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From Modal Discourse to Possible Worlds

Maxwell J. Cresswell
Studia Logica: An International Journal for Symbolic Logic
Vol. 82, No. 3, Ways of Worlds 1: On Possible Worlds and Related Notions (Apr., 2006), pp. 307-327
Published by: Springer
Stable URL: http://www.jstor.org/stable/20016786
Page Count: 21
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From Modal Discourse to Possible Worlds
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Abstract

The possible-worlds semantics for modality says that a sentence is possibly true if it is true in some possible world. Given classical propositional logic, one can easily prove that every consistent set of propositions can be embedded in a 'maximal consistent set', which in a sense represents a possible world. However the construction depends on the fact that standard modal logics are finitary, and it seems false that an infinite collection of sets of sentences each finite subset of which is intuitively 'possible' in natural language has the property that the whole set is possible. The argument of the paper is that the principles needed to shew that natural language possibility sentences involve quantification over worlds are analogous to those used in infinitary modal logic.

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