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Is mathematics somehow "scientific"? Let me explain. There is a sense in which scientific theories are ad hoc. We have a set of relevant observations, and we try to formulate a theory which (1) accounts for all of them and (2) is parsimonious. A theory here is just an explanatory principle tailored to capture the data we want. What we don't do is deduce scientific theories from foundational principles.
Axioms in math often strike me as very much like this. The only difference is that the "data" or "observations" of interest here are our intuitions about mathematics (e.g., that A+B=B+A). When I look at the axioms of ZF set theory (for example), I don't see where they're supposed to be coming from; rather, they're just one ad hoc way of justifying propositions we feel must be justified.
Isn't there something weird, though, about tweaking one's axioms to fit one's intuitions?

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