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''Ostrich Nominalism' or 'Mirage Realism'?st1=Michael Devitt', 'On the Introduction of Transfinite Numbers' and 'Logicism and Ontological Commits. of Arithmetic'
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9 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
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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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13489
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Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
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12336
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A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
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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 / 5. Definitions of Number / g. Von Neumann numbers
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18179
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For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]
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18180
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Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]
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15925
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Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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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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