[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
More information about the FOM
mailing list