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Collected Papers of Stig Kanger with Essays on His Life and Work pp 31–42Cite as

The Proof Theory of Stig Kanger: A Personal Recollection

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Part of the book series: Synthese Library ((SYLI,volume 304))

Abstract

The term Proof Theory shows a certain ambiguity. In the fifties when Stig Kanger carried out his logical work it stood for a cluster of topics pertaining to the syntactic turnstile ⊢, that is, the syntactic counterpart to the semantical notion of (logical) consequence ⊨. On the other hand, and more narrowly, it also stood for investigations of the properties of the syntactic turnstile by means of systematic transformations of derivation trees. Stig Kanger was a proof theorist only in the former sense. For him, model-theoretic semantics, couched in a rich set-theoretic framework, held pride of place, and in this he was very close to the then main European school of logic, namely the Münster School, under the leadership of Heinrich Scholz. There are indeed many questions to be asked with respect to the mere 26 (!!) non-modal pages of Provability in Logic. 1 Not the least of these is the question: where did Stig Kanger find his semantics? He admired Alfred Tarski above all other logicians. By the side of Finnegan’s Wake, Tarski-Mostowski-Robinson, Undecidable Theories,2 and, of course, Der Wahrheitsbegriff in den formalisierten Sprachen,3 would have been with him on the Desert Island. The rare off-print copy of the German (1935) version of Tarski’s masterpiece from 1933, formerly in Stockholms Högskolas Humanistiska Bibliotek, now in the University library at Stockholm, bears the mark of careful study, but it does contain the model-theoretic semantics in question only derivatively at pp. 361–62: Tarski’s official definition of truth in §3, for the general calculus of classes, is not relativized to a domain of individuals, but quantifies over a universe of everything.

Revised text of an invited lecture read at the Kanger Memorial Symposium, Uppsala University, March, 1993.

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Notes

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Authors and Affiliations

  1. Leyden University, Netherlands

    Göran Sundholm

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  1. Göran Sundholm
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Editors and Affiliations

  1. Boston University, Boston, USA

    Ghita Holmström-Hintikka

  2. Umeå University, Umeå, Sweden

    Sten Lindström

  3. Uppsala University, Uppsala, Sweden

    Rysiek Sliwinski

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© 2001 Springer Science+Business Media Dordrecht

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Sundholm, G. (2001). The Proof Theory of Stig Kanger: A Personal Recollection. In: Holmström-Hintikka, G., Lindström, S., Sliwinski, R. (eds) Collected Papers of Stig Kanger with Essays on His Life and Work. Synthese Library, vol 304. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0630-9_2

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  • DOI: https://doi.org/10.1007/978-94-010-0630-9_2

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  • Print ISBN: 978-1-4020-0112-3

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