Authors/Ockham/Summa Logicae/Book III-1/Chapter 47

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Latin English
Cap. 47. De mixtione necessarii et contingentis in prima figura Chapter 47. On the mixture of necessary and contingent propositions in the first figure.
Post praecedentem mixtionem dicendum est de mixtione necessarii et contingentis[1], et primo in prima figura; et primo quando utraque sumitur in sensu compositionis vel aequivalens. After the preceding mixture, we must speak of the mixture of the necessary and the contingent[2], and first in the first figure; and first when both are taken in the sense of composition or equivalent.
Et est primo sciendum quod si maior fuerit de necessario affirmativa et minor de contingenti, non sequitur conclusio de contingenti. Sicut non sequitur, secundum opinionem Aristotelis, 'omne album esse coloratum est necessarium; omnem hominem esse album est contingens; igitur omnem hominem esse coloratum est contingens', quia secundum eum praemissae sunt verae et conclusio falsa. Sed secundum rei veritatem difficile est invenire instantiam ubi praemissae tales sunt ƿ verae et conclusio falsa. Similiter, si maior fuerit negativa de necessario. non sequitur conclusio de contingenti, quia non sequitur 'nullum hominem esse asinum est necessarium; omne ridens esse hominem est contingens; igitur nullum ridens esse asinum est contingens’, quia praemissae sunt verae et conclusio falsa. Tamen ex praemissis taliter dispositis sequitur conclusio de possibili. Et similiter si maior fuerit de necessario affirmativa, sequitur conclusio de possibili. And it must first be known that if the major is affirmative of necessity and the minor of contingency, the conclusion of contingency does not follow. Just as it does not follow, according to Aristotle's opinion, 'every white thing being colored is necessary; every man being white is contingent; therefore, every man being colored is contingent', because according to him the premises are true and the conclusion false. But in truth it is difficult to find an instance where such premises are true and the conclusion false. Similarly, if the major is negative of necessity, the conclusion of contingency does not follow, because it does not follow 'no man being a donkey is necessary; everything that can laugh being a man is contingent; therefore, nothing that can laugh being a donkey is contingent', because the premises are true and the conclusion false. Nevertheless, from the premises thus arranged, the conclusion of possibility follows. And similarly, if the major is affirmative of necessity, the conclusion of possibility follows.
Pro quo intelligendum est quod quandocumque mixtio necessarii et possibilis est bona in quacumque figura, semper mixtio necessarii et contingentis est bona respectu conclusionis de possibili, per istas duas regulas ‘quidquid sequitur ad consequens, sequitur ad antecedens’, 'illa de contingent semper infert illam de possibili’. For which it must be understood that whenever the mixture of the necessary and the possible is good in any figure, the mixture of the necessary and the contingent is always good with respect to the conclusion of possibility, by these two rules ‘whatever follows to the consequent, follows to the antecedent’, ‘a proposition of contingency always infers a proposition of possibility’.
Et est sciendum quod quandocumque maior est de necessario negativa et minor de contingenti, si in minore sumatur sub inferius ad subiectum maioris, semper sequitur conclusio non solum de possibili sed etiam de inesse. Et per istam regulam debent glossari multa dicta Aristotelis[3], quae videntur esse contra aliqua dicta et aliqua dicenda. Sed si maior fuerit affirmativa, non sequitur conclusio de inesse, quamvis sumatur sub inferius. And it should be known that whenever the major is negative of necessity and the minor is contingent, if in the minor it is taken inferior to the subject of the major, the conclusion always follows not only of possibility but also of inherence. And by this rule many statements of Aristotle should be glossed[4], which seem to be contrary to some statements and some things to be said. But if the major is affirmative, the conclusion of inherence does not follow, although it is taken under the inferior.
