# Computer-supported Analysis of Positive Properties, Ultrafilters and Modal Collapse in Variants of G"odel's Ontological Argument

arXiv: https://arxiv.org/abs/1910.08955 · HTML: https://mlsanity.com/paper/1910.08955/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Oct 2019.

## Built on by (most cited first, 2 of 2)

- [Many Logics, One Methodology: A Plea for Logical Pluralism in Formalised Reasoning (preprint)](https://mlsanity.com/paper/2605.27246/) (2026)
- [A Simplified Variant of G"odel's Ontological Argument](https://mlsanity.com/paper/2202.06264/) (2022)

## Abstract (arXiv)

Three variants of Kurt G"odel'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 G"odel'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.