Combining Texts

All the ideas for 'Aristotle and Descartes on Matter', 'Foundations of Geometry' and 'Explanation: the state of play'

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8 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry
13472 Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD]
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]
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
12313 Explanation is for curiosity, control, understanding, to make meaningful, or to give authority [Stanford]
12314 Audience-relative explanation, or metaphysical explanation based on information? [Stanford]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
12315 We can explain by showing constitution, as well as showing causes [Stanford]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / b. Prime matter
19399 Prime matter is nothing when it is at rest [Leibniz]