Authors/Ockham/Summa Logicae/Book III-1/Chapter 14

Latin	English
Cap. 14. De syllogismis factis in tertia figura et sufficientia modorum	Chapter 14. On syllogisms of the third figure, and the sufficiency of their modes.
Post haec videndum est quomodo in tertia figura fit syllogismus.	After this we must see how the syllogism is formed in the third figure. .
Est autem primo sciendum quod in tertia figura numquam potest concludi conclusio universalis. Quod enim universalis affirmativa non possit concludi in tertia figura, patet, nam duo superiora, ordinata secundum superius et inferius, possunt universaliter praedicari de eodem contento; igitur ex hoc quod aliqua praedicantur universaliter de eodem contento, non potest haberi quod unum praedicatur universaliter de reliquo.	But it must first be known that a universal conclusion can never be concluded in the third figure. For it is clear that a universal affirmative cannot be concluded in the third figure, for two superiors, ordered according to superior and inferior, can be universally predicated of the same content; therefore, from the fact that some are predicated universally of the same content, it cannot be held that one is predicated universally of the rest.
Quod etiam universalis negativa non possit concludi, patet, nam de eodem subiecto potest unum ordinatorum secundum superius et inferius universaliter negari et reliquum universaliter affirmari. Sicut de animali universaliter negatur lapis et universaliter affirmatur substantia, et tamen lapis et substantia se habent secundum superius et inferius; igitur ex talibus praemissis numquam potest concludi unum extremum universaliter negari a reliquo.	That a universal negative cannot be concluded is clear, for of the same subject one of the ordered things can be universally denied according to the superior and inferior and the rest universally affirmed. Just as of an animal a stone is universally denied and a substance is universally affirmed, and yet a stone and a substance are related according to the superior and inferior; therefore from such premises it can never be concluded that one extreme is universally denied by the rest.
ƿ Secundo sciendum est quod in tertia figura semper debet minor esse affirmativa, ita quod nullo modo potest esse negativa. Et ratio est ista: quia de eodem potest primo aliquod superius praedicari universaliter et postea inferius removeri universaliter, et tamen ex hoc non potest concludi superius removeri ab inferiori nec universaliter nec particulariter. Unde animal praedicatur de homine universaliter et asinus removetur ab homine universaliter, et tamen animal non negatur ab homine nec universaliter nec particulariter.	Secondly, it should be known that in the third figure the minor must always be affirmative, so that it can in no way be negative. And the reason is this: because of the same thing something superior can first be predicated universally and then something inferior can be removed universally, and yet from this it cannot be concluded that the superior is removed from the inferior either universally or particularly. Hence animal is predicated of man universally and donkey is removed from man universally, and yet animal is not denied from man either universally or particularly.
Ex praedictis et duobus principiis communibus omni figurae, quorum unum est quod ‘semper altera praemissarum debet esse universalis vel singularis’ et aliud quod ‘altera praemissarum debet esse affirmativa’ sequitur quod non sunt nisi sex modi utiles in tertia figura. Nam sicut in aliis figuris per istas quatuor differentias ‘universale-particulare’, ‘affirmativum-negativum’ possunt fieri tantum sexdecim combinationes, scilicet octo, in quibus semper utraque praemissarum est negativa vel utraque est particularis; restant igitur aliae. Quia si utraque sit universalis et altera affirmativa, aut utraque est affirmativa, et habetur primus modus. Aut maior est negativa et minor affirmativa, et habetur secundus modus; aut e converso, et est modus peccans contra principium proprium istius figurae. Si autem non utraque praemissarum sit universalis sed altera, tunc aut maior est universalis et minor particularis vel e converso. Si primo modo, aut maior est affirmativa et minor negativa, et non valet, sicut patet; aut e converso, et habetur sextus modus; aut utraque est affirmativa, et habetur quartus modus. Si autem maior sit particularis et minor universalis, aut utraque est affirmativa, et est tertius modus; aut maior est negativa et minor affirmativa, et est quintus modus; aut maior est affirmativa et minor negativa, et non valet, quia peccat contra principium proprium istius figurae.	From the above and the two principles common to every figure, one of which is that ‘one of the premises must always be universal or singular’ and the other that ‘the other of the premises must be affirmative’ it follows that there are only six useful modes in the third figure. For as in the other figures, through these four differences ‘universal-particular’, ‘affirmative-negative’, only sixteen combinations can be made, namely eight, in which both of the premises are always negative or both are particular; therefore the others remain. For if both are universal and the other affirmative, or both are affirmative, and the first mode is obtained. Or the major is negative and the minor affirmative, and the second mode is obtained; or conversely, and it is a mode that violates the principle proper to that figure. But if not both of the premises are universal but the other, then either the major is universal and the minor particular, or conversely. If in the first mode, either the major is affirmative and the minor negative, and it is not valid, as is clear; or conversely, and the sixth mode is obtained; or both are affirmative, and the fourth mode is obtained. But if the major is particular and the minor universal, either both are affirmative, and it is the third mode; or the major is negative and the minor affirmative, and it is the fifth mode; or the major is affirmative and the minor negative, and it is not valid, because it violates the principle proper to that figure.
