Jan Łukasiewicz

Jan Łukasiewicz (Lviv, 1878 – Dublin, 1956) was a Polish logician, mathematician and philosopher and a central figure of the Lwów–Warsaw school. He is remembered above all for reshaping propositional logic, for the Polish notation and for being one of the first to build logical systems with more than two truth values.

He was born in Lemberg, then part of Austria-Hungary, the only child of an army officer and a civil servant's daughter. He studied in Lemberg under Kazimierz Twardowski, who gave him a demanding approach to philosophy and drew him towards mathematical logic. He earned his doctorate in 1902 with a thesis on induction and qualified for teaching in 1906. In those years he also studied in Berlin and Louvain, and he moved away from psychologistic accounts of logic.

After the First World War he took up a post at the University of Warsaw, where his lectures drew in young mathematicians. In 1919 he served as Polish Minister of Religious Denominations and Public Education, and he was twice rector of the university. Together with Stanisław Leśniewski he helped build the Lwów–Warsaw school, and his student Alfred Tarski later carried its work to an international audience.

His best-known contribution is three-valued logic, which he outlined in 1918 and presented formally in 1920. Examining future contingents, he argued that bivalence is not a logical necessity and that accepting it leads towards determinism. He therefore added a third value, possibility, to truth and falsehood, and later defended systems with infinitely many values. He also gave an elegant axiomatization of classical propositional logic.

During the German occupation he worked in clandestine teaching and, after the war, accepted an invitation from Éamon de Valera to settle in Dublin, where he remained until his death in 1956. His influence reaches the history of logic, many-valued logics and computing, where his notation inspired the use of stacks.