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Possible worlds semantics and the Liar: Reflections on a problem posed by Kaplan
Umeå University, Faculty of Arts, Department of historical, philosophical and religious studies.
2009 (English)In: The Philosophy of David Kaplan, Oxford: Oxford University Press , 2009Chapter in book (Other academic)
Abstract [en]

In this paper I discuss a paradox, due to David Kaplan, that in his view threatens the use of possible worlds semantics as a model-theoretic framework for intensional logic. Kaplan’s paradox starts out from an intuitively reasonable principle that I refer to as the Principle of Plenitude.  From this principle he derives a contradiction in what he calls Naive Possible World Theory.  Kaplan’s metatheoretic argument can be restated in the modal object language as an intensional version of the Liar paradox. To solve the paradox, Kaplan favors a ramified theory of propositions, along the lines of Russell’s ramified theory of types. I shall attempt an alternative, less drastic, modification of the standard possible worlds methodology than the one favored by Kaplan.  The idea is to regard sentences that involve propositional quantifiers, like the Liar sentence: "All propositions contemplated by Epimenides are false" as being, in a sense, indexical: one and the same sentence can express different propositions when used in different possible worlds. Using this approach, I try to show that the intensional Liar paradox can be defused and no longer poses a threat to possible worlds semantics.

Place, publisher, year, edition, pages
Oxford: Oxford University Press , 2009.
Keyword [en]
philosophy of language, philosophical logic, possible worlds semantics, paradoxes, intensionality
National Category
Languages and Literature
URN: urn:nbn:se:umu:diva-19815ISBN: 9780195367881ISBN: 019536788XOAI: diva2:207436
This paper is also published in Rojszczak, A., Cachro, J., Kurczewski, G. (eds.): Philosophical Dimensions of Logic and Science, Synthese library Vol. 320, Kluwer 2003.Available from: 2009-03-11 Created: 2009-03-11 Last updated: 2012-06-14Bibliographically approved

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Lindström, Sten
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Department of historical, philosophical and religious studies
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