Works › Prior Analytics, Books I–II
Volume 1 · pp. 594–595
Chapter XXIV. On the particular syllogisms of the mixing of the necessary and the contingent in the second figure.
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CAPUT XXIV. De particularibus syllogismis mixtionis necessarii et contingentis in secunda figura.
His autem habitis, ponendae sunt utiles et inutiles conjugationes istius mixtionis in particularibus secundae figurae syllogismis. Dicamus igitur primo, quod similiter se habet in particularibus syllogismis sicut in universalibus: quando enim in particulari syllogismo privativa fuerit et universalis et de necessario, et particularis de contingenti affirmativa, semper erit syllogismus, sicut in tertio modo secundae figurae: et sequetur duplex conclusio, scilicet et ejus quod est contingere non inesse, et ejus quod est non inesse. In illis enim conjugationibus eadem est demonstratio quae prius, scilicet per conversionem majoris simpliciter.
Quando autem universalis affirmativa fuerit de necessario, sicut in quarto secundae, nunquam erit hujus mixtionis utilis conjugatio ad syllogismum, quae sit vel de contingenti vel de inesse concludens. Inutilitas autem hujus conjugationis eodem modo probationis ostendetur, et per eosdem terminos instantiarum, quo ostensa fuit inutilitas ejusdem conjugationis in syllogismis universalibus, in quibus universalis affirmativa est de necessario et universalis negativa de contingenti.
Nec adhuc erit utilis conjugatio, quando utraeque propositiones praemissae et universalis et particularis fuerint affirmativae: inutilitas enim etiam hujus conjugationis demonstratur per eosdem terminos instantiarum, qui in universalibus syllogismis in similibus conjugationibus adducti sunt. Istae igitur sunt inutiles conjugationes simpliciter.
Est autem alia adhuc conjugatio ex opposito istius sumpta, quando scilicet utraeque propositiones fuerint privativae: universalis autem propositio sit de necessario, et negativa quae significet non inesse simpliciter et de necessitate: tunc enim per easdem propositiones quae sumptae et positae sunt non fit syllogismus, quia ex ambabus negativis nihil sequitur in aliqua figura. Sed quando convertitur propositio minor particularis quae est de contingenti secundum modum contingentis ad oppositam qualitatem, hoc est, in affirmativam, tunc fit syllogismus, sicut in tertio modo istius mixtionis dictum est, quod fit syllogismus in secunda figura.
Si autem utraeque praemissae vel indefinitae vel particulares ponantur, et una de necessario, et altera de contingenti, non potest esse syllogismus sicut et in nulla alia figura vel mixtione.
Epilogando ergo dicimus, quod manifestum ex praedictis est, quoniam quando ponitur in secunda figura in hac mixtione universalis privativa de necessario, et altera de contingenti, semper fit syllogismus et in universalibus et in particularibus ad duplicem conclusionem: non enim solum sequitur conclusio ejus quod est contingere non inesse, sed etiam sequitur conclusio ejus quod est non inesse simpliciter. Si autem affirmativa in hac mixtione ponatur de necessario, et altera de contingenti negativa, nunquam fit syllogismus neque in universalibus, neque in particularibus syllogismis.
Palam etiam est, quod tam in necessariis propositionibus, hoc est, quando propositiones sumuntur de necessario, et in his quae insunt, hoc est, quando propositiones sumuntur de inesse simpliciter, eodem modo fit et non fit syllogismus: quia propositiones de necessario similiter convertuntur cum illis de inesse, et similiter ordinantur ad mixtionem contingentis.
Palam est etiam quod omnes istius mixtionis in secunda figura syllogismi sunt imperfecti, et palam est, quia per praedictas figuras per reductionem ad primam figuram perficiuntur: quamvis enim in probatione syllogismi aliquando syllogizetur in secunda, et aliquando in tertia, tamen finalis perfectio est in reductione ad primam figuram.
CHAPTER XXIV. On the particular syllogisms of the mixing of the necessary and the contingent in the second figure.
But after these things have been had, the useful and useless conjugations of this mixing in the particular syllogisms of the second figure must be posited. Therefore let us say first that in particular syllogisms it has itself similarly as in universal ones. For when, in a particular syllogism, the privative premise is both universal and of necessity, and the particular premise about the contingent is affirmative, there will always be a syllogism, as in the third mode of the second figure; and a double conclusion will follow, namely both of that which is contingently not to inhere and of that which is not to inhere. For in those conjugations the demonstration is the same as before, namely through the conversion of the major simply.
