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'fragments/reports', 'Logicism in the 21st Century' and 'A Structural Account of Mathematics'
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6 ideas
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
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Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
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Neo-logicism founds arithmetic on Hume's Principle along with second-order logic [Hale/Wright]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
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The Julius Caesar problem asks for a criterion for the concept of a 'number' [Hale/Wright]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
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We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
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Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology [Hale/Wright]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
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Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright]
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