[FOM] Question for Nik Weaver

Bill Taylor W.Taylor at math.canterbury.ac.nz
Thu Feb 23 00:01:55 EST 2006

Nik, you made this comment in an article yesterday...

> it is possible to treat things like
> the real line and the power set of N essentially as proper classes

Presumably this apposition implies that you do NOT think of P(N) and R
as being essentially isomorphic? (OC one should remove the finite sets
from P(N) to do this most conveniently.)  I recall once seeing another
math-philosopher who refused to make this identification, but alas
I can't remember who.   Anyway, if so, what essential differences,
mathematical or philosophical, do you see between them?

Incidentally, I think this identification, accepted by many (most?)
mathematicians, and especially by almost all "pure mathematicians",
is a clear-cut example of what Friedman called "coding" just the other day.
He commented as that mathematicians loathe coding whenever they see it,
and try to avoid it at all costs.  This seems to be a counterexample.

Bill Taylor

More information about the FOM mailing list