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Ideas for
'Frege philosophy of mathematics', 'The Powers Metaphysics' and 'Russell's Mathematical Logic'
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11 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
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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 / 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 / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
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The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10039
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Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
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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 / 1. Mathematical Platonism / a. For mathematical platonism
10043
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Mathematical objects are as essential as physical objects are for perception [Gödel]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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Set theory isn't part of logic, and why reduce to something more complex? [Dummett]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
10045
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Impredicative definitions are admitted into ordinary mathematics [Gödel]
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