Combining Texts

All the ideas for 'Justified Belief as Responsible Belief', 'Foundations of Geometry' and 'Proof that every set can be well-ordered'

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9 ideas

2. Reason / A. Nature of Reason / 6. Coherence
12801 Coherentists seek relations among beliefs that are simple, conservative and explanatory [Foley]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
13472 Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / e. Countable infinity
15897 Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine]
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]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / c. Disjunctivism
12800 Externalists want to understand knowledge, Internalists want to understand justification [Foley]
13. Knowledge Criteria / B. Internal Justification / 2. Pragmatic justification
12802 We aren't directly pragmatic about belief, but pragmatic about the deliberation which precedes it [Foley]
12803 Justification comes from acceptable procedures, given practical constraints [Foley]