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'works', 'The Possibility of Metaphysics' and 'Empiricism, Semantics and Ontology'
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8 ideas
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
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Numbers are universals, being sets whose instances are sets of appropriate cardinality [Lowe]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
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Simple counting is more basic than spotting that one-to-one correlation makes sets equinumerous [Lowe]
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Fs and Gs are identical in number if they one-to-one correlate with one another [Lowe]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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Sets are instances of numbers (rather than 'collections'); numbers explain sets, not vice versa [Lowe]
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If 2 is a particular, then adding particulars to themselves does nothing, and 2+2=2 [Lowe]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
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Does the existence of numbers matter, in the way space, time and persons do? [Lowe]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
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Questions about numbers are answered by analysis, and are analytic, and hence logically true [Carnap]
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Logical positivists incorporated geometry into logicism, saying axioms are just definitions [Carnap, by Shapiro]
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