Re: [asa] Godel's theorem [Was: Re: Dawkins, religion, and children]

From: <philtill@aol.com>
Date: Thu May 10 2007 - 19:03:14 EDT

Pim,
 
Answering your two statements, taking the more interesting (2nd) one first:
 
2. I'm not assuming that nature must be able to self-exist, because personally I believe that it is God who self-exists, not nature. But it is the materialists who believe that nature self-exists, and so to examine their belief I am trying to see if nature is the kind of thing that really can self-exist. To address this I am introducing an argument from mathematics. Mathematics does not exist by itself like an equation floating in a vacuum. It is not an entity in its own right: it must be written onto something. It must be written explicitly in a Mind that is the source of all logic and mathematics, or it must be written implicitly on the fabric of some physics that displays the patterns of mathematics. Theists believe it is both; materialists believe it is only the latter. If it is only the latter, and if we believe that the physics emerged from a simpler state, then we can rightly discuss that simpler state in its relationship to its own implicit mathematics to see
  how far back we can reduce it. If we can reduce physics all the way back to an origin where it is supremely simple, then the mathematics written implicitly onto that physics at its origin must also have been supremely simple. Well, Godel tells us about the mathematics; he tells us that it cannot be reduced to any countable set of axioms if it contains arithmetic. Therefore, remembering that mathematics cannot float in a vacuum, if the mathematics have always and only been written on physics then the physics cannot be reducible to a state that supports no more than a countable set of axioms. It must have been complex enough to have the irreducible mathematics written on it. This has implications for its ability to self-exist. That was the thrust of the argument. I was not claiming that nature self-exists, but trying to argue against that belief.
 
1. I didn't assume nature must be axiomatic. I repeatedly said that one alternative is that nature cannot be reduced to axioms. I am happy with that alternative because it supports my belief that nature or whatever lies behind it cannot be simple in the reductionist sense.
 
God bless,
Phil
 
 
-----Original Message-----
From: pvm.pandas@gmail.com
To: philtill@aol.com
Cc: asa@calvin.edu
Sent: Thu, 10 May 2007 12:41 PM
Subject: Re: [asa] Godel's theorem [Was: Re: Dawkins, religion, and children]

Your argument is based on several assumptions which I believe have
made it fail to support your conclusion
 
First of all consistency versus completeness. What if nature has given
up consistency (Quantum Mechanics)
 
But that is but a minor detail, the main problems with your argument
are as follows
 
1. You assume that nature must be axiomatic
2. You assume that nature must be able to self-determine or self
exist. I fail to see why this is true or even relevant to the
argument. Within a particular system of axioms, one cannot prove that
all is true. But why should nature care about mathematical proofs of
truth? And if it were to matter, it can find another system which can
be used to explain or determine the truth.
 
As for mathematicians critiquing your argument. I have seen various
people make very similar assertions about Godel's incompleteness
theorem and have found similarly various rebuttals to such.
Not being a mathematician myself, I found it pretty trivial to find
the weaknesses in your claims which is the need for nature to be able
to self determine. However I propose that Godel's theorem says nothing
about such.
 
On 5/9/07, philtill@aol.com <philtill@aol.com> wrote:
>
> Hi Pim,
>
> you said,
>
> > As far as completeness and consistent, the two may indeed may be
> > sacrificed, one for the other. In most cases we abandon completeness
> > for consistency, but what if we were to abandon consistency for
> > completeness?
>
> I'm sorry to have to disagree but this is not correct. You are mixing
> Godel's first and second theorems. Please research it and you'll find out.
>
> Also, I am not questioning that consistent and complete systems may exist,
> or that the arithmetic inherent in nature is indeed such a system. I am
> also not questioning the ability of scientists to develop laws of physics,
> or mankind's ability to do logic and discover truth.
>
> What I am questioning is **nature's** ability to self-determine its own
> truth, and therefore to self-exist. If we conceive of nature as being
> ultimately simple, being nothing but one (or a few) mindless phenomena that
> can be described as axiomatic laws executing repeatedly to bring forth all
> the appearance of complexity in physics, then it may not strain us as hard
> to imagine the system self-existing. But since a few simple axiomatic laws
> are incapable of describing a complete and consistent arithmetical physics,
> then we must concede that nature in its essence is not simple. Indeed, the
> axioms at the essence of nature must be uncountably infinite, or rather
> nature must not be reducible to axioms at all. But then it would be truly
> amazing to think that such a complete and consistent nature self-exists
> rather than evolving slowly from a simpler state.
>
> While mathematicians have criticized the various misapplications of Godel's
> theorem, I have never run across anybody criticizing this particular take on
> it.
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Received on Thu May 10 19:03:45 2007

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