Topoi 35 (1):45-55 (2016)

Benjamin Spector
Centre National de la Recherche Scientifique
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 and false , 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
Keywords Presupposition  Vagueness  Trivalent logics  Multivalent logics  Projection  Felicity  Supervaluations  Strong kleene
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DOI 10.1007/s11245-014-9292-1
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References found in this work BETA

Vagueness, Truth and Logic.Kit Fine - 1975 - Synthese 30 (3-4):265-300.
Tolerant, Classical, Strict.Pablo Cobreros, Paul Egré, David Ripley & Robert van Rooij - 2012 - Journal of Philosophical Logic 41 (2):347-385.
On the Projection Problem for Presuppositions.Irene Heim - 1983 - In P. Portner & B. H. Partee (eds.), Formal Semantics - the Essential Readings. Blackwell. pp. 249--260.

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Yablo’s Semantic Machinery.Daniel Rothschild - 2017 - Philosophical Studies 174 (3):787-796.

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