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'fragments/reports', 'Philosophies of Mathematics' and 'Metaphysics'
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9 ideas
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
17899
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Second-order induction is stronger as it covers all concepts, not just first-order definable ones [George/Velleman]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10128
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The Incompleteness proofs use arithmetic to talk about formal arithmetic [George/Velleman]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
17843
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The idea of 'one' is the foundation of number [Aristotle]
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17850
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Each many is just ones, and is measured by the one [Aristotle]
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17851
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Number is plurality measured by unity [Aristotle]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
17902
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A successor is the union of a set with its singleton [George/Velleman]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
10133
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Frege's Theorem shows the Peano Postulates can be derived from Hume's Principle [George/Velleman]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10130
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Set theory can prove the Peano Postulates [George/Velleman]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
9793
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Mathematics studies abstracted relations, commensurability and proportion [Aristotle]
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