cbostrum (02/09/83)
I did a little research on modern treatments of the ontological
arugment for the existence of God. Most use some form of modal logic,
which renders them hard to understand just because modal logic is hard
to understand (if not thouroughly obscure). They also use a free logic
(where terms need not denote things: this is necessary to say things
like unicorns dont exist (ie to use a term without presuposing it
tohave a referent. I dont think this is a big problem and I think it
can be got around.)
Anyway, here is a formalisation of the premisses and conclusion for
the argument, in a form as taken from David Lewis, "Nous", 1970.
It uses first order logic, with Worlds as objects in the domain, which
is less obscure than modal logic.
If X is conceivable, then there is a world W where X exists.
If X is conceivable, X exists in W, but X does not exist in V then
X is greater in W than X is in V
There is some conceivable X such that X is greater in the actual world
than any other thing in any other world.
>From these, it follows that there is an X in the actual world (yes,
it really exists there) and that there doesnt exist anything any greater
in any other world.
Note that the third premiss does not assume that
there is actually in this world an X which satisfies it,
but that we can prove this from the three premisses.
I think that this argument can be defended.
(This is as Lewis gave it. I believe it needs some fixing up at the third
premiss, however).