Combining Texts
Ideas for
'W.V. Quine', 'On Platonism in Mathematics' and 'Introducing the Philosophy of Mathematics'
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8 ideas
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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10303
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Restricted Platonism is just an ideal projection of a domain of thought [Bernays]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
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8681
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The big problem for platonists is epistemic: how do we perceive, intuit, know or detect mathematical facts? [Friend]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
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8712
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Mathematics should be treated as true whenever it is indispensable to our best physical theory [Friend]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
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8473
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The logicists held that is-a-member-of is a logical constant, making set theory part of logic [Orenstein]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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10306
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Mathematical abstraction just goes in a different direction from logic [Bernays]
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6. Mathematics / C. Sources of Mathematics / 7. Formalism
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8716
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Formalism is unconstrained, so cannot indicate importance, or directions for research [Friend]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
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8706
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Constructivism rejects too much mathematics [Friend]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
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8707
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Intuitionists typically retain bivalence but reject the law of excluded middle [Friend]
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