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'fragments/reports', 'Logicism and Ontological Commits. of Arithmetic' and 'The Philosophy of Mathematics'
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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 / 3. Nature of Numbers / c. Priority of numbers
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Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett]
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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 / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
9192
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The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
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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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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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