Authors/Ockham/Summa Logicae/Book III-1/Chapter 11

Latin	English
[Cap. 11. De reductione syllogismorum secundae figurae in quatuor modos primae figura]	[Chapter 11.  On the reduction of syllogisms of the second figure into the four modes of the first figure]
Notandum est quod syllogismi in secunda figura non sunt ex se apparentes, sed habent reduci in syllogismos primae figurae, et hoc per conversionem vel per impossibile.	It should be noted that the syllogisms of the second figure are not apparent of themselves, but have to be reduced into syllogisms of the first figure, and this is by conversion by impossibility.
Per conversionem autem reducuntur tantum tres modi primi. Unde primus modus reducitur per solam conversionem maioris, quia conversa maiore fit syllogismus in prima figura, sicut de se patet. Et patet talis modus arguendi et reductio per conversionem per illam regulam ‘quidquid sequitur ad consequens, sequitur ad antecedens’. Secundus modus reducitur per conversionem minoris propositionis et transpositionem propositionum et conversionem conclusionis. Tertius modus reducitur per solam conversionem maioris.	By conversion, however, only the first three modes are reduced. Hence the first mode is reduced by the conversion of the major alone, because the major is converted into a syllogism in the first figure, as is evident in itself. And such a mode of argument and reduction by conversion is evident by that rule ‘whatever follows to the consequent, follows to the antecedent’. The second mode is reduced by the conversion of the minor proposition and the transposition of the propositions and the conversion of the conclusion. The third mode is reduced by the conversion of the major alone.
Sed quartus modus non potest reduci per conversionem, quia si sua maior converteretur, praemissae disponerentur in prima figura, sed maior esset particularis, et ita per consequens non disponerentur in modo; minor autem non potest converti, cum sit particularis negativa, quae non potest converti. Sed iste quartus modus, sicut quilibet alius, reducitur per impossibile. Unde iste quartus modus reducitur in primum modum primae figurae arguendo ex contradictoria conclusionis et maiore, inferendo contradictoriam minoris. Ut si fiat talis syllogismus in quarto modo secundae figurae ‘omnis homo est animal; quaedam substantia non est animal; igitur quaedam substantia non est homo’ accipiatur contradictoria istius conclusionis ‘quaedam substantia non est homo’, quae est ista ‘omnis substantia est homo', et arguatur sic ‘omnis homo est animal; omnis substantia est homo; igitur omnis substantia est animal’, quae est contradictors primae minoris. Et tenet omnis reductio ƿ per istam regulam ‘oppositum consequentis non stat cum antecedente, igitur consequent bona’.	But the fourth mode cannot be reduced by conversion, because if its major were converted, the premises would be arranged in the first figure, but the major would be particular, and so consequently they would not be arranged in the mode; but the minor cannot be converted, since it is a negative particular, which cannot be converted. But this fourth mode, like any other, is reduced by impossibility. Hence this fourth mode is reduced to the first mode of the first figure by arguing from the contradictory of the conclusion and the major, by inferring the contradictory of the minor. For if such a syllogism is made in the fourth mode of the second figure ‘every man is an animal; a certain substance is not an animal; therefore a certain substance is not a man’, let the contradictory of that conclusion ‘some substance is not a man’ be taken, which is that ‘every substance is a man’, and let it be argued thus ‘every man is an animal; every substance is a man; therefore every substance is an animal’, which is the contradictor of the first minor. And every reduction holds by this rule ‘the opposite of the consequent does not stand with the antecedent, therefore the consequence is good.
Unde si talis syllogismus non valeret, tunc oppositum conclusionis staret cum praemissis. Sed hoc est falsum, quia tunc possent praemissae esse verae et tamen oppositum conclusionis simul esset verum; et per consequens oppositum conclusionis et una praemissarum non inferrent oppositum alterius praemissarum, quia oppositum staret. Et ita universaliter, quando ex opposito conclusionis cum altera praemissarum infertur oppositum alterius praemissae, semper est bonus discursus per hanc regulam ‘oppositum consequentis non stat cum antecedente, igitur consequentia bona’.	Hence if such a syllogism were not valid, then the opposite of the conclusion would stand with the premises. But this is false, because then the premises could be true and yet the opposite of the conclusion would be true at the same time; and consequently the opposite of the conclusion and one of the premises would not infer the opposite of the other premises, because the opposite would stand. And so universally, when from the opposite of the conclusion with one of the premises the opposite of the other premise is inferred, there is always good discourse by this rule ‘the opposite of the consequent does not stand with the antecedent, therefore the consequence is good’.
Similiter primus modus secundae figurae reducitur in secundum modum primae figurae, arguendo ex contraria conclusionis, quae est universalis affirmativa, et ponendo eam loco minoris, et maiore negativa, qua prius, inferendo contrariam minoris, quae erit universalis negativa.	Similarly, the first mode of the second figure is reduced to the second mode of the first figure, arguing from the contraries of the conclusion, which is a universal affirmative, and putting it in place of the minor, and the major negative, as before, inferring the contraries of the minor, which will be a universal negative.
Secundus modus reducitur in primum modum primae figurae, arguendo ex eadem maiore qua prius et contraria conclusionis, quae erit universalis affirmativa, inferendo contrariam minoris, quae erit universalis affirmativa.	The second mode is reduced to the first mode of the first figure, by arguing from the same major as before and the contrary of the conclusion, which will be a universal affirmative, by inferring the contrary of the minor, which will be a universal affirmative.
Tertius modus reducitur in secundum modum primae figurae, arguendo ex eadem maiore et contradictoria conclusionis, inferendo contradictoriam minoris.	The third mode is reduced to the second mode of the first figure, by arguing from the same major and the contradictory of the conclusion, and inferring the contradictory of the minor.
Sic igitur omnis syllogismus secundae figurac reducitur in syllogismos primae figurae, scilicet in duos primos modos, arguendo semper ex maiore qua prius et contraria vel contradictoria conclusionis, inferendo contrariam vel contradictoriam minoris, semper virtute istius regulae ‘repugnans conclusionis non stat cum antecedente, igitur prima consequentia bona’..	Thus, therefore, every syllogism of the second figure is reduced to syllogisms of the first figure, namely in the two first modes, always arguing from the major which precedes and the contrary or contradictory of the conclusion, inferring the contrary or contradictory of the minor, always by virtue of that rule ‘the contrary of the conclusion does not stand with the antecedent, therefore the first consequence is good’..
Unde sciendum est quod numquam valet syllogismus in secundaƿ figura nisi possit reduci in syllogismum primae figurae vel per conversionem vel per impossibile. Et propter hoc dictum est prius quod omnis syllogismus regulatur per dici de omni vel de nullo, immediate vel mediate.	Hence it should be known that a syllogism in the second figure is never valid unless it can be reduced to a syllogism of the first figure either by conversion or by impossibility. And for this reason it was said before that every syllogism is regulated by dici de omni vel de nullo (to be said of all or none), immediately or mediately.