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'W.V. Quine', 'Review of Frege's 'Grundlagen'' 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 / 3. Nature of Numbers / b. Types of number
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8454
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The whole numbers are 'natural'; 'rational' numbers include fractions; the 'reals' include root-2 etc. [Orenstein]
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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 / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
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9992
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The 'extension of a concept' in general may be quantitatively completely indeterminate [Cantor]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
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8473
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The logicists held that is-a-member-of is a logical constant, making set theory part of logic [Orenstein]
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