From: hjort@ohstpy.mps.ohio-state.edu
Newsgroups: alt.atheism
Subject: Re: goedel's proof for existence of god
Date: 15 Apr 92 23:05:18 GMT
Distribution: na

In article <1992Apr13.172422.6509@eco.twg.com>, chall@eco.twg.com (Charles Don Hall) writes:
> 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.

Also I would like to point out that the above argument also involves (I
think) an assumtion that I don't agree with. Namely the assumtion that
existance is a property of an object (as above "_existing_ god-like being")
rather than being a property of the universe in which the object may or
maynot reside. Thus imagining an "existing god-like being" would actually
mean imagining a universe in which a god-like being exists along with
imagining a god-like being.

Actually above it seems that the above proof uses both assumtions in the
phrase:  '"existing god-like being" exists'
           ^^^^^^^^                 ^^^^^^
existance as a property of the object  ||
                                       ||
                existance as a property of the universe

All this might just be another way of explaining modal logic in the
context of the above example. I don't know.

> 
> 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.
> -- 

Acctually I have to say that this is a bogus proof in formal logic as
I know it. The conditional has the following truth table:

  A  |  B  | A->B
-----+-----+------
  T  |  T  |  T
  T  |  F  |  F
  F  |  T  |  T
  F  |  F  |  T

Thus if we know A is false (A=I am good) and that A->B is true, we still
cannot say anything about B (whatever it may be).

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

					-Hans H Hjort
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