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'Sweet Dreams', 'Russell's Metaphysical Logic' and 'The Question of Ontology'
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9 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 / a. Early logicism
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21723
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The task of logicism was to define by logic the concepts 'number', 'successor' and '0' [Linsky,B]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
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21721
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Higher types are needed to distinguished intensional phenomena which are coextensive [Linsky,B]
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21703
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Types are 'ramified' when there are further differences between the type of quantifier and its range [Linsky,B]
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21714
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The ramified theory subdivides each type, according to the range of the variables [Linsky,B]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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21713
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Did logicism fail, when Russell added three nonlogical axioms, to save mathematics? [Linsky,B]
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21715
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For those who abandon logicism, standard set theory is a rival option [Linsky,B]
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