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)

Formalism used by Leśniewski to present mathematical theory is called a radical one. According to the author, it is the implementation of the postulates of the so-called formal arithmeticians. Mathematical theory is presented as a pure game of formulas devoid of content. It is governed by the precise rules described in the metalanguage. The author stresses the difference between Leśniewski’s and Hilbert’s mathematical approaches.

Stanisław Leśniewski was one of the two originators and drivers of the Warsaw School of logic. This article describes his work chronologically, from his early philosophical work in Lvov to his highly original logical systems of protothetic, ontology and mereology. His struggles to overcome logical antinomies, his absolute commitment to logical clarity and precision, and his antipathy towards set theory made his nominalistic approach to logic among the most original of the twentieth century, while his early death and (...) the loss of his papers meant his work was only gradually discovered and appreciated outside Poland. (shrink)

"Lesniewski defined ontology, one of his three foundational systems, as 'a certain kind of modernized 'traditional logic' [On the foundations of mathematics (FM), p. 176]. In this respect it is worth bearing in mind that in the 1937-38 academic year Lesniewski taught a course called "Traditional 'formal logic' and traditional 'set theory' on the ground of ontology"; cf. Srzednicki and Stachniak, S. Lesniewski's Systems. Protothetic, 1988, p. 180. On this see Kotarbinski Gnosiology. The scientific approach to the theory of knowledge, (...) 1966, pp. 253-54 [the Polish original was published in 1929], which Lesniewski praised in [FM]: see in particular pp. 373 ff. Kotarbinski noted that Lesniewski "calls his system 'ontology' in harmony with certain terms used earlier (as in.. (shrink)

Due to the current availability of the English translation of almost all of Lesniewski's works it is now possible to give a clear and detailed picture of his ideas. Lesniewski's system of the foundation of mathematics is discussed. In abrief ouüine of his three systems Mereology, Ontology and Protothetics his positions conceming the problems of the forms of expression, proper names, synonymity, analytic and synthetic propositions, existential propositions, the concept of logic, and his views of theory of science and metaphysics (...) are sketched. The influence of Mill, Lukasiewicz, Austrian philosophy and especially Petrazycki on his thinking is evaluated and an interpretation is suggested setting him squarely in a tradition of classical Aristotelian logic. (shrink)

Due to the current availability of the English translation of almost all of Lesniewski's works it is now possible to give a clear and detailed picture of his ideas. Lesniewski's system of the foundation of mathematics is discussed. In abrief ouüine of his three systems Mereology, Ontology and Protothetics his positions conceming the problems of the forms of expression, proper names, synonymity, analytic and synthetic propositions, existential propositions, the concept of logic, and his views of theory of science and metaphysics (...) are sketched. The influence of Mill, Lukasiewicz, Austrian philosophy and especially Petrazycki on his thinking is evaluated and an interpretation is suggested setting him squarely in a tradition of classical Aristotelian logic. (shrink)

LetEO be the elementary ontology of Leniewski 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.

Insatisfait du calcul des classes et des relations de Whitehead et Russell, Leśniewski élabora en 1919-20 une théorie extensionnelle des noms qu’il nomma Ontologie. Sans entrer dans une description technique du formalisme de Leśniewski, nous montrons dans cet article que l’Ontologie permet un traitement général du distributif qui ne s’appuie à aucun moment sur une notion de classe. Nous illustrons enfin cette particularité importante du système de Leśniewski en proposant une définition logiciste de la notion de cardinalité (...) qui répond d’une manière radicale aux impératifs d’une no-class theory. (shrink)

Insatisfait du calcul des classes et des relations de Whitehead et Russell, Leśniewski élabora en 1919-20 une théorie extensionnelle des noms qu’il nomma Ontologie. Sans entrer dans une description technique du formalisme de Leśniewski, nous montrons dans cet article que l’Ontologie permet un traitement général du distributif qui ne s’appuie à aucun moment sur une notion de classe. Nous illustrons enfin cette particularité importante du système de Leśniewski en proposant une définition logiciste de la notion de cardinalité (...) qui répond d’une manière radicale aux impératifs d’une no-class theory. (shrink)

It was one of Brentano’s central ideas that all judgements are at bottom existential. In his Psychology from an Empirical Standpoint he tried to show how all traditionally acknowledged judgement forms could be reinterpreted as existential statements. Existential propositions, therefore, were a central concern for the whole Brentano School. Kazimierz Twardowski, who also accepted this program, introduced the problem of the existential reduction to his Polish students, but not all of them found this idea plausible. In 1911 Stanisław (...) class='Hi'>Leśniewski published a paper under the title “A Contribution to the Analysis of Existential Propositions” where he criticised Brentano’s translation. According to Leśniewski the consequences of Brentano’s program would be absurd because according to Leśniewski all positive existential propositions are analytically true and all negative ones are contradictory. In his later works Leśniewski repudiated all his early writings (1911–1914) as philosophically immature and formally imprecise. “[…] I regret that they have appeared in print,” he writes, “and formally ‘repudiate’ them herewith […]”. But in spite of this severe assessment, these early papers are worth considering not only from a historical standpoint. As we will see, Leśniewski’s critique of Brentano is unsound, but it casts an interesting light on his understanding of certain basic metaphysical concepts. (shrink)

