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
The facts of geometry, arithmetic or statics order themselves into theories
Axioms must reveal their dependence (or not), and must be consistent
6. Mathematics / A. Nature of Mathematics / 6. Proof in Mathematics
To decide some questions, we must study the essence of mathematical proof itself
6. Mathematics / B. Foundations for Mathematics / 2. Axioms for Geometry
The whole of Euclidean geometry derives from a basic equation and transformations
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Number / a. Axioms for numbers
Number theory just needs calculation laws and rules for integers
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