[hprotagonist]

*an empirical theory.

I can certainly prove things about, say, addition.

[solarist]

if you mean you can prove 2+2==4, it's actually tautology: | | + | | == | | | |

[hprotagonist]

no like, "addition is closed over the integers" is something you can show to be True (for all members of an infinite set, no less -- so it's not empirical.)