Universa Philosophia

I have already said in section 4 that equivalence is two equivalent propositions, of which each is of the same predicate and subject, and that it occurs by adding or removing a negation, as omnis homo currit, nullus homo non currit are equivalent, because nullus non and omnis are the same, for two negations affirm. Hence it is most clearly evident that four modal propositions of one figure are mutually equivalent. For who does not see that these propositions signify the same thing? Cursus Petri est possibilis, est contingens, non est impossibilis. Petrum a cursu cessare non est necessarium; for if the running is possible, and contingent, it is not impossible, because the possible is not the impossible; but if it is not impossible, therefore its absence is not necessary: for if Peter necessarily ceased from running, he could not run, and the running would be impossible, because when the absence of a thing is necessary, such a thing is impossible. e.g. the absence of an irrational man is necessary, therefore an irrational man is impossible, because if he were possible, he would remove that absence, which would thus be contingent, but not necessary. These things, which are most clear, are contained in the first figure amabimus, whose first and second proposition is Petrum currere est possibile, et contingens; the third, Petrum currere non est impossibile; the fourth, Petrum non currere non est necesse, because the third, concerning the impossible, with non added, is equivalent to the possible, for they are the same: est non impossibile and possibile. But the fourth, which has two negations, namely the negation of running and the negation of necessity, denies the necessity of ceasing from running; but he who does not have the necessity of ceasing from running, or of not running, can run, and accordingly his running is not impossible, is possible, and contingent.