[FOM] Cantor on Richard's Paradox

laureano luna laureanoluna at yahoo.es
Sat Jul 7 07:59:42 EDT 2007

hendrik at topoi.pooq.com wrote:

> 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.

Well, Cantor speaks of a set {B} of concepts
(Begriffe) as the set of resources we can use to
define reals. Pointing to is hardly the use of a

Anyway, this has made me notice Cantor is referring to
semantical objects (concepts, perhaps: meanings,
thoughts) and not to syntactical objects as strings of

I do not think Cantor could have believed we have an
uncountable supply of letter-strings available. So, I
wonder whether he thought those semantical objects
were in an uncountable quantity even if the
syntactical strings that should express them formed a
countable set. This is, however, still strange enough.

The letter is from 8.8.1906 and I think it can be
found in "Georg Cantor Briefe", H. Meschkowski, W.
Nilson (editors), Springer, Berlin (1991), p.446.

I haven't yet checked it.


Laureano Luna

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