Authors/Ockham/Summa Logicae/Book III-3/Chapter 16

Latin	English
CAP. 16. DE AEQUIPOLLENTIA PROPOSITIONUM DE IMPOSSIBILI.	Chapter 16. On the equivalence of propositions about the impossible.
Circa propositiones de impossibili est primo sciendum quod nulla earum est prima, quia quaelibet illarum aequipollet opposito alicuius propositionis de possibili, et ideo de qualibet quaerendum est cui aequipolleat.	Regarding propositions about the impossible, it must first be known that none of them is first, because each of them is equivalent to the opposite of some proposition about the possible, and therefore we must inquire about each one to which it is equivalent.
Et cum dictum sit quod `impossibile' aequivalet isti `non possibile', faciliter potest sciri per praedicta cui aequipollet propositio de impossibili, ponendo `non possibile' loco istius modi `impossibile'.	And since it has been said that `impossible' is equivalent to `not possible', it can easily be known from the above to what the proposition about the impossible is equivalent, by putting `not possible' in the place of that mode `impossible'.
Est igitur sciendum quod quandoque iste modus est affirmatus, ita scilicet quod negatio non negat eum; sicut hic `impossibile est omne animal esse hominem', `impossibile est aliquod animal esse hominem'.	It should therefore be known that sometimes this mode is affirmed, namely in such a way that the negation does not negate it; as here: `it is impossible for every animal to be a man', `it is impossible for any animal to be a man'.
Quandoque autem est negatus per aliam negationem, sicut hic: `non impossibile est omne animal esse hominem', `non impossibile est omnem hominem currere'.	But sometimes it is negated by another negation, as here `it is not impossible for every animal to be a man', `it is not impossible for every man to run'.
In primo casu, quando scilicet nulla negatio negat modum impossibilitatis, tunc illa de impossibili aequipollet uni de neƿcessario, sicut illa de possibili, in qua modus negatur, aequipollet uni de necessario.	In the first case, namely when no negation denies the mode of impossibility, then that of the impossible is equivalent to one of the necessary, just as that of the possible, in which the mode is denied, is equivalent to one of the necessary.
Unde ista `impossibile est omne animal esse hominem' aequipollet isti `necesse est aliquod animal non esse hominem'; et ista `impossibile est nullum animal esse hominem' aequipollet isti `necesse est aliquod animal esse hominem'; et ista `impossibile est aliquod animal esse hominem' aequipollet isti `necesse est nullum animal esse hominem'; et ista `impossibile est aliquod animal non esse hominem' aequipollet isti `necesse est omne animal esse hominem'.	Hence, `it is impossible for every animal to be a man' is equivalent to `it is necessary for some animal not to be a man'; and `it is impossible for no animal to be a man' is equivalent to `it is necessary for some animal to be a man'; and `it is impossible for any animal to be a man' is equivalent to `it is necessary for no animal to be a man'; and `it is impossible for any animal not to be a man' is equivalent to `it is necessary for every animal to be a man'.
Si autem modus impossibilitatis sit negatus, tunc mutabitur modus impossibilitatis in modum possibilitatis; sicut ista `non impossibile est omne animal esse hominem' aequipollet isti `possibile est aliquod animal esse hominem'.	But if the mode of impossibility is denied, then the mode of impossibility will be changed into the mode of possibility; just as `it is not impossible for every animal to be a man' is equivalent to `it is possible for some animal to be a man'.
Ex quo enim modus possibilitatis, quando negatur, debet mutari in modum necessitatis, et modus necessitatis, quando negatur, debet mutari in modum possibilitatis affirmatum, necesse est quod impossibile, quando negatur, mutetur in modum possibilitatis.	For since the mode of possibility, when denied, must be changed into the mode of necessity, and the mode of necessity, when denied, must be changed into the mode of possibility affirmed, it is necessary that the impossible, when denied, be changed into the mode of possibility.
Per praedicta, et per illam regulam de aequipollentiis propositionum de inesse prae contradic, post contra; prae-post que subalter potest faciliter aequipollentia propositionum modalium sciri. Et ideo ista de aequipollentis earum sufficiant.	By the above, and by that rule about the equivalences of propositions about essence before <contradic>, after <contra>; and pre--post subordination, the equivalence of modal propositions can easily be known. And therefore these things about their equivalences suffice.