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

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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.
Original languageEnglish
JournalBulletin of Symbolic Logic
Issue number3
Pages (from-to)319-335
Number of pages17
Publication statusPublished - 2018
MoE publication typeA1 Journal article-refereed

Fields of Science

  • 611 Philosophy

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