Busting a Myth About Lesniewski and Definitions
Co-authored with Rafal Urbaniak; to appear in History and Philosophy of Logic
A theory of definitions which places the eliminability and conservativeness requirements on definitions is usually... more A theory of definitions which places the eliminability and conservativeness requirements on definitions is usually called the standard theory. We examine a persistent myth which credits this theory to S. Lesniewski, a Polish logician. After a brief survey of its origins, we show that the myth is highly dubious. First, no place in Lesniewski’s published or unpublished work is known where the standard conditions are discussed. Second, Lesniewski’s own logical theories allow for creative definitions. Third, Lesniewski’s celebrated ‘rules of definition’ lay merely syntactical restrictions on the form of definitions: they do not provide definitions with such meta-theoretical requirements as eliminability or conservativeness. On the positive side, we point out that among the Polish logicians, in the 1920s and 30s, a study of these meta-theoretical conditions is more readily found in the works of J. Lukasiewicz and K. Ajdukiewicz.the works of J. Lukasiewicz and K. Ajdukiewicz.