  One might avoid this consequence by requiring only invariance under permutations that preserve the relevant structure on these domains (accessibility relations, temporal ordering). But one would then be faced with the task of explaining why this structure deserves special treatment (cf. van Benthem 1989, 334). And if we are allowed to keep some structure on the domain of worlds or times fixed, the question immediately arises why we should not also keep some structure on the domain of objects fixed: for example, the set-theoretic membership relation, the mereological part/whole relation, or the distinction between existent and nonexistent objects (see the entry on free logics). Whatever resources we appeal to in answering this question will be doing at least as much work as permutation invariance in the resulting demarcation of logical constants.