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'Defending the Axioms', 'Explanation - Opening Address' and 'Constructibility and Mathematical Existence'
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6 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 / b. Type theory
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Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro]
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We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
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Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro]
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