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Computer-supported Analysis of Positive Properties, Ultrafilters and Modal Collapse in Variants of Gödel's Ontological Argument
Bulletin of the Section of Logic, Tome 49 (2020) no. 2 Cet article a éte moissonné depuis la source Library of Science

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Three variants of Kurt Gödel's ontological argument, proposed by Dana Scott, C. Anthony Anderson and Melvin Fitting, are encoded and rigorously assessed on the computer. In contrast to Scott's version of Gödel's argument the two variants contributed by Anderson and Fitting avoid modal collapse. Although they appear quite different on a cursory reading they are in fact closely related. This has been revealed in the computer-supported formal analysis presented in this article. Key to our formal analysis is the utilization of suitably adapted notions of (modal) ultrafilters, and a careful distinction between extensions and intensions of positive properties.
Keywords: computational metaphysics, ontological argument, higher-order modal logic, higher-order logic, automated reasoning, modal ultrafilters 
@article{BSL_2020_49_2_a3,
     author = {Benzm\"uller, Christoph and Fuenmayor, David},
     title = {Computer-supported {Analysis} of {Positive} {Properties,} {Ultrafilters} and {Modal} {Collapse} in {Variants} of {G\"odel's} {Ontological} {Argument}},
     journal = {Bulletin of the Section of Logic},
     year = {2020},
     volume = {49},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BSL_2020_49_2_a3/}
}
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Benzmüller, Christoph; Fuenmayor, David. Computer-supported Analysis of Positive Properties, Ultrafilters and Modal Collapse in Variants of Gödel's Ontological Argument. Bulletin of the Section of Logic, Tome 49 (2020) no. 2. http://geodesic.mathdoc.fr/item/BSL_2020_49_2_a3/