Authors/Ockham/Summa Logicae/Book III-1/Chapter 32
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| Cap. 32. De mixtione necessarii et de inesse in secunda figura |
Chapter 32. On the mixture of necessary and assertoric (of inherence) propositions in the second figure. |
| In secunda figura[1], 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 [2], if the syllogism of the necessary is taken in the sense of composition, for the mixture to be good it is required that the proposition of inherence be of inherence simply. For if it is of inherence as of now, whatever is of the necessary, the conclusion of the necessary does not follow. For if the affirmative were of the necessary, it does not follow, just as this does not follow: ‘it is necessary for every God to be in action; no man is in action; therefore it is necessary for no man to be God’. For if no man were in action, 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 the negative is of the necessary, 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 humanity; every man is humanity; 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 of necessity and in the affirmative something lower than the middle term is taken as the middle, whether it is lower 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 lower to the subject is necessary’. And it follows from this rule that there is always a good consequence from the higher to the lower negatively and with distribution. But here I call ‘lower’ 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[3]. 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 ass, 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 of the necessary when taken in the sense of composition, as was said before [4]. And therefore in the first figure in a negative syllogism, the major existing of the necessary in the sense of composition and taken under something inferior to the subject, whether the minor is of inherence simply or of inherence as of now, there is always a good consequence. Hence this is a good discourse ‘it is necessary that no man be an ass; a white man is a man; therefore it is necessary that a white man not be an ass’. |
| 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 of the necessary in the sense of composition and the universal negative of inherence, the conclusion of the necessary does not follow. For it does not follow that ‘every being in action is necessary to be a being; no man is a being; therefore it is necessary for no man to be in action. 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 higher distributed to the lower 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 of necessity and the affirmative of inherence, however much the lesser extreme is inferior to the middle term, the conclusion of necessity does not follow, so in the second figure if the affirmative is of necessity the conclusion of necessity 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 of the necessary or negative, the conclusion of the necessary does not follow, even though in the affirmative the higher is predicated of the lower. 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 of inherence is valid in the second figure when that of the necessary 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 of necessity is taken in the sense of division, the mixture is not valid, whether affirmative or negative of necessity. For that it is not valid if the affirmative is if necessity 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 lesser 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[5], 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. | |
| 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. | |
| 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[6] 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[7] 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[8]. ƿ |
