        On the assumption that there is a (nonempty) set of all possible       worlds and a set of all possible individuals, we can define       “objective” notions of truth at a world and of truth       simpliciter, that is, notions that are not simply       relative to formal, mathematical interpretations but, rather,       correspond to objective reality in all its modal glory. Let       ℒ be a modal language whose names and predicates represent       those in some fragment of ordinary language (as in our examples       (5) and (6) above). Say that M is the        “intended” interpretation of ℒ if (i) its set       W of “possible worlds” is in fact the set of       all possible worlds, (ii) its designated “actual       world” is in fact the actual world, (iii) its set D       of “possible individuals” is in fact the set of all       possible individuals, and (iv) the referents assigned to the       names of ℒ and the intensions assigned to the predicates       of ℒ are the ones they in fact have. Then, where M        is the intended interpretation of ℒ, we can say that       a sentence φ of ℒ is        true at a possible world w just in case φ        is trueM at w, and       that φ is true just in case it is       trueM at the actual world. (Falsity at       w and falsity, simpliciter, are defined accordingly.) Under the       assumption in question, then, the modal clause above takes on pretty much the       exact form of our informal principle Nec.