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Single Idea 13622

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

Full Idea

Notably axiomatisations of first-order logic are by Frege (1879), Russell and Whitehead (1910), Church (1956), Lukasiewicz and Tarski (1930), Lukasiewicz (1936), Nicod (1917), Kleene (1952) and Quine (1951). Also Bostock (1997).

Gist of Idea

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

Source

David Bostock (Intermediate Logic [1997], 5.8)

Book Ref

Bostock,David: 'Intermediate Logic' [OUP 1997], p.232

A Reaction

My summary, from Bostock's appendix 5.8, which gives details of all of these nine systems. This nicely illustrates the status and nature of axiom systems, which have lost the absolute status they seemed to have in Euclid.

Related Ideas

Idea 13610 A logic with ¬ and → needs three axiom-schemas and one rule as foundation [Bostock]

Idea 13619 Quantification adds two axiom-schemas and a new rule [Bostock]

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]