Natural Language Semantics 16 (2):115-128 (2008)

The exclusive component of unembedded disjunctions is standardly derived as a conversational implicature by assuming that or forms a lexical scale with and. It is well known, however, that this assumption does not suffice to determine the required scalar competitors of disjunctions with more than two atomic disjuncts (McCawley, Everything that linguists have always wanted to know about logic* (But were ashamed to ask). Chicago University Press, Chicago, 1993, p. 324; Simons, “Or”: Issues in the semantics and pragmatics of disjunction. Ph.D. thesis, Cornell University, Ithaca, NY, 1998). To solve this, Sauerland (Linguist Philos 27(3): 367–391, 2004) assumes that or forms a lexical scale with two otherwise unattested silent connectives ( ${\mathbb{L}}$ and ${\mathbb{R}}$ ) that retrieve the left and right terms of a disjunction. A number of recent works have proposed an Alternative Semantics for indefinites and disjunction to account for their interaction with modals and other propositional operators (Kratzer and Shimoyama, In: Otsu Y (ed) The Proceedings of the Third Tokyo Conference on Psycholinguistics. Hituzi Syobo, Tokyo, pp. 1–25, 2002; Aloni, In: Weisgerber M (ed) Proceedings of the Conference “SuB7—Sinn und Bedeutung”. Arbeitspapier Nr. 114. Konstanz, pp. 28–37, 2003; Simons, Nat Lang Semantics 13: 271–316, 2005; Alonso-Ovalle, Disjunction in alternative semantics. Ph.D. thesis, University of Massachusetts, Amherst, MA, 2006). We note that the McCawley–Simons problem does not arise in an Alternative Semantics, if we assume that the set of pragmatic competitors to a disjunction is the closure under intersection of the set of propositions that it denotes. An adaptation of the strengthening mechanism presented in Fox (In: Sauerland U, Stateva P (eds) Presupposition and implicature in compositional semantics. MacMillan, Palgrave, pp. 71–120, 2007) allows for the derivation of the exclusive component of disjunctions with more than two atomic disjuncts without having to rely on the ${\mathbb{L}}$ and ${\mathbb{R}}$ operators. The proposal extends to the case of disjunctions with logically dependent disjuncts
Keywords Disjunction  Scalar implicatures  Alternative Semantics
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DOI 10.1007/s11050-008-9027-1
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References found in this work BETA

Elements of Symbolic Logic.Hans Reichenbach - 1947 - London: Dover Publications.
A Natural History of Negation.Laurence Horn - 1989 - University of Chicago Press.
What 'Must' and 'Can' Must and Can Mean.Angelika Kratzer - 1977 - Linguistics and Philosophy 1 (3):337--355.
A Theory of Focus Interpretation.Mats Rooth - 1992 - Natural Language Semantics 1 (1):75-116.

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Citations of this work BETA

Economy and Embedded Exhaustification.Danny Fox & Benjamin Spector - 2018 - Natural Language Semantics 26 (1):1-50.
Counterfactuals, Correlatives, and Disjunction.Luis Alonso-Ovalle - 2009 - Linguistics and Philosophy 32 (2):207-244.

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