Authors/Ockham/Summa Logicae/Book III-1/Chapter 3

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Latin English
[Cap. 3 De syllogismis factis in prima figura] [Chapter 3. Of syllogisms constructed in the first figure]
Istis visis videndum est primo de syllogismo primae figurae. Et est primo sciendum quod, cum dictum sit omnes syllogismos primae figurae regulari immediate per dici de omni vel per dici de nullo, oportet circa modos primae figurae servare duo principia. With these matters seen, we should first look at the syllogism of the first figure. And it should first be known that, since we said that all syllogisms of the first figure are governed by dici de omni, or by dici de nullo, we have to keep two principles concerning the modes of the first figure.
Primum est quod maior sit propositio universalis. Si enim maior esset particularis, patet manifeste quod talis discursus non posset regulari per dici de omni nec per dici de nullo. Tunc enim aliquis syllogismus regulatur per dici de omni quando per primam propositionem denotatur de omni illo de quo dicitur subiectum here dici praedicatum, et per secundanl propositionem denotatur subiectum primae propositionis vere dici de aliquo assumpto. The first is that the major is a universal proposition. For if the major were particular, it is manifestly clear that such a discourse could not be governed by dici de omni, or by dici de nullo. For then some syllogism is governed by by dici de omni when it is denoted by the first proposition that of everything the subject is predicated, the predicate is truly predicated, and by the second proposition it is denoted that the subject of the first proposition is truly predicated of some assumed thing.
Sicut per istam propositionem 'omnis homo est animal' denotatur quod de quocumque dicitur 'homo' de eodem dicitur 'animal'; per istam autem secundam 'Sortes est homo' denotatur quod 'homo', qui fuit subiectum primae propositionis, vere dicitur de Sorte; propter quod evidenter sequitur quod hoc praedicatum 'animal' vere dicitur de Sorte. Et ideo iste syllogismus est regulatus per dici de omni 'omnis homo est animal; Sortes est homo; igitur Sortes est animal'. For example, it is denoted by the proposition "every man is an animal" that whatever 'man' is predicated of, 'animal' is predicated of, and by the second "Socrates is a man" it is denoted that 'man', which was the subject of the first proposition, is truly predicated of Socrates, on account of which it evidently follows that the predicate 'animal' is truly predicated of Socrates. And therefore the syllogism "Every man is an animal, Socrates is an animal, therefore Socrates is an animal" is governed by dici de omni.
Et eodem modo, proportionaliter, dicendum est de syllogismo regulato per dici de nullo. Sed nihil tale potest denotari per propositionem particularem, igitur numquam propositio particularis potest esse maior in prima figura. And we should speak in the same way of the syllogism governed by dici de omni. But nothing such can be denoted by a particular proposition, therefore a particular proposition can never be the major in the first figure.
Ex eodem patet quod minor semper debet esse affirmativa, quia semper per minorem debet denotari quod illud quod in prima propositione fuit subiectum vere praedicatur de aliquo determinato assumpto, quod non potest esse nisi per propositionem affirmativam. From the same thing it is clear that the minor always ought to be affirmative, for it should always be denoted by the minor that what was the subject in the first premiss is truly predicated of some determinate assumed thing, which can only be the case in an affirmative proposition.
Ex praedictis sequitur quod in prima figura sunt tantum quatuor modi in quibus fiunt utiles coniugationes. Nam combinando duas propositiones per universalem et particularem, per affirmativam et negativam, sexdecim erunt combinationes, quarum duodecim peccabunt contra praedicta principia. Quod patet sic. Si sint duae propositiones, aut utraque est universalis aut utraque particularis, aut una universalis et alia particularis. Si autem utraque sit universalis, aut utraque est affirmativa aut utraque negativa, aut una affirmativa et alia negativa. Si utraque sit affirmativa, sic est primus modus et utilis, si utraque sit negativa, sic est alia coniugatio et est inutilis, quia habet minorem negativam. Si una sit affirmativa et alia negativa, aut maior est negativa et minor affirma tiva, vel e converso; si primo modo, habetur tertia coniugatio, et est utilis; si e converso, est quarta et inutilis, quia habet minorem negativam. From this it follows that there are only four modes in the first figure in which useful conjunctions can be made. For in combining two propositions by universal and particular, and by affirmative and negative, there will be sixteen combinations, of which twelve will err against the previous principles. Which is clear as follows. If there are two propositions, either both are universal or both particular, or one universal and the other particular. But if both are universal, either both are universal or both negative, or one is affirmative and the other negative. If both are affirmative, it is the first mode and useful. If both are negative, it is the other conjunction and is useless, because it has a negative minor. If one is affirmative and the other negative, other the major is negative and the minor affirmative, or conversely. If the first mode, it would have the third conjunction, and is useful. If conversely, it is the fourth and useless, for it has a negative minor.
Si utraque sit propositio particularis, sic fiunt quatuor combinationes per affirmativam et negativam, sicut prius, sed omnes erunt inutiles, quia omnes habebunt maiorem particularem. If both are particular propositions, then there will be four combinations of affirmative and negative, just as before, but all will be useless, for all will have a particular minor.
Si autem una sit universalis et alia particularis, aut maior est universalis et minor particularis, aut e converso. Si primo modo, aut utraque est affirmativa et habetur nona coniugatio et utilis, aut utraque negativa, et est decima coniugatio et inutilis, quia minor est negativa. Aut una est affirmativa et alia negativa, et tunc est aut maior affirmativa et minor negativa, et est undecima coniugatio et inutilis, quia minor est negativa; aut maior est negativa et minor affirmativa, et est duodecima coniugatio et utilis. Si autem maior sit particularis et minor universalis, sic fiunt quatuor combinationes per affirmativam et negativam, sed omnes erunt inutiles, quia quaelibet illarum habet maiorem particularem.  But if one is universal and the other particular, either the major is universal and the minor particular, or conversely. If the first mode, either both are affirmative and we have the ninth conjunction and useful, or both are negative, and we have the tenth conjunction and useless, for the minor is negative. Or one is affirmative and the other negative, and then either the major is affirmative and the minor negative, which is the eleventh conjunction and is useless, for the minor is negative, or the major is negative and the minor affirmative, and it is the twelfth conjunction and useful. But if the major is particular and the minor universal, then there will be four combinations of affirmative and negative, but all will be useless, for all of these have a particular major.
Ex quibus omnibus manifeste patet quod tantum sunt quatuor modi utilium coniugationum, scilicet primus et tertius et nonus et duodecimus. Duodecim vero alii sunt inutiles, quia soli quatuor possunt regulari per dici de omni vel per dici de nullo; alii non possunt, quia semper habent maiorem particularem vel minorem negativam, quorum utrumque repugnat syllogismo regulato per dici de omni vel per dici de nullo.  From all of these cases it is manifestly clear that there are only four modes of useful conjunctions, namely the first, the third, the ninth and the twelfth. But the twelve others are useless, for only four are governed by dici de omni or by dici de nullo. The others cannot, because they always have a particular major or negative minor, of which both conflict with a syllogism governed by dici de omni or by dici de nullo.

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