From: chall@eco.twg.com (Charles Don Hall)
Newsgroups: alt.atheism
Subject: Re: goedel's proof for existence of god
Keywords: god,goedel
Date: 13 Apr 92 17:24:22 GMT
Distribution: na
Organization: The Wollongong Group (East Coast Operations)

In <atten.702563771@groucho.phil.ruu.nl> atten@phil.ruu.nl (Mark van Atten) writes:

>First, this is not repeat not an attempt to apply Goedel's theorem to a
>religious question (or any other not concerning formal systems). However,
>I read somewhere that Goedel did not find it surprising that his theorem was
>used for this kind of argument, arguing that it is justified in some sense.
>(Oh, I remember: he wrote that in a letter to his mother, quoted in 'Reflections on Kurt Goedel' by Hao Wang; I will give the full quote next time, ok?)
>Goedel was very much influenced by the philosophy of Leibniz, which he studied
>very intensively 1943-1944. Goedel made this formalization of Leibniz' proof of
>the existence of God (perhaps as outlined in Monadology par.44-45)
>I would welcome all comments (theologians, logicians, thinkers, dreamers ... 
>unite!)

I've always believed that this was one of the better proofs of God's
existence, because logicians had to develop a new kind of logic to punch
holes in the argument. This particular version has some extraneous
elements and vaguenesses in it, though...a more streamlined version
is something like:

Q. Can you imagine that a "god-like being" exists?
A. Yes.
Q. So you can imagine that an "existing god-like being" exists?
A. Sure, that's the same thing!
Q. Can you imagine that an "existing god-like being" doesn't exist?
A. Well, no, that's a contradiction.
Q. So it must be the case that an "existing god-like being" exists,
   because the converse is unimaginable!
A. But...but...but...but...but...
Q. Come on, spit it out!
A. I want to change one of my previous answers. I can imagine that
   a "god-like being" exists, but not that an "existing god-like
   being" exists.
Q. But one of the attributes of godhood is omnipresence, so any
   "god-like being" is neccessarily an "existing god-like being".
A. Then I guess I can't imagine that a "god-like being" exists.
Q. Hmmph. Most people can at least IMAGINE a god-like being. You're
   not being very open-minded.

To expose the flaw in the argument, you use "modal logic", which
distinguishes between "conditional" truths (things which can be
imagined; things which are true in some possible worlds), and
"universal" truth (things which are true in all possible worlds).
So "a god-like being exists" is a conditional truth, and "all
existing god-like beings exist" is a universal truth. When you
state arguments in English, it is very easy to blur the line
between conditionals and universals.

By the way, have you seen this argument?
PREMISE: If the statement "If I am good, then I will go to Heaven" is true,
	 then God exists.
PREMISE: I am not good.
CONCLUSION: God exists.

If you translate that into propositional logic, you really can
derive the conclusion from the premisses. You can't in modal
logic, because "If I am good, then I will go to Heaven" needs
to be universally true, and "I am not good" is only conditionally
true.
-- 

===========================================================
Charles Don Hall, Licensed Philosopher  (chall@eco.twg.com)
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