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'Metaphysics: the logical approach', 'Is Mathematics purely Linguistic?' and 'On Second-Order Logic'
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5 ideas
6. Mathematics / A. Nature of Mathematics / 2. Geometry
3332
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Greeks saw the science of proportion as the link between geometry and arithmetic [Benardete,JA]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
3330
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Negatives, rationals, irrationals and imaginaries are all postulated to solve baffling equations [Benardete,JA]
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3337
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Natural numbers are seen in terms of either their ordinality (Peano), or cardinality (set theory) [Benardete,JA]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10833
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Many concepts can only be expressed by second-order logic [Boolos]
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6. Mathematics / C. Sources of Mathematics / 7. Formalism
21570
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Numbers are just verbal conveniences, which can be analysed away [Russell]
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