Combining Texts

All the ideas for 'works', 'Zettel' and 'Axiomatic Thought'

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10 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
2626 A philosopher is outside any community of ideas [Wittgenstein]
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]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
6569 'This sentence is false' sends us in a looping search for its proposition [Wittgenstein, by Fogelin]
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]
13. Knowledge Criteria / C. External Justification / 2. Causal Justification
3790 Causes of beliefs are irrelevant to their contents [Wittgenstein]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / b. Defining ethics
5319 Avoid punishment, then get rewards, avoid rejection, avoid guilt, accept contracts, follow conscience [Kohlberg, by Wilson,EO]
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]