But when the universal affirmative is of necessity, as in the fourth mode of the second figure, there will never be a useful conjugation of this mixing for a syllogism that concludes either about the contingent or about inherence. But the uselessness of this conjugation will be shown by the same mode of proof, and through the same terms of instances, by which the uselessness of the same conjugation was shown in universal syllogisms, in which the universal affirmative is of necessity and the universal negative about the contingent.
Nor again will there be a useful conjugation when both premise-propositions, the universal and the particular, are affirmative; for the uselessness of this conjugation too is demonstrated through the same terms of instances which were adduced in universal syllogisms in similar conjugations. These, therefore, are the useless conjugations simply.
But there is still another conjugation taken from the opposite of this, when namely both propositions are privative: let the universal proposition be of necessity, and let the negative signify not-inhering simply and of necessity. For then, through the same propositions which have been taken and posited, no syllogism is made, because from both negatives nothing follows in any figure. But when the minor particular proposition, which is about the contingent, is converted according to the mode of the contingent to the opposite quality, that is, into an affirmative, then a syllogism is made, just as it was said in the third mode of this mixing that a syllogism is made in the second figure.
But if both premises are posited either indefinite or particular, and one of necessity and the other about the contingent, there cannot be a syllogism, as neither in any other figure or mixing.
Therefore by way of epilogue we say that it is manifest from the aforesaid things that, when in the second figure in this mixing a universal privative of necessity is posited, and the other proposition is about the contingent, a syllogism is always made both in universals and in particulars to a double conclusion; for not only does a conclusion of that which is contingently not to inhere follow, but also a conclusion of that which is not to inhere simply follows. But if the affirmative in this mixing is posited as of necessity, and the other proposition is a negative about the contingent, a syllogism is never made, neither in universals nor in particular syllogisms.
It is also plain that both in necessary propositions, that is, when propositions are taken of necessity, and in those which inhere, that is, when propositions are taken of inherence simply, a syllogism is made and is not made in the same way, because propositions of necessity are converted similarly with those of inherence, and are similarly ordered to the mixing of the contingent.
It is also plain that all syllogisms of this mixing in the second figure are imperfect, and it is plain because they are perfected through the aforesaid figures by reduction to the first figure. For although in the proof of the syllogism one sometimes syllogizes in the second figure and sometimes in the third, nevertheless the final perfection is in reduction to the first figure.
Hic tamen dubitatio est de quarto modo secundae figurae, in quo secundum ea quae dicta sunt non videtur hujus mixtionis esse utilis conjugatio. Quartus enim habet majorem universalem affirmativam, et minorem particularem negativam, et non potest esse utilis conjugatio universali affirmativa existente de necessario, et particulari existente de contingenti, nec e converso, sicut per antedicta manifestum est. Contra hoc autem objicitur, sit quod major sit de contingenti et minor de necessario, sic, contingit omne B esse A, necesse est quoddam C non esse A, ergo quoddam C non est B: ex opposito enim conclusionis et majori sequitur oppositum minoris in prima figura per mixtionem contingentis et inesse, sic, contingit omne B esse A, omne C est B, ergo contingit omne C esse A. Ad hoc autem dici potest, quod syllogismus mixtus nullus est: quia oppositum conclusionis de inesse quod assumit, potest esse de inesse ut nunc: in mixtione autem contingentis et inesse debet esse de inesse simpliciter.
Sed tunc oritur objectio de contingenti pro possibili: contingens enim pro possibili videtur sequi sic, quod ex opposito conclusionis et majoris videtur sequi oppositum minoris in prima figura per mixtionem contingentis et necessarii, sic, contingit omne B esse A, necesse est omne C esse B, haec enim aequipollet opposito conclusionis: ergo contingit omne C esse A, de contingenti ad utrumlibet: et est modus perfectus, et major est de contingenti tali. Adhuc autem ostenditur idem per expositionem: quia si quoddam C de necessitate non est A, sit illud F et tunc erit verum dicere, quod de necessitate nullum F est A: syllogizetur ergo sic, contingit omne B esse A, de necessitate nullum F est A: ergo contingit nullum F esse B: hoc enim sequi videtur in secundo secundae per utilem istius mixtionis conjugationem: sed si contingit nullum F esse B, et F est aliquod C, ergo contingit aliquod C non esse B: et est conclusio negativa de contingenti pro possibili: et ex hoc videtur, quod regula illa falsa sit quae dicit, quod si universalis negativa non fuerit de necessario, est inutilis conjugatio. Et dicendum videtur, quod ista conclusio sequitur. Sed tamen non reputantur utiles conjugationes, nisi quae descendunt a primo modo secundae figurae, in quo est major universalis negativa: et non reputantur utiles illae particulares conjugationes quae descendunt a secundo secundae, ubi est major universalis affirmativa, et minor est universalis negativa, a qua descendit quartus secundae figurae. Et hujus causa est secundum quosdam, quod hic non debent reputari utiles conjugationes quae per conversionem non possunt reduci in primam figuram, quia debitam non habent originem: non possunt autem reduci in primam figuram per conversionem, nisi quae habent majorem universalem negativam de necessario: et ideo illae solae reputantur utiles.1
Si autem quaeritur de sufficientia harum conjugationum, dicendum quod a principio supponendum, quod in hac mixtione major debet esse universalis negativa: et tunc patet quod tantum sex sunt conjugationes utiles hic in hac mixtione, quatuor scilicet universales, et duae particulares, et sex inutiles, sicut in mixtione praecedenti quae fuit de contingenti et inesse.
