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.

The same is evident in these propositions, Petrum non currere est possibile, est contingens, non est impossibile, Petrum currere non est necessarium: for if Peter can exist without running, therefore Peter's not running is contingent, therefore it is not impossible, therefore there is no necessity of running, for if he had to run necessarily, he could not cease from running. But these four propositions are so openly equivalent in the second figure, edentuli, whose first and second proposition is possibile, et contingens est, Petrum non currere (that is, to lack running); the third, non est impossibile Petrum non currere; but the fourth, non est necessarium Petrum currere.

Nor are these more difficult, Petrum non currere non est possibile, non est contingens, est impossibile, Petrum currere est necessarium: for it is evident even to the eyes that he who runs necessarily cannot not run: because not to be able not to run is altogether the same as to have the necessity of running; but if he cannot not run, but necessarily runs, therefore not running is not contingent to him, therefore it is impossible, because the non-contingent and the impossible are the same. But these four so clear propositions are contained in their order in the third figure, purpurea, whose first and second is Petrum non currere (that is, to lack running) non est possibile, non contingens. The third, Petrum non currere est impossibile. The fourth, Petrum currere est necessarium.

Likewise these are known per se, Petrus currere non potest, nec illi potest contingere, est illi impossibile, est illi necessarium cursu carere: for if he cannot run, neither is it contingent; but if it cannot happen, therefore it is impossible to run; but if it is impossible to run, therefore not to run is necessary; but this doctrine is contained in the fourth figure, illiace, whose first and second is Petrum currere non est possibile, non contingens. The third, it is impossible. The fourth, Petrum non currere est necessarium.

Where note that the two first propositions are affirmative or negative in altogether the same way. But the third is negative as to the mode, when the two former are affirmative as to the same mode: because if in the first possible and contingent are affirmed, in the third impossible must be denied, so that with it denied possibility may be affirmed. But when the first and second deny the mode, the third must affirm it, because if in the first and second possibility is denied, in the third equivalent to them impossibility must be affirmed, so that with it affirmed possibility may be denied. But the fourth proposition has for its dictum the contradictory of the dicta of the preceding ones; for if in the three former the dictum is positive or affirmative, in the fourth it is privative or negative; for example, if in the former it is said Petrum currere, in the fourth it is said Petrum non currere; but if in the former it is said non currere, in the fourth it is said Petrum currere, because the mode necesse demands this, otherwise they will not be equivalent. For example, in illiace it is said Petrum disputare non est possibile, non contingens, est impossibile; if it were said in the fourth Petrum disputare est necesse, it would be so far from equivalence that it would yield the opposite sense; whence it is necessarily said non disputare est necesse. And so in any figure the three first propositions are similar in affirming or denying the dictum; for if it is affirmed in the first, it is affirmed in the second and third, but in the fourth it is denied. Finally consider by which negations or which affirmations the same sense is restored; then you will render equivalent propositions. I see that these things are troublesome, but they cannot be omitted, although I omit what I can.