ƿ Exempla praedictorum possunt esse ista: ‘omnis homo est animal; omnis homo est substantia; igitur aliqua substantia est animal’; ‘nullus homo est asinus; omnis homo est animal; igitur quoddam animal non est asinus’; ‘quidam homo est animal; omnis homo est substantia; igitur quaedam substantia est animal’; ‘omnis homo est animal; quidam homo est substantia; igitur quaedam substantia est animal’; ‘aliquis homo non est asinus; omnis homo est animal; igitur quoddam animal non est asinus’; ‘nullus homo est asinus; quidam homo est animal; igitur quoddam animal non est asinus’.	Examples of the above may be: ‘every man is an animal; every man is a substance; therefore some substance is an animal’; ‘no man is a donkey; every man is an animal; therefore some animal is not a donkey’; ‘some man is an animal; every man is a substance; therefore some substance is an animal’; ‘every man is an animal; some man is a substance; therefore some substance is an animal’; ‘some man is not a donkey; every man is an animal; therefore some animal is not a donkey’; ‘no man is a donkey; some man is an animal; therefore some animal is not a donkey’.
Sciendum est etiam quod praedicti modi ita tenent in terminis accidentalibus quibuscumque sicut in terminis substantialibus. Unde tales syllogismi sunt boni ‘nullus homo est ens per accidens; aliquis homo est homo albus; igitur aliquis homo albus non est ens per accidens’; ‘nullus homo distinguitur secundum rationem ab homine; aliquis homo est homo albus; igitur homo albus non distinguitur secundum rationem ab homine’; ‘nulla essentia divina distinguitur secundum rationem ab essentia divina; essentia divina est sapientia divina; igitur sapientia divina non distinguitur secundum rationem ab essentia divina’; ‘omnis intellectus speculativus informatur habitu speculativo; intellectus speculativus est intellectus practicus; igitur intellectus practicus informatur habitu speculativo’.	It should also be noted that the aforementioned modes hold in any accidental terms as well as in substantial terms. . Hence such syllogisms are good: ‘no man is an accidental being; some man is a white man; therefore some white man is not an accidental being’; ‘no man is distinguished according to reason from man; some man is a white man; therefore a white man is not distinguished according to reason from man’; ‘no divine essence is distinguished according to reason from divine essence; divine essence is divine wisdom; therefore divine wisdom is not distinguished according to reason from divine essence’; ‘every speculative intellect is informed by a speculative habit; the speculative intellect is a practical intellect; therefore the practical intellect is informed by a speculative habit’.
Verumtamen in quibusdam praedictis potest assignari fallacia aequivocationis; sed hoc non obstat quin ita teneat forma syllogistica in terminis accidentalibus sicut in terminis substantialibus, quia talis defectus, scilicet aequivocatio, potest contingere quando termini sunt substantiales. Et ideo si de praedictis vel aliquo consimili inveniatur in aliquo auctore quod praemissae sunt verae et conclusio falsa, auctoritates sunt glossandae: vel quod loquuntur aequivoce vel non de virtute sermonis. Unde quando arguitur sic ‘nullus homo distinguitur ratione ab homine; homo est homo albus; igitur homo albus non distinguitur. ratione ab homine',ƿ conclusio potest distingui, eo quod li homo albus potest supponere personaliter et significative, et tunc est discursus bonus et conclusio vera; vel potest supponere materialiter vel simpliciter, et tunc syllogismus non valet, propter hoc quod unus terminus aequivoce accipitur in una praemissa et in conclusione. Et sicut dictum est de ista, ita potest de multis aliis consimiliter dici.	However, in some of the above, the fallacy of equivocation can be assigned; but this does not prevent the syllogistic form from holding in accidental terms as well as in substantial terms, because such a defect, namely equivocation, can occur when the terms are substantial. And therefore if about the above or something similar it is found in some author that the premises are true and the conclusion false, the authorities are to be glossed: either that they speak equivocally or not literally. Hence when it is argued thus ‘no man is distinguished by reason from man; man is a white man; therefore a white man is not distinguished by reason from man’, the conclusion can be distinguished, because the white man can supposit personally and significantly, and then the discourse is good and the conclusion true; or it can supposit materially or simply, and then the syllogism is not valid, because one term is taken equivocally in one premise and in the conclusion. And as was said about this, so can be said about many others in a similar way.
