> On 14 Dec 2018, at 12:01, Philip Thrift <cloudver...@gmail.com> wrote: > > > > On Friday, December 14, 2018 at 4:49:33 AM UTC-6, Bruno Marchal wrote: > >> On 13 Dec 2018, at 21:05, Brent Meeker <meek...@verizon.net <javascript:>> >> wrote: >> >> >> >> On 12/13/2018 3:18 AM, Bruno Marchal wrote: >>>> Automating Gödel'’s Ontological Proof of God’s Existence ¨ with >>>> Higher-order Automated Theorem Provers >>>> http://page.mi.fu-berlin.de/cbenzmueller/papers/C40.pdf >>>> <http://page.mi.fu-berlin.de/cbenzmueller/papers/C40.pdf> >>> >>> Gödel took the modal logic S5 for its proof, which is the only logic NOT >>> available for the machines. >> >> What about S5 makes it not available for machines? > > > There are no intensional variant of G leading to S5. > > The axiom “5” is the guilty one (as []p & p obeys S4, and S5 can be defined > by S4 + “5”) > > “5” is <>p -> []<>p (the opposite of incompleteness: <>p -> ~[]<>p, but also > incompatible in the logic X, Z, etc.). > > Bruno > > > > > > How does this relate to the "higher-order theorem provers" that deals with > modal systems like S5? > > > https://www.ijcai.org/Proceedings/16/Papers/137.pdf
Rather interesting. The machine makes the right critics! Not quite serious about theology though. The definition of God by St-Anselme is a bit too much post-529 for the universal machine’s view. But some paragraph, notably the requirement of symmetry, gives me the feeling that the machine’s sensibility mode ([]p & <>t & p) defined in G1* (with 1 being what they called the collapse formula: p -> []p, which does not entail any collapse in arithmetic) might make the first person sensibility “believing” in the God of St-Anselme. It would be interesting to see what aspect of the ONE would correspond to this. Bruno > > - pt > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To post to this group, send email to everything-list@googlegroups.com > <mailto:everything-list@googlegroups.com>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
