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Epistemic Comparison, Models of Uncertainty, and the Disjunction Puzzle

The best known theory of modality in linguistics (Kratzer 1991, 2012) uses a binary relation on worlds to state truth-conditions for sentences with epistemic auxiliaries, and lifts this order to an order on propositions to state meanings for epistemic comparatives and equatives with likely and probable. It has recently been observed that this theory makes incorrect predictions about the truth-conditions of epistemic comparative and equative sentences in interaction with disjunction. I analyze the source of this problem in Kratzer’s and several related theories, and consider several modifications suggested in the recent literature. All of the theories available either fail to resolve the problem, or generate incorrect predictions about the relationship between must and likely when combined with Kratzer’s semantics for the auxiliaries. Various alternative models of uncertainty are available which can be used as a semantics for likely and do not encounter the semantic problems discussed here. In particular, qualitative and numerical probability have the necessary features, as do several weaker approaches that include probability as a special case. Data involving entailments and degree modification are argued to provide a reason for preferring the probabilistic approach. I then consider several methods of integrating this approach with Kratzer’s semantics for the epistemic auxiliaries, showing that all of them wrongly invalidate the inference from must to (much) more likely than not. I conclude by stating three alternative semantics for the auxiliaries which do better, one quantificational and two probabilistic. The choice between them will depend on the resolution of three open problems involving the meanings of the auxiliaries which are detailed in the concluding section.