Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-22T08:46:58.040Z Has data issue: false hasContentIssue false
  • English
  • Français

KURT GÖDEL ON LOGICAL, THEOLOGICAL, AND PHYSICAL ANTINOMIES

Part of: Mathematical Logic and Foundations Philosophical aspects of logic and foundations

Published online by Cambridge University Press:  26 July 2021

TIM LETHEN
TIM LETHEN*
Affiliation:
DEPARTMENT OF PHILOSOPHY UNIVERSITY OF HELSINKI P.O. BOX 24 FI-00014 HELSINKIFINLANDE-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper presents hitherto unpublished writings of Kurt Gödel concerning logical, epistemological, theological, and physical antinomies, which he generally considered as “the most interesting facts in modern logic,” and which he used as a basis for his famous metamathematical results. After investigating different perspectives on the notion of the logical structure of the antinomies and presenting two “antinomies of the intensional,” a new kind of paradox closely related to Gödel’s ontological proof for the existence of God is introduced and completed by a compilation of further theological antinomies. Finally, after a presentation of unpublished general philosophical remarks concerning the antinomies, Gödel’s type-theoretic variant of Leibniz’ Monadology, discovered in his notes on the foundations of quantum mechanics, is examined. Most of the material presented here has been transcribed from the Gabelsberger shorthand system for the first time.

Keywords

Kurt Gödelantinomiesmonadologytheology

MSC classification

Primary: 03-03: Historical (must also be assigned at least one classification number from Section 01)
Secondary: 03A05: Philosophical and critical 03A10: Logic in the philosophy of science
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 27 , Issue 3 , September 2021 , pp. 267 - 297
Check for updates
Copyright
© 2021, Association for Symbolic Logic