Si autem maior fuerit de contingenti et minor de necessario, non sequitur conclusio de contingenti, sicut non sequitur 'omne album esse dulce est contingens; omne lac esse album est necessarium; igitur omne lac esse dulce est contingens'. Similiter non sequitur ‘omne producens esse Deum est contingens; Patrem esse producentem est necessarium; igitur Patrem esse Deum est contingens’. Similiter non. sequitur 'nullum ens in actu esse humanitatem est contingens; omnem Deum esse ens in actu est necessarium; igitur nullum Deum esse humanitatem est contingens', nam praemissae sunt verae et conclusio falsa. Tamen conclusio de possibili bene sequitur; sed non sequitur conclusio de inesse, quamvis inferius sumatur sub medio termino in minore. But if the major is contingent and the minor is necessary, the conclusion of contingency does not follow, just as it does not follow that 'for every white thing to be sweet is contingent; for milk to be white is necessary; therefore, for every milk to be sweet is contingent'. Similarly, it does not follow that 'For every producing thing to be God is contingent; for the Father to be producing is necessary; therefore, for the Father to be God is contingent'. Similarly, it does not follow that 'for no being to be actual is contingent; for every God to be an actual being is necessary; therefore, for no God to be human is contingent', for the premises are true and the conclusion false. Nevertheless, the conclusion of possibility follows well; but the conclusion of inherence does not follow, even if it is taken under the middle term in the minor.
Secundo videndum est de praedicta mixtione quando illa de necesƿsario sumitur in sensu compositioiiis et illa de contingenti in sensu divisionis. Secondly, we must see about the aforementioned mixture when a premise of necessity is taken in the sense of composition and a premise of contingency in the sense of division.
Et est primo sciendum quod si illa de necessario sit maior et illa de contingenti minor, in syllogismo affirmativo non sequitur conclusio de contingenti. Sicut non sequitur ‘omnem materiam informatam forma ignis esse informatam forma est necessarium; hanc materiam contingit esse informatam forma ignis; igitur hanc materiam contingit esse informatam forma', quia praemissae sunt verae et conclusio falsa, secundum opinionem Aristotelis. Similiter non sequitur 'nullum hominem esse asinum est necessarium; contingit ridentem esse hominem; igitur contingit ridentem non esse asinum'. Et ita non valet talis mixtio in syllogismo negativo. And it must first be known that if the premise of necessity is major and the premise of contingency is minor, in an affirmative syllogism the conclusion of contingency does not follow. Just as it does not follow that ‘it is necessary that all matter informed by the form of fire be informed by the form; it is contingent that this matter is informed by the form of fire, therefore, it is contingent that this material is informed by form’, because the premises are true and the conclusion false, according to Aristotle’s opinion. Similarly, it does not follow that ‘it is necessary that no man be a donkey; it is contingent that a laughing man be a man; therefore, it is contingent that a laughing man not be a donkey’. And so, such a mixture is not valid in a negative syllogism.
Secundo sciendum quod si maior fuerit de contingenti et minor de necessario, si subiectum maioris sumatur praecise pro his quae sunt, vel tam pro his quae sunt quam pro his quae contingunt, semper valet mixtio et est syllogismus regulatus per dici de omni vel de nullo respectu conclusionis de contingenti, quia dictum est prius[5] quod talis mixtio de inesse et contingentis valet; sed illa de inesse est consequens ad illam de necessario; igitur etc. Sed si subiectum maioris sumatur praecise pro his quae contingunt, non valet mixtio, sicut non sequitur ‘omne quod contingit esse ens actu contingit creari; omnem Deum esse ens actu est necessarium; igitur omnem Deum contingit creari'. Ideo etiam non sequitur ibi conclusio de possibili, quia praemissae sunt verae et conclusio falsa. Secondly, it should be known that if the major is taken precisely for things that are, or both for things that are and for things that are contingent, the mixture is always valid and is a syllogism governed by 'to be said of all or of none' with respect to the conclusion of contingency, because it was said before[6] that such a mixture is valid for inherence and contingency; but that of inherence is consequent to that of necessity; therefore etc. But if the subject of the major is taken precisely for things that are contingent, the mixture is not valid, just as it does not follow that ‘everything that happens to be a being actually happens to be created; for every God to be an actual being is necessary; therefore every God happens to be created’. Therefore, a conclusion about the possible does not follow there, because the premises are true and the conclusion false.
Tertio videndum est de ista mixtione quando illa de contingenti sumitur in sensu compositionis et illa de necessario in sensu divisionis. Thirdly, we must see about this mixture when it is taken of contingency in the sense of composition and of necessity in the sense of division.
