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'Logic (Encyclopedia I)', 'Frege philosophy of mathematics' and 'Grundgesetze der Arithmetik 1 (Basic Laws)'
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12 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
9896
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A prime number is one which is measured by a unit alone [Dummett]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
18255
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Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
18252
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Real numbers are ratios of quantities, such as lengths or masses [Frege]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
9895
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A number is a multitude composed of units [Dummett]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
9852
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We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett]
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6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
18271
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We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
10623
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Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright]
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9975
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Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
9829
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The identity of a number may be fixed by something outside structure - by counting [Dummett]
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9828
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Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
18165
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My Basic Law V is a law of pure logic [Frege]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
9876
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Set theory isn't part of logic, and why reduce to something more complex? [Dummett]
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