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)

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. (shrink)

Following an idea first proposed by Jerzy Wróblewski, this paperexamines the usefulness of formal logic for comparative legal analysis. Subject of the comparison are the doctrines of mistake and attempt in Germanand English criminal law. These doctrines are distinguished by the interaction of deontic, epistemic and alethic modalities. I propose a purely extensional logic which is based on Leśniewski’s substitutional interpretation ofquantification to analyse differences in the logical structure of the variouscriminal law doctrines.

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.

"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)

Sobocinski in his paper on Leśniewski's solution to Russell's paradox (1949b) argued that Leśniewski has succeeded in explaining it away. The general strategy of this alleged explanation is presented. The key element of this attempt is the distinction between the collective (mereological) and the distributive (set-theoretic) understanding of the set. The mereological part of the solution, although correct, is likely to fall short of providing foundations of mathematics. I argue that the remaining part of the solution which suggests a specific (...) reading of the distributive interpretation is unacceptable. It follows from it that every individual is an element of every individual. Finally, another Leśniewskian-style approach which uses so-called higher-order epsilon connectives is used and its weakness is indicated. (shrink)

Leśniewski’s metalogic is often considered to be difficult to understand because it differs greatly from its standard formulation. In this paper I try to explain the reasons of these idiosyncrasies. I claim that they have mainly two sources. First of all there is Leśniewski’s conviction that a formal system should be conceived as a set of concrete marks that can always physically and syntactically be expanded by the addition of new theses. Secondly there is Leśniewski’s conviction that definitions should neither (...) be formulas belonging to the metalanguage, nor deduction rules, but formulas belonging to the object-language and expressed with the help of the biconditional functor. The realisation of the first point is linked to the second one in so far as the metalinguistic rule for the writing out of definitions has to be formulated in a way that makes it possible to build the formal system in agreement with Leśniewski’s conception. While explaining these points I give an overview of the main peculiarities of Leśniewski’s metalogic. (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)

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 ...

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)

This article presents for the first time in english lesniewski's analysis of russell's antinomy as the analysis is given in lesniewski's 1914 paper "czy klasa klas, nie podporzadkowanych sobie, jest podporzadkowana sobie?" is the class of classes which are not subordinate to themselves subordinate to itself? it is shown how the concepts appearing in this paper, written in colloquial polish, were later incorporated and expressed as fundamental axioms and theorems of his theory of collective classes, mereology. in the (...) 1914 paper he asserted: i call any object p an object subordinate to a class k if in some sense of the expression "a" the following two conditions hold: 1) k is a class (of objects) "a", 2) p is an "a". using this explication of "p is subordinate to a class k," he showed that both of the following statements are false: a) the class of classes which are not subordinate to themselves is subordinate to itself, b) the class of classes which are not subordinate to themselves is not subordinate to itself; thus showing that russell's antinomy cannot be generated since its initial assumptions are false. (shrink)

A first-order formulation of Leśniewski's ontology is formulated and shown to be interpretable within a free first-order logic of identity extended to include nominal quantification over proper and common-name concepts. The latter theory is then shown to be interpretable in monadic second-order predicate logic, which shows that the first-order part of Leśniewski's ontology is decidable.

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)

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 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)

During 1927-1931 Leśniewski published a series of articles (169 pages) entitled 'O podstawach matematyki' [On the Foundations of Mathematics] in the journal Przeglad Filozoficzny [Philosophical Review], and an abridged English translation of this series is presented here. With the exception of this work, all of Leśniewski's publications appearing after the first World War were written in German, and hence accessible to scholars and logicians in the West. This work, however, since written in Polish, has heretofore not been accessible to most (...) Western readers, and it is hoped that this translation will encourage both the study of Leśniewski's works as well as the further development of his theories. (shrink)

This paper surveys mereology, the theory of parts and wholes, focussing on its origins in Leśniewski, and noting its intended employment as a surrogate for set theory. We examine parallel and independent work by Whitehead, Leonard and Goodman, and outline the subsequent adventures of mereology, both in its formal guises and in its now intensive application within philosophical ontology.

In this paper, we shall give another proof of the faithfulness of Blass translation of the propositional fragment \ of Leśniewski’s ontology in the modal logic \ by means of Hintikka formula. And we extend the result to von Wright-type deontic logics, i.e., ten Smiley-Hanson systems of monadic deontic logic. As a result of observing the proofs we shall give general theorems on the faithfulness of B-translation with respect to normal modal logics complete to certain sets of well-known accessibility relations (...) with a restriction that transitivity and symmetry are not set at the same time. As an application of the theorems, for example, B-translation is faithful for the provability logic \ ), that is, \ \ \ \supset \Box \phi \). The faithfulness also holds for normal modal logics, e.g., \, \, \, \. We shall conclude this paper with the section of some open problems and conjectures. (shrink)

This paper assesses those features of Lesniewski's Ontology which make it difficult to understand for logicians accustomed to more orthodox systems of logic. It is seen that certain general features of presentation and content can, by selective acceptance or modification, be accommodated with a fairly orthodox viewpoint. The chief difficulty lies in the interpretation of Le?niewski's names, and the constant ???. Four interpretations are suggested in turn: Le?niewski's names as monadic predicates; as class terms; as common nouns; and as (...) empty, singular or plural terms. This last and least orthodox interpretation is argued to be the most suitable, but it is shown how it can be made to live in harmony with either the common noun or the class interpretation. (shrink)

For the sake of explaining the merits of a Leśniewski type nominalism, it should be made clear what is meant by „nominalism” and what the characteristics of this special type of nominalism are. To the first question we can find quite a lot of mutually inconsistent answers. Therefore I will just explain the distinction between two different nominalistic traditions which I hold to be fundamental. I think we should not just focus on the question which so-called abstract entities are rejected (...) but as well look for basic entities nominalists rely on. (shrink)

The main aim of the paper is paraphrasing Heidegger's category of being in the theoretic framework of Fregean phenomenological semantics. The choice of Fregean phenomenological semantics as the tool of the paraphrase is justified by the fact that philosophy articulated in Sein und Zeit may be interpreted as the modification of Husserl's project of phenomenology which is treated, in turn, as generalisation of Frege's theory of sense and nominatum. So in the paper it is defended that Heidegger's category of being (...) stems from Frege's considerations devoted to basic semantic questions. In the first chapter there are specified in existentialistic language ten principles clarifying the notion of being. In the second part the principles are paraphrased in the phenomenological theory of noema (this category is understood in spirit of the so called Californian interpretation). This move allows us to show how the conception of being is the modification of Frege's and Husserl's semantics. In the last chapters there is reconstructed Heidegger's model of acts of reference. The formal tool of the reconstruction is Leśniewski's formal language (enriched by Ajdukiewicz) with indexes designating ways of existence and referential backgrounds. (shrink)