Abstract

A highly technical defense of a standard interpretation of “possible” and of “necessary” is given. Specifically, arguments are made for the S5 system of modal logic as background for many of the arguments in the rest of the book. These begin with arguments against analyzing metaphysical necessity in terms of narrow logical necessity (or provability). It is shown, for example, that if metaphysical necessity were narrow logical necessity, then, given Gödel's incompleteness theorems, you get absurd possibilities, like the possibility that 1 = 0 is necessary. Independent arguments are also supplied for the characteristic axioms of S4 and S5. All these arguments help motivate the minimal claim that S5 implicitly defines a coherent concept of “possibility” and of “necessity” relevant to the arguments presented.