 The worry is that a theory of meaning or content which includes impossible worlds will not be compositional. Consider what we said above about the exportation principle (Section 6.1) and the semantics of negation (Section 6.4). An impossible world may represent that \(\neg A\) independently of whether it represents that \(A\). But then, for such worlds, the truth-value of \(\neg A\) is not a function of the truth-value of \(A\). So, the worry goes, the content or proposition that \(\neg A\), understood as a set of possible and impossible worlds, will not be a function of the proposition that \(A\). (Certainly, the latter is not the set-theoretic complement of the former, as it is on the possible worlds account.) The same goes for all the other logically complex sentences. This is perhaps the most serious objection to the impossible worlds approach. If it can’t be met, it may well be fatal.