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Automating Emendations of the Ontological Argument in Intensional Higher-Order Modal Logic

  • David FuenmayorEmail author
  • Christoph BenzmüllerEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10505)

Abstract

A shallow semantic embedding of an intensional higher-order modal logic (IHOML) in Isabelle/HOL is presented. IHOML draws on Montague/Gallin intensional logics and has been introduced by Melvin Fitting in his textbook Types, Tableaus and Gödel’s God in order to discuss his emendation of Gödel’s ontological argument for the existence of God. Utilizing IHOML, the most interesting parts of Fitting’s textbook are formalized, automated and verified in the Isabelle/HOL proof assistant. A particular focus thereby is on three variants of the ontological argument which avoid the modal collapse, which is a strongly criticized side-effect in Gödel’s resp. Scott’s original work.

Keywords

Automated theorem proving Computational metaphysics Higher-order logic Intensional logic Isabelle Modal logic Ontological argument Semantic embedding 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

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

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