Combining Texts

All the ideas for 'Subjectivist's Guide to Objective Chance', 'Foundations of Geometry' and 'Moral Arguments'

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9 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]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / k. Ethics from nature
Moral judgements need more than the relevant facts, if the same facts lead to 'x is good' and 'x is bad' [Foot]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
We can't affirm a duty without saying why it matters if it is not performed [Foot]
Whether someone is rude is judged by agreed criteria, so the facts dictate the value [Foot]
Facts and values are connected if we cannot choose what counts as evidence of rightness [Foot]
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
Lewis later proposed the axioms at the intersection of the best theories (which may be few) [Mumford on Lewis]