Combining Texts
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'Parmenides', 'Grundgesetze der Arithmetik 2 (Basic Laws)' and 'Intro to Non-Classical Logic (1st ed)'
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7 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 / 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 / 1. Mathematical Platonism / a. For mathematical platonism
16150
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One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato]
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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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