Stanislaw Lesniewski’s interests were, for the most part, more philosophical than mathematical. Prior to taking his doctorate at Jan Kazimierz University in Lvov, Lesniewski had spent time at several continental universities, apparently becoming relatively attached to the philosophy of one of his teachers, Hans Comelius, to the chapters of John Stuart Mill’s System of Logic that dealt specifically with semantics, and, in general, to studies of general grammar and philosophy of language. In these several early interests are already (...) to be found the roots of the work that was to occupy Lesniewski’s life: a search for a definitive doctrine of what sorts of things there are in the world, or better, of what language must be like if it is adequately and efficiently to represent the world. (shrink)

There are two main ways in which the notion of mereological fusion is usually defined in the current literature in mereology which have been labelled ‘Leśniewski fusion’ and ‘Goodman fusion’. It is well-known that, with Minimal Mereology as the background theory, every Leśniewski fusion also qualifies as a Goodman fusion. However, the converse does not hold unless stronger mereological principles are assumed. In this paper I will discuss how the gap between the two notions can be filled, focussing in particular (...) on two specific sets of principles that appear to be of particular philosophical interest. The first way to make the two notions equivalent can be used to shed some interesting light on the kind of intuition both notions seem to articulate. The second shows the importance of a little-known mereological principle which I will call ‘Mild Supplementation’. As I will show, the mereology obtained by adding Mild Supplementation to Minimal Mereology occupies an interesting position in the landscape of theories that are stronger than Minimal Mereology but weaker than what Achille Varzi and Roberto Casati have labelled ‘Extensional Mereology’. (shrink)

The Introduction outlines, in a concise way, the history of the Lvov-Warsaw School – a most unique Polish school of worldwide renown, which pioneered trends combining philosophy, logic, mathematics and language. The author accepts that the beginnings of the School fall on the year 1895, when its founder Kazimierz Twardowski, a disciple of Franz Brentano, came to Lvov on his mission to organize a scientific circle. Soon, among the characteristic features of the School was its serious approach towards philosophical studies (...) and teaching of philosophy, dealing with philosophy and propagation of it as an intellectual and moral mission, passion for clarity and precision, as well as exchange of thoughts, and cooperation with representatives of other disciplines.The genesis is followed by a chronological presentation of the development of the School in the successive years. The author mentions all the key representatives of the School (among others, Ajdukiewicz, Lesniewski, Łukasiewicz,Tarski), accompanying the names with short descriptions of their achievements. The development of the School after Poland’s regaining independence in 1918 meant part of the members moving from Lvov to Warsaw, thus providing the other segment to the name – Warsaw School of Logic. The author dwells longer on the activity of the School during the Interwar period – the time of its greatest prosperity, which ended along with the outbreak of World War 2. Attempts made after the War to recreate the spirit of the School are also outlined and the names of followers are listed accordingly. The presentation ends with some concluding remarks on the contribution of the School to contemporary developments in the fields of philosophy, mathematical logic or computer science in Poland. (shrink)

In the period after the First World War when the various national-ideological “truths” that led to it were not well resolved which resulted in the Second World War, one of the greatest world crises occurs. In those turbulent times, one philosopher renounces his national identity (changes his religion and name), wanting not to save himself from an evil world that is emerging but to join the creation of a completely new world – the world of modern logic. This man is (...) Alfred Tarski, whom many recognize as “the man who defined truth”, linking him to the formulation of the distinction between object and metalanguage. In the paper, I argue with historians of philosophy who claim that this distinction was first set by the logician and philosopher of the Lvov-Warsaw school Stanislaw Leśniewski (whose Tarski was the only doctoral student) accusing Tarski of violating professional laws without attributing the authorship of this distinction to Leśniewski. I show that this is not true and I cite the places where Tarski clearly emphasizes Leśniewski ‘s contribution. (shrink)

By pure calculus of names we mean a quantifier-free theory, based on the classical propositional calculus, which defines predicates known from Aristotle’s syllogistic and Leśniewski’s Ontology. For a large fragment of the theory decision procedures, defined by a combination of simple syntactic operations and models in two-membered domains, can be used. We compare the system which employs `ε’ as the only specific term with the system enriched with functors of Syllogistic. In the former, we do not need an empty name (...) in the model, so we are able to construct a 3-valued matrix, while for the latter, for which an empty name is necessary, the respective matrices are 4-valued. (shrink)

