An Exposition and Development of Kanger’s Early Semantics for Modal Logic

Abstract

Stig Kanger — born of Swedish parents in China in 1924 — was professor of Theoretical Philosophy at Uppsala University from 1968 until his death in 1988. He received his Ph.D. from Stockholm University in 1957 under the supervision of Anders Wedberg. Kanger’s dissertation, Provability in Logic, was remarkably short, only 47 pages, but also very rich in new ideas and results. By combining Gentzen-style techniques with a model theory à la Tarski, Kanger obtained new and simplified proofs of central metalogical results of classical predicate logic: Gödel’s completeness theorem, Löwenheim-Skolem’s theorem and Gentzen’s Hauptsatz. The part that had the greatest impact, however, was the 15 pages devoted to modal logic. There Kanger developed a new semantic interpretation for quantified modal logic which had a close family resemblance to semantic theories that were developed around the same time by Jaakko Hintikka, Richard Montague and Saul Kripke (independently of each other and independently of Kanger).

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Earlier versions ofthis paper have been presented at the UgLLI-workshop on Philosophical Logic at Uppsala University, March 18, 1995, at the Swedish national conference in philosophy, “Filosofidagarna”, Umeä, June 7-9, 1995, and discussed with friends and colleagues. A shorter version was also published as Lindström (1996). I am especially indebted to Joseph Almog, Lennart Aqvist, Thorild Dahlquist, Bengt Hansson, Risto Hilpinen, Jaakko Hintikka, Paul Needham, Peter Pagin, Wlodek Rabinowicz, Krister Segerberg and Rysiek Sliwinski for their very helpful comments and advice. A fellowship at the Swedish Collegium for Advanced Studies in the Social Seiences (SCASSS) du ring the Autumn of 1996 provided an excellent research environment for finishing the paper.