Gradable epistemic modals, probability, and scale structure

Abstract

The epistemic modals possible, probable, likely, and certain require a semantics which explains their behavior both as modal operators and as gradable adjectives. An analysis of these items in terms of Kennedy & McNally's (2005) theory of gradability suggests that they are associated with a single, fully closed scale of possibility. An implementation using the standard theory of modality due to Kratzer is shown to make incorrect predictions in several domains. However, identifying the scale of possibility with standard numerical probability explains the facts about gradability and avoids the undesirable predictions of Kratzer's theory.Keywords: gradability, comparison, epistemic modals, probability Gradable modalsMost discussion of the semantics of English modals has focused on the meanings of modal auxiliaries such as must, should, and can, illustrated in (1).(1) a. Harry should be in Sacramento by now.b. My brother can bench press 250 pounds.c. All cameras must be checked at the door.However, English also has a substantial number of adjectival modals such as likely, obligatory, able, and evident. These items are readily gradable, just like the large and well-studied class of gradable adjectives. Some examples are given in (2a)-(2d). * Special thanks to Chris Barker and Seth Yalcin, both of whom have been enormously helpful and inspiring regarding this project. Thanks also to Anna Szabolcsi, Philippe Schlenker, Chris Kennedy, Larry Horn, Angelika Kratzer, Paul Portner, Pauline Jacobson, Julien Dutant, Chris Collins, Bob Frank, Tom Leu, Eytan Zweig, Tricia Irwin, Salvador Mascarenhas, Tim Leffel, Simon Charlow, and Mike Solomon for inspiration, discussion, copies of unpublished work, data, ideas, and/or help. My initial exposure to the idea of thinking about modality and gradability together came in Seth Yalcin's philosophy of language seminar at NYU in 2008, where he floated the idea that possible and probable were instances of minimum-and relative-standard adjectives in K&M's theory and that probability provided the relevant scale. Though most of our subsequent work was done independently, we have reached similar conclusions, as can be seen by comparing the present paper to the forthcoming Yalcin 2010b.

Probability and implicatures: A unified account of the scalar effects of disjunction under modals

“…We should note that even this account cannot explain in full the range of variability observed for closed scale adjectives. 19 For relevant work, see Swanson 2006, Yalcin 2007, Lassiter 2010, Moss 2015b,a. See also Cariani et al 2016 for an up-to-date summary of the arguments for a probabilistic semantics for likely.…”

Axiomatization in the Meaning Sciences

“…Based in part on the problematic entailment predictions of the ordering semantics above, Yalcin [2010] and Lassiter [2010Lassiter [ , 2015 have proposed semantics for epistemic comparatives based on probability models.…”

Measure semantics and qualitative semantics for epistemic modals

“…The scale for height is therefore assumed to be unbounded from above, as seems pretheoretically reasonable. 23 There is a lively current debate about these issues for words such as 'likely' and 'probable' (Lassiter 2010;Klecha 2012). One question is whether they should be interpreted in terms of a closed scale.…”

“…Given the problems raised for Kratzer's semantics in §5, Yalcin (2010) andLassiter Lassiter (2010) propose a measure semantics 8 using models M = W, R,V, F , µ as in §4 where for all w ∈ W , µ w :…”

“…By contrast, Yalcin shows that a semantics based on probability measures avoids these problems. Also motivated by entailment problems for the semantics in Kratzer 1991, Lassiter (2010, 2011 proposes a similar probability-based semantics. With this background, the question naturally arises of whether probability is necessary for an adequate semantics of epistemic comparatives in natural language.…”