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'Defending the Axioms', 'works' and 'Empiricism, Semantics and Ontology'
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5 ideas
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
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Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
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Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
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The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
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Logical positivists incorporated geometry into logicism, saying axioms are just definitions [Carnap, by Shapiro]
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Questions about numbers are answered by analysis, and are analytic, and hence logically true [Carnap]
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