Abstract
The modal collapse that afflicts Gödel’s modal ontological argument for God’s existence is discussed from the perspective of the modal square of opposition.
This work has been supported by the German National Research Foundation (DFG) under grant BE 2501/9-1,2.
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Notes
- 1.
A possible direction to remedy modal collapse, as studied e.g. by Koons [21] is to impose restrictions on the domain of properties.
References
C.A. Anderson, Some emendations of Gödel’s ontological proof. Faith Philos. 7 (3), 291–303 (1990)
A.C. Anderson, M. Gettings, Gödel ontological proof revisited, in Gödel’96: Logical Foundations of Mathematics, Computer Science, and Physics. Lecture Notes in Logic, vol. 6 (Springer, Berlin, 1996), pp. 167–172
C. Benzmüller, HOL based universal reasoning, in Handbook of the 4th World Congress and School on Universal Logic, ed. by J.Y. Beziau, A. Buchsbaum, A. Costa-Leite, A. Altair (Rio de Janeiro, 2013), pp. 232–233. http://www.uni-log.org/start4.html
C. Benzmüller, B. Woltzenlogel Paleo, Gödel’s God in Isabelle/HOL. Archive of Formal Proofs (2013). https://www.isa-afp.org/entries/GoedelGod.shtml
C. Benzmüller, B. Woltzenlogel Paleo, Gödel’s God on the computer, in Proceedings of the 10th International Workshop on the Implementation of Logics, ed. by S. Schulz, G. Sutcliffe, B. Konev. EPiC Series. EasyChair (2013). Invited abstract
C. Benzmüller, B. Woltzenlogel Paleo, Automating Gödel’s ontological proof of God’s existence with higher-order automated theorem provers, in ECAI 2014, ed. by T. Schaub, G. Friedrich, B. O’Sullivan. Frontiers in Artificial Intelligence and Applications, vol. 263 (IOS Press, Amsterdam, 2014), pp. 163–168
C. Benzmüller, L.C. Paulson, Exploring properties of normal multimodal logics in simple type theory with LEO-II, in Festschrift in Honor of Peter B. Andrews on His 70th Birthday (College Publications, London, 2008), pp. 386–406
C. Benzmüller, L.C. Paulson, Quantified multimodal logics in simple type theory. Log. Univers. (Special Issue on Multimodal Logics) 7 (1), 7–20 (2013)
C. Benzmüller, F. Theiss, L. Paulson, A. Fietzke, LEO-II - a cooperative automatic theorem prover for higher-order logic, in Proceedings of IJCAR 2008. LNAI, vol. 5195 (Springer, Berlin, 2008), pp. 162–170
Y. Bertot, P. Casteran, Interactive Theorem Proving and Program Development (Springer, Berlin, 2004)
F. Bjørdal, Understanding Gödel’s Ontological Argument, in The Logica Yearbook 1998, ed. by T. Childers (Filosofia, Prague, 1999)
J.C. Blanchette, T. Nipkow, Nitpick: a counterexample generator for higher-order logic based on a relational model finder, in Proceeding of ITP 2010. LNCS, vol. 6172 (Springer, Berlin, 2010), pp. 131–146
C.E. Brown, Satallax: an automated higher-order prover, in Proceedings of IJCAR 2012. LNAI, vol. 7364 (Springer, Berlin, 2012), pp. 111–117
S. Chatti, F. Schang, The cube, the square and the problem of existential import. Hist. Philos. Log. 34 (2), 101–132 (2013)
R. Corazzon, Contemporary bibliography on the ontological proof. http://www.ontology.co/biblio/ontological-proof-contemporary-biblio.htm
M. Fitting, Types, Tableaux and Gödel’s God (Kluver Academic Press, Dordrecht, 2002)
A. Fuhrmann, Existenz und notwendigkeit — Kurt Gödels axiomatische theologie, in Logik in der Philosophie, ed. by W. Spohn et al. (Synchron, Heidelberg, 2005)
K. Gödel, Appendix A. Notes in Kurt Gödel’s hand, in Logic and Theism: Arguments for and Against Beliefs in God (Cambridge University Press, Cambridge, 2004), pp. 144–145
P. Hajek, A new small emendation of Gödel’s ontological proof. Stud. Log. 71 (2), 149–164 (2002)
P. Hajek, Ontological proofs of existence and non-existence. Stud. Log. 90 (2), 257–262 (2008)
R. Koons, Sobel on Gödel’s ontological proof. Philos. Christi 2, 235–248 (2006)
T. Nipkow, L.C. Paulson, M. Wenzel, Isabelle/HOL: A Proof Assistant for Higher-Order Logic. LNCS, vol. 2283 (Springer, Berlin, 2002)
P.E. Oppenheimera, E.N. Zalta, A computationally-discovered simplification of the ontological argument. Australas. J. Philos. 89 (2), 333–349 (2011)
B. Woltzenlogel Paleo, Automated verification and reconstruction of Gödel’s proof of God’s existence. OCG J. 04, 4–7 (2013)
J. Rushby, The ontological argument in PVS, in Proceedings of CAV Workshop “Fun With Formal Methods”, St. Petersburg, Russia (2013)
D. Scott, Appendix B. Notes in Dana Scott’s hand, in Logic and Theism: Arguments for and Against Beliefs in God (Cambridge University Press, Cambridge, 2004), pp. 145–146
J.H. Sobel, Gödel’s ontological proof, in On Being and Saying. Essays for Richard Cartwright (MIT, Cambridge, 1987), pp. 241–261
J.H. Sobel, Logic and Theism: Arguments for and Against Beliefs in God (Cambridge University Press, Cambridge, 2004)
Acknowledgements
We would like to thank Paul Weingartner, André Fuhrmann and Melvin Fitting for several discussions about Gödel’s ontological argument.
Note About Authorship Alphabetic order has been used for the authors’ names. The extent and kind of contribution of each author cannot be inferred from the order.
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Benzmüller, C., Paleo, B.W. (2017). The Ontological Modal Collapse as a Collapse of the Square of Opposition. In: Béziau, JY., Basti, G. (eds) The Square of Opposition: A Cornerstone of Thought. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-45062-9_18
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