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'Unconscious Cerebral Initiative', 'First-Order Logic' and 'Grundgesetze der Arithmetik 2 (Basic Laws)'
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7 ideas
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 / 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 / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
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10286
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A 'set' is a mathematically well-behaved class [Hodges,W]
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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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