Aristotle says we should only require of a discipline what the domain affords (when he is establishing principles not by induction). Indeed, a perfectly servic

Aristotle says we should only require of a discipline what the domain affords (when he is establishing principles not by induction). Indeed, a perfectly serviceable philosophy of math would address what enables it to be taught and used consistently by different practitioners, so they all get the same results (or better, by some agreed metric thereof). But I think the real question is what makes one mathematical approach better than another: economy? insight? accuracy? transparency? composability with other approaches? usability? cultural value? economic relevance? Then, if you want to traverse 2,300 years, does the historical evolution of math evidence tension between the math we want and the math we got, and how (TF) to get what we want? Realizing we're wrong about math is the essence of math: it's how we got 365 days instead of 360, irrational numbers distinct from ratios ...