Constraints on the lexicalization of logical operators

Linguistics and Philosophy 36 (1):1-29 (2013)
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Abstract

We revisit a typological puzzle due to Horn (Doctoral Dissertation, UCLA, 1972) regarding the lexicalization of logical operators: in instantiations of the traditional square of opposition across categories and languages, the O corner, corresponding to ‘nand’ (= not and), ‘nevery’ (= not every), etc., is never lexicalized. We discuss Horn’s proposal, which involves the interaction of two economy conditions, one that relies on scalar implicatures and one that relies on markedness. We observe that in order to express markedness and to account for a bigger typological puzzle, namely the absence of lexicalizations of ‘XOR’ (= exclusive or), ‘all-or-none’, and many other imaginable logical operators, one must restrict the basic lexicalizable elements to a small set of primitives. We suggest that an ordering based perspective, following Keenan and Faltz (Boolean semantics for natural language, 1985), makes the stipulated primitives that we arrive at more natural. We also propose a modification to Horn’s proposal, based on recent work on implicatures, in which only the implicature condition is operative and in which markedness is part of the definition of the alternatives for scalar implicatures rather than an independent condition

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2013-05-24

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R. Singh
Brock University

Citations of this work

Update rules and semantic universals.Luca Incurvati & Giorgio Sbardolini - 2023 - Linguistics and Philosophy 46 (2):259-289.
Metalogical Decorations of Logical Diagrams.Lorenz Demey & Hans Smessaert - 2016 - Logica Universalis 10 (2-3):233-292.
The Logic of Lexical Connectives.Giorgio Sbardolini - 2023 - Journal of Philosophical Logic 52 (5):1327-1353.

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References found in this work

Introduction to mathematical philosophy.Bertrand Russell - 1919 - New York: Dover Publications.
A Natural History of Negation.Laurence R. Horn - 1989 - University of Chicago Press.
The Development of Logic.William Kneale & Martha Kneale - 1962 - Oxford, England: Clarendon Press. Edited by Martha Kneale.
Generalized quantifiers and natural language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.

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