Combining Texts

All the ideas for 'works', 'Axiomatic Thought' and 'Three-Dimensionalism v Four-Dimensionalism'

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11 ideas

5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
The facts of geometry, arithmetic or statics order themselves into theories [Hilbert]
Axioms must reveal their dependence (or not), and must be consistent [Hilbert]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
To decide some questions, we must study the essence of mathematical proof itself [Hilbert]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Number theory just needs calculation laws and rules for integers [Hilbert]
9. Objects / B. Unity of Objects / 3. Unity Problems / a. Scattered objects
If we accept scattered objects such as archipelagos, why not think of cars that way? [Hawthorne]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
Four-dimensionalists say instantaneous objects are more fundamental than long-lived ones [Hawthorne]
10. Modality / A. Necessity / 11. Denial of Necessity
A modal can reverse meaning if the context is seen differently, so maybe context is all? [Hawthorne]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / d. Knowing essences
By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert]
27. Natural Reality / C. Space / 6. Space-Time
Modern metaphysicians tend to think space-time points are more fundamental than space-time regions [Hawthorne]