Combining Texts

All the ideas for 'fragments/reports', 'The Language of Morals' and 'Axiomatic Thought'

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9 ideas

5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17963 The facts of geometry, arithmetic or statics order themselves into theories [Hilbert]
17966 Axioms must reveal their dependence (or not), and must be consistent [Hilbert]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
17967 To decide some questions, we must study the essence of mathematical proof itself [Hilbert]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
17965 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
17964 Number theory just needs calculation laws and rules for integers [Hilbert]
7. Existence / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience
16050 The goodness of a picture supervenes on the picture; duplicates must be equally good [Hare]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
3061 Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / i. Prescriptivism
2855 In primary evaluative words like 'ought' prescription is constant but description can vary [Hare, by Hooker,B]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / d. Knowing essences
17968 By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert]