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 First, no place in Leśniewski's published or unpublished work is known where the standard conditions are discussed.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)

The article describes the background of Roman Ingarden's 1922 review of Leon Chwistek's book Wielość rzeczywistości, and the back-and-forth that followed. Despite the differences, the two shared some interesting similarities. Both authors had important ties to the intellectual happenings outside Poland and were not considerd mainstream at home. In the end, however, it is these connections that allowed them to gain recognition. Ingarden, who had been a student of Husserl, became the leading phenomenologist in the postwar Poland. For Chwistek, a (...) painter, philosopher, and logician interested in Russell’s work, such connections meant that he won the competition for a professorship at the university in Lwów over Alfred Tarski. Until recently, Chwistek’s place in Polish logic remains unclear and Ingarden’s interactions with Polish logic and the Vienna Circle have not been investigated extensively. A deeper look at this intellectual fracas between Ingarden and Chwistek helps one in the study of the complicated mesh of alliances within the Lwów-Warsaw School. The article also identifies the origins of the split between phenomenology and the analytic philosophical tradition in Poland. The article is also accompanied by the translations of the reviews. (shrink)

Stanisław Leśniewski developed a system of logic and foundations of mathematics that considerably differs from Russell and Whitehead’s system. The difference between these two approaches to logic is significant primarily in the case of Leśniewski’s calculus of names, Ontology, and the concept of names that it contains. Russell’s theory of descriptions played a much more important role than Leśniewski’s concept of names in the history of philosophy. In response to that, several researchers aimed to approximate Leśniewski’s concept of names to (...) Russell’s theory. There are several such attempts. This paper presents an interpretation that was suggested by Arthur Prior. Prior interpreted Leśniewskian names as class names. This interpretation was rejected by such prominent Leśniewskian scholars as Peter Simons or Rafal Urbaniak. According to Simons, class names oppose Leśniewski’s ontological views. Urbaniak claimed that Prior’s interpretation of Leśniewskian names as class names is unclear. The aim of this paper is to demonstrate that from the formal point of view, Prior’s interpretation could be justified. (shrink)

ABSTRACT Leśniewskian Ontology (LO) is a system in which the basic subject-predicate formula takes the form of a b and express one-argument predication, e.g. John is a student. In LO’s language, there is no many-argument form of predication given that would allow for the structural expression of, for example, the sentence John is Anne’s son. In this article, a simple and natural extension of LO is suggested to encompass many-argument predication. The system thus obtained corresponds to polyadic second-order logic.

Hybrid languages are introduced in order to evaluate the strength of “minimal” mereologies with relatively strong frame definability properties. Appealing to a robust form of nominalism, I claim that one investigated language \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {H}_{\textsf {m}}$\end{document} is maximally acceptable for nominalistic mereology. In an extension \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {H}_{\textsf {gem}}$\end{document} of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {H}_{\textsf {m}}$\end{document}, a modal analog (...) for the classical systems of Leonard and Goodman and Leśniewski is introduced and shown to be complete with respect to 0-deleted Boolean algebras. We characterize the formulas of first-order logic invariant for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {H}_{\textsf {gem}}$\end{document}-bisimulations. (shrink)

In his Formal Logic, Arthur N. Prior declared that Jan Łukasiewicz's logical notation is ‘unquestionably the best logical symbolism for most purposes’. Whether he had a substantive, and...

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 ...