur a pronomine demonstrante quodcumque quod est album, sit necessaria. Ita quod si tantum sint tria alba, pro tunc per istam ‘omne album de necessitate non est asinus’ non denotatur ƿ nisi quod quaelibet istarum trium propositionum sit necessaria ‘hoc non est asinus’ et ‘illud non est asinus’ et ‘illud non est asinus’, et si quaelibet istarum trium propositionum sit necessaria, - quod erit verum si tantum tres homines sint albi -, tunc illa propositio de necessario erit vera, quia quaelibet singularis est vera. Non tamen erit illa de necessario necessaria, quia poterit habere multas singulares falsas, et per consequent erit falsa. Et ita talis de necessario aliquando est vera, quando scilicet quaelibet singularis est vera, et aliquando est falsa, quando scilicet aliqui singularis est falsa. Et hoc est summe necessarium ad sciendum quando propositio de modo in sensu divisionis quaecumque vel aequivalens ei, vel quaecumque propositio habens adverbialem determinationem determinantem compositionem, est vera et quando est falsa.	But if the negative (premise) is de necessario, the discourse is still not valid, because it does not follow that ‘every white thing is necessarily not a donkey; every tamable thing is a donkey; therefore, a tamable thing is necessarily not white’. For if no donkey is white, the premises are true and the conclusion false. For then the major is true, namely ‘every white thing is necessarily not a donkey’, for any singular is true. For whatever white thing you demonstrate, ‘this is necessarily not a donkey’ is true, because since, by chance, no white thing is a donkey, every white thing is different from a donkey and consequently cannot be a donkey, and so it is necessarily not a donkey. And the reason for the truth of such propositions is this: because, as has been frequently touched upon, by this ‘every white thing is necessarily not a donkey’ it is not denoted that that proposition is necessary in which the predicate is removed from that subject, for example from this subject ‘white’, just as it is not denoted that this ‘no white thing is a donkey’ is necessary; just as neither by this ‘a white thing can be black’ does it denote that this is possible: ‘a white thing is black’. But by this ‘every white man is necessarily not a donkey’ it is denoted that any proposition in which this predicate ‘donkey’ is removed by a verb at present from the pronoun denoting whatever is white, is necessary. So that if there are only three white men, then by this ‘every white man is necessarily not a donkey’ it is not denoted except that any one of these three propositions is necessary ‘this is not a donkey’ and ‘that is not a donkey’ and ‘that is not a donkey’, and if any one of these three propositions is necessary, - which will be true if only three men are white -, then that proposition will be true de necessario, because any singular is true. However, that proposition will not be necessary de necessario, because it could have many false singulars, and consequently it will be false. And so, such a proposition is sometimes true de necessario, namely when any singular is true, and sometimes false, namely when some singular is false. And this is highly necessary for knowing when a proposition of a mode in the sense of division, or any proposition equivalent to it, or any proposition having an adverbial determination determining composition, is true and when it is false.
Sic igitur patet quod quamvis negativa sit de necessario, non sequitur conclusio de necessario, sicut non sequitur ‘omne agens de necessitate non patitur; omnis creatura patitur; ergo omnis creatura de necessitate non est agens’. Nec sequitur ‘omnis homo de necessitate non est Deus; quaelibet persona divina est Deus; igitur quaelibet persona divina de necessitate non est homo’, nam ante incarnationem fuerunt praemissae verae et conclusio falsa.	Thus it is clear that although the negative is de necessario, the conclusion de necessario does not follow, just as it does not follow ‘every agent necessarily does not suffer; every creature suffers; therefore, every creature is not necessarily an agent’. Nor does it follow ‘every man necessarily is not God; every divine person is God; therefore, every divine person is necessarily not a man’, for before the incarnation the premises were true and the conclusion false.
Sic igitur patet quod si illa de necessario sumatur in sensu divisionis vel aliqua aequivalens ei, quod discursus mixtus non valet in secunda figura. Nec potest reduci in primam figuram per conversionem, quia dictum est prius quod talis de necessario non est convertibilis in illam de necessario sed tantum in illam de inesse; ex duabus autem de inesse non sequitur conclusio de necessario in prima figura. Similiter dictum est quod talis negativa universalis non convertitur in universalem sed in particularem de inesse, maior autem non potest esse particularis in prima figura. Similiter minor in prima figura non potest esse particularis de necessario, sicut dictum est. ƿ	Thus, it is clear that if a premise de necessario is taken in the sense of division or something equivalent to it, that the mixed discourse is not valid in the second figure. Nor can it be reduced to the first figure by conversion, because it was said before that such a proposition de necessario is not convertible into that de necessario but only into the assertoric; but from two assertoric propositions, the conclusion de necessario in the first figure does not follow. Similarly, it was said that such a universal negative is not convertible into a universal but into a particular assertoric, but the major cannot be particular in the first figure. Similarly, the minor in the first figure cannot be particular de necessario, as was said .