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'On the Question of Absolute Undecidability', 'The Concept of Law' and 'System of Logic'
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4 ideas
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
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The only axioms needed are for equality, addition, and successive numbers [Mill, by Shapiro]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
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PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
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Arithmetical undecidability is always settled at the next stage up [Koellner]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
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Arithmetic is based on definitions, and Sums of equals are equal, and Differences of equals are equal [Mill]
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