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'fragments/reports', 'Frege's Concept of Numbers as Objects' and 'Nature and Meaning of Numbers'
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16 ideas
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
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
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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17441
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Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are [Wright,C, by Heck]
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13862
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There are five Peano axioms, which can be expressed informally [Wright,C]
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17853
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Number truths are said to be the consequence of PA - but it needs semantic consequence [Wright,C]
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17854
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What facts underpin the truths of the Peano axioms? [Wright,C]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
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
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 / 5. Definitions of Number / c. Fregean numbers
13894
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Sameness of number is fundamental, not counting, despite children learning that first [Wright,C]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
10140
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We derive Hume's Law from Law V, then discard the latter in deriving arithmetic [Wright,C, by Fine,K]
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8692
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Frege has a good system if his 'number principle' replaces his basic law V [Wright,C, by Friend]
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17440
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Wright says Hume's Principle is analytic of cardinal numbers, like a definition [Wright,C, by Heck]
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13893
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It is 1-1 correlation of concepts, and not progression, which distinguishes natural number [Wright,C]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
13888
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If numbers are extensions, Frege must first solve the Caesar problem for extensions [Wright,C]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
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
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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