What’s an empirical proof? I’m not being facetious, I’m genuinely interested because I’ve never heard the term before. To me, a proof is a deductive mathematic

What’s an empirical proof? I’m not being facetious, I’m genuinely interested because I’ve never heard the term before. To me, a proof is a deductive mathematical argument that takes a claim of the form “if P then Q” and shows how Q is necessarily true when we assume P. I don’t know how to translate from reality into that formalism. All of modern mathematics does not attempt to do so. Instead, it is built up from the axioms of set theory, which take the form of rules for manipulating symbols on paper (or on a computer or even in our minds) without saying anything specific about what those symbols really mean.