Kotarbiński is one of the leading figures in the Lvov-Warsaw school of Polish philosophy. We summarize the development of Kotarbiński’s thought from his early nominalism and ‘pansomatistic reism’ to the later doctrine of ‘temporal phases’. We show that the surface clarity and simplicity of Kotarbiński’s writings mask a number of profound philosophical difficulties, connected above all with the problem of giving an adequate account of the truth of contingent (tensed) predications. The paper will examine in particular the attempts to resolve (...) these difficulties on the part of Leśniewski. It will continue with an account of the relations of Kotarbińskian reism to the ontology of things or entia realia defended by the later Brentano. Kotarbiński’s identification of Brentano as a precursor of reism is, it will be suggested, at least questionable, and the paper will conclude with a more careful attempt to situate the Brentanian and Kotarbińskian ontologies within the spectrum of competing ontological views. (shrink)

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)

The purpose of this article is to present several immediate consequences of the introduction of a new constant called Lambda in order to represent the object ``nothing" or ``void" into a standard set theory. The use of Lambda will appear natural thanks to its role of condition of possibility of sets. On a conceptual level, the use of Lambda leads to a legitimation of the empty set and to a redefinition of the notion of set. It lets also clearly appear (...) the distinction between the empty set, the nothing and the ur-elements. On a technical level, we introduce the notion of pre-element and we suggest a formal definition of the nothing distinct of that of the null-class. Among other results, we get a relative resolution of the anomaly of the intersection of a family free of sets and the possibility of building the empty set from ``nothing". The theory is presented with equi-consistency results . On both conceptual and technical levels, the introduction of Lambda leads to a resolution of the Russell's puzzle of the null-class. (shrink)

In the paper, original formal-logical conception of syntactic and semantic: intensional and extensional senses of expressions of any language L is outlined. Syntax and bi-level intensional and extensional semantics of language L are characterized categorically: in the spirit of some Husserl’s ideas of pure grammar, Leśniewski-Ajukiewicz’s theory syntactic/semantic categories and in accordance with Frege’s ontological canons, Bocheński’s famous motto—syntax mirrors ontology and some ideas of Suszko: language should be a linguistic scheme of ontological reality and simultaneously a tool of its (...) cognition. In the logical conception of language L, its expressions should satisfy some general conditions of language adequacy. The adequacy ensures their unambiguous syntactic and semantic senses and mutual, syntactic, and semantic compatibility, correspondence guaranteed by the acceptance of a postulate of categorial compatibility syntactic and semantic categories of expressions of L. From this postulate, three principles of compositionality follow: one syntactic and two semantic already known to Frege. They are treated as conditions of homomorphism partial algebra of L into algebraic models of L: syntactic, intensional, and extensional. In the paper, they are applied to some expressions with quantifiers. Language adequacy connected with the logical senses described in the logical conception of language L is, of course, an idealization, but only expressions with high degrees of precision of their senses, after due justification, may become theorems of science. (shrink)

This is the first English translation of Leon Chwistek’s “Tragedia werbalnej metafizyki,” Kwartalnik Filozoficzny, Vol. X, 1932, 46–76. Chwistek offers a scathing critique of Roman Ingarden’s Das literarische Kunstwerk and of the entire Phenomenology movement. The text also contains many hints at Chwistek’s own philosophical and formal ideas. The book that Chwistek reviews attracted wide attention and was instrumental in winning Ingarden a position as Professor of Philosophy at the University of Lwów in 1933. Chwistek’s alienation from his fellow logicians (...) of the Lvov-Warsaw school is clear from his ridicule of Leśniewski’s project. (shrink)

