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'fragments/reports', 'Philosophy of Mathematics' and 'The Rise of Analytic Philosophy 1879-1930'
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10 ideas
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10200
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We distinguish realism 'in ontology' (for objects), and 'in truth-value' (for being either true or false) [Shapiro]
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10210
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If mathematical objects are accepted, then a number of standard principles will follow [Shapiro]
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10215
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Platonists claim we can state the essence of a number without reference to the others [Shapiro]
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10233
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Platonism must accept that the Peano Axioms could all be false [Shapiro]
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6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
10244
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Intuition is an outright hindrance to five-dimensional geometry [Shapiro]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
10280
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A stone is a position in some pattern, and can be viewed as an object, or as a location [Shapiro]
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6. Mathematics / C. Sources of Mathematics / 7. Formalism
22310
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The formalist defence against Gödel is to reject his metalinguistic concept of truth [Potter]
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6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
22298
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Why is fictional arithmetic applicable to the real world? [Potter]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
10254
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Can the ideal constructor also destroy objects? [Shapiro]
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10255
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Presumably nothing can block a possible dynamic operation? [Shapiro]
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