Et est primo sciendum quod si illa de necessario fuerit maior et illa de contingenti minor, non sequitur conclusio de contingenti. Sicut non sequitur 'omnis homo de necessitate est Deus; omnem personam divinam esse hominem est contingens; igitur omnem personam divinam esse Deum est contingens', quia praemissae possunt esse verae concluƿsione exsistente falsa. Per eosdem terminos patet quod non valet syllogismus negativus, tamen conclusio de possibili sequitur. And it must first be known that if a proposition of necessity is major and a proposition of contingency is minor, the conclusion of contingency does not follow. Just as it does not follow that 'every man is God of necessity; that every divine person is man is contingent; therefore that every divine person is God is contingent', because the premises can be true while the conclusion is false. By the same terms it is clear that the negative syllogism is not valid, yet a conclusion of possibility follows.
Secundo sciendum quod si maior fuerit de contingenti et minor de necessario, non valet mixtio, quia non sequitur ‘omne suppositum esse Deum est contingens; quaelibet persona divina de necessitate est suppositum; igitur quamlibet personam divinam esse Deum est contingens’. Nec sequitur 'nullum ens actu esse humanitatem est contingens; quaelibet persona divina de necessitate est ens actu; igitur nullam personam divinam esse humanitatem est contingens’ Secondly, it should be known that if the major is contingent and the minor is necessary, the mixture is not valid, because it does not follow that ‘for every supposited thing to be God is contingent; every divine person is necessarily a supposited thing; therefore that every divine person is God is contingent’. Nor does it follow that ‘no actual being is contingent to be human; every divine person is necessarily an actual being; therefore, no divine person is contingent to be human’.
Quarto videndum est de ista mixtione quando utraque sumitur in sensu divisionis. Fourthly, we must see about this mixture when both are taken in the sense of division.
Et est primo sciendum quod si maior fuerit de necessario et minor de contingenti, non valet mixtio. Non enim sequitur 'omnis homo de necessitate est Deus; omnem humanitatem contingit esse hominem’, igitur omnem humanitatem contingit esse Deum’, nam supposito quod nullus homo esset nisi Christus, praemissae essent verae et conclusio falsa. Similiter, secundum principia Aristotelis, non sequitur ‘omne corpus caeleste luminosum de necessitate est substantia; contingit lunam esse corpus caeleste luminosum; igitur contingit lunam esse substantiam'. Per eosdem terminos patet quod syllogismus negativus non valet, tamen conclusio de possibili sequitur. And it must first be known that if the major is of necessity and the minor of contingency, the mixture is not valid. For it does not follow that 'every man is of necessity God; every human is contingently a man; therefore, every human is contingently God', for supposing that there was no man except Christ, the premises would be true and the conclusion false. Similarly, according to Aristotle's principles, it does not follow that 'every luminous heavenly body is of necessity a substance; it is contingent that the moon is a luminous heavenly body; therefore it is contingent that the moon is a substance'. By the same terms it is clear that the negative syllogism is not valid, yet the conclusion follows of possibility.
Si autem maior fuerit de contingenti et minor de necessario, semper sequitur conclusio de contingenti, sumpto subiecto conclusionis praecise pro his quae sunt, vel tam pro his quae sunt quam pro his quae contingunt, quia semper talis syllogismus rcgulatur per dici de omni vel de nullo. Si autem subiectum maioris sumatur praecise pro his quae contingunt, non valet; sicut non sequitur 'contingit omne ens creari, hoc est; omne, quod contingit esse ens, contingit creari; Deus de necessitate est ens; igitur contingit Deum creari’. ƿ But if the major is of contingency and the minor of necessity, the conclusion always follows of contingency, taking the subject of the conclusion precisely for those things that are, or both for those things that are and for those things that are contingent, because such a syllogism is always governed by 'to say of all or of none'. But if the subject of the major is taken precisely for those things that are contingent, it is not valid; just as it does not follow that 'it is contingent

that every being is created, that is; everything that is contingent to be a being is contingent to be created; God is a being of necessity; therefore it is contingent that God be created'.

Notes

  1. ↑ Cf. Aristot., Anal. Prior, I, c. 16 (35b 23 - 36b 25).
  2. ↑ Cf. Aristotle, Anal. Prior, I, c. 16 (35b 23 - 36b 25).
  3. ↑ Cf. Aristot., loco cit.
  4. ↑ Cf. Aristotle, in place of cit.
  5. ↑ Supra, cap. 37, lin. 24-35.
  6. ↑ Supra, cap. 37, lin. 24-35.
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