God created the real numbers

I'm an enthusiastic Cantor skeptic, I lean very heavily constructivist to the point of almost being a finitist, but nonetheless I think the thesis of this article is basically correct.

Nature and the universe is all about continuous quantities; integral quantities and whole numbers represent an abstraction. At a micro level this is less true -- elementary particles specifically are a (mostly) discrete phenomenon, but representing the state even of a very simple system involves continuous quantities.

But the Cantor vision of the real numbers is just wrong and completely unphysical. The idea of arbitrary precision is intrinsically broken in physical reality. Instead I am off the opinion that computation is the relevant process in the physical universe, so approximations to continuous quantities are where the "Eternal Nature" line lies, and the abstraction of the continuum is just that -- an abstraction of the idea of having perfect knowledge of the state of anything in the universe.

>I'm an enthusiastic Cantor skeptic

A skeptic in what way? He said a lot.

Here I'm referring to the cloud of things that Hilbert called "Cantor's Paradise". Basically everything around the notion of cardinality of infinities.

Please say more, I don't see how you can be _skeptical_ of those ideas.

Math is math, if you start with ZFC axioms you get uncountable infinites.

Maybe you don't start with those axioms. But that has nothing to do with truth, it's just a different mathematical setting.

I loosely identify with the schools of intuitinalism/construtivism/finitism. Primary idea is that the Law of the Excluded Middle is not meaningful.

So yes, generally not starting with ZFC.

I can't speak to "truth" in that sense. The skepticism here is skepticism of the utility of the ideas stemming from Cantor's Paradise. It ends up in a very naval-gazing place where you prove obviously false things (like Banach-Tarski) from the axioms but have no way to map these wildly non-constructive ideas back into the real world. Or where you construct a version of the reals where the reals that we can produce via any computation is a set of measure 0 in the reals.

I don't understand why you believe Banach-Tarski to be obviously false. All that BT tells me is that matter is not modeled by a continuum since matter is composed of discrete atoms. This says nothing of the falsity of BT or the continuum.