Authors/Ockham/Summa Logicae/Book III-3/Chapter 35

Latin	English
CAP. 35. DE INDUCTIONE UNIVERSALIUM DE POSSIBILI.	On the Induction of Universal Possibilities
Circa inductionem universalium de possibili est sciendum quod ex singularibus non sequitur universalis, quia ista regula non valet `omnes singulares sunt possibiles, igitur universalis est possibilis'. Sicut non sequitur `haec est possibilis: haec propositio contingens est vera; et haec est possibilis: ista propositio contingens est vera, et sic de singulis; igitur haec est possibilis: omnis propositio contingens est vera'.	Regarding the induction of universals from the possible, it must be known that the universal does not follow from the particular, because this rule does not hold: 'all particulars are possible, therefore the universal is possible'. Just as it does not follow that this is possible: this proposition is contingently true; and this is possible: this proposition is contingently true, and so on about individuals; therefore this is possible: every contingent proposition is true.
Et ita frequenƿter universalis est impossibilis, et tamen quaelibet singularis est possibilis. Et ideo talis consequentia non valet `secundum illud signum continuum esse actu divisum est possibile, et secundum illud signum continuum esse actu divisum est possibile, et sic de singulis, igitur secundum omne signum continuum esse actu divisum est possibile'.	And so often the universal is impossible, and yet every particular is possible. And therefore such a conclusion does not hold: 'According to that continuous sign it is possible to be actually divided, and according to that continuous sign it is actually possible to be divided, and so about each, therefore according to every continuous sign it is actually possible to be divided'.
Et hoc, accipiendo omnes propositiones in sensu compositionis; nam si acciperentur in sensu divisionis, conclusio esset vera, quia ista est vera `secundum omne signum potest continuum dividi'.	And this is so, taking all propositions in the sense of composition; for if they were taken in the sense of division, the conclusion would be true, because this is true, `according to every sign a continuum can be divided.'
Et si dicatur quod sicut ex possibili non sequitur impossibile, ita ex possibilibus non sequitur impossibile, dicendum est quod ex possibilibus et compossibilibus non sequitur impossibile, tamen ex possibilibus et incompossibilibus bene sequitur impossibile.	And if it is said that just as the impossible does not follow from the possible, so the impossible does not follow from the possible, it must be said that the impossible does not follow from the possible and the impossible, yet the impossible does well follow from the possible and the impossible.
Et ita est in proposito, quia singulares talium propositionum universalium impossibilium etsi sint possibiles sunt tamen simul cum hoc incompossibiles.	And so it is in a proposition, because the particulars of such universal impossible propositions, even if they are possible, are nevertheless at the same time incommensurable.
Est tamen hic notandum quod quandoque unius universalis sunt infinitae singulares. Et quando sic est, possibile est quod universalis sit impossibilis et quaelibet singularis possibilis, et tamen nullae duae singulares sunt incompossibiles, immo nullae singulares finitae sunt incompossibiles, sed quaelibet una accepta est incompossibilis omnibus aliis simul sumptis.	It must be noted here, however, that sometimes there are infinite particulars of one universal. And when this is so, it is possible for the universal to be impossible and every singular possible, and yet no two particulars are incompatible, indeed no finite singulars are incompatible, but each one taken alone is incompatible with all the others taken together.
Quandoque autem unius universalis singulares sunt finitae; et tunc si universalis sit impossibilis, necesse est quod aliqua singularis sit impossibilis vel quod aliquae singulares in numero certo sint incompossibiles. Notandum est etiam quod ista regula non est vera `universalis est possibilis, igitur suae singulares sunt possibiles'; sicut si nullus homo sit albus et multi asini sint albi, haec universalis est possibilis `omne album est homo', et tamen nulla singularis est possibilis, quia quocumque albo ƿ demonstrato haec est impossibilis `hoc album est homo'. Tamen si universalis sit possibilis, oportet quod possit habere omnes singulares possibiles; sicut, illo posito, ista `omne album est homo' nullam habet singularem possibilem, et tamen potest habere, quia posito quod nihil esset album nisi homo, tunc istius `omne album est homo' omnes singulares essent possibiles.	And sometimes the particulars of one universal are finite; and then if the universal is impossible, it is necessary that some particular be impossible, or that some particulars in a certain number be incomposable. It must also be noted that this rule is not true: `the universal is possible, therefore its particulars are possible'; just as if no man were white and many asses were white, this universal statement is possible, `every white man is a man,' and yet no singular is possible, because wherever white is pointed out, this statement is impossible, `this white man is a man.' . However, if the universal is possible, it must be able to have all possible particulars; just as, on that positing, the statement `all white is man' has no singular possibility, and yet it can have, because if it were posited that nothing was white but man, then all singulars would be possible for this `all white is man'.