Measure semantics and qualitative semantics for epistemic modals

Abstract

In this paper, we explore semantics for comparative epistemic modals that avoid the entailment problems shown by Yalcin (2006Yalcin ( , 2009Yalcin ( , 2010 to result from Kratzer's (1991) semantics. In contrast to the alternative semantics presented by Lassiter (2010, 2011) based on finitely additive measures, we introduce semantics based on qualitatively additive measures, as well as semantics based on purely qualitative orderings, including orderings on propositions derived from orderings on worlds in the tradition of Kratzer (1991Kratzer ( , 2012. All of these semantics avoid the entailment problems that result from Kratzer's semantics. Our discussion focuses on methodological issues concerning the choice between different semantics.

Modality, Scale Structure, and Scalar Reasoning

“…The third is controversial, and it may well turn out that likely is associated with a weaker scale which is not connected, but mimics additivity among comparable propositions. (See Keynes, ; Holliday and Icard, and many others.) Non‐connected scales have been suggested for various non‐modal adjectives as well (e.g.…”

“…For reasons that we have already seen, this argument is correctly rendered invalid if likely lives on a probability scale. This is a good result, but not, of course, proof that probability is the right scale: there are weaker logics for likelihood which also invalidate this inference and have other desirable features (Holliday and Icard, ).…”

Alternatives and Truthmakers in Conditional Semantics

“…Following Kratzer (1981bKratzer ( , 1991Kratzer ( , 2012, I assume that if -clauses work as restrictors of the domain of quantification (modal base) of modals. Moreover, following recent work (Yalcin 2010, Lassiter 2011, Holliday & Icard 2013, I assume that probably has a probabilistic semantics (or at least a semantics that yields an equivalent logic). Roughly, probably ϕ says that the probability of ϕ is higher than .5.…”

Fatalism and the Logic of Unconditionals

“…40 By contrast, versions of this argument pattern involving epistemic comparatives like more probable and at least as likely aren't unrestrictedly valid. See Yalcin (2010); Lassiter (2010Lassiter ( , 2017; Holliday & Icard (2013) for discussion. 41 I assume here that valid (deductively good) inferences preserve support.…”