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'Parmenides', 'The Question of Ontology' and 'The Tarskian Turn'
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8 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
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15364
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English expressions are denumerably infinite, but reals are nondenumerable, so many are unnameable [Horsten]
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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 / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
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15360
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ZFC showed that the concept of set is mathematical, not logical, because of its existence claims [Horsten]
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15369
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Set theory is substantial over first-order arithmetic, because it enables new proofs [Horsten]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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16150
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One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato]
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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 / 10. Constructivism / d. Predicativism
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15370
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Predicativism says mathematical definitions must not include the thing being defined [Horsten]
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