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

Tutkimustuotos: ArtikkelijulkaisuArtikkeliTieteellinenvertaisarvioitu

Abstrakti

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.
Alkuperäiskielienglanti
LehtiBulletin of Symbolic Logic
Vuosikerta24
Numero3
Sivut319-335
Sivumäärä17
ISSN1079-8986
DOI - pysyväislinkit
TilaJulkaistu - 2018
OKM-julkaisutyyppiA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä, vertaisarvioitu

Tieteenalat

  • 611 Filosofia

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