Works › Prior Analytics, Books I–II
Volume 1 · pp. 732–734
Treatise III, Chapter IV
A marker with ≈ is an approximate page boundary, placed by measure of the text; the page photographs remain the authority. In the paired views, clicking a page marker brings that page into view.
CAPUT IV.
De secundae figurae conversivis syllogismis tam particularibus quam universalibus.
In secunda autem figura eam quidem propositionem quae est ad majorem extremitatem (et est major in syllogismo ante facto) non est sive contingit interimere contrarie, hoc est, contrariam conclusionis in universalibus syllogismis cum minori assumendo, quolibet modo sive quocumque modo facta conversione conclusionis: sive scilicet assumendo contrariam conclusionis sive contradictoriam. Cujus causa est, quia conclusio conversivi syllogismi interimentis majorem semper fit in tertia figura: eo quod sicut in prima figura, ita et in secunda major non interimitur nisi per tertiam figuram: sed in tertia figura non fit syllogismus universalem habens conclusionem. Contraria autem universalis conclusionis est universalis; et ideo contraria majoris in universalibus syllogismis secundae figurae concludi non potest per conversivum syllogismum: alteram autem propositionem, scilicet minorem in duobus primis universalibus syllogismis similiter interimemus conversione. Dico autem similiter, quia si conclusio convertitur contrarie, fit interemptio minoris contrarie (hoc est, per contrariam minoris). Si autem opposite convertitur conclusio in contradictoriam, fit destructio minoris per suam contradictoriam.
Hoc autem quod dictum est, ostendatur in modis singulis secundae figurae, et primo in universalibus, deinde particularibus. In universalibus autem hoc ostendendo incipiamus a modo secundo secundae figurae: quia in illo prima est universalis affirmativa, et secunda universalis negativa: in primo autem modo e converso est prima negativa, et secunda affirmativa, et ambae universales.
Ponamus enim A medium omni B inesse, et idem A dicamus nulli inesse C, conclusio erit quod nullum C est B, sic, omne B A, nullum C A, ergo nullum C B. Si ergo sumatur contraria conclusionis hujus quae dicit, quod omne C est B et propositio major maneat (haec scilicet, omne B A) syllogizatur contraria minoris, quod scilicet A omni C inerit: tunc enim fit prima figura sic, omne B A, omne C B, ergo omne C A. Hic est primus modus primae figurae. Si autem contraria conclusionis sumatur cum minori propositione, per tertiam figuram syllogizatur contradictoria majoris et non contraria; cujus exemplum est, quod sumatur contraria conclusionis, quod scilicet B inest omni C, et apponatur minor, scilicet quod A nulli C inest: sequitur quod A non omni inest B, sic, nullum C A, omne C B, ergo aliquod B non est A. Hic enim est secundus modus tertiae figurae.
Si autem non contrarie sed opposite per contradictionem convertatur conclusio, eadem contradictoria accepta cum majori, syllogizabit contradictoriam minoris; et accepta cum minori, syllogizabit contradictoriam majoris, sicut patet in eodem secundo modo secundae figurae. Si enim opposite per contradictionem convertatur conclusio B C prioris syllogismi, tunc propositio major quae est A B similiter ostendetur, sicut prius: A C autem quae propositio minor, ostendetur opposite, hoc est, per suam contradictoriam: nam si B inest alicui C (sicut dicit conclusionis contradictoria) et assumatur minor quae dicit quod A nulli C inest: sequitur quod A alicui B non inerit, quae est contradictoria majoris, sic, nullum C est A, quoddam C est B, ergo quoddam B non est A. Eadem autem sumpta cum majori, syllogizabit contradictoriam minoris, sic, omne B A, quoddam C B, ergo aliquod C est A, quae est contradictoria minoris.
CHAPTER IV.
On The Conversive Syllogisms Of The Second Figure, Both Particular And Universal.
But in the second figure, the proposition which is toward the greater extreme, and is the major in the syllogism made before, cannot, or does not happen to, be destroyed contrarily, that is, by taking the contrary of the conclusion in universal syllogisms with the minor, in any mode or in whatever way the conversion of the conclusion is made, namely whether by taking the contrary of the conclusion or the contradictory. The cause of this is that the conclusion of a conversive syllogism destroying the major is always made in the third figure, because just as in the first figure, so also in the second, the major is not destroyed except through the third figure; but in the third figure a syllogism having a universal conclusion is not made. But the contrary of a universal conclusion is universal; and therefore the contrary of the major in universal syllogisms of the second figure cannot be concluded through a conversive syllogism. But the other proposition, namely the minor in the first two universal syllogisms, we shall destroy similarly by conversion. I say similarly because, if the conclusion is converted contrarily, the destruction of the minor is made contrarily, that is, through the contrary of the minor. But if the conclusion is converted oppositely into the contradictory, the destruction of the minor is made through its contradictory.
But let what has been said be shown in the several modes of the second figure, first in the universals, then in the particulars. In showing this in the universals, let us begin from the second mode of the second figure, because in that mode the first is universal affirmative and the second universal negative; but in the first mode, conversely, the first is negative and the second affirmative, and both are universal.
