Ideas from 'Axiomatic Thought' by David Hilbert [1918], by Theme Structure
[found in 'From Kant to Hilbert: sourcebook Vol. 2' (ed/tr Ewald,William) [OUP 1996,0-19-850536-1]].
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5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
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The facts of geometry, arithmetic or statics order themselves into theories
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Axioms must reveal their dependence (or not), and must be consistent
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6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
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To decide some questions, we must study the essence of mathematical proof itself
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6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
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The whole of Euclidean geometry derives from a basic equation and transformations
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
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Number theory just needs calculation laws and rules for integers
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26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / d. Knowing essences
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By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge
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