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.