This paper is a contribution to the reconstruction of Tarski’s semantic background in the light of the ideas of his master, Stanislaw Lesniewski. Although in his 1933 monograph Tarski credits Lesniewski with crucial negative results on the semantics of natural language, the conceptual relationship between the two logicians has never been investigated in a thorough manner. This paper shows that it was not Tarski, but Lesniewski who first avowed the impossibility of giving a satisfactory theory of truth for ordinary language, (...) and the necessity of sanitation of the latter for scientific purposes. In an early article (1913) Lesniewski gave an interesting solution to the Liar Paradox, which, although different from Tarski’s in detail, is nevertheless important to Tarski’s semantic background. To illustrate this I give an analysis of Lesniewski’s solution and of some related aspects of Lesniewski’s later thought. (shrink)

In this paper, we want to present the genesis of Stanisław Leśniewski’s mereology. Although ‘mereology’ comes from theword ‘part’, mereology arose as a theory of collective classes. That is why we present the differences between the concepts of being a distributive class and being a collective class. Next, we present Leśniewski’s original mereology from 1927, but with a modern approach. Leśniewski was inspired to create his concept of classes and their elements by Russell’s antinomy. To face (...) it, Leśniewski had to define the concept of being an element of based on the concept of being part of. Leśniewski showed that in his theory, there is no equivalent to Russell’s antinomy. We will show that his solution has nothing to do with the original approach because, in both cases, we are talking about objects of a different kind. Russell’s original antinomy concerned distributive classes, and Leśsniewski’s considerations concerned collective classes. (shrink)

Since Kazimierz Twardowski introduced the notions of “symbolomania” and “pragmatophobia,” the relationship between logic and reality was the focus of the philosophers from the Lvov-Warsaw School — inter alia two prominent logicians of the group, Stanisław Leśniewski and Jan Łukasiewicz. Bolesław Sobociński has pointed out, however, that there was a contrast between their approach to logic and reality. Despite being members of the same philosophical group and even colleagues from the same department, their philosophical views on the position (...) of logic in reality differed considerably. Yet they both agreed that reality has a certain importance for logic and that logic could be valuable for reality. The aim of this paper is to introduce their divergent positions and describe in more detail how Leśniewski and Łukasiewicz understood the relationship between logic and the real world. (shrink)

Zbigniew Tworak The early Leśniewski and the Liar AntinomyIn his early, prelogistic article „Critique of the Logical Principle of Excluded Middle” (1913) Stanislaw Leśniewski presents a certain solution to the Liar Antinomy. He argues that the Logical Principle of Excluded Middle is false but he defends the so-called Principle of Contradictory Sentences (the weaker version of the Logical Principle of Excluded Middle) and the Logical Principle of Contradiction. The paper discusses this solution. Leśniewski’s solution to the Liar (...) antinomy differs from Tarski’s in several important details. On the one hand, there is a connection between the proposition and a medieval solution to insolubilia, the so-called restrictio theory. A restrictio is a doctrine which has it that self-reference is illegitimate (either in all cases or in some cases only). On the other hand, there is a connection between the proposition and the contextual approach (what is communicated by the sentence varies with the context of use of the sentence). Keywords: Stanislaw Leśniewski, Liar Antinomy, restrictio theory. (shrink)

The logical theories of Stanislaw Leśniewski differ profoundly form classical formal systems. Unlike the latter, they do not have an entirely predetermined vocabulary. Nor do they have a determined list of functors of syntactical-semantical categories. Due to formalized directives for definitions, the logics of Leśniewski are constructed progressively, making new theses and consequently functors of new syntactical-semantical categories accesible. In this article we present the genetic aspect associated with these theses-definitions. We also show that the property of creativity (...) makes it possible to bridge some of the fundamental gaps in contemporary classical logics. (shrink)

The logical theories of Stanislaw Leśniewski differ profoundly form classical formal systems. Unlike the latter, they do not have an entirely predetermined vocabulary. Nor do they have a determined list of functors of syntactical-semantical categories. Due to formalized directives for definitions, the logics of Leśniewski are constructed progressively, making new theses and consequently functors of new syntactical-semantical categories accesible. In this article we present the genetic aspect associated with these theses-definitions. We also show that the property of creativity (...) makes it possible to bridge some of the fundamental gaps in contemporary classical logics. (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 (...) class='Hi'>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)

