Leśniewski’s Logic and its Relation to Classical and Free Logics

Abstract

Understanding the relationship between the logical system of Stanisław Leśniewski and those of the Frege-Russell tradition is made difficult by a number of factors, some of them circumstantial, some substantial. The circumstantial ones include the fact that Leśniewski died in 1939, having published only a small fraction of his work, and his manuscripts were destroyed in the Nazi occupation of Poland. What survives is often compressed almost to the point of unintelligibility. His punctilious insistence on utmost rigour and his preference for an interesting but idiosyncratic notation isolated him from all but his students and a few contemporaries. While of those surviving some have, with their own pupils, reconstructed many of Leśniewski’s achievements and pushed his work forward, they have tended not to spare much time for publicising Leśniewski’s work to a wider audience. There exists to date no mtroductury logic textbook (outside Japan!) which devotes so much as a chapter to presenting even Leśniewski’s basic ideas. On the substantial side, many of his opinions were then, and surprisingly many still are, uncompromisingly, even inconveniently radical.