From: barry@arnold.math.ucla.edu (Barry Merriman)
Subject: Re: Proof of God's Existence
Organization: UCLA, Mathematics Department
Date: Tue, 8 Sep 92 21:59:51 GMT

In article <1992Sep8.044743.1221@cltr.uq.OZ.AU> gar@cltr.uq.oz.au (Greg  
Restall) writes:
> barry@arnold.math.ucla.edu (Barry Merriman) writes:
> 
> *Zorn's lemma is more or less an axiom of set theory. It seems 
> *a bit pointless to take an axiom of set theory, and
> *simply say this axiom applies to causality...
> 
> Zorn's lemma applies to sets.  If it's true, it must 
> apply to sets of causes.  It's interesting to know that 
> if it is true, and if a couple of other somewhat plausible
> conditions hold, then there is a first cause.  You may not
> be so impressed by such a result, but I think it's neat.

I'll reiterate: I wouldn't deign to call it a ''result''. 
-Zorn's lemma is an *axiom* for partially ordered sets. 
-Its a mere assumption about the properties of such sets.
-Its a _first principle_ about such sets!

To say events ordered by causality is a partially ordered set, 
with one or two properties, and by the _axioms_ of such things, 
there is a first event, is hardly much of a result, is it?

There is little difference between this and simply postulating
the is a first event, as far as I can see, since all his
'argument' is wrapped up in his initial claim that the set
of events is a thing to which Zorn applies.



> 
> *The trick is, I don't go of the metaphysical 
> *deep end trying to irrefutably justify my claim. I just 
> *say: look at the historical evidence.> A number of points:
> 
> 1.  No-one was asking you to `irrefutably' justify
> your claim.  
> Where we were taking you to task is to realise that
> your claim is fudgy, and that any attempt to justify
> it means taking a philosophical stance.

No, dude. I'm saying look at the historical record and see how
well a purely philosophical, platonic approach to understaning
nature has worked. Not Too Well. Why is an appeal to the historical
record a philosophical claim?

> 
> 4.  The conclusion of Bob's argument --- that there is a 
> first cause --- looks like a rather difficult thing to
> test by way of experiment.  What Bob does is show that its
> existence is equivalent to the axiom of choice (for sets
> of causes) under certain plausible conditions.  What I 
> can't see for the life of me is what you could have against
> such an argument.  It's just saying that what we're after
> (whether or not there is a first cause) is a consequence
> of some other things.  Well, now we have a better idea
> of one way the universe could be, if it has a first
> cause.  

What I have against it is this: is a lot of mathematical
smoke and mirrors to obscure the simple claim that there
is a first cause. He's trying to lend legitimacy to this 
age old philosophical riddle by simply sucking in some
fancy mathematical things like set theory and Zorn's lemma.
It really contributes nothing to our understaning, since
he just makes a bunch of standard claims about causality, and
then using an *axiom* to achieve the desired conclusion 
(the one that has allays been achieved by philosophers anyway). 
There is no content to this argument. Its all axioms whose
''truth'' cannot be known.

(e.g. Why not adopt the rejection of Zorn's lemma, and conclude there need
not be a first cause? )


> 
> ------------------+------------------------------------------------
> Greg Restall      | Philosophy Department, University of Queensland
> gar@cltr.uq.oz.au | Queensland, 4072  Australia.
> ------------------+------------------------------------------------
--
Barry Merriman
UCLA Dept. of Math
UCLA Inst. for Fusion and Plasma Research
barry@math.ucla.edu (Internet; NeXTMail is welcome)


Newsgroups: sci.philosophy.tech