Single Idea 13622

[catalogued under 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 Reference

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]