Combining Philosophers
Ideas for Ion, Harr�,R./Madden,E.H. and Kurt Gdel
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6 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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10132
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There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
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15273
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Points can be 'dense' by unending division, but must meet a tougher criterion to be 'continuous' [Harré/Madden]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
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15274
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Points are 'continuous' if any 'cut' point participates in both halves of the cut [Harré/Madden]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
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10046
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The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel]
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10868
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The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
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13517
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If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
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