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Studia Logica

, Volume 107, Issue 1, pp 31–51 | Cite as

Gödel on Deduction

  • Kosta Došen
  • Miloš AdžićEmail author
Article

Abstract

This is an examination, a commentary, of links between some philosophical views ascribed to Gödel and general proof theory. In these views deduction is of central concern not only in predicate logic, but in set theory too, understood from an infinitistic ideal perspective. It is inquired whether this centrality of deduction could also be kept in the intensional logic of concepts whose building Gödel seems to have taken as the main task of logic for the future.

Keywords

Deduction Sequent Set Extension Concept Intension General proof theory Proof-theoretic semantics 

Mathematics Subject Classification

03A05 (Philosophical and critical) 03F03 (Proof theory, general) 

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Notes

Acknowledgements

Work on this paper was supported by the Ministry of Education, Science and Technological Development of Serbia, while the Alexander von Humboldt Foundation has supported the presentation of matters related to it by the first-mentioned of us at the conference General Proof Theory: Celebrating 50 Years of Dag Prawitz’s “Natural Deduction”, in Tübingen, in November 2015. We are grateful to the organizers for the invitation to the conference, for their care, and in particular to Peter Schroeder-Heister, for his exquisite hospitality. We are also grateful to Gabriella Crocco for making Gödel’s deciphered notes [37] available to us, and for allowing us to quote a sentence from them translated in [45]. The publishing of [37] is part of the project Kurt Gödel Philosopher: From Logic to Cosmology, which is directed by Gabriella Crocco and funded by the French National Research Agency (Project ANR-09-BLAN-0313). She and Antonio Piccolomini d’Aragona were also very kind to invite us to the workshop Inferences and Proofs, in Marseille, in May 2016, where the first-mentioned of us delivered a talk based partly on this paper, and enjoyed their especial hospitality. We are grateful to the Institute for Advanced Study in Princeton for granting us, through the office of its librarian Mrs. Marcia Tucker and its archivist Mr. Casey Westerman, the permission to quote this sentence; we were asked to give credit for that with the following text: “All works of Kurt Gödel used with permission. Unpublished Copyright (1934–1978) Institute for Advanced Study. All rights reserved by Institute for Advanced Study.”

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Authors and Affiliations

  1. 1.Faculty of PhilosophyUniversity of BelgradeBelgradeSerbia
  2. 2.Mathematical InstituteSerbian Academy of Sciences and ArtsBelgradeSerbia

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