> 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.
I've often wondered about similar issues myself.
For one thing, we could argue that there is a difference between our interpretation of certain mathematical notions, such as completed infinite sets, and what we're actually doing, which is writing finitely many symbols down on paper in certain ways. There's no reason for which I can see that, because we can write certain symbols down in certain ways, that certain interpretations of what we're doing, above and beyond this, must follow. Add to this the fact that the act of writing down these symbols is only possible by the nature of our reality. Or at least, I don't see how we could prove its independence from our reality in a way that we would understand, because it seems to me that any such metaproof must also be within, and hence a feature of, our reality.