A Note on the Cardinalities of Sets of Scalar Alternatives

Bibliographic Data

ID19064007
AuthorsSalvador Mascarenhas (0000-0003-3381-8688, Institut Jean Nicod, Département d’études cognitives, ENS, EHESS, CNRS, PSL University, France, corresponding author)
Year2021
Volume38
Issue3
Pages473-482
Publication date2021-06-24
Open AccessYes
TypeARTICLE
VenueJournal of Semantics (JOURNAL)
Journal identifiersISSN: 0167-5133 • E-ISSN: 1477-4593
PublisherOxford University Press (OUP) (PUBLISHER)
DOI10.1093/jos/ffab011
OpenAlexW3174642060
LanguageEN
Citations received2
References cited11

Formal theories of scalar implicature appeal crucially to a set of alternatives. These are the alternative statements that a speaker could have made but chose not to in pragmatic accounts, and the alternative statements that figure in the computation of exhaustivity operators in grammatical approaches. I show that the three sufficiently explicit theories of alternatives in the literature generate sets of alternatives that grow at least exponentially as a function of the input, and that these theories generate very large sets even for relatively small inputs. For pragmatic accounts of scalar implicature, I argue these results are hard or impossible to square with what we know independently about manipulating alternatives from the psychology of human reasoning. I propose that they pose a weaker but more general challenge for grammatical approaches, since alternatives as required by exhaustivity operators occur elsewhere in grammar, for example as part of the semantics of operators like “only” and “even.”

Appeal · Assertion · Epistemology · Grammar · Implicature · Linguistics · Mathematical economics · Pragmatics · Programming language · Advanced Algebra and Logic · Computer Science · Law · Linguistics and Discourse Analysis · Mathematics · Philosophy · Syntax, Semantics, Linguistic Variation

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