A Case Study on Computational Hermeneutics: E. J. Lowe’s Modal Ontological Argument

Part of the Sophia Studies in Cross-cultural Philosophy of Traditions and Cultures book series (SCPT, volume 34)


Computers may help us to better understand (not just verify) arguments. In this chapter we defend this claim by showcasing the application of a new, computer-assisted interpretive method to an exemplary natural-language argument with strong ties to metaphysics and religion: E. J. Lowe’s modern variant of St. Anselm’s ontological argument for the existence of God. Our new method, which we call computational hermeneutics, has been particularly conceived for use in interactive-automated proof assistants. It aims at shedding light on the meanings of words and sentences by framing their inferential role in a given argument. By employing automated theorem proving technology within interactive proof assistants, we are able to drastically reduce (by several orders of magnitude) the time needed to test the logical validity of an argument’s formalization. As a result, a new approach to logical analysis, inspired by Donald Davidson’s account of radical interpretation, has been enabled. In computational hermeneutics, the utilization of automated reasoning tools effectively boosts our capacity to expose the assumptions we indirectly commit ourselves to every time we engage in rational argumentation and it fosters the explicitation and revision of our concepts and commitments.



Author “Christoph Benzmüller” was funded by Volkswagen Foundation.


  1. Alama, J., P. E. Oppenheimer, and E. N. Zalta. 2015. Automating Leibniz’s theory of concepts. In Automated Deduction - CADE-25 - 25th International Conference on Automated Deduction, Berlin, Germany, August 1–7, 2015, Proceedings, ed. A. P. Felty and A. Middeldorp, vol. 9195, 73–97. Lecture Notes in Computer Science. Berlin: Springer.Google Scholar
  2. Baumberger, C., and G. Brun. 2016. Dimensions of objectual understanding. Explaining Understanding. New Perspectives from Epistemology and Philosophy of Science, 165–189. New York: Routledge.Google Scholar
  3. Baumgartner, M., and T. Lampert. 2008. Adequate formalization. Synthese 164 (1): 93–115.Google Scholar
  4. Benzmüller, C. 2013. A top-down approach to combining logics. In Proceedings of the 5th International Conference on Agents and Artificial Intelligence (ICAART), ed. J. Filipe and A. Fred, vol. 1, 346–351, Barcelona, Spain. SCITEPRESS – Science and Technology Publications, Lda.Google Scholar
  5. ——. 2017. Recent successes with a meta-logical approach to universal logical reasoning (extended abstract). In Formal Methods: Foundations and Applications - 20th Brazilian Symposium, SBMF 2017, Recife, Brazil, November 29 - December 1, 2017, Proceedings, ed. S. A. da Costa Cavalheiro and J. L. Fiadeiro. Lecture Notes in Computer Science, vol. 10623, 7–11. Cham: Springer.Google Scholar
  6. Benzmüller, C., and L. Paulson. 2013. Quantified multimodal logics in simple type theory. Logica Universalis (Special Issue on Multimodal Logics) 7 (1): 7–20.Google Scholar
  7. Benzmüller, C., and B. Woltzenlogel Paleo. 2014. Automating Gödel’s ontological proof of God’s existence with higher-order automated theorem provers. In ECAI 2014. Frontiers in Artificial Intelligence and Applications, ed. T. Schaub, G. Friedrich, and B. O’Sullivan, vol. 263, 93–98. Amsterdam: IOS Press.Google Scholar
  8. ——. 2016. The inconsistency in Gödel’s ontological argument: A success story for AI in metaphysics. In Proceedings of the IJCAI 2016.Google Scholar
  9. Benzmüller, C., L. Weber, and B. Woltzenlogel Paleo. 2017. Computer-assisted analysis of the Anderson-Hájek controversy. Logica Universalis 11 (1): 139–151.Google Scholar
  10. Blanchette, J., and T. Nipkow. 2010. Nitpick: A counterexample generator for higher-order logic based on a relational model finder. In Proceedings of ITP 2010. Lecture Notes in Computer Science, vol. 6172, 131–146. Heidelberg: Springer.Google Scholar
  11. Blanchette, J., S. Böhme, and L. Paulson. 2013. Extending Sledgehammer with SMT solvers. Journal of Automated Reasoning 51 (1): 109–128.Google Scholar
  12. Block, N. 1998. Semantics, conceptual role. In Routledge Encyclopedia of Philosophy. Routledge: Taylor and Francis.Google Scholar
  13. Brandom, R. B. 1994. Making It Explicit: Reasoning, Representing, and Discursive Commitment. Cambridge: Harvard University Press.Google Scholar
  14. Brun, G. 2014. Reconstructing arguments. formalization and reflective equilibrium. Logical Analysis and History of Philosophy 17: 94–129.Google Scholar
  15. Davidson, D. Jan. 1994. Radical interpretation interpreted. Philosophical Perspectives 8: 121–128.CrossRefGoogle Scholar
  16. ——. 2001a. Essays on Actions and Events: Philosophical Essays, vol. 1. Oxford: Oxford University Press (on Demand).Google Scholar
  17. ——. Sept. 2001b. On the very idea of a conceptual scheme. In Inquiries into Truth and Interpretation. Oxford: Oxford University Press.Google Scholar
