Completeness in modal logic

University essay from Lunds universitet/Teoretisk filosofi

Abstract: This paper is mainly inspired by formal research results and philosophical considerations in ?A guide to intensional semantics?, written in 1973 by Bengt Hansson and Peter Gärdenfors. That essay was focused on the philosophy of semantics for modal logics, with special attention to completeness results. The purpose of the essay was to exhibit a negative trend in modal logic regarded as a philosophical discipline; the enterprise of completeness proving has become largely ?l?art pour l?art?, as the authors express it, and semantics often seem to be viewed by logicians as mere ?collectors of completeness results? rather than tools for actually interpreting modal logics. To illustrate this point, they constructed a semantics that makes every classical modal logic come out complete. Completeness as such is a trivial property for all even moderately interesting modal logics.

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