According to Kratzer’s influential account of epistemic must and might, these operators involve quantification over domains of possibilities determined by a modal base and an ordering source. Recently, this account has been challenged by invoking contexts of ‘epistemic tension’: i.e., cases in which an assertion that mustϕ\documentclass[12pt]{minimal}
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\begin{document}$$\lnot \phi $$\end{document}, and cases in which speakers try to downplay a previous assertion that mustϕ\documentclass[12pt]{minimal}
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\begin{document}$$\lnot \phi $$\end{document}. Epistemic tensions have been invoked from two directions. Von Fintel and Gillies (Nat Lang Semant 18(4):351–383, 2010) propose a return to a simpler modal logic-inspired account: must and might still involve universal and existential quantification, but the domains of possibilities are determined solely by realistic modal bases. In contrast, Lassiter (Nat Lang Semant 24(2):117–163, 2016), following Swanson (Interactions with context. Ph.D. thesis, MIT, 2006; and in A. Eagan and B. Weatherstone, eds., Epistemic Modality, Oxford UP, 2011), proposes a more revisionary account which treats must and might as probabilistic operators. In this paper, we present a series of experiments to obtain reliable data on the degree of acceptability of various contexts of epistemic tension. Our experiments include novel variations that, we argue, are required to make progress in this debate. We show that restricted quantificational accounts à la Kratzer fit the overall pattern of results better than either of their recent competitors. In addition, our results help us identify the key components of restricted quantificational accounts, and on that basis propose some refinements and general constraints that should be satisfied by any account of the modal auxiliaries.
