Re: Platonism

Victor Yodaiken (
Wed, 9 Nov 1994 14:15:35 -0700

On Nov 9, 12:46pm, Randall Holmes wrote:
Subject: Re: Platonism
>(responding to yodaiken's question)
>It depends on what level one is working. Suppose that I prove
>mathematically that there is a proof of theorem X, even prove it
>constructively. The computer code generated by following the procedure
>outlined in my proof may be so large as not to be implementable.
>I'm doing metamathematics, but it is not implementable directly.

Sure, but I do not see why this requires one to have faith that
the syntactic objects (which clearly exist) represent similarly
"real" objects.

>Of course, this can be avoided by making the theory in which
>metamathematical reasoning is to be carried out sufficiently weak;
>but I don't think that PRA is weak enough to forbid metamathematical
>results of this kind (comments on this question are invited?) One's

There is no number less than 100! that has property X:
proof: for i=1 to 100! test X on i

If you can define exponentiation or factorial you are able to define
infeasible computations.