Jan Łukasiewicz

Jan Łukasiewicz was a Polish logician and a leading figure of the Lwów–Warsaw school, who taught in Lwów and Warsaw and, after the Second World War, in Dublin. Motivated by Aristotle's problem of future contingents, such as tomorrow's sea battle, he constructed a three-valued logic in which some statements are neither true nor false but indeterminate. This opened the field of many-valued logic. He also introduced prefix ('Polish') notation and reinterpreted the history of ancient logic.

Key ideas

• Statements about undetermined future events are neither true nor false but take a third value, indeterminate.
• Accepting a third value means giving up the principle of bivalence, and with it some classical laws.
• Logical formulas can be written without brackets using prefix notation.
• Aristotle's syllogistic and Stoic logic can be reconstructed rigorously with the tools of modern formal logic.

Major works

• O zasadzie sprzeczności u Arystotelesa (On the Principle of Contradiction in Aristotle, 1910)
• "O logice trójwartościowej" (On Three-Valued Logic, 1920)
• Aristotle's Syllogistic from the Standpoint of Modern Formal Logic (1951)

In the conversation

• Debate The analytic/continental split is mostly an accident of the 1930s, not a philosophical divide Tomasz Wójcik · 7 replies
• Question Strong Kleene, weak Kleene, Łukasiewicz: what actually differs between the tables? Pieter de Jong · 4 replies