Re: [asa] Goedel's theorem and religion

As a logician, I have to say that any study that involves logic beyond
the level of the sentential, is affected by Goedel's theorem. It does not
interfere with derivations within limits, as it also does not restrict a
proof in geometry or number theory. But it presents a strong claim: there
are true statements in all these areas that cannot be proved true.

Let me take a different tack. What are the foundational claims of your
theology? How do you prove them true? You can't do it from within, and
from without it establishes that there is something superior to your
theology. But then you have to demonstrate that this superior study is
consistent and covers all that's necessary, which Goedel has shown can't
be done.

On the other hand, there is something at which human beings excel,
believing contradictory claims. This provides that all statements are
true, the /consequentia mirabilis/ of the medieval logicians. But, rather
than accepting these consequences, practitioners only accept what they
want to accept, becoming very upset when they are charged with promoting
nonsense.
Dave

On Fri, 13 Oct 2006 11:11:11 +1300 Don Nield <d.nield@auckland.ac.nz>
writes:
> Thank you, Ian. Another ASA memeber has contacted me privately,
> making a
> similar comment, and I was already approaching the topic with
> caution.
> On the other hand, when a person as experienced as John Polkinghorne
>
> thinks that Goedel's theorem has some relevance outside formal
> mathematical logic then I have to take that seriously.
> Yes, Goedel left behind an unpublished manuscript on a form of the
> ontological argument, separate from incompleteness theorems. It is
>
> unclear whether his failure to publish this was due to his
> dissatisfaction about the strength of his argument or whether
> Goedel,
> who was an intensely private person, just wished to keep out of
> controversy about religion.
> Don
>
> Iain Strachan wrote:
>
> > Don,
> >
> > I don't claim to be an expert in this field, but purely in my own
>
> > personal opinion, I think Godel's theorem is a bit of a red
> herring as
> > far as religion is concerned. It applies only to the
> comparatively
> > narrow field of symbolic logic, and states that consistent systems
> of
> > symbolic logic are necessarily incomplete, in that there will
> exist
> > formally undecidable propositions within that system. The kind of
>
> > formally undecidable propositions that occur seem to be to do with
>
> > self-referential statements, like the equivalent of "THIS
> STATEMENT IS
> > FALSE". I think Godel constructed an assertion that effectively
> said
> > "THIS STATEMENT IS FORMALLY UNDECIDABLE". Since this is only an
> > existence theorem by construction, I don't see that it has any
> general
> > use in defining the limits of knowledge - only that this kind of
> > self-referential statement is formally undecidable. There is no
> proof
> > that statements not of this class are formally undecidable.
> >
> > As I understand it, from a brief web-browse, Goedel also
> constructed
> > some form of "argument for God" based on the ontological argument,
> but
> > it appears that this has nothing to do with the incompleteness
> theorems.
> >
> > Iain
> >
> > On 10/11/06, *Don Nield* <d.nield@auckland.ac.nz
> > <mailto:d.nield@auckland.ac.nz>> wrote:
> >
> > For better or for worse, I have just accepted the job of
> writing a
> > short
> > handbook article on Goedel's theorem in the context of science
> and
> > religion. If anyone in this forum has any expertise in the
> > subject (or
> > strong views on the subject!) I would like to hear (privately
> or
> > otherwise) from him or her. I have in front of me Stephen
> Barr's book
> > "Modern Physics and Ancient Faith". Barr discusses the work of
> John
> > Lucas and Roger Penrose. I am also aware that Stanley Jaki
> has
> > written
> > on the subject, and that people like John Polkinghorne mention
> Goedel
> > from time to time. What other books or papers should I be
> reading?
> > Don Nield
> >
> > To unsubscribe, send a message to majordomo@calvin.edu
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> >
> >
> >
> >
> > --
> > -----------
> > After the game, the King and the pawn go back in the same box.
> >
> > - Italian Proverb
> > -----------
>
>
>
>
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>
>

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Received on Fri Oct 13 00:06:04 2006