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KURT GÖDEL’S FIRST STEPS IN LOGIC: FORMAL PROOFS IN ARITHMETIC AND SET THEORY THROUGH A SYSTEM OF NATURAL DEDUCTION

Published online by Cambridge University Press:  25 October 2018

JAN VON PLATO
JAN VON PLATO*
Affiliation:
UNIVERSITY OF HELSINKI, FINLAND 00014 HELSINKI, FINLANDE-mail: jan.vonplato@helsinki.fi
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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

01A60030303F03Gödelformal proofnatural deduction
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 24 , Issue 3 , September 2018 , pp. 319 - 335
Copyright
Copyright © The Association for Symbolic Logic 2018 

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