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)
Stanisław Brzozowski formulated the ideal of modern man in the polemic with the contemporary man, who has ceased to believe in truth and moral values and is devoid of the will to act. For Brzozowski modernity involves the discovery of truth about the human condition: about man as an autonomous subject, a creator of values, who struggles with non-human reality. This truth was formulated in Kant’s idea of autonomy and in Marx’ idea of a collective conquest of the world of (...) nature. For Brzozowski, ideal modern man is “the conscious labourer,” who labours because he wants to proudly impose a human law on the non-human world. At the same time Brzozowski used the term “modernity” to describe life of constant change in the modern world, understood as a set of results of man’s reign over nature. For the sake of human maturity, Brzozowski expected the truly modern man to perceive modern life as an unquestionable value. Undoubtedly, there is an evident tension in Brzozowski’s ideal of modern man between the affirmation of creativity in the world of change and the necessity of disciplined production, including unchangeable moral foundations of labour. There is also a major shift in this ideal, stemming from Brzozowski’s change of attitude towards religion. (shrink)
The essay examines Stanisław Brzozowski’s ideas on mutual interactions between the sphere of culture and the realm of the political. It shows how Brzozowski made use of literary texts in order to elucidate social and political processes. In doing so, he insisted on a specific form of knowledge accessible through texts of literature and literary criticism, which are not limited by the mere “logic of notions.” Following Vico and Sorel Brzozowski detected an “irrational core” at the bases of human collectivities (...) such as above all modern nations, and it is through literature that this core can be revealed. Brzozowski’s understanding of political ideas and concepts is informed—to a decisive degree—by the literary imagination. This can be shown by a semantic and rhetorical analysis of some of his later writings. (shrink)
Stanisław Brzozowski was active as philosopher and literary critic for only a few years at the turn of the twentieth century, yet his writings are still inspire contemporary thinkers and critics. In every important phase of the development of Polish literary criticism, Polish intellectuals have acknowledged Brzozowski as a writer who had the courage and critical acumen to confront modernity and examine closely contemporary trends of thought from the perspective of social and individual life. This continued presence of the celebrated (...) critic cannot but be interesting for the researcher who is led to ask, what is so intriguing in Brzozowski’s work, why do successive generations of critics and intellectuals return to Brzozowski? Drawing on many important interpretations of Brzozowski’s work (Burek, Głowiński, Nycz), I want to show that in Brzozowski’s work it is possible to find everything contemporary criticism and thought needs, because his books contain, in nuce , projects and strategies which can be (and are) used in different ways by critics representing different ideologies and worldviews. Brzozowski worked out, or rather attempted to work out, ideas which are a source of modern critical projects but in addition his work comprises a repertoire of possibilities which contemporary critical thought can turn to its advantage. Brzozowski’s work can be also treated as a performative act, calling forth the reader’s response, in this way shedding new light on it. I also show that “performative consciousness” is both close to Brzozowski’s practice of writing and deeply rooted in his philosophical conviction. Brzozowski can be considered a representative of modernist, critical literature, in which reading and writing become a mode of experience, a privileged social discourse, and a “leaven,” an act and an activity. (shrink)
This book introduces the English-speaking reader to the thought of Stanislaw Brzozowski (1878-1911), the outstanding Polish philosopher and literary critic. Although practically unknown in the West, Brzozowski is an important but neglected forerunner of the intellectual tradition of `Western Marxism', most commonly associated with Georg Lukács and Antonio Gramsci. -/- Concentrating first on the early phase of Brzozowski's thought, Professor Walicki goes on to analyse his ideas on the working class and its relation to the intelligentsia and contemporary working-class (...) ideologies. Finally he deals with aspects of his thought which go beyond the Marxian problematic and round off the intellectual portrait of the man. -/- Brzozowski's anti-naturalistic approach resulted in a radical reinterpretation of Marxism which dealt with many of the problems of the revolt against positivism in European philosophy. Professor Walicki argues that the retrieval of the philosophical and humanist aspect of Marxism, and its separation from the Engels-inspired `scientific Marxism', was the achievement of Brzozowski and not, as frequently assumed, of Lukács, who came to similar conclusions only some ten years later. -/- By placing Brzozowski within the cross-currents of the various philosophical, sociological, literary, and political streams of Western and Eastern European thought in which Marxism was situated, Professor Walicki produces a fascinating study of an early East European challenge to orthodox Marxism. (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)
LetEO be the elementary ontology of Leniewski formalized as in Iwanu , 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.
