[FOM] A formalism for Ultrafinitism

[Robbie Lindauer]

On May 20, 2004, at 7:52 PM, W.Taylor at math.canterbury.ac.nz wrote:

> An ultrafinitist who doesn't
> want 10^10^10 or whatever, can merely add an axiom that
> the top number has certain appropriate properties.

Why is it necessary to have a top number?  Why not just recognize that 
there is no top number?  E.g. take induction as proof that there is no 
greatest number, no number of numbers, etc., since for all x, x < x + 
1.

This would have a lot in common with adding a "large cardinal axiom" in 
"normal" set theoretic terms too.  It just has an ad-hoc feeling to it. 
  "What do we do about this biggest number?"

Best Wishes,

Robbie Lindauer