Computer-supported Analysis of Positive Properties, Ultrafilters and Modal Collapse in Variants of Gödel's Ontological Argument
This work addresses formal logic and philosophical arguments for researchers in automated reasoning, but it is incremental as it builds on existing variants without introducing new paradigms.
The authors tackled the problem of analyzing variants of Gödel's ontological argument by encoding and assessing three versions (Scott, Anderson, Fitting) on a computer, revealing that Anderson and Fitting's variants avoid modal collapse and are closely related despite apparent differences.
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.