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)

In this paper, I try to accomplish two goals. The first is to provide a general characterization of a method of proofs called — in mathematics — the diagonal argument. The second is to establish that analogical thinking plays an important role also in mathematical creativity. Namely, mathematical research make use of analogies regarding general strategies of proof. Some of mathematicians, for example George Polya, argued that deductions is impotent without analogy. What I want to show is that there exists (...) a direct line leading from Cantor’s diagonal argument to constructions that underlies of the proofs of several important theorems of the mathematical logic (in particular, Church’s theorem concerning the undecidability of formal arithmetic, Gödel’s theorem concerning the incopleteness of formal arithmetic, Tarski’s theorem concerning truth, and Turing’s theorem concerning the Halting Problem), and that the line could be described as an analogical mapping. In other words, Cantor’s diagonal argument and the proofs of the limitative theorems are structurally the same. Hence they can be represented as instances (or special cases) of the same general scheme. (shrink)

The basic philosophical idea of intuitionism is that mathematical entities exist only as mental constructions and that the notion of truth of a proposition should be equated with its verification or the existence of proof. However different intuitionists explained the existence of a proof in fundamentally different ways. There seem to be two main alternatives: the actual and potential existence of a proof. The second pro-posal is also understood in two alternative ways: as knowledge of a method of con-struction of (...) a proof or as knowledge-independent and tenseless existence of a proof. This paper is a presentation and analysis of these alternatives. (shrink)

The Knower Paradox is an element of the class of paradoxes of self-reference. It demonstrates that any theory Ó which (1) extends Robinson arithmetic Q, (2) includes a unary knowledge predicate K, and (3) contains certain elementary epistemic principles involving K is inconsistent. In this paper I present different versions of the Knower Paradox (both in the framework of the first-order arithmetic and in the modal logic). There are several solutions of the paradox. Some of them I discuss in detail, (...) namely solution developed within modal logic, solution proposed by C. A. Anderson and solution proposed by P. Égré. The common defect of these proposals is that they developed a connection between the concepts of knowledge and provability. Finally, I suggest a solution using the basic ideas of the revision theory of definitions. (shrink)

In this paper, I try to give an account of situations in which self-reference is likely to occur. Generally, self-reference or circularity is relation in which something refers to itself (directly or via another, intermediate, objects). Self-referential objects sometimes lead to antinomies (inconsistencies) and sometimes do not. We can distinguish between vicious and innocuous self-referential objects. There is controversy whether all antinomies essentially involve some form of self-reference (S. Yablo has given an ingenious liar-style antinomy that, he claims, avoids self-reference). (...) I suggest that self-reference is necessarily involved in finite antinomies, but not in infinity ones. (shrink)

The paper discusses the debate on the human nature in the sophistic thought. Focusing on the "nature-culture" controversy it presents the evolution of the views of the sophists: from Protagoras' optimistic contention of the progress of mankind and his appraisal of culture to its criticism and the radical turn to nature in Antiphon, Hippias, Trasymachos, and Callicles. The paper aims at presenting the analysis of the ongoing discussion, with the stress laid on reconstruction of the arguments and concepts as well (...) as the attitudes that are associated with various positions of this debate. -/- . (shrink)

These are the excerpts from the book "Sztuka a prawda. Problem sztuki w dyskusji między Gorgiaszem a Platonem" concerning Gorgias' theory of apate (deception).

In the paper I argue that Kant’s philosophy underlies both contemporary individualism and personalism. The Kantian categorical imperative may be, in my opinion, interpreted in an anti-egotistical way and in an entirely individualistic one. The first kind of interpretation not only made a contribution to the emergence of numerous and manifold kinds of personalism, but it also inspired many critics of individualism. The second kind of interpretation, together with the Kantian analyses of human self, became essential to the conceptualization of (...) modern individualism. I argue that Kantian tradition in many respects appears to be close to Thomism as far as the conception of person and human individual is concerned. As the dispute between American Thomists, discussed in the paper, reveals, Thomistic personalists found, in Kant’s philosophy issues which filled some gaps in the scholastic heritage, especially in anthropology, ethics, and social problems. (shrink)

