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William of Soissons lived in Paris in the 12th century. Hij is known as the first one to proof ex contradictione quod libet, or that from a contradiction every assertion may be inferred as true ,[1]. Later Clarence Irving Lewis formalized this proof as follows [2]:
Proof [bewerken]
A &¬ A : beïng a contradiction.
B : beïng any possible assertion.
(1) A &¬ A → A
(2) A → A∨B
(3) A &¬ A → A∨B
(4) A &¬ A → ¬A
(5) A &¬ A → (A∨B) &¬A
(6) (A∨B) &¬A → B
(7) A &¬ A → B
Sources
^ Graham Priest, 'What's so bad about contradictions?' in Priest, Beal and Armour-Garb, The law of non-contradicton, p. 25.
^ Christopher J. Martin, William’s Machine, Journal of Philosophy, 83, 1986, pp. 564 – 572. In particular p. 565
