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5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof

[proofs built up from some initially accepted truths]

7 ideas
Boole's method was axiomatic, achieving economy, plus multiple interpretations [Boole, by Potter]
Frege produced axioms for logic, though that does not now seem the natural basis for logic [Frege, by Kaplan]
Quantification adds two axiom-schemas and a new rule [Bostock]
Axiom systems from Frege, Russell, Church, Lukasiewicz, Tarski, Nicod, Kleene, Quine... [Bostock]
No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider]
Good axioms should be indisputable logical truths [Sider]
Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths) [Rumfitt]