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Answer by Marcin for Has philosophy ever clarified mathematics?

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Would you expect to learn much about how to practice science (or any sub-branch thereof) from the philosophy of science? I hope the answer would be no; that falls within the study of science.

The philosophy of science and mathematics exists to examine the philosophical underpinnings of those disciplines which lie outside the purview of those disciplines themselves (e.g. do numbers have some kind of objective existence separate from the minds of reasoning beings), and philosophical topics related to them (such as the ethics of scientific and mathematical enquiry).

Now, that is not to say that this stuff is useless - it can guide the actions of scientists and mathematicians, and identify limitations in the discipline and its methods. However, you're not going to find material which has a simple relationship to the practice of the discipline, and certainly not in introductory texts aimed at people who are not mathematicians.


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