Combining Texts

All the ideas for 'fragments/reports', 'In Defence of Three-Dimensionalism' and 'Axiomatic Thought'

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13 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 / E. Objects over Time / 3. Three-Dimensionalism
3-D says things are stretched in space but not in time, and entire at a time but not at a location [Fine,K]
Genuine motion, rather than variation of position, requires the 'entire presence' of the object [Fine,K]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
4-D says things are stretched in space and in time, and not entire at a time or at a location [Fine,K]
You can ask when the wedding was, but not (usually) when the bride was [Fine,K, by Simons]
9. Objects / E. Objects over Time / 5. Temporal Parts
Three-dimensionalist can accept temporal parts, as things enduring only for an instant [Fine,K]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
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 / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]