We derive a probabilistic account of the vagueness and context-sensitivity of scalar adjectives from a Bayesian approach to communication and interpretation. We describe an iterated-reasoning architecture for pragmatic interpretation and illustrate it with a simple scalar implicature example. We then show how to enrich the apparatus to handle pragmatic reasoning about the values of free variables, explore its predictions about the interpretation of scalar adjectives, and show how this model implements Edgington's (Analysis 2:193-204,1992, Keefe and Smith (eds.) Vagueness: a reader, 1997) account of the sorites paradox, with variations. The Bayesian approach has a number of explanatory virtues: in particular, it does not require any special-purpose machinery for handling vagueness, and it is integrated with a promising new approach to pragmatics and other areas of cognitive science. Edgington (1992Edgington ( , 1997 proposes an attractive unified approach to the Sorites, Lottery, and Preface paradoxes. According to Edgington, these puzzles are all explained by a generalization of classical logic which has the formal structure of the probability calculus, with an accompanying generalized notion of valid reasoning. She gives a number of strong arguments to the effect that a degree-based theory of vagueness with the formal structure of probabilities is preferable to one with the structure of classical fuzzy logic. However, she explicitly disavows the idea that the degrees involved in B Daniel Lassiter

How do comprehenders reason about pragmatically ambiguous scalar terms like some in complex syntactic contexts? In many pragmatic theories of conversational implicature, local exhaustification of such terms ('only some') is predicted to be difficult or impossible if the result does not entail the literal meaning, whereas grammatical accounts predict such construals to be robustly available. Recent experimental evidence supports the salience of these local enrichments, but the grammatical theories that have been argued to account for this evidence do not provide explicit mechanisms for weighting such construals against others. We propose a probabilistic model that combines previous work on pragmatic inference under 'lexical uncertainty' with a more detailed model of compositional semantics. We show that this model makes accurate predictions about new experimental data on embedded implicatures in both non-monotonic and downward-entailing semantic contexts. In addition, the model's predictions can be improved by the incorporation of neo-Gricean hypotheses about lexical alternatives. This work thus contributes to a synthesis of grammatical and probabilistic views on pragmatic inference.

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Relative adjectives in the positive form exhibit vagueness and context-sensitivity. We suggest that these phenomena can be explained by the interaction of a free threshold variable in the meaning of the positive form with a probabilistic model of pragmatic inference. We describe a formal model of utterance interpretation as coordination, which jointly infers the value of the threshold variable and the intended meaning of the sentence. We report simulations exploring the effect of background statistical knowledge on adjective interpretation in this model. Motivated by these simulation results, we suggest that this approach can account for the correlation between scale structure and the relative/absolute distinction while also allowing for exceptions noted in previous work. Finally, we argue for a probabilistic explanation of why the sorites paradox is compelling with relative adjectives even though the second premise is false on a universal interpretation, and show that this account predicts Kennedy’s (2007) observation that the sorites paradox is more compelling with relative than with absolute adjectives.

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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.

Consideration of the metalinguistic effects of utterances involving vague terms has led Barker [1] to treat vagueness using a modified Stalnakerian model of assertion. I present a sorites-like puzzle for factual beliefs in the standard Stalnakerian model [28] and show that it can be resolved by enriching the model to make use of probabilistic belief spaces. An analogous problem arises for metalinguistic information in Barker's model, and I suggest that a similar enrichment is needed here as well. The result is a probabilistic theory of linguistic representation that retains a classical metalanguage but avoids the undesirable divorce between meaning and use inherent in the epistemic theory [34]. I also show that the probabilistic approach provides a plausible account of the sorites paradox and higher-order vagueness and that it fares well empirically and conceptually in comparison to leading competitors.

Relative adjectives in the positive form exhibit vagueness and context-sensitivity. We suggest that these phenomena can be explained by the interaction of a free threshold variable in the meaning of the positive form with a probabilistic model of pragmatic inference. We describe a formal model of utterance interpretation as coordination, which jointly infers the value of the threshold variable and the intended meaning of the sentence. We report simulations exploring the effect of background statistical knowledge on adjective interpretation in this model. Motivated by these simulation results, we suggest that this approach can account for the correlation between scale structure and the relative/absolute distinction while also allowing for exceptions noted in previous work. Finally, we argue for a probabilistic explanation of why the sorites paradox is compelling with relative adjectives even though the second premise is false on a universal interpretation, and show that this account predicts Kennedy’s (2007) observation that the sorites paradox is more compelling with relative than with absolute adjectives.