[FOM] The characteristic S5 axiom and the ontological argument

[Paul Hollander]

> For what the skeleton of the argument proves is that: if it is possible
> that God exists necessarily then God exists necessarily, which is but an
> instance of the characteristic S5 axiom.

I recall that Godel is regarded as drawing this conclusion on the basis 
of weaker modal axioms than S5, bolstered with his own second-order 
special axioms and definitions regarding "essence," "being God-like," 
"positive property," etc.  Those same second-order axioms and 
definitions also serve to warrant the conclusion that being God-like is 
possibly exemplified.  So (as I recall) Godel accomplishes both goals of 
(1) deriving that a God-like being possibly exists, and (2) deriving 
that if a God-like being possibly exists then a God-like being 
necessarily exists (i.e., being God-like is necessarily exemplified -- a 
second-order claim), without appeal to S5.

I believe Norman Malcolm, Charles Hartshorne and Alvin Plantinga have 
explicitly used S5 in their versions of the ontological argument, with 
Plantinga's being the most widely discussed.  There also may be more 
recent versions that I just don't know about.

-paul