[FOM] Cantor on Richard's Paradox

hendrik@topoi.pooq.com hendrik at topoi.pooq.com
Wed Jul 4 23:22:47 EDT 2007

On Wed, Jul 04, 2007 at 03:54:37PM +0200, laureano luna wrote:
> It looks like Cantor is pointing at a kind of
> indefinite extensibility in human natural linguistic
> competence, since he refers in general to our
> resources to define reals.
> Moreover, Cantor seems to think that all reals are
> definable, since any limitation on the cardinality of
> the set of defining resources results for him in a
> corresponding limitation on the cardinality of the
> continuum.
> This, I think, has little to do with the philosophy of
> mathematics generally ascribed to him. 

He may have a physicist's intuition about definability -- that if you 
can point to a position on a number line (perhaps on a ruler of a 
pressure guage) you have defined a real number.    This is much less 
formal than definability on a formal system.  And the quantizatoin of 
physics happened long after his work.

-- hendrik

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