For let us posit A as middle to be present in every B, and let us say the same A to be present in no C; the conclusion will be that no C is B, thus: every B is A, no C is A, therefore no C is B. Therefore if the contrary of this conclusion is taken, which says that every C is B, and the major proposition remains, namely this, every B is A, the contrary of the minor is syllogized, namely that A will be present in every C. For then the first figure is made thus: every B is A, every C is B, therefore every C is A. This is the first mode of the first figure. But if the contrary of the conclusion is taken with the minor proposition, the contradictory of the major and not the contrary is syllogized through the third figure. An example of this is that the contrary of the conclusion is taken, namely that B is present in every C, and the minor is added, namely that A is present in no C; it follows that A is not present in every B, thus: no C is A, every C is B, therefore some B is not A. For this is the second mode of the third figure.
But if the conclusion is converted not contrarily but oppositely through contradiction, the same contradictory, accepted with the major, will syllogize the contradictory of the minor, and accepted with the minor, will syllogize the contradictory of the major, as is clear in the same second mode of the second figure. For if the conclusion B C of the prior syllogism is converted oppositely through contradiction, then the major proposition, which is A B, will be shown similarly, as before; but A C, which is the minor proposition, will be shown oppositely, that is, through its contradictory. For if B is present in some C, as the contradictory of the conclusion says, and the minor is assumed, which says that A is present in no C, it follows that A will not be present in some B, which is the contradictory of the major, thus: no C is A, some C is B, therefore some B is not A. But the same proposition, taken with the major, will syllogize the contradictory of the minor, thus: every B is A, some C is B, therefore some C is A, which is the contradictory of the minor.
Unde rursum formando eumdem syllogismum ad interimendum minorem sumatur contradictoria conclusionis: quia si detur B alicui C inesse, haec est enim conclusionis opposita, A autem dicatur inesse omni B, quae est major: sequitur quod A inerit alicui C, quae est contradictoria minoris, sic, omne B A, aliquod C B, ergo aliquod C A. Hic est syllogismus in tertio modo primae figurae. Similiter autem ostendetur in primo modo secundae figurae, in quo e converso se habent propositiones ad modum secundum: est enim in primo major negativa universalis, et in secundo minor negativa universalis.
Si autem in parte sive in particulari fiat syllogismus, et conclusio convertatur contrarie, quia hoc vocamus in subcontrariam converti, neutra propositionum praemissarum prioris syllogismi interimitur per talem conversivum syllogismum, quamvis fiat syllogismus, quemadmodum etiam est in particulari syllogismo primae figurae. Sed si convertatur conclusio opposite (hoc est, in sibi contradictorie oppositam) et jungatur cum altera praemissarum, utraeque praemissae interimuntur per syllogizatas sibi contradictorias. Et gratia exempli formetur tertius secundae figurae sic, nullum B A, aliquod C est A, ergo aliquod C non est B. Si enim ponatur in majori A medium nulli B majori extremo inesse, conclusio erit B C propositio, hoc est, quod quoddam C non est B, hic enim est tertius figurae secundae. Si ergo convertatur conclusio in subcontrariam, ita quod dicatur B alicui C inesse, et A B propositio major maneat, quae dicit nullum B esse A, conclusio quae sequitur erit quod A alicui C non inest. Sed per illam non interimitur minor quae posita est ex principio altera esse praemissarum prioris syllogismi: contingit enim A alicui C inesse, et alicui C non inesse in contingenti materia.
Hence again, in forming the same syllogism for destroying the minor, let the contradictory of the conclusion be taken; for if it is granted that B is present in some C, for this is the opposite of the conclusion, and A is said to be present in every B, which is the major, it follows that A will be present in some C, which is the contradictory of the minor, thus: every B is A, some C is B, therefore some C is A. This is the syllogism in the third mode of the first figure. But it will be shown similarly in the first mode of the second figure, in which the propositions stand conversely to the second mode; for in the first the major is universal negative, and in the second the minor is universal negative.
But if a syllogism is made in part or particularly, and the conclusion is converted contrarily, because we call this to be converted into the subcontrary, neither of the premise-propositions of the prior syllogism is destroyed through such a conversive syllogism, although a syllogism is made, just as it is also in a particular syllogism of the first figure. But if the conclusion is converted oppositely, that is, into the contradictorily opposite to itself, and is joined with one of the premises, both premises are destroyed through the contradictories syllogized for them. And for the sake of example let the third of the second figure be formed thus: no B is A, some C is A, therefore some C is not B. For if in the major A is posited as the middle to be present in no B, the greater extreme, the conclusion will be the B C proposition, that is, that some C is not B; for this is the third of the second figure. Therefore, if the conclusion is converted into the subcontrary, so that B is said to be present in some C, and the major proposition A B remains, which says that no B is A, the conclusion which follows will be that A is not present in some C. But through that the minor is not destroyed, which was posited from the beginning to be the other of the premises of the prior syllogism; for it happens in contingent matter that A is present in some C and is not present in some C.
