On Thu, 13 Jul 2006 10:31:00 -0400, Hatto von Aquitanien <abbot@AugiaDives.hre> wrote:
>Robert J. Kolker 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. > >Isn't that Chruch's theorem?
I suspect that the theorem you're referring to is the fact that there is no algorithm to decide whether a given statement is a theorem. This is true, in contrast to what Robert said, which is false.
>> We still need Inspiration. If you regard all, so-called "mental" >> processes, as really physical then your assertion may have some basis. > >The only thing I am asserting with absolute conviction that will never be >shaken is that the thought processes which we call mathematics are governed >by the Laws of Nature. That is to say Physical Laws. Whether that amounts >to "finitary algorithmic means" is less certain. Everything else was >intended contingently. > >Note that my comment regarding proofs involved verification, not production.