[FOM] High Complexity without Infinity

[Randall Holmes]

Dear FOM'ers,

Re Taranovsky's posting on "high complexity without infinity" I wanted
to comment that it is exactly this notion of "sufficiently rapidly
increasing finite function" which lay behind at least my adaptations of
Bryan Ford's purported argument against Con(ZFC) (I extracted an
argument against Con(PA), a much more disturbing creature --
fortunately an incorrect one!).  Of course the argument is not valid
precisely because "sufficiently rapidly increasing finite function" is
not in fact definable in PA, so the truth definitions which can be
given for PA using this concept do not lead to paradox.

It would be interesting to hear whether anyone else agrees with
Taranovsky that this is arguably a finitary concept.