Rursum si subcontraria conclusionis jungatur cum minori, ut si dicatur quod B inest alicui C, quae est subcontraria conclusionis: et dicatur A inesse alicui C, quae est minor prioris syllogismi: tunc non erit syllogismus, quia ambae praemissae sunt particulares, et neutrum eorum (quae sumpta sunt pro praemissis) est universale: propter quod A B major propositio non potest interimi per talem conversionem conclusionis.
Si autem in eodem modo tertio secundae figurae conclusio convertatur opposite in suam contradictoriam, interimuntur utraeque propositiones prioris syllogismi per conversive syllogizatas suas contradictorias: nam si convertatur conclusio quae dicit quoddam C non esse B, in suam contradictoriam universalem affirmativam: et dicatur B inesse omni C, et jungatur cum majori quae dicit A nulli B inesse, sequitur contradictoria minoris, quae dicit aliquod C A esse: sequitur enim quod nulli C inest A; sic autem facile est formare hujusmodi syllogismos.
Rursum si B omni C dicatur inesse (quae est contradictoria conclusionis) et jungatur cum minori quae dicit A alicui C inesse: sequitur quod alicui B inest A per tertiam figuram, quae est contradictoria majoris. Eadem est demonstratio in conversivo syllogismo in quarto secundae figurae, in quo major est universalis praedicativa sive affirmativa. Notandum ergo est hic quod in secunda figura semper per conversivum syllogismum interimitur major propositio per tertiam figuram, minor autem semper per primam. Item notandum quod ubique oppositum conclusionis ponendum est pro minori in syllogismo conversivo.
Notandum etiam quod sunt in hac figura duodecim conjugationes conversivi syllogismi. Aut enim sumitur contraria conclusionis, aut contradictoria. Si contraria: aut in syllogismo universali, aut particulari. Si in particulari sumitur contraria, neutra praemissarum interimitur. Si est circa universalem: aut ergo juxta modum primum, aut juxta secundum. Si juxta primum, sic sunt duo. Et si juxta secundum, sic sunt alii qui fiunt quatuor supponendo contrariam conclusionis in modo universali. Adhuc si supponatur contradictoria: hoc iterum est aut juxta syllogismum universalem, aut juxta particularem. Si universalis aut est primus, et circa illum sunt duo: et si est secundus, circa illum sunt iterum duo. Si autem est circa particularem: tunc sunt duo juxta tertium, et duo juxta quartum. Et sic supposita contradictoria fiunt hic octo conversivi syllogismi, qui cum aliis quatuor faciunt hic in universo duodecim syllogismos conversivos, sicut et in prima figura duodecim fuerunt.
Again, if the subcontrary of the conclusion is joined with the minor, as if it is said that B is present in some C, which is the subcontrary of the conclusion, and A is said to be present in some C, which is the minor of the prior syllogism, then there will not be a syllogism, because both premises are particular, and neither of those things which have been taken for premises is universal. On account of this the major proposition A B cannot be destroyed through such a conversion of the conclusion.
But if in the same third mode of the second figure the conclusion is converted oppositely into its contradictory, both propositions of the prior syllogism are destroyed through their contradictories syllogized conversively. For if the conclusion which says that some C is not B is converted into its universal affirmative contradictory, and B is said to be present in every C, and it is joined with the major which says that A is present in no B, the contradictory of the minor follows, which says that some C is A; for it follows that A is present in no C. Thus, moreover, it is easy to form syllogisms of this kind.
Again, if B is said to be present in every C, which is the contradictory of the conclusion, and it is joined with the minor which says that A is present in some C, it follows through the third figure that A is present in some B, which is the contradictory of the major. The same demonstration holds in the conversive syllogism in the fourth of the second figure, in which the major is universal predicative or affirmative. Therefore it must be noted here that in the second figure the major proposition is always destroyed through the third figure by a conversive syllogism, but the minor always through the first. Likewise it must be noted that everywhere the opposite of the conclusion must be put for the minor in the conversive syllogism.
It must also be noted that in this figure there are twelve conjugations of the conversive syllogism. For either the contrary of the conclusion is taken, or the contradictory. If the contrary is taken, it is either in a universal syllogism or in a particular one. If the contrary is taken in a particular syllogism, neither premise is destroyed. If it is around a universal one, then either according to the first mode or according to the second. If according to the first, then there are two. And if according to the second, then there are others which become four, by supposing the contrary of the conclusion in the universal mode. Again, if the contradictory is supposed, this again is either according to a universal syllogism or according to a particular one. If it is universal, either it is the first, and around it there are two, or if it is the second, around it there are again two. But if it is around a particular, then there are two according to the third, and two according to the fourth. And thus, when the contradictory is supposed, there are made here eight conversive syllogisms, which with the other four make here in the whole twelve conversive syllogisms, just as in the first figure there were twelve.
If a page does not appear, its photograph has not been uploaded yet.