Authors/Ockham/Summa Logicae/Book III-1/Chapter 9

 

Latin	English
[Cap. 9. De syllogismo ex propositionibus de inesse sumptis in obliquo]	[Chapter 9.  On syllogisms from assertoric propositions in an oblique case]
Circa syllogismum de obliquis est sciendum quod quando maior est de obliquo et minor de recto semper sequitur conclusio de obliquo et regulatur per dici de omni vel de nullo, dummodo obliquitas cadat a parte eiusdem extremi in conclusione a parte cuius cadit in maiore ita quod si subiectum maioris sit terminus obliquus, oportet quod subiectum conclusionis sit terminus obliquus. Unde omnes tales syllogismi regulantur per dici de omni vel de nullo ‘omnem hominem videt asinus; Sortes est homo; igitur Sortem videt asinus’; ‘cuiuslibet hominis est asinus; Sortes est homo; igitur Sortis est asinus’; ‘omnis homo videt asinum; Sortes est homo; igitur Sortes videt asinum’; ‘nullum asinum videt homo; Brunellus est asinus; igitur Brunellum non videt homo’;nullus homo est asini; Sortes est homo; igitur Sortes non est asini’.	Concerning syllogisms in the oblique case, it should be known that when the major is in an oblique case, and the minor in a direct [nominative] case, a conclusion in the oblique case always follows, and it is governed by the dici de omni, provided that the obliqueness falls on the side of the same extreme in the conclusion as it falls in the major, so that if the subject of the major is an oblique term, the subject of the conclusion has to be an oblique term. Hence all such syllogisms are governed by the dici de omni: "every man is seen by a donkey, Socrates is a man, therefore Socrates is seen by a donkey", "to every man there belongs a donkey, Socrates is a man, therefore to Socrates there belongs a donkey", "every man sees a donkey, Socrates is a man, therefore Socrates sees a donkey", "no donkey is seen by a man, Brunellus is a donkey, therefore Brunellus is not seen by a man", "no man belongs to a donkey, Socrates is a man, therefore Socrates does not belong to a donkey".
Sciendum est etiam quod variis modis potest esse terminus obliquus in syllogismo: quia aliquando utraque praemissarum est de obliquo, aliquando altera tantum. Similiter, aliquando utriusque subiectum est ƿ terminus aliquando praedicatum utriusque; aliquando subiectum unius est terminus obliquus, aliquando praedicatum alterius. Et aliis modis possunt fieri combinationes, quas longum foret enarrare.	It should be known also that an oblique term in a syllogism can be in various modes.  For sometimes both premisses are oblique, sometimes only one of them. Similarly, sometimes the subjects of both are the [oblique] term, sometimes the predicates of both. Sometimes the subject of one is the oblique term, sometimes the predicate of the other.  And there can occur combinations in other modes, which it would take a long time to relate.
Hoc tamen sciendum est quod praeter praedictos modos regulatos per dici de omni vel de nullo, in quatuor casibus est bonus discursus, ubi aliqua praemissarum est de obliquo, et non in aliis.	But nevertheless it should be known that beyond the previous modes governed by dici de omni, in four cases there is a good discourse, where some of the premisses are in an oblique case, and not in others.
(1) Primus est, quando maior est universalis negativa cuius subiectum est terminus obliquus, et minor est affirmativa, habens terminum praedicatum obliquum; et tunc sequitur conclusio de recto et non de obliquo Bene enim sequitur ‘nullum hominem videt asinus; omne risibile videt hominem; igitur nullum risibile est asinus'; similiter bene sequitur nullius hominis est asinus; omne risibile est hominis; igitur nullum risibile est asinus'; quia impossibile est quod conclusio sit falsa si praemissae sint verae.	The first is when the major is a universal negative whose subject is an oblique term, and the minor is affirmative, having an oblique predicate term, and then the conclusion follows in the direct case, and not the oblique.  For 'No man is seen by a donkey, everything capable of laughter sees a man, therefore nothing capable of laughter is a donkey" follows well.  Similarly "to no man belongs a donkey, everything capable of laughter is a man, therefore nothing capable of laughter is a donkey" follows well, for it is impossible that the conclusion is false if the premisses are true.
