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Single Idea 13688

[filed under theme 5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof ]

Full Idea

Since they are the foundations on which a proof rests, the axioms in a good axiomatic system ought to represent indisputable logical truths.

Gist of Idea

Good axioms should be indisputable logical truths

Source

Theodore Sider (Logic for Philosophy [2010], 2.6)

Book Ref

Sider,Theodore: 'Logic for Philosophy' [OUP 2010], p.46

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The 7 ideas with the same theme [proofs built up from some initially accepted truths]:

22277

Boole's method was axiomatic, achieving economy, plus multiple interpretations [Boole, by Potter]

13609

Frege produced axioms for logic, though that does not now seem the natural basis for logic [Frege, by Kaplan]

13619

Quantification adds two axiom-schemas and a new rule [Bostock]

13622

Axiom systems from Frege, Russell, Church, Lukasiewicz, Tarski, Nicod, Kleene, Quine... [Bostock]

13687

No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider]

13688

Good axioms should be indisputable logical truths [Sider]

12198

Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths) [Rumfitt]