This article questions the belief expressed in various histories of pharmacy that the tenth-century Arab physician Avicenna introduced the tradition of coating pills with gold and silver. Although an examination of his Canon documents Avicenna's interest in the medicinal application of gold and silver, no mention is made of coating pills. Nor do other Islamic physicians seem to have been familiar with this practice, any more than such medieval European authors as Arnaldus of Villanova, Raymund Lull or Johannes de Rupescissa. (...) The same is true of medicinal compendia representative of later periods, such as the Ortus sanitatis, Valerius Cordus' Dispensatorium or the Secrets of Alessio Piemontese. The earliest known mention of coating pills with precious metals occurs in a non-medical book, The Golden Fleece , and the earliest mention in the professional literature seems to appear only in the second half of the seventeenth century. The practice of coating pills with gold and silver was to be practiced in Europe into the first half of the twentieth century. (shrink)

Classical Political Philosophy in Popular Discourse combines two scientific paradigms-classical political philosophy and contemporary, empirical sociology. The chief aim of this unique scientific project is to explore, operationalize, and reconstruct a political doctrine appearing in social discourse, exemplified by Polish society.

This book presents Tocqueville’s vision of the European continent, exploring his ideas of liberty, virtue, religion, patriotism, civic participation and democracy. Although Tocqueville is often revered as a classic writer on the subject of American democracy, this book focuses on the multifaceted importance of his ideas within a European context.

Scanlon grounds all moral principles in claims about "what individuals have reasons to agree to." Analyzing Scanlon's groundwork, I discuss his central reason for being concerned with morality and why personal and impersonal reasons for moral conduct cannot co-exist in his contractualism. I demonstrate that personal values and reasons are incommensurable with impersonal values and reasons. Thus, Scanlon needs to exclude impersonal reasons from the moral theory he advocates. But I argue that there may be a means of inclusion of (...) both the personal and impersonal values and reasons. I propose Aristotelian virtue ethics as a plausible foundation for subordinating the impersonal values and reasons to the value of human rationality in its full capacity. This subordination may provide the defensible condition that Scanlon's contractualism requires to justify moral principles to each person on the grounds of respect for human rationality. (shrink)

The author aims at evaluating the activities on the Facebook profiles of three regional media editorials – namely the ‘TVP 3 Łódź’ TV channel, the ‘Radio Łódź’ radio channel, and the Express Ilustrowany daily – particularly in terms of including local and regional information in their posts. Another objective was to attempt to quantify and compare these activities. The used research method is the analysis of profile content on Facebook, and the study was conducted within the period of one month.

Carl Jung paid a short visit to Taos, New Mexico, in January 1925. A brief account of his stay at the Pueblo appeared in Memories, Dreams, Reflections, edited by Aniela Jaffe in 1963. Remembering his conversations with Mountain Lake, Jung wrote of the confrontation between the “European consciousness,” or the “European thought,” with the Indian “unconscious.” My article provides a reading of Jung’s text as a meeting ground of the aesthetic, emotional, visionary and of the analytical, rational, explanatory. Like many (...) other European and Anglo-American visitors to Taos Pueblo, Jung rediscovers its capacity to mirror the inner needs of the visitor; he examines the significance of the encounter with the Southwestern landscape and with the Pueblo Indians’ religious views in terms of self-reflection and of the return to the mythical. As Carl Jung’s “inner comprehension” of the Pueblo Indian’s philosophy is mediated through language, aware both of its desire and its inability to become liberated from the European perspectives, Mountain Lake’s attitude towards his visitor from Switzerland remains ultimately unknown; Mountain Lake does, however, communicate his readiness to assume the archetypal role of a teacher and a spiritual guide whose insights reach beyond the confines and mystifications of language. According to Jung’s account, during this brief encounter of the two cultures, he and his Indian host experienced a sense of satisfaction and fulfillment, the sources of which, as they both understood them in their own individual ways, resided in the comprehension of universal sharing. (shrink)

The bookplate which Bruno Schulz designed in 1919 for his friend, Stanisław Weingarten, anticipates the motifs of his later literary work: a book, the Book, a collection of books reflecting the collector’s preferences but dependent on the laws undermining the notions of authorship and ownership. Standing on the margin of the artistic and literary scene, Pierrot/schulz acknowledges the relatedness of his and Weingarten’s “private“ vision with the recurrent, universal themes of world art and literature. The scene designed for the emblem (...) of Weingarten’s library demonstrates Schulz’s awareness that the pleasure of discovering spaces of textual cross-fertilizations belongs to the realm of discoveries made by “standard” narratives of psychoanalysis. The scene also demonstrates Schulz’s readiness to imaginatively play with that awareness. The essay traces correspondences between the elements of the 1919 Pierrot ex-libris and the books from Weingarten’s collection which, with time, included and gave privileged position to the works of Bruno Schulz. Among the authors referred to are Rainer Maria Rilke, Alfred Kubin, and Jules Laforgue. (shrink)

