Montague's Theorem and Modal Logic

Erkenntnis 79 (3):551-570 (2014)

Abstract
In the present piece we defend predicate approaches to modality, that is approaches that conceive of modal notions as predicates applicable to names of sentences or propositions, against the challenges raised by Montague’s theorem. Montague’s theorem is often taken to show that the most intuitive modal principles lead to paradox if we conceive of the modal notion as a predicate. Following Schweizer (J Philos Logic 21:1–31, 1992) and others we show this interpretation of Montague’s theorem to be unwarranted unless a further non trivial assumption is made—an assumption which should not be taken as a given. We then move on to showing, elaborating on work of Gupta (J Philos Logic 11:1–60, 1982), Asher and Kamp (Properties, types, and meaning. Vol. I: foundational issues, Kluwer, Dordrecht, pp 85−158, 1989), and Schweizer (J Philos Logic 21:1–31, 1992), that the unrestricted modal principles can be upheld within the predicate approach and that the predicate approach is an adequate approach to modality from the perspective of modal operator logic. To this end we develop a possible world semantics for multiple modal predicates and show that for a wide class of multimodal operator logics we may find a suitable class of models of the predicate approach which satisfies, modulo translation, precisely the theorems of the modal operator logic at stake
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DOI 10.1007/s10670-013-9523-7
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References found in this work BETA

Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2002 - Cambridge University Press.
Formal Philosophy. [REVIEW]Richard Montague - 1975 - Canadian Journal of Philosophy 4 (3):573-578.
Truth and Paradox.Anil Gupta - 1982 - Journal of Philosophical Logic 11 (1):1-60.
Towards a Proper Treatment of Quantification in English.Richard Montague - 1974 - In Richmond H. Thomason (ed.), Formal Philosophy. Yale University Press.

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