Chapter 11 Leśniewski’s Intuitive Formalism
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Abstract
When Stanisław Leśniewski read in 1911 Jan Łukasiewicz’s book The Principle of Contradiction in Aristotle he discovered modern symbolic logic and the Russellian antinomy of the classes, that do not contain themselves. He started then to look for a solution to this antinomy and elaborated his formal theory of wholes and parts. However, if he adopted the new formal tools of logistics, he refused to proceed in his building of formal systems as a “pure formalist”. In particular, for Leśniewski, a formal system must not be interpreted after having been built. An intuitive interpretation must be given from the beginning, the formal system being only a means to communicate the “logical intuitions” of the author. That is the reason why Leśniewski’s unconventional position has been called an “intuitive formalism” by Kearns or an “intuitionistic formalism” by Tarski. In this paper, I try to make these expressions more precise and explain how exactly the relation between intuition and formal systems must be understood according to Leśniewski.