Yet here there is a doubt about the fourth mode of the second figure, in which, according to the things that have been said, there does not seem to be a useful conjugation of this mixing. For the fourth has a universal affirmative major and a particular negative minor, and the conjugation cannot be useful when the universal affirmative is of necessity and the particular is about the contingent, nor conversely, as is manifest through the things said before. But against this it is objected: let the major be about the contingent and the minor about the necessary, thus: every B contingently is A; it is necessary that some C not be A; therefore some C is not B. For from the opposite of the conclusion and the major the opposite of the minor follows in the first figure through the mixing of the contingent and inherence, thus: every B contingently is A; every C is B; therefore every C contingently is A. But to this it can be said that there is no mixed syllogism, because the opposite of the conclusion of inherence which it assumes can be of inherence as now, whereas in the mixing of the contingent and inherence it ought to be of inherence simply.
But then an objection arises about the contingent for the possible. For the contingent for the possible seems to follow in this way, because from the opposite of the conclusion and of the major the opposite of the minor seems to follow in the first figure through the mixing of the contingent and the necessary, thus: every B contingently is A; it is necessary that every C be B, for this is equipollent to the opposite of the conclusion; therefore every C contingently is A, concerning the contingent toward either alternative; and it is a perfect mode, and the major is about such a contingent. Again the same thing is shown by exposition: because if some C of necessity is not A, let that be F, and then it will be true to say that of necessity no F is A. Therefore let it be syllogized thus: every B contingently is A; of necessity no F is A; therefore no F contingently is B. For this seems to follow in the second mode of the second figure through the useful conjugation of this mixing. But if no F contingently is B, and F is some C, therefore some C contingently is not B; and it is a negative conclusion about the contingent for the possible. And from this it seems that that rule is false which says that if the universal negative is not of necessity, the conjugation is useless. And it seems one must say that this conclusion follows. Yet nevertheless no conjugations are judged useful except those which descend from the first mode of the second figure, in which there is a universal negative major; and those particular conjugations are not judged useful which descend from the second mode of the second figure, where there is a universal affirmative major and the minor is a universal negative, from which the fourth mode of the second figure descends. And the cause of this, according to certain people, is that here those conjugations ought not to be judged useful which cannot be reduced to the first figure through conversion, because they do not have the due origin; but none can be reduced to the first figure through conversion except those which have a universal negative major of necessity; and therefore those alone are judged useful.1
But if one asks about the sufficiency of these conjugations, one must say that from the beginning it must be supposed that in this mixing the major ought to be universal negative; and then it is clear that there are only six useful conjugations here in this mixing, namely four universal and two particular, and six useless, as in the preceding mixing, which was about the contingent and inherence.
Notes
- This solution is ambiguous. On the contrary: then the modes of proving which Aristotle often uses would be none. Besides, then by parity Baroco and Bocardo in those syllogisms of inherence would be imperfect modes, because they cannot be reduced through conversion; indeed they would be useless. And therefore I would say to the first that that inferred conclusion, the universal affirmative about the contingent, does not contradict the particular negative of necessity which was the minor in the first syllogism. Yet nevertheless it contradicts that proposition and its subcontrary when taken under a disjunction. To the second it must be said that the argument concludes no more insofar as it is the second mode of the second figure, and not insofar as it is the fourth of the same. P. J. (Haec solutio est ambigua. Contra: tunc modi probandi quibus saepe utitur Aristoteles nulli essent. Praeterea, tunc a pari baroco et bocardo in illis de inesse essent modi imperfecti, quia non possunt reduci per conversionem; imo essent inutiles. Et ideo ego dicerem ad primum, quod illa conclusio illata universalis affirmativa de contingenti non contradicit particulari negativae de necessario quae fuit minor in primo syllogismo. Sed tamen contradicit illi et suae subcontrariae sumptis sub disjunctione. Ad secundum dicendum quod argumentum non plus concludit ut est secundus secundae, et non in quantum quartus ejusdem. P. J.) ↩
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