Authors/Ockham/Summa Logicae/Book III-3/Chapter 14

Latin	English
CAP. 14. DE AEQUIPOLLENTIIS PROPOSITIONUM IN QUIBUS PONITUR ISTE MODUS `NECESSARIUM'.	Chapter 14. Concerning the equivalent propositions in which the 'necessary' mode is placed.
Istis praemissis, tamquam quibusdam praeambulis, videndum est de aequipollentiis istarum propositionum. Et causa brevitatis tantum dicendum est de modalibus famosis, quia ex istis potest studiosus conicere quid de aliis est dicendum.	With these premises, as some preambles, it is necessary to see the equivalence of these propositions. And for the sake of brevity it is necessary to say only about the well-known modalities, because from these the student can guess what is to be said about the others.
Primo autem videndum est de propositione in qua ponitur iste modus `necessarium'. De qua dicendum est quod negatio aut non negat modum aut negat modum.	First, however, we must look at the proposition in which this `necessary' mode is used. Of which we must say that negation either does not negate the mode or negates the mode.
Si primo modo, semper talis propositio aequivalet alicui primae de necessario, quia in tali casu, retento eodem modo, dicendum est consimiliter de aequipollentia illius et de aequipollentia suae de inesse. Unde sicut ista `non omne animal est homo' aequipollet isti `aliquod animal non est homo', ita ista `necesse est non omne animal esse hominem' aequivalet isti `necesse est aliquod animal non ƿ esse hominem'. Et ita est generaliter de omnibus talibus.	If, in the first way, such a proposition is always equivalent to something of the first necessity, because in such a case, retained in the same way, it must be said similarly about the equivalence of that and the equivalence of its existence. Hence, just as this `not every animal is a man' is equivalent to `some animals are not man', so this `it is necessary that not every animal is a man' is equivalent to `it is necessary that some animal is not a man'. And so it is generally with all such things.
Si autem modus necessitatis negetur et etiam signum, si habeat signum, tunc modus negatus mutandus est in modum quem infert, scilicet in possibile affirmatum et residuum in contradictorium; sicut ista `non necesse est omne animal esse hominem' aequipollet isti `possibile est aliquod animal non esse hominem'. Si autem modus negetur et non signum, solum modus mutabitur in possibile affirmatum; unde ista `nullus homo de necessitate est animal' aequipollet isti `omnis homo potest non esse animal'. Et ideo non est quaerendum cui aequipollet ista `omnis homo de necessitate non est animal', sed cui aequipollet ista `nullus homo de necessitate est animal'. Et est dicendum sicut nunc dictum est. Et hoc, quia istae aequipollent `omnis homo de necessitate non est animal' et `necesse est nullum hominem esse animal'; ista autem `non omnis homo de necessitate est animal' aequivalet isti `aliquis homo potest non esse animal'. Et ita est de aliis.	Now if the mode of necessity is denied and also the sign, if it has a sign, then the negated mode must be changed into the mode which it implies, that is, the affirmative in the possible and the remainder into the contradictory; just as this `it is not necessary for every animal to be a man' is equivalent to this `it is possible for some animal not to be a man'. But if the mode is denied and not the sign, only the mode will be changed in the affirmative; whence the statement `no man is necessarily an animal' is equivalent to these `every man can not be an animal'. And therefore it is not necessary to ask to whom the statement `every man is not necessarily an animal' is equivalent, but to whom the statement `no man is necessarily an animal' is equivalent. And it must be said as it has now been said. And this, because these are equivalent to `every man is not necessarily an animal' and `it is necessary for no man to be an animal'; But this statement `not every man is necessarily an animal' is equivalent to this `some man may not be an animal.' And so it is with others.
Et sicut dictum est de propositionibus de necessario respectu propositionum de possibili, ita est dicendum, proportionaliter, de propositionibus de possibili respectu propositionum de necessario. Nam quando modus possibilitatis remanet affirmatus, non est mutandus modus, sed quantum ad residuum accipienda est proportionaliter aequipollentia sicut in illis de inesse. Unde ista `possibile est non omnem hominem esse animal' aequipollet isti `possibile est aliquem hominem non esse animal'.	And just as it was said of propositions of the necessary with respect to propositions of the possible, so it must be said, proportionally, of propositions of the possible with respect to propositions of the necessary. For when the mode of possibility remains affirmed, there is no need to change the mode, but as to the remainder it is to be taken proportionally equivalent as in those of being. Hence this statement `it is possible that not every man is an animal' is equivalent to `it is possible that some man is not an animal'.
