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Ideas for 'Defending the Axioms', 'Theories of Everything' and 'Axiomatic Thought'

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4 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]
Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
If two mathematical themes coincide, that suggest a single deep truth [Maddy]