Combining Texts
Ideas for
'Sententia on 'De Caelo'', 'Briefings on Existence' and 'Mathematics without Foundations'
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12 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
12335
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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
12333
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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 / 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 / 1. Foundations for Mathematics
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I do not believe mathematics either has or needs 'foundations' [Putnam]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
9939
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It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam]
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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
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 / 4. Mathematical Empiricism / a. Mathematical empiricism
9940
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Maybe mathematics is empirical in that we could try to change it [Putnam]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
9941
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Science requires more than consistency of mathematics [Putnam]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
12331
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Logic is definitional, but real mathematics is axiomatic [Badiou]
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