[FOM] Remedial mathematics?

[Andre.Rodin at ens.fr]

Timothy Y. Chow:

> Some skeptics, like Nelson, of course have an answer---they don't believe
> in N.  But this is a pretty radical position, and I think skeptics should
> be forced to acknowledge how radical a position they are taking and how
> much standard mathematical practice they are throwing out with the
> bathwater.

In my sense in order to not "believe in N" one doesn't need to be a sceptic.
Would you call a sceptic someone who did not believe in Euclid's 5th Postulate
before the non-Euclidean geometries were well established? Actually the
brightest mathematicians didn't believe it and continued to work hard on it. In
fact the discovery of the non-Euclidean geometries didn't require one to throw
away any essential part of the earlier practice - albeit it required to give up
certain philosophical ideas about the geometrical space. The situation with N
may turn to be similar. I admit that for the moment this is a sheer speculation
but I think it is important not only to be open for but also try to push such
possible developments.

Andrei