Also available as arXiv:2205.08628
This work is an illustration of Computational Philiosophy and, in addition, shows how these methods can help detect and rectify errors in modal reasoning.
The latest version includes a new postscript that considers alternative premises due to Andrzej Bilat (April 2021)
Updated version with better typesetting, some small addenda, and a
new postscript
here
and also available as
arXiv:2205.08628
HTML version available courtesy of arXiv:2205.08628
PVS dump file: start PVS 7 and do "M-x undump" this file to recreate the specifications and proofs used in the paper.
A Technical Report describes the embedding of modal logics in PVS that is used here.
Note: for those not familiar with these topics, St. Anselm was Archbishop of Canterbury and a contemporary of William the Conqueror. His Ontological Argument is a 3-line proof of the existence of God that has fascinated logicians for nearly 1,000 years.
This paper is concerned with the Proslogion III (modal) form of the Argument. Another recent paper examines the Proslogion II (traditional) Ontological Argument rendered in classical (first- and higher-order) logics, while another extends the analysis to first order modal treatments of that argument. Please email me if you would like to receive a draft copy of any of these papers.
@article{Rushby21:ijpr,
TITLE = {Mechanized Analysis of {Anselm's} Modal Ontological Argument},
AUTHOR = {John Rushby},
JOURNAL = {International Journal for Philosophy of Religion},
VOLUME = 89,
PAGES = {135--152},
MONTH = apr,
YEAR = 2021,
NOTE ={First published online 4 August 2020}
}