Published in 1542, Álvar Núñez Cabeza de Vaca’s La relación is a chronicle of the Pánfilo de Narváez’s 1527 expedition to the New World in which Cabeza de Vaca was one of the four survivors. His account has received considerable attention. It has been appreciated and critically examined as a narrative of conquest and colonization, a work of ethnographic interest, and a text of some literary value. Documenting and fictionalizing for the first time in European history the experience of travelling/trekking (...) in the region which now constitutes the Southwest in the United States, Cabeza de Vaca’s story testifies to the sense of disorientation, as well as to the importance of psychological and cultural mechanisms of responsiveness and adaptability to a different environment. What allows the Moroccan-American contemporary writer Laila Lalami to follow that perspective in her book The Moor’s Account is an imaginative transfer of the burden and satisfaction of narrating the story of the journey to the black Moroccan slave whose presence in the narratives of conquest and exploration was marginal. In Lalami’s book, Estebanico becomes the central character and his role is ultimately identified with that of a writer celebrating the freedom of diversity, one who survives to use the transcultural experience of the past creatively in ways well suited to the needs of the current moment. (shrink)

The author characterizes and explains a phenomenon of neomessianism in catholic moral teaching of John Paul II and cardinal Ratzinger. According to these Christian moralists, the modern world is being destroyed by antichristian liberalism, “wild capitalism” and ethical relativism and that is why it need a new evangelization. It is also a church which suffers from secularization and therefore the mission, the revived idea of Christ and moral examples should begin.

In the paper we discuss the problem of limitations of freedom in mathematics and search for criteria which would differentiate the new concepts stemming from the historical ones from the new concepts that have opened unexpected ways of thinking and reasoning. We also investigate the emergence of category theory and its origins. In particular we explore the origins of the term functor and present the strong evidence that Eilenberg and Carnap could have learned the term from Kotarbiński and Tarski.

The aim of this paper is to present a conception of the triple nature of mathematics. It is argued that the nature of mathematics is best served by distinguishing deep ideas (of concepts or propositions), their surface representations (signs which can be perceived by senses) and their formal models (in axiomatic theories). For instance, the concept „number π” has several different models in set theory (those based on Dedekind cuts and on Cantor's equivalence classes of Cauchy sequences) and yet all (...) working mathematicians in the world have the same object π in mind. They have a common deep idea of π. Generally, the deep idea of a concept X is a well-formed mental construction of X which controls reasoning. It manifests itself in a characteristic, definite feeling of purpose, in firm certainty of the meaning of X in various contexts, and in robustness of understanding of X in cases of typical cognitive conflicts. Epistemic deep ideas are intersubjective and have been formed in phylogeny whereas individual deep ideas (or deep intuitions) are formed in ontogeny. In certain situations a deep idea may be described in terms of intuition, of meaning or sense, or of understanding, but none of these terms can provide a satisfactory description fitting all cases. (shrink)

This paper explores some variants and aspects of multi-quantificational criteria of existence, examining these in the context of the debate between monism and pluralism in analytical philosophy. Assuming familiarity with the findings to date, we seek to apply to these the newly introduced concepts of “substitution” and “substitutional model”. Possible applications of formal theories involving multiple types of existential quantifier are highlighted, together with their methods of construction. These considerations then lead to a thesis asserting the irrelevance of both multi-quantificational (...) criteria and assumptions involving quantificational ontology to the debate between monism and pluralism in ontology. Many quantifiers cannot properly distinguish different modes of existence–as we aim to show by furnishing a general method for constructing counter-examples to any theory that assumes that different types of existential quantifier correspond to different modes of existence. (shrink)

Brzezinski predicts that the interface between ethics and science will be the new frontier of politics, and it will place on the shoulders of democratic leaders and those concerned with human rights, the obligation to be at least part-time scientists and philosophers.