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)

Gaston Bachelard (1884-1962) was a seminal figure in contemporary French philosophy. Together with Michel Foucault, Georges Canguilhem and Jean Cavailles, he shaped the 'French epistemological' school of philosophy of science. In France, Bachelard is a towering presence; in the English-speaking world, he is little known. Now, Zbigniew Kotowicz gives us the first English language, in-depth presentation of the entire spectrum of Bachelard's work: epistemology, poetic imagination and temporality. And he explores an old philosophical tradition that Bachelard's thought opens up (...) - atomism - a doctrine that has been almost forgotten and is much misunderstood ". (shrink)

The author of this book speaks out again in regard to the Enlightenment. His inspiration comes not only from new observations occasioned by own studies, but also from the recently read material as well as opinions and appraisals of the era articulated lately at academic conferences. Although they have not led the author to perform a fundamental revision of his views in regard to the nature of Enlightenment and its crucial contributions to the Western culture, they did afford a better (...) understanding of its complexity. They also made him more aware that his interpretation and presentation of that era depends considerably on what its prominent representatives had to say, as well as on the worldview-based assumptions and methods of appraisal adopted by its later observers and interpreters. (shrink)

This book focuses on the standards of philosophical rationality, corresponding to a philosophy that aspires to be more than the wisdom that stems from and addresses everyday human needs. It is a search for standards that would, as it were, show the way to philosophical wisdom for anyone who is willing and able to assess it. One of the problems is that people have had a different understanding of the basic concept of rationality, which is the rationale. (Series: Development in (...) Humanities - Vol. 1). (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.

The treatment of Descartes' philosophy within this book takes it to be a specific instance of rationalism. Descartes gave the human intellect the central role in this system; thus, it is considered a variant of an intellectual rationalism.

W artykule tym autor wskazuje zarówno na określone luki pojęciowe w systemie kartezjańskim, jak i wyjaśnia potrzebę wypełnienia tych luk – w przekonaniu autora może się to przyczynić zarówno do większej jasności wypowiedzi Kartezjusza, jak i do ich większej spójności logicznej. Szczegółowo analizuje jedynie dwa z takich pojęć, tj. metodyki i metodologii. Oba mają charakter kategorialny, ale pierwsze z nich jest ogólniejsze niż drugie. Krótko rzecz ujmując, metodyka dotyczyć może zarówno zasad poznawczych, jak i moralnych, wyznaniowych i innych jeszcze, natomiast (...) metodologia tych reguł, które są zalecane i stosowane w którymś z tych obszarów problemowych. Autor przyjmuje również, że z metodyką mamy do czynienia wówczas, gdy mowa jest o czynnościach przygotowawczych do intelektualnego wkroczenia na każdy z tych obszarów myślenia i praktycznego postępowania i poszukujemy tych racji, które sprawiają, że to myślenie i postępowanie staje się racjonalne. Natomiast z metodologią mamy do czynienia wówczas, gdy już znajdujemy się na którymś z tych obszarów i zmierzamy – w sposób racjonalnie zaplanowany – do wytyczonych na nim celów. (shrink)

There is not much disagreement that the recent spectacular establishment of parliamentary democracies and market economies in Eastern Europe and the even more breathtaking events in most Soviet republics – which should culminate in the reemergence of the Baltic nations as independent states – may be convincingly conceived of as the triumph of civil society over the Marxist-Leninist system. Both the collapse of the Marxist-Leninist system and the reemergence of civil society may be discussed in terms of theories which deal (...) with the relationship between human nature and sociopolitical systems. (shrink)

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.

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.