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Ideas for 'Lectures on the History of Philosophy', 'Mathematics without Numbers' and 'Scientific Attitude and Fallibilism'

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5 ideas

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

14775

Numbers are just names devised for counting [Peirce]

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism

8698	Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]

9557	Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]

10263

Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism

14776

That two two-eyed people must have four eyes is a statement about numbers, not a fact [Peirce]