Sed talis modus arguendi ex affirmativis non valet. Non enim sequitur ‘omnem hominem videt asinus; omnis equus videt hominem; igitur omnis equus est asinus’.	But such a mode of arguing from affirmatives is not valid.  For "every man is seen by a donkey, every horse sees a man, therefore every horse is a donkey" does not follow.
(2) Secundus casus est quando maior est universalis negativa, habens praedicatum obliquum, et minor est affirmativa, habens subiectum obliquum; et tunc sequitur conclusio de recto. Bene enim sequitur ‘nullus asinus videt hominem; omne rudibile videt asinus; igitur nullum rudibile est homo’. Sed si praemissae sint affirmativae, non sequitur conclusio; non enim sequitur ‘omnis homo videt asinum; omnem equum videt homo; igitur omnis equus est asinus'.	The second case is when the major is a universal negative, having an oblique predicate, and the minor is affirmative, having an oblique subject, and then the conclusion follows in the direct case. For "no donkey sees a man, everything capable of laughter is seen by a donkey, therefore nothing capable of laughter is a man" follows well. But if the premisses are affirmative, the conclusion does not follow, for "every man sees a donkey, every horse is seen by a man, therefore every horse is a donkey" does not follow.
(3) Tertius casus est quando maior est universalis affirmativa de recto et minor est affirmativa habens subiectum obliquum; et tunc sequitur conclusio habens subiectum obliquum. Sicut bene sequitur ‘omnis asinus currit; Sortis est asinus; igitur Sortis est currens’. Bene etiam sequitur 'omnis homo est animal; Sortem videt homo; igitur Sortem videt animal’. Sed si maior sit negativa, non sequitur; non enim sequitur 'nullus equus est asinus; cuiuslibet hominis est equus; igitur nullius hominis est asinus'.	The third case is when the major is universal affirmative in the direct case, and the minor is an affirmative having an oblique subject, and then a conclusion having an oblique subject follows. For example "every donkey runs, to Socrates belongs a donkey, therefore something belonging to Socrates runs". But if the major is negative, it does not follow, for "no horse is a donkey, to every man there belongs a horse, therefore to no man there belongs a horse" does not follow.
(4) Quartus casus est quando maior est affirmativa de recto et minor habens praedicatum obliquum; et tunc sequitur conclusio habens praeƿdictum obliquum. Nam sequitur ‘omnis homo est animal; asinus est hominis; igitur asinus est animalis’. Similiter bene sequitur ‘omnis homo currit; Sortes videt hominem; igitur Sortes videt currentem’. Sed si maior sit negativa, non sequitur; non enim sequitur ‘nullum risibile est asinus; omnis homo videt risibile; igitur nullus homo videt asinum’.	The fourth case is when the major is affirmative in the direct case and the minor has an oblique predicate, and then a conclusion with a predicate in the oblique case follows.  For "every man is an animal, a donkey belongs to a man, therefore a donkey belongs to an animal" follows. Similarly "every man runs, Socrates sees a man, therefore Socrates sees someone running" follows well. But if the major is negative, it does not follow, for "nothing capable of laughter is a donkey, every man sees something capable of laughter, therefore no man sees a donkey" does not follow.
In aliis casibus non tenet processus quando aliqua praemissa est de obliquo, sed semper servandae sunt regulae positae in prioribus capitulis. Propter quod tales discursus non valent ‘omnis homo videt asinum; tantum risibile est homo; igitur tantum risibile videt asinum'; 'omnis hominis est asinus; omne album praeter Sortem est homo; igitur omnis albi praeter Sortem est asinus', et huiusmodi, sive arguatur ex terminis praecise importantibus res creatas sive increatas.	The procedure does not hold in other cases when some premiss is in the oblique case, but the rules given in the previous chapters always hold.  Because of this, such discourses as "every man sees a donkey, the only thing capable of laughter is a man, therefore the only thing capable of laughter sees a donkey", "to every man belongs a donkey, everything white apart from Socrates is a man, therefore to everything white apart from Socrates there belongs a donkey", and similar discourses are not valid, whether the argument is from terms precisely conveying created or uncreated things.