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Ideas for 'works', 'Metaphysics: the logical approach' and 'Empiricism, Semantics and Ontology'

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5 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry

3332	Greeks saw the science of proportion as the link between geometry and arithmetic [Benardete,JA]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number

3330	Negatives, rationals, irrationals and imaginaries are all postulated to solve baffling equations [Benardete,JA]

3337	Natural numbers are seen in terms of either their ordinality (Peano), or cardinality (set theory) [Benardete,JA]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism

13936

Questions about numbers are answered by analysis, and are analytic, and hence logically true [Carnap]

8748	Logical positivists incorporated geometry into logicism, saying axioms are just definitions [Carnap, by Shapiro]