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'Logicism and Ontological Commits. of Arithmetic', 'Grundgesetze der Arithmetik 2 (Basic Laws)' and 'Human Flourishing, Ethics and Liberty'
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10 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 / b. Types of number
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9886
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Cardinals say how many, and reals give measurements compared to a unit quantity [Frege]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
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9889
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Real numbers are ratios of quantities [Frege, by Dummett]
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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 / c. Fregean numbers
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10553
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A number is a class of classes of the same cardinality [Frege, by Dummett]
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10020
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Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege]
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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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6. Mathematics / C. Sources of Mathematics / 7. Formalism
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9887
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Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett]
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8751
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Only applicability raises arithmetic from a game to a science [Frege]
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