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Jeremy Shipley
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This commits a complex question fallacy. It presumes that philosophers are ignorant of mathematical and scientific issues pertinent to their work. We are not. The recent literature on structuralism in the philosophy of mathematics and the philosophy of science, for example, contains deep engagement with category theory, quantum field theory, and other deep and difficult mathematics and scientific topics. A case might be made that some traditional epistemologists should learn more probability theory, but recent years have seen an ascendant formal epistemology that is deeply informed by probability theory and an increased interaction between traditional and formal methods. Just about every semi-important epistemologist these days knows at least a bit of probability and is familiar with Bayes theorem. To be sure, there may be some philosophers who don't find gravity or Markov processes really pertinent to, let's say, GE Moore's open question argument in meta-ethics, but then there are physicists, no doubt, who believe silly things about ethics. I object to the presupposition of this question that philosophers are not, to the extent that it is pertinent, learning the things we need to from mathematics. A better question (which I have begun to answer) is not what should but rather what are philosophers drawing from engagement with mathematics.