Mathematicians and scientists have vague folk theories of what math and science are that both are blurred ancestral memories of pre-WWII logical positivism.
These theories are totally wrong, but do little *direct* harm because they are mainly ignored in practice.
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(the book is Tymoczko's 'New Directions in the Philosophy of Mathematics: An Anthology')
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Would you recommend it? ("This provocative book goes beyond foundationalist questions to offer what has been called a “postmodern” assessment of the philosophy of mathematics — one that addresses issues of theoretical importance in terms of mathematical experience.") —blurb
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