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From: gsmith@brahms.BERKELEY.EDU (Gene Ward Smith)
Newsgroups: net.religion,talk.religion,net.origins
Subject: Re: The Cosmological Argument
Message-ID: <15449@ucbvax.BERKELEY.EDU>
Date: Fri, 29-Aug-86 05:06:25 EDT
Article-I.D.: ucbvax.15449
Posted: Fri Aug 29 05:06:25 1986
Date-Received: Tue, 9-Sep-86 04:02:15 EDT
References: <15222@ucbvax.BERKELEY.EDU> <112@methods.UUCP>
Sender: usenet@ucbvax.BERKELEY.EDU
Reply-To: gsmith@brahms.UUCP (Gene Ward Smith)
Organization: University of California, Berkeley
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Xref: linus net.religion:10642 talk.religion:29 net.origins:3442

In article <112@methods.UUCP> cary@methods.UUCP (Cary Timar (U of W co-op)) writes:
>In article <15222@ucbvax.BERKELEY.EDU> gsmith@brahms.UUCP (Gene Ward Smith) writes:

>>   We can do this a little differently: we can look at everything that exists
>>and the relation "<" of ontological dependence ...
>>Zorn's lemma says that there are maxima under ontological dependence.

>Extrapolating logic and set theory outside our universe is questionable,
>at best.  I see no reason why any theoretical god need be bound by some
>descriptive laws invented by men to describe the behavior of
>mathematical sets that they created to describe the universe around
>them.

   Well, I agree with you, sort of. But I think logic and set theory are 
more universal than you think. In particular, set theory was invented to
talk about mathematical reality (sets of real numbers, etc.) and not 
the universe around us.

>In particular, I cannot see why we should grant Zorn's Lemma.
>Mathematicians generally prefer to have proofs that do not depend on the
>Axiom of Choice or its equivalents.

   Most mathematicians could care less, a few strange ones do. By the way,
there is an old joke to the effect that the existence of God is equivalent
to the Axiom of Choice: since Zorn's lemma => God exists and God exists =>
God can do the choice routine, and hence the Axiom of Choice is true.

>I feel that somehow any theoretical god is belittled by being dependent
>for its very existence on Zorn's Lemma.

   This is not what the argument says, so I wouldn't worry about it. 

ucbvax!brahms!gsmith    Gene Ward Smith/UCB Math Dept/Berkeley CA 94720
    "*That* the world is, is the mystical." -- Ludwig Wittgenstein