Combining Texts
Ideas for
'Mahaprajnaparamitashastra', 'Foundations of Geometry' and 'Grounding Concepts'
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8 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 / a. The Infinite
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17730
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Combining the concepts of negation and finiteness gives the concept of infinity [Jenkins]
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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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17719
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Arithmetic concepts are indispensable because they accurately map the world [Jenkins]
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17717
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Senses produce concepts that map the world, and arithmetic is known through these concepts [Jenkins]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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17724
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It is not easy to show that Hume's Principle is analytic or definitive in the required sense [Jenkins]
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