This essay is an attempt to analyze an important decision Brzozowski took at the end of his life, i.e. his late turn towards Catholicism, which, despite his own objections, we should nonetheless call a religious conversion. The main reason why Brzozowski resisted the traditional rhetoric of conversion lies in his often repeated conviction that faith cannot invalidate life, because “what is not biographical, does not exist at all.” Brzozowski, therefore, rejects conversion understood as a radical and abrupt revolution of the (...) soul, which annuls everything that happened before, and turns to a model of religiosity (“Catholicism, undoubtedly”) which preserves his entire biographical past. In this manner, Brzozowski seeks his own formula of faith, more adequate to the “situation” of the modern man who lives in and through History. I argue that the model of “conversion without conversion” Brzozowski chose as representative of modern man is typically, though avant la lettre , post-secular: closer to the Jewish sources of past-oriented tschuva than to the mystical timelessness of traditionally Christian metanoia . The idea that redemption consists not in a liberation of a pure spirit but in a patient working-through of the universal history of creation is an implicit credo of the whole modern age, first fully articulated by Brzozowski and only later in the writings of Hermann Cohen, Franz Rosenzweig, and Walter Benjamin. Brzozowski emerges as a relatively early precursor of the future post-secular option whose advocates, like the author of The Diary , will not allow themselves to “lose a single moment,” either of their lives or the world’s history. (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)
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)
In this article, Brzozowski’s much discussed connections with fascism are reconsidered in the context of interpretations of fascism by Sternhell and Gentile. At the end of his life, Brzozowski tried to reconcile socialism and nationalism. He criticized orthodox Marxism and liberal democracy, underlined the political and cultural importance of the nation, praised irrationalism, strength, imperialism, heroism, asceticism, the labourer and the soldier as ideal attitudes with regard to the world. He wanted to turn Poland into a modern nation, but feared (...) some consequences of modernity. Brzozowski’s ambivalent attitude towards modernity precludes finding an adequate description for them, in particular in the Polish and Central European context, although his concepts were similar to those of some of his contemporaries from France or Italy, such as Georges Sorel or the “La Voce” group, as well as “antimoderns” as described by Antoine Compagnon. At present labels such as “fascism” or even “proto-fascism” seem to be too ambiguous to grasp the originality of Brzozowski’s thinking. The Polish thinker’s case suggests a reconsideration of Sternhell’s thesis that Eastern-European Marxism remained loyal to the Heglian, rationalist, and materialist essence of Marxism. (shrink)
The volumes of G¨ odel’s collected papers under review consist almost entirely of a rich selection of his philosophical/scientific correspondence, including English translations face-to-face with the originals when the latter are in German. The residue consists of correspondence with editors (more amusing than of any scientific value) and five letters from G¨ odel to his mother, in which explains to her his religious views. The term “selection” is strongly operative here: The editors state the total number of items of personal (...) and scientific correspondence in G¨ odel’s Nachlass to be around thirty-five hundred. The correspondence selected involves fifty correspondents, and the editors list the most prominent of these: Paul Bernays, William Boone, Rudolph Carnap. Paul Cohen, Burton Dreben, Jacques Herbrand, Arend Heyting, Karl Menger, Ernest Nagel, Emil Post, Abraham Robinson, Alfred Tarski, Stanislaw Ulam, John von Neumann, Hao Wang, and Ernest Zermelo. The correspondence is arranged alphebetically, with A-G in Volume IV. The imbalance results from the disproportionate size of the Bernays correrspondence: 85 letters are included (almost all of them), spanning 234 pages) including the face-to-face originals and translations). Each volume contains a calendar of all the items included in the volume together with separate calendars listing all known correspondence (whether included or not) with the major correspondents (seven in Volume IV and ten in Volume V). Let me recommend to the reader the review of these same volumes by Paolo Mancosu in the Notre Dame Journal of Formal Logic 45 (2004):109- 125. This essay very nicely describes much of the correspondence in terms of broad themes relating, especially, to the incompleteness theorems—their origins in G¨ odel’s thought, their reception, their impact on Hilbert’s program. (shrink)
An argument against multiply instantiable universals is considered in neglected essays by Stanislaw Lesniewski and I.M. Bochenski. Bochenski further applies Lesniewski’s refutation of universals by maintaining that identity principles for individuals must be different than property identity principles. Lesniewski’s argument is formalized for purposes of exact criticism, and shown to involve both a hidden vicious circularity in the form of impredicative definitions and explicit self-defeating consequences. Syntactical restrictions on Leibnizian indiscernibility of identicals are recommended to forestall Lesniewski’s paradox.
