Modality and expressibility

Review of Symbolic Logic:1-39 (forthcoming)
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When embedding data are used to argue against semantic theory A and in favor of semantic theory B, it is important to ask whether A could, after all, make sense of those data. It is possible to ask that question on a case-by-case basis. But suppose we could show that A can make sense of all the embedding data which B can possibly make sense of. This would, in one fell swoop, undermine all arguments in favor of B over A on the basis of embedding data. And, provided that the converse does not hold—that is, that A can make sense of strictly more embedding data than B can—it would also show that there is a precise sense in which B is more constrained than A, yielding a pro tanto simplicity-based consideration in favor of B. In this paper I develop formal tools which allow us to make comparisons of this kind, which I call comparisons of potential expressive power. I motivate the development of these tools by way of the recent debate about epistemic modals. These tools show that several prominent revisionary theories which have been developed in response to facts about how epistemic modals embed are strictly less expressive than the standard relational theory, in the sense that the relational theory can make sense of any embedding data involving epistemic modals which those theories can make sense of, but not vice versa. This necessitates a fundamental reorientation in how to think about the choice between these semantics for epistemic modals, and yields a formal tool for comparing different semantics of fragments of natural language with broad applicability. In concluding I consider in more detail the empirical picture concerning the behavior of epistemic modals in attitude contexts and what this tells us about the theory of epistemic modals in light of the foregoing results.
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First archival date: 2018-11-06
Latest version: 2 (2018-12-18)
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