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'Pragmatism - eight lectures', 'Letters to Queen Charlotte' and 'Introduction to Mathematical Philosophy'
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6 ideas
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
23026
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We know mathematical axioms, such as subtracting equals from equals leaves equals, by a natural light [Leibniz]
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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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Any founded, non-repeating series all reachable in steps will satisfy Peano's axioms [Russell]
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'0', 'number' and 'successor' cannot be defined by Peano's axioms [Russell]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
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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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What matters is the logical interrelation of mathematical terms, not their intrinsic nature [Russell]
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