Meta-metamathematics

[Hendrik Boom]

On Thu, Jan 06, 2022 at 01:46:45AM -0500, JOSEPH SHIPMAN wrote:

> 
> I propose the following:
> 
> “There is no physical experiment which could ever provide persuasive evidence for or against statements of set theory that are not absolute. Mathematicians who firmly disagree about such a statement, but who agree about fundamental physics, will never be able to settle the matter by doing computations or any other physical processes.”
> 
> If this proposition is correct, then arguing about, say, the continuum hypothesis can be viewed as a “religious dispute”. Even though CH is refuted by ZFC+RVM, CH-believers will not have to regard, say, physical evidence for the consistency of cardinals below a measurable as evidence toward RVM, because direct evidence for CH itself will not be something that correct physical theories can provide. Attention should be focused on axioms with new arithmetical (or at least absolute) consequences.
> 
> What is your opinion of this proposition? I especially want to hear from physicists.

Physicists do appear to act as if the consistency of the Quantum-mechanical
Standard  Model were an axiom.

This isn't the continuum hypothesis, but is it 
the kind of mathematical axiom you are talking about?

Or is it instead part of the physics?

-- hendrik