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'works', 'What is Cantor's Continuum Problem?' and 'Grundgesetze der Arithmetik 2 (Basic Laws)'
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9 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
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
9889
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Real numbers are ratios of quantities [Frege, by Dummett]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10868
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The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
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13517
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If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
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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10553
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A number is a class of classes of the same cardinality [Frege, by Dummett]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
10271
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Basic mathematics is related to abstract elements of our empirical ideas [Gödel]
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6. Mathematics / C. Sources of Mathematics / 7. Formalism
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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