[FOM] A formalism for Ultrafinitism
robblin at thetip.org
Sun May 23 12:51:22 EDT 2004
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 +
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?"
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