Quando autem tam signum quam modus negatur, tunc modus possibilitatis mutandus est in modum necessitatis et reliquum in contradictorium, sicut sua de inesse. Unde ista `non est possibile omne animal esse hominem' aequivalet isti `necesse est aliquod animal non esse hominem'.	But when both the sign and the mode are denied, then the mode of possibility must be changed into the mode of necessity, and the rest into a contradictory one, as of its being. Hence this statement `it is not possible for every animal to be a man' is equivalent to this `it is necessary for some animal not to be a man'.
Quando autem signum non negatur sed tantum modus possibilitatis, tunc praecise mutandus est modus possibilitatis in modum necessitatis et non signum universale in signum particulare, nec e converso.	But when the sign is not negated but only the mode of possibility, then precisely the mode of possibility must be changed into the mode of necessity and not a universal sign into a particular sign, nor vice versa.
Sicut ista `nullus homo potest esse animal' aequipollet isti `omnis homo de necessitate non est animal'. Et tunc, quamvis modus universalis non mutetur in modum particularem nec e converso, tamen modus univerƿsalis negativus mutandus est in modum universalem affirmativum, non negatum sed affirmatum, sicut patet in exemplo proposito.	Just as the statement `no man can be an animal' is equivalent to `every man is necessarily not an animal'. And then, although the universal mode is not changed into a particular mode, nor vice versa, yet the negative mode of the universal must be changed into the universal affirmative mode, not denied but affirmed, as is evident in the proposed example.
Ex istis faciliter patere possunt aequipollentiae propositionum in quibus ponuntur isti modi 'necessarium', `possibile'. Ex quibus etiam faciliter patere potest quae propositiones repugnant, scito quae propositiones primae repugnant et quae non.	From these it can easily be seen that the equivalence of propositions in which the terms 'necessary' and 'possible' are placed. From which it is also easily evident which propositions are contradictory, knowing which propositions are incompatible with the first and which are not.
Unde sciendum est quod istae propositiones `omnis homo de necessitate est animal', `omnis homo de necessitate non est animal' repugnant contrarie, sicut istae `necesse est omnem hominem esse animal', `necesse est nullum hominem esse animal'.	Hence it must be known that these propositions, `every man is necessarily an animal', `every man is not necessarily an animal,' are mutually contradictory, just as these propositions, `it is necessary for every man to be an animal,' and `it is necessary for no man to be an animal'.
Istae etiam sunt repugnantes `omnis homo de necessitate est animal', `aliquis homo de necessitate non est animal'; non tamen proprie contrarie, eo quod non utraque est universalis.	These are also contradictory: `every man is necessarily an animal', `some man is not necessarily an animal'; not, however, properly on the contrary, inasmuch as both are not universal.
Nec sunt contradictoriae, quia possunt simul esse falsae; et ita plus conveniunt cum contrariis, eo quod possunt simul esse falsae, sed non possunt simul esse verae. Eodem modo dicendum est de istis `omnis homo de necessitate non est animal', `aliquis homo de necessitate est animal'.	Nor are they contradictory, because they can be false at the same time; and thus they agree more with their opposites, in that they can be false at the same time, but they cannot be true at the same time. In the same way it must be said of these: 'every man is not of necessity an animal', 'some man is of necessity an animal'.
Istae autem propositiones `omnis homo de necessitate est animal', `aliquis homo potest non esse animal' sunt contradictoriae. Et similiter istae `omnis homo de necessitate non est animal', `aliquis homo potest esse animal'.	But these propositions, `every man is necessarily an animal', `some man may not be an animal' are contradictory. And in the same way as these `every man is not necessarily an animal', `some man can be an animal'.
Istae autem propositiones `omnis homo potest esse animal' `omnis homo potest non esse animal' non repugnant. Nec istae `omnis homo potest non esse animal', `aliquis homo potest esse animal'. Nec istae `omnis homo potest esse animal', `aliquis homo potest non esse animal'.	But these propositions, `every man can be an animal,' and `every man can not be an animal,' do not contradict each other. Nor are these `every man may not be an animal', `any man may be an animal'. Nor are these `every man can be an animal', `some man can not be an animal'.
Sed istae contradicunt `omnis homo potest esse animal', `aliquis homo de necessitate non est animal'; et similiter `omnis homo potest non esse animal' et `aliquis homo de necessitate est animal'.	But these are contradictory: `every man can be an animal', `some man is not necessarily an animal'; and likewise, "every man may not be an animal," and "some man is of necessity an animal."