A Computationally Assisted Reconstruction of an Ontological Argument in Spinoza’s The Ethics

Jack K. Horner 1
  • 1 , Lawrence, United States of America

Abstract

The comments accompanying Proposition (Prop.) 11 (“God ... necessarily exists”) in Part I of Spinoza’s The Ethics contain sketches of what appear to be at least three more or less distinct ontological arguments. The first of these is problematic even on its own terms. More is true: even the proposition “God exists” (GE), a consequence of Prop. 11, cannot be derived from the definitions and axioms of Part I (the “DAPI”) of The Ethics; thus, Prop. 11 cannot be derived from the DAPI, either. To prove these claims, I use an automated deduction system (ADS) to show that Prop. 11 is independent of the DAPI. I then augment the DAPI with some auxiliary assumptions I believe Spinoza would accept and that sustain an automated derivation of (GE). The results illustrate how an ADS can facilitate the analysis of arguments and yield an apparently novel argument cast in the style of Spinoza.

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  • Anselm. Prosologium. Trans. by S. N. Deane. In St. Anselm: Basic Writings. Second Edition. Chicago: Open Court, 1962.

  • Aquinas. On Being and Essence. Trans. by Armand Maurer, Second Revised Edition. Toronto : The Pontifical Institute of Medieval Studies, 1968.

  • Aristotle. Prior Analytics. Trans. by A. J. Jenkinson. In The Basic Works of Aristotle. Ed. by Richard McKeon. New York : Random House, 1941.

  • Aristotle. Metaphysics. Trans. by W. D. Ross. In Richard McKeon, ed. The Basic Works of Aristotle. New York : Random House, 1941.

  • Benzmüller, Cristoph, and Paleo, Bruno W. “Automating Gödel’s ontological proof of God’s existence with higher-order automated theorem provers.” Proceedings of the 2014 European Conference on Artificial Intelligence, 93-98. IOS Press, 2014.

  • Chang, Chen C, and Keisler, H. Jerome. Model Theory. Third Edition. New York : Dover Publications, 2012.

  • Church, Alonzo. Introduction to Mathematical Logic. Part I. Princeton : Princeton University Press, 1956.

  • Cocchiarella, Nino B., and Freund, Max A. Modal Logic: An Introduction to its Syntax and Semantics. Oxford : Oxford University Press, 2008.

  • Descartes. Meditations on First Philosophy. Trans. by L. J. Lafleur. Indianapolis : Bobbs-Merrill Company, 1960.

  • Drews, Samuel, and Albarghouthi, Aws. “Effectively Propositional Interpolants.” In Chaudhuri S., and Farzan A. (eds.). Computer Aided Verification (CAV 2016). Published in Lecture Notes on Computer Science, Vol. 9780. Switzerland: Springer, Cham, 2016, 210-229.

  • Gödel, Kurt. (1970). “Ontological proof”. Reprinted in Solomon Feferman, John W. Dawson, Jr., Warren Goldfarb, Charles Parsons, and Robert N. Solovay (eds.) Kurt Gödel: Collected Works. Volume III. Oxford : Oxford University Press, 1995.

  • Journal of Automated Reasoning. New York: Springer.

  • Kalman, John A. Automated Reasoning with Otter. Princeton : Rinton Press, 2001.

  • Kant. Critique of Pure Reason. Trans. by Norman Kemp Smith. New York : St. Martin’s Press LLC, 2007.

  • Leitsch, Alexander. The Resolution Calculus. New York : Springer, 1997.

  • Locke. An Essay Concerning Human Understanding. Ed. by R. Woodhouse. London : Palgrave, 2004.

  • McCune, William W. prover9 and mace4. http://www.cs.unm.edu/~mccune/prover9/. 2009. Accessed 30 December 2018.

  • Nadler, Stephen. Spinoza’s Ethics: An Introduction. Cambridge : Cambridge University Press, 2006.

  • Oppenheimer, Paul, and Zalta, Edward. “A computationally-discovered simplification of the ontological argument.” Australasian Journal of Philosophy 89/2 (2011), 333-349.

  • Oppy, Graham. Ontological Arguments and Belief in God. Cambridge: Cambridge University Press, 1995.

  • Oppy, Graham. “Ontological Arguments.” In Edward Zalta (ed.). Stanford Encyclopedia of Philosophy.http://plato.stanford.edu/entries/ontological-arguments/. 2011. Accessed 30 December 2018.

  • Quaife, Art. Automated Development of Fundamental Mathematical Theories. Dordrecht: Kluwer Academic Publishers, 1992.

  • Scott, Dana. “Notes in Dana Scott’s Hand.” In Sobel, Jordan H. Logic and Theism: Arguments for and Against Beliefs in God. Cambridge : Cambridge University Press, 2004. Appendix B, 145-146.

  • Spinoza. The Ethics. In Benedict de Spinoza. On the Improvement of the Understanding, The Ethics, Correspondence. Unabridged trans. by R. H. M. Elwes (1883). New York : Dover Publications reprint, 1955.

  • Symons, John F., and Horner, Jack K. “Software error as a limit to inquiry for finite agents: Challenges for the post-human scientist.” In Powers, Tom (ed.) Philosophy and Computing: Essays in Epistemology, Philosophy of Mind, Logic, and Ethics. New York : Springer, 2017.

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