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.
[Editor’s Note: This essay is part of Scientia Salon’s special “scientism week” and could profitably be read alongside other entries on the same topic on this site, such as this one by John Shook and this one by yours truly. My take on the issue is very different from that of the authors who contributed to this special series, and indeed close to that of Putnam and Popper — as it should be clear from a recent presentation I did at a workshop on scientism I organized. Also, contra the author of the third essay in this series (but, interestingly, not the author of the first two!) I think the notion that mathematics is a part of science is fundamentally indefensible. Then again, part of the point of the SciSal project is to offer a forum for a variety of thoughtful perspectives, not just to serve as an echo chamber…
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