1. One theory or many? In 2004 a very interesting and readable article by Lenore Blum, entitled “Computing over the reals: Where Turing meets Newton,” appeared in the Notices of the American Mathematical Society. It explained a basic model of computation over the reals due to Blum, Michael Shub and Steve Smale (1989), subsequently exposited at length in their influential book, Complexity and Real Computation (1997), coauthored with Felipe Cucker. The ‘Turing’ in the title of Blum’s article refers of course (...) to Alan Turing, famous for his explication of the notion of mechanical computation on discrete data such as the integers. The ‘Newton’ there has to do to with the well known numerical method due to Isaac Newton for approximating the zeros of continuous functions under suitable conditions that is taken to be a paradigm of scientific computing. Finally, the meaning of “Turing meets Newton” in the title of Blum’s article has another, more particular aspect: in connection with the problem of controlling errors in the numerical solution of linear equations and inversion of matrices,Turing (1948) defined a notion of condition for the relation of changes in the output of a computation due to small changes in the input that is analogous to Newton’s definition of the derivative. The thrust of Blum’s 2004 article was that the BSS model of computation on the reals is the appropriate foundation for scientific computing in general. By way of response, two years later another very interesting and equally readable article appeared in the Notices, this time by Mark Braverman and Stephen Cook (2006) entitled “Computing over the reals: Foundations for scientific computing,” in which the authors argued that the requisite foundation is provided by a quite different “bit computation” model, that is in fact prima facie incompatible with the BSS model. The bit computation model goes back to ideas due to Stefan Banach and Stanislaw Mazur in the latter part of the 1930s, but the first publication was not made until Mazur (1963).. (shrink)
My favorite poststructuralist is Gilles Deleuze (with or without Guattari). I like to think that he was really writing an elaborate series of works of science fiction, in a non-fictional format (much as Stanislaw Lem did in Imaginary Magnitude and A Perfect Vacuum ), only without letting anyone in on the joke. Partly this is because there are moments where what he says is almost right (such as the definition of "relation" he gives in his interview with Claire Parnet, (...) where he visibly reaches for, but can't quite grasp, the notion of a set of ordered pairs), much as many science fiction writers get things almost right. That, plus the fact that he was obviously channeling La Mettrie, which seems to have escaped many people. (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)
The aim of this paper is to present a certain kind of argumentation against the idea of the Turing test (we call it CCSC—Complete Conversation System Claim) and to discuss the issue of its first formulation. Ned Block, with his idea of “Aunt Bubbles” argument, is thought of as a founding father of CCSC, but we present the results of our bibliographical researches which clearly show that the first formulation of CCSC should be ascribed to Polish writer and philosopher (...) Stanisław Lem. (shrink)
Three chapters contain the results independent of each other. In the first chapter I present a set of axioms for the propositional calculus which are shorter than the ones known so far, in the second one I give a method of defining all ternary connectives, in the third one, I prove that the probability of propositional functions is preserved under reversible substitutions.
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 paper presents major ethical, legal and methodological problems related to the use of placebo in mental disorders, especially in depression. It is pointed out that although authoritative groups of experts and numerous publications in the field of psychopharmacology indicate advisability of the double blind design with placebo in clinical trials of antidepressants, in recent years there have been more and more voices questioning legitimacy of this method. Objections of an ethical nature are raised, and reliability of this approach is (...) put into doubt from the methodological viewpoint. These issues are discussed in more detail in the paper. Available alternative solutions should be implemented in psychotropic drug studies. The author shares these objections and doubts of an ethical nature, and believes that the placebo procedure is not a necessity in clinical trials of antidepressants. (shrink)
The paper discusses the impact of the thought of Stanisław Brzozowski (1878–1911) on several Polish emigré writers, including Józef Czapski and Gustaw Herling-Grudziński, but first of all Czesław Miłosz (1911–2004) and Aleksander Wat (1900–1967). Miłosz’ approach oscillated between early fascination through an unjust rejection during the war, due to the “appropriation” of Brzozowski’s thought by the right wing publicists, to the new phase of fascination after the war, culminating in the publication of a book on Brzozowski ( A Man Among (...) Scorpions , 1962) and prolonged in several important articles till the very end of his life. Wat’s approach shifted from the communist practice of “overcoming” Brzozowski through the affirmation of his criticism and rejection of catholic obscurantism to the process of the internalization of the catholic faith. (shrink)
stanislaw lesniewski, Collected Works, Edited by Stanislaw J. Surma, Jan T. Srzednicki and D. I. Barnett, with an annotated bibliography by V. Frederick Rickey. Warsaw:PWN?Polish Scientific Publishers; and Dordrecht, Boston, London: Kluwer. 2 vols., xvi + 794 pp. $274/£163/Dfl. 480.
The aim of the paper is to give a new definition of real number. The logical type of any number defined is that of the function B = h(A) which assigns to a class of sets A a class of sets B. I give some conditions which the function h has to fulfill to be considered as number; an intuitive sense of the conditions is as follows: a function, which is number, assigns a class of sets of measure h·m to (...) a class A of sets of equal measure, where m is the measure of A. (shrink)