Combining Texts
Ideas for
'Intro to Naming,Necessity and Natural Kinds', 'Grundgesetze der Arithmetik 2 (Basic Laws)' and 'Introducing the Philosophy of Mathematics'
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7 ideas
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 / 7. Formalism
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9887
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Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett]
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8751
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Only applicability raises arithmetic from a game to a science [Frege]
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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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