Some afterthoughts on my previous remarks about “ontological pluralism.” I said there that
A “string of symbols” cannot “come out true in some languages but false in others, while meaning what it actually means,” because “what it actually means” is not specifiable language-independently. To suppose that a string of symbols “actually” means something independently of the language it is expressed in is just to take an external statement literally, at face value.
Of course there may be multiple explicata for a single explicandum, but this is not a case of a string of symbols coming out true in some languages but false in others; the different explications are not prima facie comparable; they mean different things as they are framed in different languages, just as positive-integer-valued real numbers are not (without further ado) to be identified with the natural numbers resulting from the Dedekind axioms. Nor are the Dedekind natural numbers to be identified, initially, with the Frege-Russell natural numbers. Of course we can seek to conjoin the two languages, or locate both within a single larger language, such as ZFC, but even then “number” means something different under the two proposed explications, even though they are within the same linguistic framework.
Something Howard Stein pointed out over two decades ago, but is almost invariably missed in discussions of Carnapian explication — not only among would-be Carnapian metaphysicians — is the fact that, since explicandum and explicatum are generally embedded in different languages, the relation between them is not internal but external, in the sense that the question whether a given explication is a good one, or whether its uses “sufficiently resemble” those of its explicandum (for given purposes), or whether one explication is preferable to another, are external questions, framed in a third language that (in that case) includes pragmatic or normative components (see Stein’s 1992 paper, linked to above, p. 280).
Carnap’s pluralism was consistently linguistic. He did not regard ontological assertions as having cognitive significance, though he thought some of them could, at a stretch, be given practical (normative) significance — but only with respect to choices among languages or explications (i.e. to choices among “worlds” only insofar as these are linguistic proposals).