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'On the Question of Absolute Undecidability', 'Moral Dilemmas Revisited' and 'Introduction to Mathematical Philosophy'
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7 ideas
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
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14431
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The definition of order needs a transitive relation, to leap over infinite intermediate terms [Russell]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
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14422
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Any founded, non-repeating series all reachable in steps will satisfy Peano's axioms [Russell]
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14423
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'0', 'number' and 'successor' cannot be defined by Peano's axioms [Russell]
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17887
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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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17891
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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 / d. Hume's Principle
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14425
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A number is something which characterises collections of the same size [Russell]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
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14434
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What matters is the logical interrelation of mathematical terms, not their intrinsic nature [Russell]
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