Combining Texts
Ideas for
'Possibility', 'Briefings on Existence' and 'Infinity: Quest to Think the Unthinkable'
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17 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
10880
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Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg]
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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 / 3. Nature of Numbers / e. Ordinal numbers
10861
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Beyond infinity cardinals and ordinals can come apart [Clegg]
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10860
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An ordinal number is defined by the set that comes before it [Clegg]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
10854
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Transcendental numbers can't be fitted to finite equations [Clegg]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / k. Imaginary numbers
10858
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By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
10853
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Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10866
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Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10869
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The Continuum Hypothesis is independent of the axioms of set theory [Clegg]
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12327
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The undecidability of the Continuum Hypothesis may have ruined or fragmented set theory [Badiou]
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10862
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The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg]
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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 / 6. Logicism / d. Logicism critique
12331
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Logic is definitional, but real mathematics is axiomatic [Badiou]
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