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'Defending the Axioms', 'Thinking About Logic' and 'Problems in Personal Identity'
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4 ideas
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10979
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Although second-order arithmetic is incomplete, it can fully model normal arithmetic [Read]
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Second-order arithmetic covers all properties, ensuring categoricity [Read]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
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Von Neumann numbers are helpful, but don't correctly describe numbers [Read]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
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Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
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