[FOM] Monsieur, x^p = x (mod p), donc Dieu existe. Repondez !
Vaughan Pratt
pratt at cs.stanford.edu
Fri Mar 11 02:33:25 EST 2011
On 3/10/2011 6:55 PM, Daniel Mehkeri wrote:
> Now, it might be thought there could be an alternate ultrafinitary
> proof. Here is a reason to think otherwise: suppose for example
> Bounded Arithmetic could prove it.
For us nonparticipants in this game it would be helpful to know the
ground rules.
I heard Yessenin-Volpin talk on his version of ultrafinitism at MIT in
the 1970s. While it did not make sense to me then, it occurs to me now
that one might base such a notion on the Blum axioms (q.v. on Wikipedia)
for a choice of complexity measure on an acceptable Goedel numbering of
the partial recursive functions, along with a plausible limit on how
long a program can run, such as some estimate of the lifetime to date of
the universe in Planck time units, or (much) more generously Parikh's
number 2^1000. In particular one can imagine proving that there must be
only finitely many feasible numbers in a suitable (but non-vague) sense,
hence a least infeasible number and a greatest feasible number. What
has been accomplished along such lines?
Anything less general would seem to smack of arbitrariness, while
anything more general would seem hard to prove however defined.
Vaughan Pratt
More information about the FOM
mailing list