Combining Texts
Ideas for
'The Evolution of Modern Metaphysics', 'Intro to 'The Reason's Proper Study'' and 'Set Theory and Its Philosophy'
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4 ideas
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
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It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter]
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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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