Jan Łukasiewicz

Works

• 1920On Three-Valued Logic

  Introduces a third truth value, “possible”, for statements about the undetermined future – one of the first many-valued logics.

• 1951Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic

  Reconstructs Aristotle’s syllogistic as an axiomatic system of propositional and term logic.

Position

Łukasiewicz began as a critic of received logic: in his 1910 book he argued that Aristotle’s principle of contradiction is neither self-evident nor strictly provable and has above all a practical and ethical justification. In 1920 he introduced a third truth value for statements about the open future, such as the statement that he would be in Warsaw at a certain hour a year later; if such statements were already true or false, he argued, determinism would follow. He soon generalised the system to logics with any finite and with infinitely many values. His bracket-free notation, in which connectives precede their arguments, became known as Polish notation and, reversed, entered computing. In 1951 he reconstructed Aristotle’s syllogistic as an axiomatic theory. Emil Post developed many-valued systems independently at about the same time; Arthur Prior used Łukasiewicz’s notation and built on his work in tense logic, and infinite-valued logic became a model for fuzzy logic. Critics object that the third value does not capture possibility correctly, since a contradiction about the future then also receives the middle value, and John Corcoran and Timothy Smiley (1972–74) argued that Aristotle’s syllogistic is better read as a system of natural deduction than as an axiomatic theory.

Life & context

Jan Łukasiewicz was born on 21 December 1878 in Lwów (now Lviv), then in Austrian Galicia, the son of an army officer. He studied law and then philosophy and mathematics at Lwów University and took his doctorate under Kazimierz Twardowski in 1902; he habilitated in 1906 and lectured in Lwów, where his book “On the Principle of Contradiction in Aristotle” appeared in 1910. In 1915 he went to the reopened University of Warsaw, where he became professor. In 1919 he was minister of religious affairs and public education in the government of Ignacy Paderewski, and he was twice rector of the university (1922–23 and 1931–32). With Stanisław Leśniewski he built up the Warsaw school of logic, whose students included Alfred Tarski. In September 1939 his house and library were destroyed in the bombardment of Warsaw; during the German occupation he taught at the underground university. In 1944 he and his wife left Warsaw for Germany, where the logician Heinrich Scholz helped them in Münster; in 1946 he went via Belgium to Ireland. He held a chair at the Royal Irish Academy in Dublin and died there on 13 February 1956.

Further main works

• On the Principle of Contradiction in Aristotle (O zasadzie sprzeczności u Arystotelesa, 1910)
• Elements of Mathematical Logic (Elementy logiki matematycznej, 1929)
• Investigations into the Sentential Calculus (with Alfred Tarski, Untersuchungen über den Aussagenkalkül, 1930)
• On the History of the Logic of Propositions (Zur Geschichte der Aussagenlogik, 1934)