Works › Prior Analytics, Books I–II
Volume 1 · pp. 577–578
Chapter XVIII. Because there cannot be a uniform generation from the contingent in the second figure.
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CAPUT XVIII. Quia non potest esse generatio uniformis de contingenti in secunda figura.
Acturi autem de generatione uniformi syllogismorum de contingenti in secunda figura inutilium et utilium conjugationum, primo ponendae sunt regulae per quas regulantur hujusmodi syllogismi, si fieri possunt in secunda figura. Prima autem regula est, quod in secunda sive media figura, quando utraeque propositiones praemissae sunt contingentes sive de contingenti ad utrumlibet qualitercumque combinentur ad modum aliquem constituendum, non fit syllogismus in secunda figura.
Secunda vero regula per quam regulari habent syllogismi contingentis et inesse, sive in mixtione contingentis et inesse, in secunda figura est haec, quod in secunda figura fit mixtio contingentis et inesse, si una propositionum fuerit affirmativa et altera negativa: et si illa propositio quae est de inesse, fuerit universalis affirmativa, non erit syllogismus in secunda figura. Si autem illa de inesse fuerit universalis negativa, erit syllogismus in secunda figura ex mixtione contingentis et inesse.
Tertia regula est secundum quam regulatur mixtio contingentis et necessarii in secunda figura, et est haec, quod eodem modo est in mixtione contingentis et necessarii in secunda figura sicut est in mixtione contingentis et inesse in secunda figura, quod scilicet universali negativa existente de necessario, fit syllogismus, sed non fit syllogismus, universali affirmativa existente de necessario.
His autem ita positis, adhuc addendum est quod contingens quod concluditur in conclusionibus syllogismorum secundae figurae oportet accipere eodem modo, quemadmodum et in prioribus est acceptum, hoc est, quod in tota ista generatione syllogismorum de contingenti secundum mixtiones contingentis et inesse et necessarii et contingentis, non concluditur nisi contingens pro possibili. Si enim syllogismus talis vel talis mixtionis reducatur in primam figuram, erit in prima figura major universalis negativa, vel de inesse, vel de necessario: propter quod sicut talis conjugatio in prima figura non concludit nisi contingens pro possibili, sic nec in secunda figura universales syllogismi, de quibus hic loquimur, non possunt concludere nisi contingens pro possibili.
Has autem regulas verificabimus hoc modo, quibus verificatis satis patet generatio syllogismorum uniformium et mixtorum in secunda figura. Ad verificationem ergo primae praeponimus istam rationem: quoniam si perfici debeat syllogismus secundae figurae, oportet quod aut per conversionem propositionis de contingenti perficiatur, aut per deductionem ad impossibile. Sed neutro istorum modorum potest perfici syllogismus secundae figurae, qui est ex utraque de contingenti. Ergo utraque existente de contingenti in secunda figura non erit syllogismus.
CHAPTER XVIII. Because there cannot be a uniform generation from the contingent in the second figure.
But since we are about to deal with the uniform generation of syllogisms about the contingent in the second figure, of useless and useful conjugations, first the rules must be posited by which syllogisms of this kind are regulated, if they can be made in the second figure. But the first rule is that in the second or middle figure, when both premise propositions are contingent or about the contingent toward either alternative, however they are combined to constitute some mode, no syllogism is made in the second figure.
But the second rule by which syllogisms of the contingent and inherence, or in the mixing of the contingent and inherence, have to be regulated in the second figure is this: that in the second figure a mixing of the contingent and inherence is made if one of the propositions is affirmative and the other negative; and if that proposition which is of inherence is a universal affirmative, there will not be a syllogism in the second figure. But if that proposition of inherence is a universal negative, there will be a syllogism in the second figure from the mixing of the contingent and inherence.
The third rule, according to which the mixing of the contingent and the necessary is regulated in the second figure, is this: that it is in the same way in the mixing of the contingent and the necessary in the second figure as it is in the mixing of the contingent and inherence in the second figure, namely that, when the universal negative is about the necessary, a syllogism is made; but a syllogism is not made when the universal affirmative is about the necessary.
But with these things thus posited, it must still be added that the contingent which is concluded in the conclusions of syllogisms of the second figure must be accepted in the same way as it was accepted also in the prior matters, that is, that in this whole generation of syllogisms about the contingent according to the mixings of the contingent and inherence and of the necessary and the contingent, nothing is concluded except the contingent for the possible. For if a syllogism of this or that mixing is reduced to the first figure, in the first figure the major will be universal negative, either of inherence or of necessity. For this reason, just as such a conjugation in the first figure concludes only the contingent for the possible, so also in the second figure the universal syllogisms about which we are speaking here cannot conclude except the contingent for the possible.
But we shall verify these rules in this way; when they have been verified, the generation of uniform and mixed syllogisms in the second figure is sufficiently clear. Therefore for the verification of the first rule we set before it this reasoning: because if a syllogism of the second figure ought to be perfected, it must be perfected either through the conversion of the proposition about the contingent or through a deduction to the impossible. But a syllogism of the second figure which is from each proposition about the contingent cannot be perfected by either of those modes. Therefore, when both propositions are about the contingent, there will not be a syllogism in the second figure.
