Combining Texts

All the ideas for 'Foundations of Geometry', 'Structure and Ontology' and 'Why Reason Can't be Naturalized'

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6 ideas

3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
8828 Truth is rational acceptability [Putnam]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
13472 Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
9546 Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara]
18742 Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew]
18217 Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
9626 A structure is an abstraction, focussing on relationships, and ignoring other features [Shapiro]