Combining Texts

All the ideas for 'fragments/reports', 'Philosophical Essay on Probability' and 'Foundations of Geometry'

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8 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]
13. Knowledge Criteria / C. External Justification / 7. Testimony
The reliability of witnesses depends on whether they benefit from their observations [Laplace, by Hacking]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
If a supreme intellect knew all atoms and movements, it could know all of the past and the future [Laplace]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]