Combining Texts

All the ideas for 'Foundations of Geometry', 'On Multiplying Entities' and 'De primae philosophiae emendatione'

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9 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor
8207 The quest for simplicity drove scientists to posit new entities, such as molecules in gases [Quine]
8208 In arithmetic, ratios, negatives, irrationals and imaginaries were created in order to generalise [Quine]
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]
7. Existence / B. Change in Existence / 4. Events / c. Reduction of events
8205 Explaining events just by bodies can't explain two events identical in space-time [Quine]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
12716 The concept of forces or powers best reveals the true concept of substance [Leibniz]
10. Modality / A. Necessity / 11. Denial of Necessity
8206 Necessity could be just generalisation over classes, or (maybe) quantifying over possibilia [Quine]