Democracy - hope or illusion? Blooming, failing or declining? Our doubts and hesitation make part of unbending efforts to endorse and explain democracy. Who is right - the custodians of promise or the prophets of decline? The book concentrates on doubts. The author tries to explore «the other side of the moon», emphasizing the role of critical thinking, opposing a main-current optimism. Defending democracy we want to generate hope, but hoping may be a dangerous craft. Protecting our hope we are (...) prone to believe that democracy - even if it is not a full success story - is justified in its nature and out of question. How much do we have to forget to sanction this view? This is, in fact, the main question the book raises. It gives voice to those who never, in their writing on democracy, used a flattering tone. Starting with Greek giants - Plato and Aristotle - up to modern and most recent times, going through a broad field of revealing criticism, leaving us with an unsettling feeling that democracy is rather something to be explained than something to be celebrated. Living in democracy, lamenting its underperformances, we must not overlook a fundamental question - in what part do our disappointments reflect the «art of forgetting», allowing us to cast into oblivion all serious doubts originating in a critical discourse on modernity and democracy? (shrink)

The book by professor Stanisław Kowalczyk, renowned scholar in the field of social philosophy, is, without doubt, one of the most important studies on the idea of freedom. The concept of freedom is as old as mankind. It has many meanings and has been interpreted in many different ways. For instance, we also have the word „liberty," which means „freedom or right" and is synonymous with the word freedom, which means „the condition of being free." The author indicates that (...) in our times the notion of freedom is most frequently used; however, it is often misused or deceptive. Mass media and people of all walks of life talk of liberty; everyone talks of freedom and, for many, it is the highest value. Longing for freedom is rooted in the heart of every human being, for freedom is an existential correlate and the fulfilment of the rational human being. The semantic confusion about the notion of freedom leads to many misuses of the concept. Personalism, as a philosophical concept in which a person stands in the centre of all discussion, serves as a framework for the author's delineation on the concept of freedom. He further states that the appropriate understanding of this value is possible in the context of the personalistic interpretation of a human being. This is the focus of this informative and insightful book. (shrink)

In the first part I focus on the issue of progress, in particular progress in philosophy. Philosophical progress has a special property that it shares with the process of becoming a better person. It is constantly finding yourself “on the way”. This path is not only anchored in the Absolutely Perfect but it conditions and stimulates the reflection towards the truth about the relationship between Him and us. We can assume that the core of this reflection is philosophy. The second (...) part is devoted to the paradoxical nature of the most generally understood memory. I assume that the condition of awareness of a certain content is its outdatedness, that is, its transfer to the sphere of memory. Memory is a constantly updated and constantly re-ordered picture of everything that the subject has ever relegated from being, so that it can be replaced by something else. The foundation of this order is a certain axiology. In the third part I show how the sketched concept of memory is used to describe the mechanism of the evolution of philosophical thought. The “on the way” philosophy would consist of two constantly repeated activities: on reconstructing what is to be denied, and thus on the recognition of the previous philosophical achievements in its totality, and on its negation. This denial would concern the whole of this achievement as an axiologically reconstructed unity. The new system is only realized as a series of consequences of the negation of the current state. The vast majority of philosophical reflection focuses on the constitution of this current state, its supposed unity. In the short part of the fourth, I draw up prospects for further deliberations. (shrink)

The book is devoted to the thought of one of the 20th century's most interesting philosophers of religion. Heschel, a traditional Polish Jew who became a modern thinker, was also an impressive prophet of interreligious dialogue.

Stosunek polskiej filozofii katolickiej do Augusta Cieszkowskiego był ambiwalentny. Z jednej strony, uważano go za wybitnego filozofa polskiego, żarliwie religijnego i inspirowanego tradycją chrześcijańską, z drugiej strony, jego myśl budziła liczne zastrzeżenia doktrynalne (ewolucyjna perspektywa religii, możliwość realizacji Królestwa Bożego na ziemi, wątki panteizujące, ograniczanie wolnej woli, uzurpowanie sobie prawa do absolutyzmu poznawczego, jeśli chodzi o "Boże plany", uznanie Boga przed stworzeniem świata za nierozwiniętą jeszcze Możność, "elitarna" koncepcja nieśmiertelności jednostkowej za zasługi). Z dzisiejszej perspektywy filozofia Cieszkowskiego budzi opór ze (...) względu na próbę "totalizacji" rzeczywistości i eksponowanie utopijnego modelu ustroju teokratycznego. (shrink)

Polish conservative thinker Władysław Leopold Jaworski developed an interest for the theories of Austrian philosopher Othmar Spann. Both accepted universalism, both also believed that universalism was inspired by romantic tradition, although Spann sought its roots much further back in history, even as far as Aristotle. Both authors staunchly criticized modern-day individualism and liberalism, which they considered fatal. In their opinion individualism and liberalism upset the primacy of totality in social thought, which led to multiple pathologies. Despite their accentuation of totality, (...) both philosophers displayed very decided anti-totalitarian convictions typical for many conservatives. (shrink)