Combining Texts
Ideas for
'fragments/reports', 'What is Cantor's Continuum Problem?' and 'Foundations of Geometry'
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7 ideas
6. Mathematics / A. Nature of Mathematics / 2. Geometry
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13472
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Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
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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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6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
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9546
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Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara]
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18742
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Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew]
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18217
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Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
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10271
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Basic mathematics is related to abstract elements of our empirical ideas [Gödel]
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