On Thu, 13 Jul 2006 09:43:42 -0500, "Robert J. Kolker" <email@example.com> wrote:
>Hatto von Aquitanien wrote: > >> >> I know this was addressed to someone else, but I would also like to offer my >> thoughts on this matter. I contend that mathematics _is_ constrained by >> physical reality. The underlying logic which determines mathematics is a >> manifestation of physical reality. I believe what you are asserting is >> that mathematics should not be required to produce physically measurable >> results as a test of its validity. I really have to wonder if such a >> requirement is unrealistic. It's interesting to observe that some people >> are wont to point to the fact that formal proofs can be verified by >> computer programs. > >But formal proofs generally cannot be discovered by finitary algorithmic >means.
That's nonsense. Given a formal theory, enumerate all finite strings in a language suitable for describing formal proofs in that theory. As each one appears, check to see whether it's a proof. Every proof in the theory will eventually appear.
If you meant to be talking about _efficient_ algorithms you should say so.
> We still need Inspiration. If you regard all, so-called "mental" >processes, as really physical then your assertion may have some basis. > >Bob Kolker