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Semantic Analysis of some Variants of Anderson-like Ontological Proofs

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Abstract

The aim of this paper is to prove strong completeness theorems for several Anderson-like variants of Gödel’s theory wrt. classes of modal structures, in which: (i). 1st order terms order receive only rigid extensions in the constant objectual 1st order domain; (ii). 2nd order terms receive non-rigid extensions in preselected world-relative objectual domains of 2nd order and rigid intensions in the constant conceptual 2nd order domain.

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Correspondence to Miroslaw Szatkowski.

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Szatkowski, M. Semantic Analysis of some Variants of Anderson-like Ontological Proofs. Stud Logica 79, 317–355 (2005). https://doi.org/10.1007/s11225-005-3610-y

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Keywords

  • Ontological proof
  • 2nd order modal logic
  • positive properties
  • completeness