Logica Universalis

, Volume 11, Issue 1, pp 139–151 | Cite as

Computer-Assisted Analysis of the Anderson–Hájek Ontological Controversy

Article

Abstract

A universal reasoning approach based on shallow semantical embeddings of higher-order modal logics into classical higher-order logic is exemplarily employed to analyze several modern variants of the ontological argument on the computer. Several novel findings are reported which contribute to the clarification of a long-standing dispute between Anderson and Hájek. The technology employed in this work, which to some degree realizes Leibniz’s dream of a characteristica universalis and a calculus ratiocinator for solving philosophical controversies, is ready to be fruitfully adopted in larger scale by philosophers.

Keywords

Ontological argument Universal reasoning Shallow semantical embedding Higher-order modal logic Classical higher-order logic Higher-order automated theorem proving 

Mathematics Subject Classification

03A10 03B15 03B45 

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  • C. Benzmüller
    • 1
  • L. Weber
    • 1
  • B. Woltzenlogel Paleo
    • 2
  1. 1.Department of Mathematics and Computer ScienceFreie Universität BerlinBerlinGermany
  2. 2.WienAustria

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