Ostendamus autem primo quod non potest perfici per conversionem, ita scilicet quod universalis negativa convertatur in terminis secundum idem genus contingentis: sed bene convertitur in terminis in contingens commune, quod est contingens pro possibili, sicut a principio istius libri determinatum est: nullo modo tamen convertitur illa negativa de contingenti ad utrumlibet secundum idem genus contingentis. Quod autem non convertatur de contingenti ad utrumlibet universalis negativa, supponamus ex prius habitis, quia convertitur illa de tali contingenti in oppositam qualitatem. Dicamus igitur hoc supposito, quod in contingere non convertitur universalis privativa, ut si dicamus, quod A contingit nulli B, quod nullum B contingit esse A, non est necesse per consequentiam conversionis, quod e converso B contingat nulli A, hoc est, quod nullum A contingat esse C: hoc autem ostenditur deducendo ad impossibile. Faciamus ergo istam consequentiam conversionis sic, nullum B contingit esse A, ergo nullum A contingit esse B: si enim sequitur hoc, detur haec, nullum B contingit esse A; quoniam ergo jam ostensum est quod in contingenti convertuntur affirmationes negationibus, ita quod contraria in contrariam, et contrajacentes sibi per contradictionem in suas contrajacentes convertuntur, ita quod sint affirmati modi, et contrarie vel contradictorie in dicto sive propositione quae modificatur: tunc ex hoc sequitur si nullum A contingit esse B, quod omne A contingit esse B, sed hoc est falsum: non enim sequitur, si aliquod praedicatum alicui subjecto omni sive universaliter contingit inesse, quod etiam e converso subjectum illud omni praedicato per conversionem contingat inesse: quare si contingit nullum A esse B, non sequitur quod contingat nullum B esse A: si enim hoc detur, sequitur quod contingit omne A esse B, quod falsum est: quia universalis affirmativa non convertitur simpliciter in terminis. Hoc autem sequitur ex hoc, quod ponitur universalis negativa converti in terminis in contingenti. Ergo talis hypothesis est impossibilis.
Hoc autem idem per instantiam in terminis ostenditur sic: quia nihil prohibet in quibusdam terminis A quidem praedicatum nulli B contingere: et tamen B subjectum alicui quod est sub A praedicato de necessitate non inesse: sit enim B homo, et A album: contingit enim album omni homini non inesse, sive nulli homini inesse: quia contingit nullum hominem esse album; quod probatur per hoc, quia contingit omnem hominem esse album propter conversionem in oppositam qualitatem: non tamen contingit nullum album esse hominem: quia quaedam alba necesse est non esse hominem sicut cygnum, et nivem, et margaritam, et hujusmodi. Quod autem necessarium est
But first let us show that it cannot be perfected through conversion, namely in such a way that a universal negative is converted in terms according to the same genus of contingent; but it is indeed converted in terms into the common contingent, which is the contingent for the possible, as was determined from the beginning of this book. Nevertheless that negative about the contingent toward either alternative is in no way converted according to the same genus of contingent. But that a universal negative is not converted about the contingent toward either alternative, let us suppose from the things previously held, because that proposition about such a contingent is converted into the opposite quality. Therefore, with this supposed, let us say that in the case of contingently inhering the universal privative is not converted, so that if we say that A contingently belongs to no B, then that no B contingently is A does not make it necessary through the consequence of conversion that, conversely, B contingently belongs to no A, that is, that no A contingently is C. But this is shown by leading to the impossible. Therefore let us make this consequence of conversion thus: no B contingently is A; therefore no A contingently is B. For if this follows, let this be given: no B contingently is A. Therefore, since it has already been shown that in the contingent affirmations are converted with negations, so that contraries are converted into contraries, and those opposed to each other by contradiction into their own opposed propositions, in such a way that the modes are affirmed, and the opposition is contrarily or contradictorily in the dictum or proposition which is modified, then from this it follows, if no A contingently is B, that every A contingently is B. But this is false. For it does not follow, if some predicate contingently belongs to every subject or universally, that conversely that subject also contingently belongs to every predicate through conversion. Therefore, if no A contingently is B, it does not follow that no B contingently is A; for if this is granted, it follows that every A contingently is B, which is false, because a universal affirmative is not converted simply in terms. But this follows from the fact that a universal negative is posited to be converted in terms in the contingent. Therefore such a hypothesis is impossible.
But this same thing is shown through an instance in terms thus: because nothing prevents, in certain terms, A as predicate from contingently belonging to no B, and yet B as subject from not belonging of necessity to something which is under A as predicate. For let B be man, and A white. For white contingently does not belong to every man, or belongs to no man, because it is contingent that no man be white; this is proved through this, that every man contingently is white on account of conversion into the opposite quality. Nevertheless it is not contingent that no white thing be a man, because certain white things must not be man, such as a swan, snow, pearl, and things of this kind. But that which is necessary is
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