Combining Texts

All the ideas for 'Foundations of Geometry', 'The Will to Believe' and 'Morals and Modals'

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7 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry
Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara]
Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew]
Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
If we are told the source of necessity, this seems to be a regress if the source is not already necessary [Blackburn]
If something underlies a necessity, is that underlying thing necessary or contingent? [Blackburn, by Hale/Hoffmann,A]
23. Ethics / E. Utilitarianism / 4. Unfairness
Imagine millions made happy on condition that one person suffers endless lonely torture [James]