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'The Elm and the Expert', 'The Question of Ontology' and 'On What There Is'
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7 ideas
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
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12215
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The existence of numbers is not a matter of identities, but of constituents of the world [Fine,K]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
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12211
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It is plausible that x^2 = -1 had no solutions before complex numbers were 'introduced' [Fine,K]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
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12209
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The indispensability argument shows that nature is non-numerical, not the denial of numbers [Fine,K]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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1613
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Logicists cheerfully accept reference to bound variables and all sorts of abstract entities [Quine]
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6. Mathematics / C. Sources of Mathematics / 7. Formalism
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1616
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Formalism says maths is built of meaningless notations; these build into rules which have meaning [Quine]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
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1615
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Intuitionism says classes are invented, and abstract entities are constructed from specified ingredients [Quine]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
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1614
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Conceptualism holds that there are universals but they are mind-made [Quine]
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