Combining Texts
Ideas for
'The Evolution of Modern Metaphysics', 'Intro to 'The Reason's Proper Study'' and 'Scientific Attitude and Fallibilism'
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6 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 / 4. Axioms for Number / g. Incompleteness of Arithmetic
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The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
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If structures are relative, this undermines truth-value and objectivity [Hale/Wright]
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The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright]
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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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6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
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The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright]
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