Computer-supported Assessments of Gödel’s ontological variant 

(and its variants by Scott, Anderson, Fitting)

Background reading

Kurt Gödel's ontological argument and emendations of it (including Dana Scott’s variant) are discussed in various texts, including:

Recommended readings on Gödel’s ontological argument (and on ontological arguments in general) also include:

Computer-supported formal assessment of Gödel’s ontological argument (and also Scott’s variant)

In 2013 Gödel’ ontological argument was formally reconstructed and assessed by us on the computer:

The findings include: Gödel’s 1970 variant is inconsistent, Scott’s variant is consistent, modal collapse and monotheism is implied, the argument works already in higher-order modal logic KB. 

Different aspects of our initial studies were presented at several conferences and events:

Assessment of the inconsistency in Gödel’s 1970 variant (which was unknowingly corrected by Scott)

The inconsistency in Gödel’s 1970 variant, which is avoided in Scott’s variant, is assessed in more detail in the following papers:

Assessment of the Anderson-Hajek controversy on Gödel’s ontological argument

  • Computer-Assisted Analysis of the Anderson-Hájek Controversy (Christoph Benzmüller, Leon Weber, Bruno Woltzenlogel Paleo), In Logica Universalis, volume 11, number 1, pp. 139-151, 2017. (Preprint: [bibtex] [doi] [url]
  • Can Computers Help to Sharpen our Understanding of Ontological Arguments? (Christoph Benzmüller, David Fuenmayor), In Mathematics and Reality, Proceedings of the 11th All India Students' Conference on Science & Spiritual Quest (AISSQ), 6-7 October, 2018, IIT Bhubaneswar, Bhubaneswar, India (Sudipto Gosh, Ramgopal Uppalari, K. Vasudeva Rao, Varun Agarwal, Sushant Sharma, eds.), The Bhaktivedanta Institute, Kolkata,, pp. 195-226, 2018. (Preprint: [bibtex]  

A formal assessment of Melvin Fitting’s intensional variant of Gödel’s ontological argument (see his 2002 book):

We also formalised Fitting’s intensional variant on the computer, and we assessed it and compared it with the variants of Scott and Anderson:

The latter paper starts using (modal) ultrafilters as a mathematical tool for the comparison of the different variants.

Ultrafilter-based assessments and simplifications of Gödel’s ontological argument 

Using (modal) ultrafilters, Gödel’s ontological argument can be more deeply studied, and it can be further simplified: 

Further references in which our computer-supported assessments of Gödel’s ontological argument is discussed:

Studies of other, related ontological arguments with our technique and tools:

Related pioneering works on computational metaphysics by Ed Zalta and colleagues is mentioned in: