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How much do you need to know about mathematics to begin learning about the philosophy of mathematics or, for example, read something like The Principles of Mathematics or Principia Mathematica by Bertrand Russell?

How much do you need to know about science to begin learning about the philosophy of science? Some but not a great deal if you are interested in very general metaphysical questions about e.g. the nature of explanation, laws and causation, and in very general methodological questions about how scientific theories are confirmed and refuted. You'll need to know quite a lot more if you are interested in understanding more specific foundational questions about the interpretation of quantum mechanics or are worrying about the nature of natural selection. Similarly, how much do you need to know about mathematics to begin learning about the philosophy of mathematics? Some but not a great deal if you are interested in very general metaphysical and epistemological questions about e.g. the nature of numbers and the nature of our knowledge of such things (if they are "things"). Quite a lot more if you are bugged by more specific questions about how we are to settle axioms for set theory or to decide...

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