Combining Texts

All the ideas for 'Necessary Existents', 'works' and 'Foundations of Geometry'

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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]
14. Science / B. Scientific Theories / 1. Scientific Theory
You have only begun to do real science when you can express it in numbers [Kelvin]
19. Language / D. Propositions / 3. Concrete Propositions
Propositions (such as 'that dog is barking') only exist if their items exist [Williamson]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / a. Energy
Energy has progressed from a mere formula, to a principle pervading all nature [Kelvin]