In the paper, various notions of the logical semiotic sense of linguistic expressions – namely, syntactic and semantic, intensional and extensional – are considered and formalised on the basis of a formal-logical conception of any language L characterised categorially in the spirit of certain Husserl's ideas of pure grammar, Leśniewski-Ajdukiewicz's theory of syntactic/semantic categories and, in accordance with Frege's ontological canons, Bocheński's and some of Suszko's ideas of language adequacy of expressions of L. The adequacy ensures their unambiguous syntactic and (...) semantic senses and mutual, syntactic and semantic correspondence guaranteed by the acceptance of a postulate of categorial compatibility of syntactic and semantic (extensional and intensional) categories of expressions of L. This postulate defines the unification of these three logical senses. There are three principles of compositionality which follow from this postulate: one syntactic and two semantic ones already known to Frege. They are treated as conditions of homomorphism of partial algebra of L into algebraic models of L: syntactic, intensional and extensional. In the paper, they are applied to some expressions with quantifiers. Language adequacy connected with the logical senses described in the logical conception of language L is, obviously, an idealisation. The syntactic and semantic unambiguity of its expressions is not, of course, a feature of natural languages, but every syntactically and semantically ambiguous expression of such languages may be treated as a schema representing all of its interpretations that are unambiguous expressions. (shrink)

The paper contains an overview of the most important results presented in the monograph of the author "Teorie Językow Syntaktycznie-Kategorialnych" ("Theories of Syntactically-Categorial Languages" (in Polish), PWN, Warszawa-Wrocław 1985. In the monograph four axiomatic systems of syntactically-categorial languages are presented. The first two refer to languages of expression-tokens. The others also takes into consideration languages of expression-types. Generally, syntactically-categorial languages are languages built in accordance with principles of the theory of syntactic categories introduced by S. Leśniewski [1929,1930]; they are connected (...) with- the Ajdukiewicz’s work [1935] which was a continuation of Leśniewski’s idea and further developed and popularized in the research on categorial grammars, by Y. Bar-Hillel [1950,1953,1964]. To assign a suitable syntactic category to each word of the vocabulary is the main idea of syntactically-categorial approach to language. Compound expressions are built from the words of the vocabulary and then a suitable syntactic-category is assigned to each of them. A language built in this way should be decidable, which means that there should exist an algorithm for deciding about each expression of it, whether it is well-formed or is syntactically connected . The traditional, originating from Husserl, understanding of the syntactic category confronts some difficulties. This notion is defined by abstraction using the concept of affiliation of two expressions to the same syntactic category. (shrink)

This is a collection of new investigations and discoveries on the history of a great tradition, the Lvov-Warsaw School of logic , philosophy and mathematics, by the best specialists from all over the world. The papers range from historical considerations to new philosophical, logical and mathematical developments of this impressive School, including applications to Computer Science, Mathematics, Metalogic, Scientific and Analytic Philosophy, Theory of Models and Linguistics.

The Introduction outlines, in a concise way, the history of the Lvov-Warsaw School—a most unique Polish school of worldwide renown, which pioneered trends combining philosophy, logic, mathematics and language. The author accepts that the beginnings of the School fall on the year 1895, when its founder Kazimierz Twardowski, a disciple of Franz Brentano, came to Lvov on his mission to organize a scientific circle. Soon, among the characteristic features of the School was its serious approach towards philosophical studies and teaching (...) of philosophy, dealing with philosophy and propagation of it as an intellectual and moral mission, passion for clarity and precision, as well as exchange of thoughts, and cooperation with representatives of other disciplines. The genesis is followed by a chronological presentation of the development of the School in the successive years. The author mentions all the key representatives of the School, accompanying the names with short descriptions of their achievements. The development of the School after Poland’s regaining independence in 1918 meant part of the members moving from Lvov to Warsaw, thus providing the other segment to the name—Warsaw School of Logic. The author dwells longer on the activity of the School during the Interwar period—the time of its greatest prosperity, which ended along with the outbreak of World War 2. Attempts made after the War to recreate the spirit of the School are also outlined and the names of continuators are listed accordingly. The presentation ends with some concluding remarks on the contribution of the School to contemporary developments in the fields of philosophy, mathematical logic or computer science in Poland. (shrink)

The Warsaw School of Logic (WSL) was the famous branch of the Lvov-Warsaw School (LWS) – the most important movement in the history of Polish philosophy. Logic made the most important field in the activities of the WSL. The aim of this work is to highlight the role and significance of the WSL in the history of logic in the 20th century.