Combining Texts
Ideas for
'Mathematics without Numbers', 'Scientific Attitude and Fallibilism' and 'Reply to Fifth Objections'
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5 ideas
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
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Numbers are just names devised for counting [Peirce]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
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Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
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Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
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Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
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That two two-eyed people must have four eyes is a statement about numbers, not a fact [Peirce]
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