Combining Philosophers
Ideas for Eubulides, David S. Oderberg and Harold Hodes
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5 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
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Mathematics is higher-order modal logic [Hodes]
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The Aristotelian view is that numbers depend on (and are abstracted from) other things [Oderberg]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
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Arithmetic must allow for the possibility of only a finite total of objects [Hodes]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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It is claimed that numbers are objects which essentially represent cardinality quantifiers [Hodes]
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Numerical terms can't really stand for quantifiers, because that would make them first-level [Hodes]
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