[FOM] The characteristic S5 axiom and the ontological argument
paul at paulhollander.com
Wed Apr 8 13:33:11 EDT 2009
> 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.
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