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5 To be sure, a necessary proposition c~ which is true in every case a f o r t i o r i has to be true in at least one case, hence a is possible. But this principle or the corresponding quantificational law (Vxct --+ 3zc~) cannot be correctly derived from the presupposed equivalence (Vxa ~ ~3x-,c~) plus the law of double negation, (---~a ~ a) in the way a t t e m p t e d by Leibniz. e. e. 3x-~-~c~! It cannot be overlooked, however, t h a t the t r u t h conditions quoted from the early De Conditionibus, even when combined with Leibniz's later views on possible worlds, fail to come up to the standards of modern possible worlds semantics, since in Leibniz's work nothing corresponds to the accessability relation among worlds.

65Cf. ] omne necessarium est possible. Nam semper, si omnis est, etiam quidam est. Si enim Omnis est, non quidam non est seu quidam non non est. Ergo quidam est". 42 Wolfgang Lenzen (NEC 5) [--]a ~ [--IWlc~. Poser pointed out to the following passage in "De Affectibus": "For what can impossibly be actually the case, that can impossibly be possible ''66 which rather convincingly shows that, in Leibniz's view, any impossible proposition is impossibly possible: (NEC 6) -~(}c~ -+ ~ ( } ~ a . However, Poser failed to give any quotation (or any other compelling reason) to show that Leibniz would also have accepted the stronger S5-principle (}a -+ [--l~a, according t o w h i c h any possible proposition would be necessarily possible.

But it is necessary that A and B have nothing in common" (C. 267, # 29). 23 A precise definition of this new relation presupposes t h a t one first introduces the more familiar relation 'A contains B' or its converse 'A is contained in B', formally A C_ B, as follows: A + Y = C means 'A is in C', or 'C contains A'. (cf. C. 265, # # 10). , 268). 22 Wolfgang Lenzen T h a t is, C contains A iff there is some set Y such t h a t the union of A and Y equals C. As Leibniz noted in Prop. 13 and Prop.