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From: gmonro@gov.nt.ca (Graham Monroe)
Subject: Re: rereRe: The end of god
Message-ID: <1994Oct25.052916.3600@gov.nt.ca>
Organization: Government of the NWT, Canada
References: <Cxzo7E.91v@gpu.utcc.utoronto.ca> <Harmon.776.000A2404@psyvax.psy.utexas.edu> <Cy72p4.B1r@gpu.utcc.utoronto.ca>
Date: Tue, 25 Oct 1994 05:29:16 GMT
Lines: 59

In article <Cy72p4.B1r@gpu.utcc.utoronto.ca> pindor@gpu.utcc.utoronto.ca (Andrzej Pindor) writes:
>In article <Harmon.776.000A2404@psyvax.psy.utexas.edu>,
>Michael G. Harmon <Harmon@psyvax.psy.utexas.edu> wrote:
>>In article <Cxzo7E.91v@gpu.utcc.utoronto.ca> pindor@gpu.utcc.utoronto.ca (Andrzej Pindor) writes:
>>
>>>Your example just illustrates the Goedel theorem.  The point I was trying to 
>>>make was that to know something 'for sure' we also use mathematics, even
>>>if applied to a system external to the one in which this something is true.
>>>Short of divine inspiration, what we hold to be true in science is arrived at
>>>by logical reasoning at some level. We may propose various conjectures and
>>>even have a deep, unfaltering belief that such a conjecture is true, it only
>>>becomes a scientific truth if proven using logic. Penrose seems to suggest
>>>that there are some scientific (mathematical) truths which logic cannot prove.
>>>I have yet to hear an example. Yours does not cut it.
>>
>>>Andrzej
>>
>>It may be that Penrose is saying there are some truths that are not 
>>scientific in nature that will subsequently remain unprovable by scientific 
>>method.  It might be that such phenomenon that would be agreed upon as valid 
>>solely by the concurrance of a sufficient number of credentialed members of 
>>the scientific community who either try the idea out in their own minds and 
>>admit a certain reasonance with respect to the rest of what they know or 
>>perhaps be able to gain a statisical basis by experimenting with the 
>>subjective perceptions of a group of subjects who claim to be able to directly 
>>percieve aspects of the 'truth' in question.  
>
>How would this differ from widely accepted cojectures? These would just
>be plausible guesses, wouldn't they? Are you suggesting to turn mathematics
>into a democracy and determine mathematical truths by voting? I hope not.

I may be diverging from your conversation somewhat (I haven't been
consistently following the thread) but as I understand the Goedel
theorem, there are, in any sufficiently powerful logical system,
statements that can neither be proven true nor false. This means they
have no truth value and the statements, or their negations, can be
taken as axioms. Asking whether the statement is true or false is
in effect asking a meaningless question.

In the case of a statement about the physical world that fits this 
description the truth or falsehood could in principle be determined
by experiment, or if it could not, then it would be outside the realm
of physics.

On the other hand, this does not mean that we could perform the
experiment necessary to determine the truth value of the statement.
We are limited by technology, energy limits, and even conceivably,
by observer interactive phenomena.

Graham
>
>Andrzej
>-- 
>Andrzej Pindor                        The foolish reject what they see and 
>University of Toronto                 not what they think; the wise reject
>Instructional and Research Computing  what they think and not what they see.
>pindor@gpu.utcc.utoronto.ca                           Huang Po


