Abstract
In this short note I shall make a few comments on the interpretation of quantification in modal logic. My points of departure are the formal language L of the lower predicate logic with modalities, and an interpretation of L. The interpretation I have in mind has the form of the valuation given in my paper The Morning Star Paradox (Theoria 23 (1957), 1-11), except that the valuation shall apply to the formulas of L and not only to the statements.
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Notes
In my essay Provability in Logic, Stockholm 1957,I adopted (x) instead of (UX). We may note, however, that the preference of (x) to (Ux) does not affect the contents of the essay except at two points, viz. the definition of an ontological modality (p. 34, lines 6-7) and the formulas (13)-(15) on p. 36. These lines could well have been omitted.
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© 2001 Springer Science+Business Media Dordrecht
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Holmström-Hintikka, G., LindstrÖm, S., Sliwinski, R. (2001). A Note on Quantification and Modalities. In: Holmström-Hintikka, G., Lindström, S., Sliwinski, R. (eds) Collected Papers of Stig Kanger with Essays on his Life and Work. Synthese Library, vol 303. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0500-5_4
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DOI: https://doi.org/10.1007/978-94-010-0500-5_4
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