Busting a Myth about Leśniewski and Definitions

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 Le?niewski, a Polish logician. After a brief survey of its origins, we show that the myth is highly dubious. First, no place in Le?niewski's published or unpublished work is known where the standard conditions are discussed. Second, Le?niewski's own logical theories allow for creative definitions. Third, Le?niewski'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 ?ukasiewicz and Ajdukiewicz.     

On Blass Translation for Leśniewski’s Propositional Ontology and Modal Logics

Studia Logica - In this paper, we shall give another proof of the faithfulness of Blass translation (for short, B-translation) of the propositional fragment $$\mathbf{L}_1$$ of...     

Embedding the elementary ontology of stanisław Leśniewski into the monadic second-order calculus of predicates

LetEO be the elementary ontology of Le?niewski formalized as in Iwanu? [1], and letLS be the monadic second-order calculus of predicates. In this paper we give an example of a recursive function ?, defined on the formulas of the language ofEO with values in the set of formulas of the language of LS, such that ? _EO A iff ? _LS ?(A) for each formulaA.     

Leśniewski’s <Emphasis Type="Italic">characteristica universalis</Emphasis>

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.     

On Jaśkowski's discussive logics

We expose the main ideas, concepts and results about Jakowski's discussive logic, and apply that logic to the concept of pragmatic truth and to the Dalla Chiara-di Francia view of the foundations of physics.Partially supported by grants from JNICT (Portugal) and FAPESP (Brazil), Philosophy Section. Portions of this paper were concluded while the second author visited the Math-Phys Seminar at the University of Algarve (Portugal).Presented byCecylia Rauszer     

A semantical investigation into Leśniewski's axiom of his ontology

A structure A for the language L, which is the first-order language (without equality) whose only nonlogical symbol is the binary predicate symbol , is called a quasi -struoture iff (a) the universe A of A consists of sets and (b) a b is true in A ([p) a = {p } & p b] for every a and b in A, where a(b) is the name of a (b). A quasi -structure A is called an -structure iff (c) {p } A whenever p a A. Then a closed formula in L is derivable from Leniewski's axiom x, y[x y u (u x) u; v(u, v x u v) u(u x u y)] (from the axiom x, y(x y x x) x, y, z(x y z y x z)) iff is true in every -structure (in every quasi -structure).