Skip to main content Accessibility help
×
Home
Hostname: page-component-768dbb666b-6zkrn Total loading time: 0.269 Render date: 2023-02-05T02:23:18.449Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

THE DEVELOPMENT OF GÖDEL’S ONTOLOGICAL PROOF

Published online by Cambridge University Press:  20 September 2019

ANNIKA KANCKOS
Affiliation:
DEPARTMENT OF PHILOSOPHY UNIVERSITY OF HELSINKI P.O. BOX 24 (UNIONINKATU 40 A), FI - 00014 FINLANDE-mail: annika.kanckos@helsinki.fiE-mail: lethen@cs.uni-saarland.de
TIM LETHEN
Affiliation:
DEPARTMENT OF PHILOSOPHY UNIVERSITY OF HELSINKI P.O. BOX 24 (UNIONINKATU 40 A), FI - 00014 FINLANDE-mail: annika.kanckos@helsinki.fiE-mail: lethen@cs.uni-saarland.de

Abstract

Gödel’s ontological proof is by now well known based on the 1970 version, written in Gödel’s own hand, and Scott’s version of the proof. In this article new manuscript sources found in Gödel’s Nachlass are presented. Three versions of Gödel’s ontological proof have been transcribed, and completed from context as true to Gödel’s notes as possible. The discussion in this article is based on these new sources and reveals Gödel’s early intentions of a liberal comprehension principle for the higher order modal logic, an explicit use of second-order Barcan schemas, as well as seemingly defining a rigidity condition for the system. None of these aspects occurs explicitly in the later 1970 version, and therefore they have long been in focus of the debate on Gödel’s ontological proof.

Type
Research Article
Copyright
© Association for Symbolic Logic 2019

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

BIBLIOGRAPHY

Adams, R. A. (1995). Introductory Note to *1970, in: [10], Oxford University Press.Google Scholar
Anderson, C. A. (1990). Some emendations of Gödel’s ontological proof. Faith and Philosophy, 7 (3), 291303.CrossRefGoogle Scholar
Anderson, C. A. & Gettings, M. (1996). Gödel’s ontological proof revisited. In Hájek, P., editor. Gödel ’96: Logical Foundations of Mathematics, Computer Science and Physics—Kurt Gödel’s Legacy, Brno, Czech Republic, August 1996, Proceedings. Berlin: Springer-Verlag, pp. 167172.CrossRefGoogle Scholar
Benzmüller, C. & Fuenmayor, D. (2018). Can computers help to sharpen our understanding of ontological arguments? In Gosh, S., Uppalari, R., Vasudeva Rao, k., Agarwal, V., and Sharma, S., editors. Mathematics and Reality, Proceedings of the 11th All India Students’ Conference on Science & Spiritual Quest, 6-7 October, 2018, IIT Bhubaneswar, Bhubaneswar, India. Kolkata: The Bhaktivedanta Institute, pp. 195226.Google Scholar
Benzmüller, C., Brown, C., & Kohlhase, M. (2004). Higher-order semantics and extensionality. Journal of Symbolic Logic, 69(4), 10271088.CrossRefGoogle Scholar
Benzmüller, C., Weber, L., & Woltzenlogel Paleo, B. (2017). Computer-assisted analysis of the Anderson-Hájek ontological controversy. Logica Universalis, 11, 139151.CrossRefGoogle Scholar
Bjørdal, F. (1999). Understanding Gödel’s ontological argument. In Childers, T., editor. The Logica Yearbook 1998. Praha: Filosofia, pp. 214217.Google Scholar
Fitting, M. (1999). Barcan both ways. Journal of Applied Non-Classical Logics, 9(2–3), 329344.CrossRefGoogle Scholar
Fitting, M. (2002). Types, Tableaus, and Gödel’s God. Amsterdam: Springer Netherlands.CrossRefGoogle Scholar
Gödel, K. (1995). Kurt Gödel Collected Works: Unpublished Essays and Lectures, Vol. 3. New York: Oxford University Press.Google Scholar
Gödel, K. (2003). In Feferman, S., Dawson, J. W. Jr., Goldfarb, W., Parsons, C., and Solovay, R. M., editors. Kurt Gödel Collected Works: Correspondence H–Z. Oxford: Clarendon.Google Scholar
Hájek, P. (1996). Magari and others on Gödel’s ontological proof. In Ursini, A., and Aglianò, P., editors. Logic and Algebra. New York: Marcel Dekker, pp. 125136.Google Scholar
Hájek, P. (2002). A new small emendation of Gödel’s ontological proof. Studia Logica, 71(2), 149164 .CrossRefGoogle Scholar
Hartshorne, C. (1962). The Logic of Perfection. LaSalle, Il.: Open Court Publishing Company.Google Scholar
Hartshorne, C. (1965). Anselm’s Discovery – A Re-Examination of the Ontological Proof for God’s Existence. LaSalle, Il.: Open Court Publishing Company.Google Scholar
Kanckos, A. & Woltzenlogel Paleo, B. (2017). Variants of Gödel’s ontological proof in a natural deduction calculus. Studia Logica, 105(3), 553586.CrossRefGoogle Scholar
Koons, R. C. 2006. Sobel on Gödel’s ontological proof, in Philosophia Christi, 8 (2006), 235247.Google Scholar
Kovač, S. (2012). Modal collapse in Gödel’s ontological proof. In Szatkowski, Mirosław, editor. Ontological Proofs Today, Chapter 15. Frankfurt: Ontos, pp. 323343.CrossRefGoogle Scholar
Scott, D. (1970). Notes in Dana Scott’s hand. In Sobel, J. H., editor. Logic and Theism: Arguments for and against Beliefs in God. New York: Cambridge University Press, pp. 145146.Google Scholar
Sobel, J. H. (1987). Gödel’s ontological proof. In Thompson, J. J., editor. On being and Saying: Essays for Richard Cartwright. Cambridge, MA: MIT Press, pp. 241261.Google Scholar
Sobel, J. H. (2001). Logic and Theism: Arguments for and against Beliefs in God. Cambridge: Cambridge University Press.Google Scholar
Wang, H. (1987). Reflections on Kurt Gödel. Cambridge, MA: The MIT Press.Google Scholar
Wang, H. (1996). A Logical Journey: From Gödel to Philosophy. Cambridge, MA: The MIT Press.Google Scholar
4
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

THE DEVELOPMENT OF GÖDEL’S ONTOLOGICAL PROOF
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

THE DEVELOPMENT OF GÖDEL’S ONTOLOGICAL PROOF
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

THE DEVELOPMENT OF GÖDEL’S ONTOLOGICAL PROOF
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *