Leśniewski, negation, and the art of logical subtlety
pp. 113-120
in: Sandra Lapointe, Jan Woleński, Mathieu Marion, Wioletta Miskiewicz (eds), The Golden age of Polish philosophy, Berlin, Springer, 2009Abstract
Leśniewski essentially developed three theories: Protothetic, Ontology, and Mereology. Since his death in 1939, none of the efforts to reawaken interest in Leśniewski have had much success. In spite of his successive burials, I am among those who persevere in thinking that Leśniewski's systems present more than a merely historical interest. The richness of Leśniewski's alternative lies in his approach to truth and falsity, the idea of predicative levels and his conception of logic as something which, so to say, freely "expands". Leśniewski's systems can be called to task when it comes to the study of formal languages, the development of higher order logics, definitional procedures, the search for extreme metalinguistic rigor and the quest for an ontologically neutral language. In this paper, I focus on the following three issues. First, I consider the question of the number of operators a formal system must or can possess.
