> 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?
> 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. -- Nil conscire sibi