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Tricia Irwin, Salvador Mascarenhas, Tim Leffel, Simon Charlow, and Mike Solomon for inspiration, discussion, copies of unpublished work, data, ideas, and/or help.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.

Verbal Probabilities: An Alternative Approach

“…The tendency to identify certain with the lower end and possible with the high end of a distribution is also compatible with linguistic analyses of at least and at most readings of numbers, discussed in the introduction. Such readings seem to be particularly frequent in interaction with modals (Lassiter, 2010;Musolino, 2004). Our results add to these analyses by showing empirically that the reverse relationship also applies, namely that epistemic modals induce speakers to select numbers in accordance with such readings.…”

“….5 would more accurately be described as likely (Yalcin, 2010). Lassiter (2010) has shown that these three epistemic modals (certain, probable/ likely, and possible) span an underlying "totally closed" scale (i.e., a scale with definite lower and upper bounds; cf. Kennedy & McNally, 2005), similar to the metric (0, 1) probability scale.…”

Gradability across grammatical domains

“…'Gauzner-Michl is more likely to be the murderer than Kastenjakl. ' Lassiter (2010Lassiter ( , 2011Lassiter ( , 2014Lassiter ( , 2017ab) and Villalta (2008), among others, explicitly model modal meanings using abstract scales. Lassiter 2010, following Yalcin (2010), proposes a model of English gradable epistemic modals like possible and likely in which they are associated with a scale of numerical probabilities.…”

“…goodness, leaving open the possibility that multiple worlds could 24. Lassiter (2010) argues that distinctions in scale type (described as open versus closed scales by Kennedy and McNally 2005 in the context of gradable adjectives) are relevant to an analysis of gradable epistemic modals. Logoori kudoka is not sensitive to distinctions in scale type, so we do not discuss these differences in our paper.…”

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.…”