History and Philosophy of Logic 31 (4):349-379 (2010)

Curtis Franks
University of Notre Dame
The papers where Gerhard Gentzen introduced natural deduction and sequent calculi suggest that his conception of logic differs substantially from the now dominant views introduced by Hilbert, Gödel, Tarski, and others. Specifically, (1) the definitive features of natural deduction calculi allowed Gentzen to assert that his classical system nk is complete based purely on the sort of evidence that Hilbert called ?experimental?, and (2) the structure of the sequent calculi li and lk allowed Gentzen to conceptualize completeness as a question about the relationships among a system's individual rules (as opposed to the relationship between a system as a whole and its ?semantics?). Gentzen's conception of logic is compelling in its own right. It is also of historical interest, because it allows for a better understanding of the invention of natural deduction and sequent calculi.
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DOI 10.1080/01445340.2010.522365
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References found in this work BETA

Grundlagen der Arithmetik.Gottlob Frege - 1884 - Breslau: Wilhelm Koebner Verlag.
Die Grundlagen der Arithmetik.Gottlob Frege - 1988 - Felix Meiner Verlag.
From Frege to Gödel.Jean Van Heijenoort (ed.) - 1967 - Cambridge: Harvard University Press.
Tonk, Plonk and Plink.Nuel Belnap - 1962 - Analysis 22 (6):130-134.

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Citations of this work BETA

The Context of Inference.Curtis Franks - 2018 - History and Philosophy of Logic 39 (4):365-395.
Early Structural Reasoning. Gentzen 1932.Enrico Moriconi - 2015 - Review of Symbolic Logic 8 (4):662-679.
Rule-Irredundancy and the Sequent Calculus for Core Logic.Neil Tennant - 2016 - Notre Dame Journal of Formal Logic 57 (1):105-125.
The Deduction Theorem.Curtis Franks - 2021 - History and Philosophy of Logic 42 (2):129-159.

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