Young Łukasiewicz studied mathematics and philosophy at the University of Lviv, earning his doctorate sub auspiciis wiperatoris, a rare honor, in 1902.
Young Łukasiewicz studied mathematics and philosophy at the University of Lviv, earning his doctorate sub auspiciis wiperatoris, a rare honor, in 1902.
Jan Łukasiewicz was a Polish logician and philosopher. His work was centered on philosophical logic, mathematical logic, and history of logic.
Background
Łukasiewicz was born on December 21, 1878, in Lemberg, Galicia, Austria-Hungary (now Lviv, Ukraine). His father, Paweł Łukasiewicz, was a captain in the Austrian army: his mother, the former Leopoldina Holtzer, was the daughter of an Austrian civil servant. The family was Roman Catholic, and the language spoken at hone was Polish.
Education
Young Łukasiewicz studied mathematics and philosophy at the University of Lviv, earning his doctorate sub auspiciis wiperatoris, a rare honor, in 1902. He was a pupil of philosopher Kazimierz Twardowski.
At the University of Lviv, Łukasiewicz received his Habilitation (1906) and lectured in logic and philosophy, as Privatdozent until 1911, then as an extraordinary professor. In 1915 Łukasiewicz accepted an invitation to lecture at the University of Warsaw, then in German-occupied territory.
Between the world wars, as a citizen of independent Poland, Łukasiewicz was minister of education (1919), professor at the University of Warsaw (1920-1939), twice rector of that institution, an active member of scientific societies, and the recipient of several honors. He and Stanislaw Leśniewski founded the Warsaw school of logic, which A. Tarski helped make world famous. Viewing mathematical logic as an instrument of inquiry into the foundations of mathematics and the methodology of empirical science, Łukasiewicz succeeded in making it a required subject for mathematics and science students in Polish universities. His lucid lectures attracted students of the humanities as well.
In 1946 Łukasiewicz, then an exile in Belgium, accepted a professorship at the Royal Irish Academy, Dublin, where he remained until his death.
Using modern formal techniques, Łukasiewicz reconstructed and reevaluated ancient and medieval logic. Through his work in this area, we have changed our view of the history of logic.
During his last years in Ireland, Łukasiewicz published important studies on modal and intuitionistic logic, and he again made logical history with a detailed and novel study of Aristotle’s syllogistic. Essentially he interpreted syllogisms in Aristotle to be theorems of logic, not rules of derivations.
After some early essays on the principles of noncontradiction and excluded middle (1910), Łukasiewicz arrived by 1917 at the conception of a three-valued propositional calculus. His subsequent researches on many-valued logics is regarded by some as his greatest contribution. He viewed these "non-Aristotelian" logics as representing possible new ways of thinking, and he experimented with interpreting them in modal terms and in probability terms. The nonstandard systems he developed have value independently of the philosophy that inspired them or of tile usefulness of those interpretations. Łukasiewicz created the elegant "Łukasiewicz system" for two-valued propositional logic and the parenthesis-free "Polish notation."
The metalogic (a term he coined on the model of Hilbert’s terminology) of propositional calculi, notably the theory of their syntactic and semantic completeness, owes much to Łukasiewicz and his school. He regarded these studies as a prelude to analogous investigations for the rest of logic, which were then carried out by Tarski.