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Single Idea 13687

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

Full Idea

Axiomatic systems do not allow reasoning with assumptions, and therefore do not allow conditional proof or reductio ad absurdum.

Gist of Idea

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

Source

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

Book Ref

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

A Reaction

Since these are two of the most basic techniques of proof which I have learned (in Lemmon), I shall avoid axiomatic proof systems at all costs, despites their foundational and Ockhamist appeal.

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]