From: tycchow+@cs.cmu.edu (Timothy Chow)
Newsgroups: sci.philosophy.tech
Subject: Re: Proof of God's Existence
Date: 9 Sep 92 04:01:29 GMT
Article-I.D.: cs.BuALuI.Cqo.2
Organization: None.  This saves me from writing a disclaimer.

O.K., I'll confess that I did the unforgivable and actually went back
and READ CAREFULLY all the articles in this thread.  :-)

In <Bu13pL.C83@usenet.ucs.indiana.edu> David Chalmers quotes the paper:

  So what is being claimed here, at least, is a sound argument to a
  true conclusion.  It is only reasonable to add the usual disclaimers.
  All that the argument seeks to establish is that there is a First Cause.
                                                   ^^^^^^^^^^^^^^^^^^^^^^
Greg Restall claims that the paper seeks to establish a *conditional*
result.  Note that the underlined phrase is *unconditional*---I think
this is what ired Barry Merriman.  We can resolve this by assuming that
the author had tongue firmly in cheek when he said his paper establishes
a first cause, and that what he *really meant* was a conditional result.

Given this, then the question remains as to whether the argument has any
relvance to the physical universe.  Barry Merriman complains that the
argument is "purely contemplative" and hence cannot "prove" anything
about the physical universe.  I think he is right that before the
argument can claim to have any implications about the physical universe,
the assumptions need to be backed up by empirical evidence.  This,
however, is only an argument against the *unconditional* form of Meyer's
claim; if Meyer really intended only a *conditional* result then I don't
think Merriman would deny its validity.

On the other hand Merriman also seems to argue that the *conditional*
result is close to vacuous:

BM: Zorn's lemma is more or less an axiom of set theory. It seems 
BM: a bit pointless to take an axiom of set theory, and
BM: simply say this axiom applies to causality, and so there
BM: is a first cause. Why not just postulate a first cause, 
BM: and dispense with the philosophical prestidigitation?

Consider the following argument: It seems a bit pointless to take an
axiom of set theory, and simply say that this axiom applies to
topological spaces, and so the product of compact sets is compact.  Why
not just postulate that the product of compact sets is compact, and
dispense with the mathematical prestidigitation?

Since most mathematicians think that the equivalence of the axiom of
choice with Tychonoff's theorem is non-trivial, Merriman's argument is a
bit too simplistic.  Arguably, all of mathematics amounts to exploring
the consequences of axioms.  To give another example, how about the
derivation of the Lorentz transformation equations from the constancy of
the speed of light, the principle of relativity, etc.?  Why not just
postulate the Lorentz transformation equations and dispense with the
mathematical prestidigitation?

The REAL question is whether or not the inference of the first cause from
Zorn's lemma is a trivial one.  If it isn't trivial, then the paper is
at least of some mathematical interest.  However, I would argue that the
inference is pretty much trivial.  Hence Merriman's complaint is
essentially justified.  There is only a minuscule difference between

	If there is a first cause then there is a first cause.
and	If Zorn's lemma applies to causal sets then there is a first cause.

because both claims are trivial.

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

By this reasoning, every theorem of mathematics is "hardly much of a
result."  To say that a metric space is a topological space, with one or
two properties, and by the _axioms_ of such things, every metric space
is paracompact, is hardly much of a result, is it?

Perhaps what you mean is that if we are ONLY appealing to axioms DIRECTLY
instead of to lemmas or theorems then the result can't be much more than
trivial.  In that case I pretty much agree with you.

BM: It really contributes nothing to our understaning, since
BM: he just makes a bunch of standard claims about causality, and
BM: then using an *axiom* to achieve the desired conclusion 

I'm not sure it "contributes nothing to our understanding."  For
example, you yourself suggested that the picture that current physics
paints, of an infinitely receding chain of causal events, refutes any
argument of the existence of a first cause.  But this is one of the main
points of the paper: the existence of such chains in no way precludes
the existence of a first cause.  Consider the set S = {-1} U {x: x>0}.
This set has a first cause, in spite of the behavior as you approach
zero from above.  Now, I'm not saying I buy the paper's arguments, but
simply that it contributes a little bit to our understanding.

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

This is not precluded by the paper, if you accept the conditional reading.

One problem I see with the paper (here I am sharpening an argument I
made in another article) is its claimed EQUIVALENCE of Zorn's lemma
with the existence of a first cause.  If this is to be more than a
mathematical statement (i.e., if the mathematical concepts in the paper
are intended to model the real world) then we need to assume something
like:

	Every partially ordered set (with properties blah blah blah)
	can be REALIZED as (or "models" if you like) an actual set of
        causal events of the real world.

This seems even more dubious than the other assumptions of the paper.
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