[btilly]

While interesting, that doesn't matter for what I said.

An example of a key question is whether mathematical constructions can use the absolute truth of statements in mathematical constructions. Even if those absolute truths are not themselves something that can be settled by any algorithm.

If they can, then we get all of the weirdness of infinite set theory, such as that there must be more reals than rationals. If they can't, then all of mathematics could fit within a countable universe, and things like Cantor's diagonalization proof just demonstrates a Halting problem kind of self-reference in the definitions of the real numbers.

And this brings us to my point. It doesn't matter whether the universe is continuous and measured to finite precision, or discrete. The set of measurements that we could potentially ever make within this universe is finite (though large). The set of measurements that could be made in principle from the principles that we can discover within this universe is countable. And we have no way to produce an oracle that can always decide truth or falsity. And therefore reality cannot encompass the actual existence of the uncountable infinites that ZFC claim must exist.