Combining Texts
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'Philebus', 'teaching' and 'Nature and Meaning of Numbers'
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6 ideas
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
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13508
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Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
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18096
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Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
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18841
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Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
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14130
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Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
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8924
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Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
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9153
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Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K]
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