Combining Texts
Ideas for
'Unconscious Cerebral Initiative', 'Foundations of Geometry' and 'Structuralism'
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5 ideas
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 / 7. Mathematical Structuralism / a. Structuralism
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8921
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Structuralism is now common, studying relations, with no regard for what the objects might be [Hellman]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
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8922
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Maybe mathematical objects only have structural roles, and no intrinsic nature [Hellman]
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