Combining Philosophers
Ideas for H.Putnam/P.Oppenheim, Thomas Reid and Ian Rumfitt
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5 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
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Maybe an ordinal is a property of isomorphic well-ordered sets, and not itself a set [Rumfitt]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
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A single object must not be counted twice, which needs knowledge of distinctness (negative identity) [Rumfitt]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
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Infinitesimals do not stand in a determinate order relation to zero [Rumfitt]
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6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
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Cantor and Dedekind aimed to give analysis a foundation in set theory (rather than geometry) [Rumfitt]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
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Some 'how many?' answers are not predications of a concept, like 'how many gallons?' [Rumfitt]
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