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'Foundations of Geometry', 'The Question of Realism' and 'Recent Debates on the A Priori'
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5 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
9226
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If mathematical theories conflict, it may just be that they have different subject matter [Field,H]
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6. Mathematics / A. Nature of Mathematics / 2. Geometry
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Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD]
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6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
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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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Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew]
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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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