Sobocinski in his paper on Leśniewski's solution to Russell's paradox (1949b) argued that Leśniewski has succeeded in explaining it away. The general strategy of this alleged explanation is presented. The key element of this attempt is the distinction between the collective (mereological) and the distributive (set-theoretic) understanding of the set. The mereological part of the solution, although correct, is likely to fall short of providing foundations of mathematics. I argue that the remaining part of the solution which suggests a specific (...) reading of the distributive interpretation is unacceptable. It follows from it that every individual is an element of every individual. Finally, another Leśniewskian-style approach which uses so-called higher-order epsilon connectives is used and its weakness is indicated. (shrink)

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 Leśniewski, a Polish logician. After a brief survey of its origins, we show that the myth is highly dubious. First, no place in Leśniewski's published or unpublished work is known where the standard conditions are discussed. Second, Leśniewski's own logical theories allow for creative definitions. Third, Leśniewski'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 1930s, a study of these meta-theoretical conditions is more readily found in the works of Łukasiewicz and Ajdukiewicz. (shrink)

This paper discusses the resolution principle in the context of non-classical logics.

The triangle in general or the man as such are general objects. These are objects that possess the properties common to all the individual objects in their range. Stanisław Leśniewski and Tadeusz Kotarbiński, two Polish philosophers and logicians belonging to the Lvov-Warsaw School, produced several proofs aiming to show that such objects are impossible because the principles that govern them lead to a contradiction. In this paper I first clarify the structure of their proofs. Then I suggest a way to (...) elude their conclusion. In order to do that I use two Meinongian distinctions: the distinction between complete and incomplete objects, on the one hand, and the distinction between nuclear and extranuclear properties, on the other hand. I claim first that general objects are incomplete objects, i.e. they do not satisfy the ontological principle of the excluded middle, and second that the principle that governs the relations between the properties of general objects and the properties of the individual objects in their range should be restricted to nuclear properties. (shrink)

The paper presents a method of truth-graph by truth-tables. On the one hand, the truth-graph constituted by truth value coordinate and circumference displays a more visual representation of the different combinations of truth-values for the simple or complex propositions. Truth-graphs make sure that you don’t miss any of these combinations. On the other hand, they provide a more convenient tool to discern the validity of a complex proposition made up by simple compositions. The algorithm involving in setting up all the (...) truth conditions is proposed to distinguish easily among tautologous, contradictory and consistent expressions. Furthermore, the paper discusses a certain connection between the truth graphs and the symbols for propositional connectives proposed by Stanisław Leśniewski. (shrink)

Leśniewski’s systems deviate greatly from standard logic in some basic features. The deviant aspects are rather well known, and often cited among the reasons why Leśniewski’s work enjoys little recognition. This paper is an attempt to explain why those aspects should be there at all. Leśniewski built his systems inspired by a dream close to Leibniz’s characteristica universalis: a perfect system of deductive theories encoding our knowledge of the world, based on a perfect language. My main claim is that Leśniewski (...) built his characteristica universalis following the conditions of de Jong and Betti’s Classical Model of Science (2008) to an astounding degree. While showing this I give an overview of the architecture of Leśniewski’s systems and of their fundamental characteristics. I suggest among others that the aesthetic constraints Leśniewski put on axioms and primitive terms have epistemological relevance. (shrink)

With material on his early philosophical views, his contributions to set theory and his work on nominalism and higher-order quantification, this book offers a uniquely expansive critical commentary on one of analytical philosophy’s great ...