The original philosophical foundation of mathematics would be Pythagoreanism [1].
For instance, that there is a special, transcendent meaning to "oneness" or "twoness" — or more generally, that there is a basic harmony within mathematics that manifests in the harmonies of the cosmos.
That's fine. It's just that when you get to the very bottom of axioms, it can get a little weird. Like, is the underlying basis the one, the nothing or the all? Is it being or not being? That is metaphysical -- and has implications for the foundation of any axiom, no?
I'm not sure what it even means for the underlying basis to be one or nothing or everything (basis of what specificly?). That doesn't sound like an axiom thing to me.
For instance, that there is a special, transcendent meaning to "oneness" or "twoness" — or more generally, that there is a basic harmony within mathematics that manifests in the harmonies of the cosmos.
Here is a nice article on the sources of his mathematical contributions. https://www.sciencedirect.com/science/article/pii/0315086089...
[1] https://en.m.wikipedia.org/wiki/Pythagoras