Kurt gödel’s first steps in logic: Formal proofs in arithmetic and set theory through a system of natural deduction

Bulletin of Symbolic Logic 24 (3):319-335 (2018)
Authors
Jan Von Plato
University of Helsinki
Abstract
What seem to be Kurt Gödel’s first notes on logic, an exercise notebook of 84 pages, contains formal proofs in higher-order arithmetic and set theory. The choice of these topics is clearly suggested by their inclusion in Hilbert and Ackermann’s logic book of 1928, the Grundzüge der theoretischen Logik. Such proofs are notoriously hard to construct within axiomatic logic. Gödel takes without further ado into use a linear system of natural deduction for the full language of higher-order logic, with formal derivations closer to one hundred steps in length and up to four nested temporary assumptions with their scope indicated by vertical intermittent lines.
Keywords Kurt Gödel  formal proof  natural deduction
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DOI 10.1017/bsl.2017.42
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References found in this work BETA

Gödel’s Natural Deduction.Kosta Došen & Miloš Adžić - 2018 - Studia Logica 106 (2):397-415.
On Gödel's Way In: The Influence of Rudolf Carnap.Warren Goldfarb - 2005 - Bulletin of Symbolic Logic 11 (2):185-193.
Gödel’s Notre Dame Course.Miloš Adžić & Kosta Došen - 2016 - Bulletin of Symbolic Logic 22 (4):469-481.

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