Combining Philosophers
Ideas for Herodotus, Georg Kreisel and Harold Hodes
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6 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
10027
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Mathematics is higher-order modal logic [Hodes]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
10026
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Arithmetic must allow for the possibility of only a finite total of objects [Hodes]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
17809
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Gödel showed that the syntactic approach to the infinite is of limited value [Kreisel]
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6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
17810
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The study of mathematical foundations needs new non-mathematical concepts [Kreisel]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10021
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It is claimed that numbers are objects which essentially represent cardinality quantifiers [Hodes]
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10022
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Numerical terms can't really stand for quantifiers, because that would make them first-level [Hodes]
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