I have to admit to pretty much agreeing with Coel’s main points in this post, which anyone who read my recent post on logic probably won’t find too surprising.  The idea of math and logic resting on empirical foundations seems to be ferociously resisted, I think because those foundations don’t feel empirical, mainly because we don’t learn them empirically.  The human brain is not a blank slate.  It comes with pre-wiring for a number of capacities, including logic and some math.  We don’t always use it, but we evolved it, probably due to its survival advantages.

However, unlike Coel, I’m not insistent on mathematics being a part of science.  I’m content to leave science to endeavors that involve a heavy amount of empirical investigation, and the logical and mathematical consequences of that investigation.   Mathematics may have empirical foundations, but I think it’s pretty obvious that mathematicians aren’t doing empirical work, but finding interesting and (sometimes) useful tautologies.