FOM: Assorted other replies

[JOE SHIPMAN, BLOOMBERG/ SKILLMAN]

To Neil T: By "reproof" I think Berlinski meant both rebuke and redemonstration.
I hope your first quote will put an end to all further talk about barbers.

To Thayer: The various set-theoretical ways of developing real analysis, while
disagreeing on whether e is a member of pi, all provably have the same theorems
*of real analysis* (in a language which doesn't allow talk about reals being
members of each other).  Is the same true for the choices of a topos for r.a.?

To Davis: I agree with you 100%.  A related important f.o.m. issue is the nature
of the certainty attainable for mathematical statements where we don't have a
formalizable classical proof (I will discuss several types in an upcoming post).

To Harvey: Bravo (at last)!  But please tell us all what k-subtle cardinals are.

To Riis: You have humor too.  I hope Vaughan can take a joke.     -- Joe Shipman