Combining Texts

All the ideas for 'Moral Dilemmas Revisited', 'Axiomatic Thought' and 'On Metaphysics (frags)'

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9 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]
20. Action / C. Motives for Action / 5. Action Dilemmas / a. Dilemmas
There is no restitution after a dilemma, if it only involved the agent, or just needed an explanation [Foot, by PG]
I can't understand how someone can be necessarily wrong whatever he does [Foot]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / c. Purpose denied
Theophrastus doubted whether nature could be explained teleologically [Theophrastus, by Gottschalk]
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]