Notandum est etiam quod regulae datae de prima figura et secunda sunt etiam servandae in tertium homo esa. Et propter hoc iste discursus non valet ‘omnis homo est animal; tantum homo est risibilis; igitur tantum risibile est animal’, et ita est de aliis.	It should also be noted that the rules given for the first and second figures must also be observed for the third. . And for this reason, this discourse is not valid: ‘every man is an animal; only man is laughable; therefore only a laughable thing is an animal’, and so it is with the others.
Notandum est etiam quod sicut in prima figura aliqui modi concludunt indirecte, ita etiam in tertia figura. Nam quilibet modus affirmativus concludit duas conclusiones, scilicet unam directam et suam conversam, modi autem negativi concludunt tantum unam, quia particularis negativa non convertitur.	It should also be noted that just as in the first figure some modes conclude indirectly, so also in the third figure. For each affirmative mode concludes two conclusions, namely one direct and its converse, but negative modes conclude only one, because the particular negative is not converted.
Sciendum est etiam quod omnes syllogismi tertiae figurae reducuntur in primam figuram, vel per conversionem vel per impossibile. Unde primus modus reducitur in tertium primae per conversionem minoris. Secundus reducitur in quartum modum per conversionem minoris. Tertius reducitur in tertium per conversionem maioris et transpositionem propositionum et conversionem conclusionis. Quartus reducitur per conversionem minoris. Sextus reducitur per conversionem minoris. Sed quintus modus non potest reduci per conversionem, quia non est in eo aliqua propositio convertibilis nisi universalis affirmativa, quae non convertitur nisi in particularem, et tunc in syllogismo in prima figura utraque praemissa esset particularis; quod non est verum. Et ideo iste modus reducitur praecise per impossibile, sicut etiam omnes alii per impossibile reducuntur. Unde sciendum quod quilibet syllogismus factus in tertia figura reducitur in primam figuram, arguendo ex ƿ opposito contradictorie conclusionis et minore, inferendo oppositum contradictorie maioris. Et tenet talis reductio per istam regulam ‘oppositum conclusionis non stat cum antecedente, igitur consequentia bona’.	It should also be known that all syllogisms of the third figure are reduced to the first figure, either by conversion or by the impossible. Hence the first mode is reduced to the third of the first by the conversion of the minor. The second is reduced to the fourth mode by the conversion of the minor. The third is reduced to the third by the conversion of the major and the transposition of the propositions and the conversion of the conclusion. The fourth is reduced by the conversion of the minor. The sixth is reduced by the conversion of the minor. But the fifth mode cannot be reduced by conversion, because there is no convertible proposition in it except a universal affirmative, which is not converted except into a particular, and then in the syllogism in the first figure both premises would be particular; which is not true. And therefore this mode is reduced precisely by the impossible, just as all the others are also reduced by the impossible. Hence it should be known that any syllogism made in the third figure is reduced to the first figure by arguing from the opposite of the contradictory of the conclusion and the minor, inferring the opposite of the contradictory of the major. And such a reduction holds by this rule 'the opposite of the conclusion does not agree with the antecedent, therefore the consequence is good'.
Sciendum est tamen quod si in quinto modo maior esset singularis, posset reduci per conversionem minoris. Verumtamen talis syllogismus non plus deberet poni in isto quinto modo quam, in secundo, propter hoc quod singularis non plus convenit cum particulari quam cum universali sed minus.	It should be noted, however, that if the major were singular in the fifth mode, it could be reduced by converting the minor. However, such a syllogism should not be posited in this fifth mode any more than in the second, because the singular does not agree more with the particular than with the universal, but less.