Combining Philosophers
Ideas for Paul Bernays, Alain Badiou and Craig Bourne
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12 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
9812
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In mathematics, if a problem can be formulated, it will eventually be solved [Badiou]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
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Numbers are for measuring and for calculating (and the two must be consistent) [Badiou]
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12334
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There is no single unified definition of number [Badiou]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
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Each type of number has its own characteristic procedure of introduction [Badiou]
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12322
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Must we accept numbers as existing when they no longer consist of units? [Badiou]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
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Mathematics shows that thinking is not confined to the finite [Badiou]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
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The undecidability of the Continuum Hypothesis may have ruined or fragmented set theory [Badiou]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
12329
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If mathematics is a logic of the possible, then questions of existence are not intrinsic to it [Badiou]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10303
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Restricted Platonism is just an ideal projection of a domain of thought [Bernays]
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12328
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Platonists like axioms and decisions, Aristotelians like definitions, possibilities and logic [Badiou]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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Logic is definitional, but real mathematics is axiomatic [Badiou]
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10306
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Mathematical abstraction just goes in a different direction from logic [Bernays]
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