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)

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)

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)

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)

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)

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)

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)

Artykuł analizuje problem kosztów powstałych w wyniku realizacji obowiązku udzielenia pomocy osobie znajdującej się w niebezpieczeństwie. Autorzy prezentują trzy odmienne stanowiska dotyczące tego problemu, rozważając scenariusz, w którym osoba decyduje się, z własnej woli lub przymuszona za pomocą prawa, uratować inną osobę, w sytuacji, w której taka pomoc wiąże się z naruszeniem praw trzeciej strony. Przykładowo, A ratuje tonącego B, ale w trakcie ratowania narusza prawa C. Pytanie, które stawiają autorzy brzmi: zakładając, że istnieje obowiązek udzielenia pomocy osobie znajdującej się (...) w niebezpieczeństwie, kto powinien ponieść koszty odszkodowania za naruszenie praw trzeciej strony? Autorzy rozważają następujące możliwości: koszty pomocy powinny zostać poniesione przez (a) ratującego, (b) osobę, której prawa zostały naruszone, (c) ratowanego, (d) całe społeczeństwo. (shrink)

The purpose of the essay is to critically analyze the influence of J. Derrida’s deconstruction on David J. Gunkel’s book Deconstruction (MIT Press 2021). Gunkel’s handbook is aimed at making deconstruction a tool of critical thinking accessible to non-professionals. It turns out that accomplishing this task comes at the expense of precisely the critical potential of deconstruction itself. Gunkel is well aware that his arguments are sometimes superficial and overlook deeper problems that should be addressed. Such a failure takes the (...) form of a fetishistic denial, which in psychoanalysis is summarized by the formula “I know well, but all the same.” In turn, deconstruction itself, insofar as it is separated from Kant’s transcendental philosophy and Hegel’s dialectics, becomes an academic ideology. Restoring its proper subversive potential can only be done by returning to a philosophy of reflection, in which the thinker himself must ultimately consider his own position as an author and bring it under criticism. This is the path that Gunkel avoids, because he could then no longer be the author of a handbook on deconstruction, rather than someone who practices deconstruction. -------------------------- Received: 4/11/2022. Reviewed: 13/12/2022. Accepted: 20/12/2022. (shrink)

The article reviews the book Philosophia Vitam Alere. Prace dedykowane Profesorowi Romanowi Darowskiemu SJ z okazji 70-lecia urodzin, edited by Stanisław Ziemiański S.J.

The Cognitive Science of Religion represents a contemporary attempt at a naturalistic explanation of religion. There is debate as to whether its account of how religious beliefs arise is reconcilable with the religious account, which holds that religious beliefs are caused by God. In my paper, I argue that these two accounts cannot be reconciled when it comes to the specific question of how Christian religious beliefs arise if one accepts an important theological doctrine of the supernaturality of Christian belief. (...) This doctrine implies that there can be no natural explanation for how Christian beliefs arise because they are a gift of divine grace. This leads to a conundrum for Christian theists: they can either reject the CSR account of how their religious beliefs arise, or they can reject the supernaturality of Christian belief. I argue that the latter is preferable. I then draw on the work of the theologian Denis Edwards to illustrate how one can drop this doctrine without abandoning some other fundamental tenets of Christian theology. (shrink)

We show that for every enumeration degree $a < 0'_e$ there exists an e-degree c such that $a \leq c < 0'_e$, and all degrees b, with $c \leq b < 0'_e$, are properly $\Sigma^0_2$.