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Making sense of (in)determinate truth: the semantics of free variables
Philosophy and History, KTH, School of Architecture and the Built Environment (ABE), Philosophy and History of Technology, Philosophy. Swedish Coll Adv Study, Thunbergsvagen 2, SE-75238 Uppsala, Sweden..
2018 (English)In: Philosophical Studies, ISSN 0031-8116, E-ISSN 1573-0883, Vol. 175, no 11, p. 2715-2741Article in journal (Refereed) Published
Abstract [en]

It is argued that truth value of a sentence containing free variables in a context of use (or the truth value of the proposition it expresses in a context of use), just as the reference of the free variables concerned, depends on the assumptions and posits given by the context. However, context may under-determine the reference of a free variable and the truth value of sentences in which it occurs. It is argued that in such cases a free variable has indeterminate reference and a sentence in which it occurs may have indeterminate truth value. On letting, say, x be such that x(2) = 4, the sentence 'Either x = 2 or x = -2' is true but the sentence 'x = 2' has an indeterminate truth value: it is determinate that the variable x refers to either 2 or -2, but it is indeterminate which of the two it refers to, as a result 'x = 2' has a truth value but its truth value is indeterminate. The semantic indeterminacy is analysed in a 'radically' supervaluational (or plurivaluational) semantic framework closely analogous to the treatment of vagueness in McGee and McLaughlin (South J Philos 33: 203-251, 1994, Linguist Philos 27: 123-136, 2004) and Smith (Vagueness and degrees of truth, Oxford University Press, Oxford, 2008), which saves bivalence, the T-schema and the truth-functional analysis of the boolean connectives. It is shown that on such an analysis the modality 'determinately' is quite clearly not an epistemic modality, avoiding a potential objection raised by Williamson (Vagueness, Routledge, London, 1994) against such 'radically' supervaluational treatments of vagueness, and that determinate truth (rather than truth simpliciter) is the semantic value preserved in classically valid arguments. The analysis is contrasted with the epistemicist proposal of Breckenridge and Magidor (Philos Stud 158: 377-400, 2012) which implies that (in the given context) 'x = 2' has a determinate but unknowable truth value.

Place, publisher, year, edition, pages
Springer, 2018. Vol. 175, no 11, p. 2715-2741
Keywords [en]
Indeterminate truth, Determinate truth, Indeterminacy, Free variables, Supervaluations, Reference, Supertruth, Arbitrary reference, Arbitrary objects, Plurivaluations
National Category
Philosophy
Identifiers
URN: urn:nbn:se:kth:diva-235864DOI: 10.1007/s11098-017-0979-1ISI: 000445388800003Scopus ID: 2-s2.0-85029575750OAI: oai:DiVA.org:kth-235864DiVA, id: diva2:1254443
Note

QC 20181009

Available from: 2018-10-09 Created: 2018-10-09 Last updated: 2018-10-09Bibliographically approved

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