On 9/14/2012 11:53 AM, John Clark wrote:
On Thu, Sep 13, 2012 at 7:55 AM, Stephen P. King
<stephe...@charter.net <mailto:stephe...@charter.net>> wrote:
> Godel numberings are not unique.
True, there are a infinite number of ways you could do Godel numbering.
Hi John,
Yes, but my point here is that this is the same thing as having an
infinite number of names for one and the same thing. This makes it
impossible to be absolutely sure of what "John Clark" or "Stephen P.
King" is.
> Thus there is no a single abslute structure of relations, there
is an infinity
And you can use any one of those Godel numbering schemes to show that
there is not a single one of those infinite number of structural
relationships that are powerful enough to do arithmetic and be
consistent and complete. The hope is that the scheme mathematicians
are using is consistent but incomplete, if it's inconsistent that
would be a disaster.
Mathematicians get around this problem by defining a unique naming
scheme. My point is that this cannot be done at a meta-theoretical level
when we have to include a multiplicity of names for the same of multiple
entities that are evaluating models of the mathematical scheme.
John K Clark
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Onward!
Stephen
http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html
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