From: kevin@vaxc.cc.monash.edu.au
Newsgroups: sci.math
Subject: GOD - THE FINAL CHAPTER
Date: 8 Sep 92 00:16:27 +1000
Organization: Computer Centre, Monash University, Australia

I posted earlier the following argument:
1. It is possible to imagine a world epistemically quivalent to ours, in which
god exists.
2. Likewise, where God doesn't exist.
Thus, given the existence of these worlds, a proof of the existence of God
is impossible.
Criticisms that have been recently raised are the following:
First, is it so clear that both worlds exists?
Take the first. Imagine simply the scenario of the detatched God, a God who
made the universe, then completely ignored it; left it to itself and the
laws of nature, and didn't interfere. Sure, the existence of this god will
have absolutely no effect on it, apart from its existence, but still, he's 
there. It seems to me that this is an EPISTEMIC possibility, i.e, a 
possibility completely consistent with all your current 'knowledge' of 
the universe. Although it may be unlikely, whatever that may mean, still,
it's logically possible. It seems that even a hard line aethiest must concede
this.
Now take the second, and more controversial. Once again, I will suggest a
possible state of affairs, epistemically equivalent to ours, in which there
is no God. I'm not denying that what I'm about to suggest is crazy - but
logically consistent with our epistemic data. Simply this - imagine that you
(the reader) have been taken since birth, and embedded in a tank by a mad
psychiatrist who has connected electrodes to every part of your brain. All
the sense datum - in fact everything (inluding thoughts that aren't sensory
in nature) are fed to you from him - and no-one else. You have absolutely
no idea about the 'real' world - only the world the mad scientist has created
for you. In fact, the real world can consist of anything logically consistent,
perhaps epistemically wildly different from our own - in particular, a
world in which God don't exist. It seems likely that even a God fearing
man must concede this as an EPISTEMIC possibility - no matter how much
an insult to his dignity this may be.

Thus, it seems that these two worlds can exists as EPISTEMIC possibilities -
i.e, worlds indistinguishable from our own .
(I challenge anyone to show me otherwise- these sorts of examples, in 
particular the latter, have been running around philosophy since Descartes, 
and, it seems, though silly, can't be resolved. Do not take the bizzare
but logically possible lightly - this is the whole topic of conversation - 
PROOFS of the existence of God - i.e, where such possibilities can be
logically eliminated.)

The second point raised in critisism was the notion of existence. What do I
mean when I say these worlds 'exist'? Am I conceding that there are actually
two different world existing, one in which god is, and the other in which
he aint? A bit of model theory should resolve this problem. Take an 
undecidable statement about the (standard) natural numbers. The way we can
show such a statement undecidable is by constructing two models, M and M' of
the axioms of the arithmetic, one in which the statement is true, and the other
in which it's false. Neither of these models need be the standard one, none-
theless, it gives us information about the standard model. Note also, that
in thestandard model, the statement is still precisely one of true or false - 
its just that we can't get to it using the axioms.
Let's consider this as an analogy. I have constructed two worlds - M and M',
one in which a certain statement is true - the other in which it's false.
Now, I'm not claiming either of them actually correspond to the real world.
Nonetheless, both model all knowledge any individual has, had has and ever 
may have. Thus- whatever you take as axioms (I have mentioned problems with
this previously)- they can be nothing more than epistimological statements - 
all of which are true in both worlds.
Certainly, however, in the real world God either exists or doesn't exist.
All I'm saying, is we can't decide in an EPISTEMIC fashion which one is the
case. Ultimately, what's needed is faith - which is necessarily irrational
(be it faith in the existence or non-existence of God.)
I hope that answers all queries - further queries (all answerable, of course)
are welcomed both in private or in public.

In closing, I have also noted another line of argument running - something
like the following.
1. God is existence.
2. You can prove the existence of existence in some modified set theory
(Of course, in normal set theory, you can't.)
Actually, I have a problem with both points.
First, din't kid yourself. This sort of New Testament "God is existence" 
new-age lets be philosophical and use words which we don't really understand
so no-one can really pin us down IS WRONG.
God is more than existence - he must be, because pretty much all aethiests
agree exsitence exists. God is more than that. God is a creature who makes
moral judgements. God tells us what's good and whats bad. God gives tablets
to old men on mountain tops. God blows up ancient cities with too many
homosexuals in them. God has a son who rises from the dead. 
Existence is not a creature who makes moral judgements. Existence doesn't
tell us what's good or bad. Existence doesn't give tables to old men on 
mountain tops. Existence doesn't blow up ancient cities with too many
homosexuals in them. That's just absurd.
You are misrepresenting religion if you just claim God is existence - few
would argue that existence doesn't exist. God -to any Christian - is a lot
more than that. That cannot be denied while maintaining credibility.
But lets look at point 2- you can prove the existence of existence in some
modified set theory. Well, how odd. It sounds to me, (and do correct me if
I'm worng) that what's being claimed is that there is some modified set
theory, of which one can prove the constintency, from within. Well, the
second theorem of Godel tells us then that that system can't even code
in a uniform way each recursive set! So it couldn't be too much of
a set theory could it let alone EXISTENCE ITSELF - i.e, GOD!
What would dear old john paul say when he opened the local mathematical
bulletin and read
THEOREM: God's missing a recursive set !!!!
Please, darlings!!!!!!!!!!
Love
Kevin Davey
Monash University
Australia.



From: sec@otter.hpl.hp.com (Simon Crouch)
Date: Thu, 10 Sep 1992 15:08:43 GMT
Subject: Re: Freedman-Donaldson Theorem
Organization: Hewlett-Packard Laboratories, Bristol, UK.