>>10203769

>You said physicists use infinities and limits (computations with infinitely many steps) to describe things in the universe. However, the things they describe do not make these infinitely many steps explicitly visible. We do not know whether physical processes actually perform infinitely many steps, we only know that our predictions on infinitist axioms they match well.

I was responding to the claim that nonfinite mathematics does not correspond to reality, so saying that some specific thing is not "visible" is irrelevant of you admit that physics uses infinity in many ways.

>However that is an underdetermined theory, i.e. there are alternative models that fit just as well, namely finite approximations.

If they are approximations then by definition they don't fit "just as well."

>In addition, we have plenty of evidence of a discrete quantum graph,

What about quantum graphs with infinite or semi-infinite edges?

>but NO good evidence of infinities, e.g. no infinitely dense or hot things.

What about the density of a black hole?

Regardless, as I already said, claiming the absence of specific infinite things does not respond to the fact that indignities are used.

>Conversely, axiom systems involving infinities have dreadful theoretical issues like uncomputability/undecideability, counterintuitive results like nondenumerability, Banach-Tarski.

So what?

> I'd say finite theories are backed up by more evidence and are nicer in many ways, so they should be preferred.

When Wildberger does all physics without infinity then you can claim it has more evidence, until then, it doesn't.

>E.g. very large numbers instead of infinities or a truncated sum instead of an infinite one.

That's what a finite approximation is, I'm asking what you're approximating.