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adžić, M. and Došen, K., Logic lectures: Gödel's basic logic course at Notre dame, preprint, 2017, arXiv:1705.02601.Google Scholar
Boolos, G., A new proof of the Gödel incompleteness theorem . Notices of the American Mathematical Society, vol. 36 (1989), pp. 388–390.Google Scholar
Braithwaite, R.B. (ed.), The Foundations of Mathematics and Other Logical Essays, Routledge and Keegan Paul, London, 1931.Google Scholar
Chaitin, G.J., The Berry paradox , Complex Systems and Binary Networks (R. López-Peña, H. Waelbroeck, R. Capovilla, R. García-Pelayo, and F. Zertuche, editors), Springer, Berlin, 1995, pp. 23–31.CrossRefGoogle Scholar
Chaitin, G.J., Elegant lisp programs , People & Ideas in Theoretical Computer Science (C. S. Calude, editor), Springer, Berlin, 1999, pp. 32–52.Google Scholar
Dawson, J.W., Logical Dilemmas: The Life and Work of Kurt Gödel, A. K. Peters, Natik, MA, 1996.CrossRefGoogle Scholar
Gödel, K., Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I . Monatshefte für Mathematik und Physik, vol. 38 (1931), no. 1, pp. 173–198.CrossRefGoogle Scholar
Gödel, K., Russell's mathematical logic, The Philosophy of Bertrand Russell (Schilpp, P. A., editor), Northwestern University, Evanston and Chicago, 1944, pp. 123–153.Google Scholar
Goldfarb, W. et al., Kurt G ö del, Collected Works. Vol. III. Unpublished Essays and Lectures, Oxford University Press, New York, 1995.Google Scholar
Goodstein, R.L., Recursive Number Theory: A Development of Recursive Arithmetic in a Logic-Free Equation Calculus, North-Holland, Amsterdam, Netherlands, 1957.Google Scholar
Hilbert, D. and Ackermann, W., Grundzüge der theoretischen Logik, Julius Springer, Berlin, 1928.Google Scholar
Hilbert, D. and Bernays, P., Grundlagen der Mathematik I, Springer, Berlin, 1934.Google Scholar
Hindley, J.R., BCK and BCI logics, condensed detachment and the 2-property . Notre Dame Journal of Formal Logic, vol. 34 (1993), no. 2, pp. 231–250.CrossRefGoogle Scholar
Hindley, J.R., Basic Simple Type Theory, Cambridge University Press, Cambridge, 1997.CrossRefGoogle Scholar
Kahle, R., David Hilbert über Paradoxien. Pré-Publicações do Departamento de Matemática, Universidade de Coimbra, Coimbra, Portugal, 2006. Available at http://www.mat.uc.pt/preprints/ps/p0617.pdf.Google Scholar
Kanckos, A. and Lethen, T., The development of Gödel's ontological proof . The Review of Symbolic Logic to appear. https://doi.org/10.1017/S1755020319000479.Google Scholar
Kanckos, A. and Lethen, T., Kurt Gödel's reception of Charles Hartshorne's ontological proof , The Vienna Circle and Religion (E. Ramharter, editor), Springer, Cham, to appear.Google Scholar
Kikuchi, M., Kurahashi, T., and Sakai, H., On proofs of the incompleteness theorems based on Berry's paradox by Vopěnka, Chaitin, and Boolos . Mathematical Logic Quarterly, vol. 58 (2012), no. 4–5, pp. 307–316.CrossRefGoogle Scholar
Lethen, T., Kurt Gödel's anticipation of the Turing machine: A vitalistic approach . History and Philosophy of Logic, vol. 41 (2020), no. 3, pp. 252–264.CrossRefGoogle Scholar
Lethen, T., Mistakes in the Bible—Kurt Gödel's biblical studies, manuscript submitted for publication, 2020.Google Scholar
Lethen, T., Kurt Gödel's dogmatic theology , The Vienna Circle and Religion (E. Ramharter, editor), Springer, Cham, to appear.Google Scholar
Lethen, T. and Passon, O. (eds.), Kurt Gödels Notizen zur Quantenmechanik , Springer Spektrum, Berlin, to appear.Google Scholar
Ott, L., Fundamentals of Catholic Dogma, Mercier, Cork, RI, 1957.Google Scholar
Peckhaus, V. and Kahle, R., Hilbert's paradox . Historia Mathematica, vol. 29 (2002), no. 2, pp. 157–175.CrossRefGoogle Scholar
von Plato, J., Logic lectures: Gödel's basic logic course at Notre Dame [book review] . History and Philosophy of Logic, vol. 39 (2018), no. 4, pp. 396–403.CrossRefGoogle Scholar
von Plato, J., Kurt Gödel's first steps in logic: Formal proofs in arithmetic and set theory through a system of natural deduction, this Journal, vol. 24 (2018), no. 3, pp. 319–335.Google Scholar
von Plato, J., Can Mathematics Be Proved Consistent? Gödel's Shorthand Notes & Lectures on Incompleteness, Springer, Berlin, 2020.CrossRefGoogle Scholar
von Plato, J., Chapters from Gödel's Unfinished Book on Foundational Research in Mathematics , 2021, to appear.Google Scholar
Ramsey, F.P., The foundations of mathematics . Proceedings of the London Mathematical Society, vol. 2 (1926), no. 1, pp. 338–384.CrossRefGoogle Scholar
Sobel, J. H., Gödel's ontological proof , On Being and Saying: Essays for Richard Cartwright (J. J. Thompson, editor), MIT Press, Cambridge, 1987, pp. 241–261.Google Scholar
Sobel, J. H., Logic and Theism: Arguments for and Against Beliefs in God, Cambridge University Press, Cambridge, 2003.CrossRefGoogle Scholar
Sørensen, M.H. and Urzyczyn, P., Lectures on the Curry–Howard Isomorphism, Elsevier, Amsterdam, 2006.Google Scholar
Wang, H., A Logical Journey: From Gödel to Philosophy, MIT Press, Cambridge, MA, 1996.Google Scholar