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From: ccb8m@viper.cs.Virginia.EDU (Charles C. Bundy)
Subject: Re: Is Penrose Right?
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References: <44oo23$s07@newsflash.concordia.ca <457p9j$820@aurora.cs.athabascau.ca> <481925744wnr@smithg.demon.co.uk>
Date: Wed, 18 Oct 1995 14:44:57 GMT
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In article <481925744wnr@smithg.demon.co.uk> Chris@smithg.demon.co.uk writes:
>In article: <457p9j$820@aurora.cs.athabascau.ca>  burt@cs.athabascau.ca (Burt 
>Voorhees) writes:
>> 
>> <earlier discussion of Penrose snipped>
>> 
>My reading of Penrose is that he claims that there are certain
>truths which mathematicians know 'unassailably'. I take this to mean that
>such Platonic truths are known with certainty, rather than near certainty. For
>such truths (presumably 1+1 = 2 would be an example), the type of subjective
>error you mention would not be a possibility. In other words, mathematicians 
>see these truths through a glass, clearly.
>

[snip]

>'through a glass, darkly' proposition contradictions would not matter.
>Mathematicians would not claim to know anything with unassailable 
>certainty. The highest degree of belief would be 'near certainty', and so It 
>would not be too surprising if contradictions were found occasionally.
>
>It is difficult to imagine that a statement such as 1+1 = 2 could be incorrect,
>but my preference would be to say that we see even truths such as this 
>'through a glass, darkly'. My point is that Penrose's argument only works
>if he insists that he can see 'through a glass, clearly'.

I agree.  1 of something is a symbolic mapping to a unit of something with
"clearly" defined boundaries.  The mathematical definition of 1 is 
a clear truth, but it's physical counterpart is uncertain (dark truth).  IE 

   1 -> car,  car + car = 2 cars 

seems resonable eh?  but does

   1 -> drop of water, drop of water + drop of water = 2 drops of water

Sounds like fuzzy set theory to me :)

>-- 
>Chris Gordon-Smith
>London
>UK
>Email: chris@smithg.demon.co.uk
>

Charles C. Bundy IV
ccb8m@virginia.edu

