### Abstract

A computer-formalisation of the essential parts of Fitting's textbook "Types, Tableaus and Gödel's God" in Isabelle/HOL is presented. In particular, Fitting's (and Anderson's) variant of the ontological argument is verified and confirmed. This variant avoids the modal collapse, which has been criticised as an undesirable side-effect of Kurt Gödel's (and Dana Scott's) versions of the ontological argument. Fitting's work is employing an intensional higher-order modal logic, which we shallowly embed here in classical higher-order logic. We then utilize the embedded logic for the formalisation of Fitting's argument. (See also the earlier AFP entry “Gödel's God in Isabelle/HOL”.)

### License

BSD License

### Topics

- Logic/Philosophical aspects

### Session Types_Tableaus_and_Goedels_God

- Relations
- IHOML
- IHOML_Examples
- GoedelProof_P1
- GoedelProof_P2
- FittingProof
- AndersonProof

## Cite

×

Types_Tableaus_and_Goedels_God-AFP

    @article{Types_Tableaus_and_Goedels_God-AFP,
      author  = {David Fuenmayor and Christoph Benzmüller},
      title   = {Types, Tableaus and Gödel’s God in Isabelle/HOL},
      journal = {Archive of Formal Proofs},
      month   = {May},
      year    = {2017},
      note    = {\url{https://isa-afp.org/entries/Types_Tableaus_and_Goedels_God.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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