Será S5 o sistema de lógica modal correto para a modalidade metafísica?

Abstract

This work is in a simultaneous investigation in both modal logic and modal metaphysics. We seek to the system of modal propositional logic correct for metaphysical modality or modality tout court. Being understood as 'metaphysical modality' the modality with respect to the ways of truth; if the truth value of a proposition (true / false) is necessary or possible. An arbitrary proposition, , can be true while necessarily , (ï ), can be false. For other hand, can be false while possibly , (³ ), can be true. In addition to the actual truth value of the proposition, its truth value in alternative possible worlds is indispensable. Suppose two propositions: i) there are objects that travel faster than light, and ii) there are round squares. Both are actually false, but sometimes it is said that there are possible worlds in which i) is true; the way how i) is false is contingent (¬.. ³..). But have ii) is false in all possible worlds, the way how ii) is false is necessary (¬.. ¬³..). Even who thinks that i) is necessarily false, can still accept that if things had been different from the way of they actually are, maybe i) could have been true while ii) for all alternative ways of being of things, could not have been true. Thus, i) is impossible under some ways of being of things and ii) is impossible under any ways of being of things. Iteration cases of modal operators are particularly important here. Is the conditional if necessary , then necessarily necessary true? It depends. Are presented here five modal systems: K, T, B, S4 and S5 in order of strength, with the strongest S5. In S4 and S5 the conditional is true, in the weaker systems it is false. S5 is conventionally accepted as the appropriate modal system for metaphysical modality. Here, however, some objections to this common place and answers to them are presented and discussed. The modal logic with the possible-worlds semantics and some notions of modal metaphysics are presented as preliminary study.