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From: jwhrpr@mailserv.mta.ca (Jonathan Harpur)
Subject: Re^5: The end of god
Message-ID: <jwhrpr.10.000EFB20@mailserv.mta.ca>
Summary: blathering for hours, seemingly interminably
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References: <Cxzo7E.91v@gpu.utcc.utoronto.ca> <Harmon.776.000A2404@psyvax.psy.utexas.edu> <Cy72p4.B1r@gpu.utcc.utoronto.ca> <1994Oct25.052916.3600@gov.nt.ca>
Date: Fri, 4 Nov 1994 10:43:53 GMT

In article <1994Oct25.052916.3600@gov.nt.ca> gmonro@gov.nt.ca (Graham Monroe) writes:
>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:

I can't figure out who wrote what... but SOMEONE listed above wrote:
>>>>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.
[Snip]

...and someone else wrote:
>>>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.  

Yet another person, or maybe the first person, wrote:
>>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. 
[Snip]

I think people here are missing the point - Mathematics _is_ democratic - 
there is an accepted value of one - or any unitary measurement - as is all
precepts and systems of thought, including other forms of logic. Numbers, no
matter how many people agree on it, are still an arbitrary mental construct, 
and as such exist only in the heads of some sentient beings (and some humans, 
too. Heh.) The concept of "one", for instance, is empiric in the framework of 
integers, but this does not keep it from existing in the set of real 
numbers too; This does not prove the existence of "one", though, it just 
states that in a predefined set of ideas (like, er, numbers) "one" makes 
sense. To us, anyway. Many cultures had no representation of "zero" or "nil".
There is no way to say that their system of thought is less true for it though 
- who knows, maybe it's more true... Science as a whole is tarred to the same 
stick as mathematics, above - it's just a set of models that reflects to some 
degree of accuracy what we perceive in the outside world, and which is 
communicated to others, who concur with what we see and think. Proof in the 
system is no more true than the basis for the system itself. If we think the 
earth is flat and that space is curved... (think about that more before you 
reject it out of hand...)                                   See what I mean? 
Okay, you system purists: Convention, which is all you fellas are working 
with, is democratic, and there's no getting around that. Logic is a set of 
rules (read: conventions) the same way mathematic is, bound by the same 
(fallible) rules. The truths generated by logic only apply within the system, 
and when you export these truths outside of the system and introduce it to 
real life in an attempt to apply it to something practical, the "truth" will 
have the same flaws as the system. Unless the system is flawless, which is to 
say there are never any exceptions to the rules, ever, then the resulting 
truth is similarly flawed.
I have an Aloe plant handy...
Jonathan Harpur
