In reply to Jimbo W:
> So in that case, is mathematics provisional in the same way that scientific theories about
> reality are provisional?
Yes.
> If, rather, mathematics is provisional, in what way is it provisional ...
For example, all humans (all mathematicians) could have a delusional blind-spot about some aspect of logic, and so always get something wrong. (The fact that I answered "yes" above doesn't mean that things can't be proved well beyond reasonable doubt, just as much of science, though formally provisional, is well beyond reasonable doubt.)
> So reality and maths are both agency independent?
I would say so (though noting the formally provisional nature of any such conclusion).
> Is it? Or is it a tool that we use to access it?
Both. Yes it is a tool, a tool fashioned out of empirical enquiry, in the same way that a telescope is both derived from empirical enquiry and a tool towards further enquiry.
> Is it more fundamental than that?
Is maths more fundamental than reality? I'd say no, and I'm not even sure how it could be. To me maths is a description of reality, and the description/nature of something has the same fundamentalness (if that's a word) as the thing itself.
> Why the machine metaphor ...
The brain is a tool, a "machine" is a tool.
> What sort of environmental evolutionary pressure would drive this?
Our higher mathematical ability is likely a spandrel, something not directly selected for, but a by-product of things that are selected for.