  18. ——. Sept. 2001c. Radical interpretation. In Inquiries into Truth and Interpretation. Oxford: Oxford University Press.Google Scholar
  19. Eder, G., and E. Ramharter. Oct. 2015. Formal reconstructions of St. Anselm’s ontological argument. Synthese: An International Journal for Epistemology, Methodology and Philosophy of Science 192 (9): 2795–2825.CrossRefGoogle Scholar
  20. Elgin, C. 1999. Considered Judgment. Princeton: Princeton University Press.Google Scholar
  21. Fuenmayor, D., and C. Benzmüller. 2017. Automating emendations of the ontological argument in intensional higher-order modal logic. In KI 2017: Advances in Artificial Intelligence 40th Annual German Conference on AI, Dortmund, Germany, September 25–29, 2017, Proceedings. LNAI, vol. 10505, 114–127. Cham: Springer.Google Scholar
  22. ——. Sept. 2017. Computer-assisted reconstruction and assessment of E. J. Lowe’s modal ontological argument. Archive of Formal Proofs., Formal proof development.
  23. ——. May 2017. Types, Tableaus and Gödel’s God in Isabelle/HOL. Archive of Formal Proofs., Formal proof development.
  24. Godlove, T. F., Jr. 1989. Religion, Interpretation and Diversity of Belief: The Framework Model from Kant to Durkheim to Davidson. Cambridge: Cambridge University Press.Google Scholar
  25. ——. 2002. Saving belief: on the new materialism in religious studies. In Radical Interpretation in Religion, ed. N. Frankenberry. Cambridge: Cambridge University Press.Google Scholar
  26. Hales, T., M. Adams, G. Bauer, T. D. Dang, J. Harrison, L. T. Hoang, C. Kaliszyk, V. Magron, S. Mclaughlin, T. Nguyen, and et al. 2017. A formal proof of the kepler conjecture. Forum of Mathematics, Pi 5: e2.Google Scholar
  27. Harman, G. 1987. (Nonsolipsistic) conceptual role semantics. In Notre Dame Journal of Formal Logic, ed. E. Lepore, 242–256. New York: Academic.Google Scholar
  28. Horwich, P. 1998. Meaning. Oxford: Oxford University Press.Google Scholar
  29. Lowe, E. J. 2010. Ontological dependence. In The Stanford Encyclopedia of Philosophy, ed. E. N. Zalta, spring 2010 ed. Metaphysics Research Lab, Stanford University.Google Scholar
  30. ——. 2013. A modal version of the ontological argument. In Debating Christian Theism, ed. J. P. Moreland, K. A. Sweis, and C. V. Meister, 61–71. Oxford: Oxford University Press.Google Scholar
  31. Nipkow, T., L. C. Paulson, and M. Wenzel. 2002. Isabelle/HOL — A Proof Assistant for Higher-Order Logic. Lecture Notes in Computer Science, vol. 2283. Heidelberg: Springer.Google Scholar
  32. Oppenheimer, P., and E. Zalta. 2011. A computationally-discovered simplification of the ontological argument. Australasian Journal of Philosophy 89 (2): 333–349.Google Scholar
  33. Pagin, P. Mar. 1997. Is compositionality compatible with holism? Mind & Language 12 (1): 11–33.Google Scholar
  34. ——. 2008. Meaning holism. In The Oxford Handbook of Philosophy of Language, ed. E. Lepore. Oxford: Oxford University Press (1. publ. in paperback edition).Google Scholar
  35. Pelletier, F. J. Feb. 2012. Holism and compositionality. In The Oxford Handbook of Compositionality, ed. W. Hinzen, E. Machery, and M. Werning. 1st ed. Oxford: Oxford University Press.Google Scholar
  36. Pelletier, F. J., G. Sutcliffe, and C. Suttner. Aug. 2002. The development of CASC. AI Communications 15 (2,3): 79–90.Google Scholar
  37. Peregrin, J. 2014. Inferentialism: Why Rules Matter. New York: Springer.CrossRefGoogle Scholar
  38. Peregrin, J., and V. Svoboda. 2013. Criteria for logical formalization. Synthese 190 (14): 2897–2924.CrossRefGoogle Scholar
  39. ——. 2017. Reflective Equilibrium and the Principles of Logical Analysis: Understanding the Laws of Logic. Routledge Studies in Contemporary Philosophy. Routledge: Taylor and Francis.Google Scholar
  40. Portoraro, F. 2014. Automated reasoning. In The Stanford Encyclopedia of Philosophy, ed. E. N. Zalta, winter 2014 ed. Metaphysics Research Lab, Stanford University.Google Scholar
  41. Rushby, J. 2013. The ontological argument in PVS. In Proc. of CAV Workshop “Fun With Formal Methods”, St. Petersburg, Russia.Google Scholar
  42. Sutcliffe, G., and C. Suttner. Oct. 1998. The TPTP problem library. Journal of Automated Reasoning 21 (2): 177–203.Google Scholar
  43. Tarski, A. 1956. The concept of truth in formalized languages. Logic, Semantics, Metamathematics 2: 152–278.Google Scholar
  44. Wiedijk, F. 2006. The Seventeen Provers of the World: Foreword by Dana S. Scott. (Lecture Notes in Computer Science/Lecture Notes in Artificial Intelligence). New York/Secaucus: SpringerGoogle Scholar
  45. Williams, M. Nov. 1999. Meaning and deflationary truth. Journal of Philosophy XCVI (11): 545–564.Google Scholar
  46. Williamson, T. 2013. Modal Logic as Metaphysics. Oxford: Oxford University Press.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Freie Universität BerlinBerlinGermany
  2. 2.University of LuxembourgEsch-sur-AlzetteLuxembourg

Personalised recommendations