From: holmes@opal.idbsu.edu (Randall Holmes)
Subject: Re: GOD - THE FINAL CHAPTER
Organization: Boise State University Math Dept.
Date: Tue, 8 Sep 1992 16:41:28 GMT

In article <1992Sep8.001627.90029@vaxc.cc.monash.edu.au> kevin@vaxc.cc.monash.edu.au writes:
>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.

The hard-line atheist must agree that the creation of the world by God
is a logical possibility for this to work.  This is open to doubt.

>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.

Here, you _assume_ that the non-existence of God is logically
consistent.  Not a legitimate move.  (I agree with your conclusions,
but your argument is invalid).

>
>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.

It gives you information about the _theory_; what does it tell you
about the standard model, exactly?

 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.

First, I was not entirely serious.  But suppose that I were.

Second, I am not being "New Age"; I intended to be taken literally.
Conclusions follow -- see below.

>God is more than existence - he must be, because pretty much all aethiests
>agree exsitence exists.

Maybe they thereby admit the existence of God without knowing it.
Spinoza claims to prove in his _Ethics_ that everyone loves God,
including the atheists...

 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.

One of the points of my posting on "God is existence" was to draw the
conclusion that God is V (the logical universe), which certainly does
not do any of these things!
 
>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.

Thus God does not do any of these things either, since God = Existence!

>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.

I am not a Christian.  I'm not misrepresenting -- I am refuting (at
least humorously).  The philosophical concept of God is hard to
distinguish from the logical universe; I follow Spinoza (for
argument's sake, at least) and take the philosophical concept to be
God and the rest to be mythology.

>But lets look at point 2- you can prove the existence of existence in some
>modified set theory.

Actually, the existence of V is an _axiom_ of NFU ( a case of the
comprehension scheme), so the proof is very short.

 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.

Nope.  The consistency is proved in ZFC See R. B. Jensen, The
consistency of a slight (!) variation on Quine's 'New Foundations',
Synthese, vol. 19.  I am a professional set theorist; I do know what I
am doing (as set theorist, if not theologian).

 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 !!!!

See above.

>Please, darlings!!!!!!!!!!
>Love
>Kevin Davey
>Monash University
>Australia.
>
>
>



-- 
The opinions expressed		|     --Sincerely,
above are not the "official"	|     M. Randall Holmes
opinions of any person		|     Math. Dept., Boise State Univ.
or institution.			|     holmes@opal.idbsu.edu