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Article Dans Une Revue Topoi Année : 2016

Multivalent Semantics for Vagueness and Presupposition

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Benjamin Spector

Résumé

Both the phenomenon of presupposition and that of vagueness have motivated the use of one form or another of trivalent logic, in which a declarative sentence can not only receive the standard values true (1) and false (0), but also a third, non-standard truth-value which is usually understood as 'undefined' (#). The goal of this paper is to propose a multivalent framework which can deal simultaneously with presupposition and vagueness, and, more specifically, capture their projection properties as well as their different roles in language. Now, there is a prima facie simple way of doing this, which simply consists in assimilating the two phenomena, and using an appropriate type of trivalent logic. On this view, we just need a compositional system that deals with the 'undefined' truth-value, and does not care about whether the source of undefinedness is 'presuppositional' or related to vagueness. I will argue that such a simple solution cannot succeed, and point out a number of desiderata that any successful approach must meet. I will then present and discuss two seven-valued semantics, inspired, respectively, by the Strong Kleene semantics and by supervaluationism, which meet these desiderata.
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Dates et versions

hal-03877285 , version 1 (29-11-2022)

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Benjamin Spector. Multivalent Semantics for Vagueness and Presupposition. Topoi, 2016, 35 (1), pp.45-55. ⟨10.1007/s11245-014-9292-1⟩. ⟨hal-03877285⟩
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