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)

This is the translation of Protagoras' life from Diogenes Laertius' "Lives of eminent Philosophers" (IX, 8).

The paper examines the interest of the Sophists in the problems of the Pre-socratic philosophy of nature.

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)

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.

L'auteur a l'intuition que Descartes avait directement lu, autant, voire plus que les thomistes, saint Augustin ; mieux, malgré ou en vertu de sa réticence à l'avouer, il en avait aussi subi l'influence indirecte, sous le poids des débats théologiques et philosophiques de son temps. Une série de rapprochements entre les textes canoniques de Descartes et certains passages de saint Augustin.

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)

Protagoras u Sekstusa Empiryka (PH I 216) a platoński Teajtet Dzieła Sekstusa Empiryka stanowią ważne źródło doksograficzne, zawierając m. in. fragmenty i przekazy poświęcone sofistyce. Są wśród nich omówienia poglądów Protagorasa. W świetle problemów, jakie stwarza rekonstrukcja myśli tego sofisty, warto poddać badaniu źródła i perspektywę Sekstusa, zwracając szczególną uwagę na krótkie przedstawienie tez Protagorasa zawarte w Zarysach Pyrrońskich (PH I 216). Porównując omówienie Sekstusa i przedstawienie Platona w Teajtecie, dostrzec możemy podobieństwo prezentowanych poglądów. W przekazie Seksusa podobnie jak w (...) Teajtecie główny akcent położony jest na tezę homo-mensura, z którą wiąże się dwa inne podstawowe dla platońskiego dialogu wątki: zmienności rzeczy oraz "prywatności" spostrzeżeń. Mimo charakterystycznej dla sceptycyzmu modyfikacji strony pojęciowej, nadinterpretacji oraz wyrwania tez z dialogowego kontekstu przedstawienia obu wątków wykazują daleko idące paralele z Teajtetem. Bez względu na to, czy omówienie to jest dziełem samego Sekstusa, czy zaczerpnięte zostało z jakiegoś wcześniejszego źródła mającego charakter sceptycznej "ściągawki", możemy na jego podstawie wnioskować, że dialog Teajtet uważany był w późnej starożytności za wiarygodne źródło informacji na temat poglądów Protagorasa. Należy jednak podkreślić, że przekaz Sekstusa stanowi jedynie interpretację treści zawartych w platońskim Teajtecie i – wbrew praktyce wielu uczonych - nie może być brany pod uwagę jako niezależne źródło wiedzy o myśli Protagorasa. (shrink)

The paper is devoted to the sophistic method of "two-fold arguments" (antilogic). The traditional understanding of antilogic understood as an expression of agonistic and eristic tendencies of the sophists has been in recent decades, under the influence of G.B. Kerferd, replaced by the understanding of antilogic as an independent argumentative technique, having its own sources, essence, and goals. Following the interpretation of G.B. Kerferd, according to which the foundation of the antilogic is the opposition of two logoi resulting from contradictions (...) or opposites, necessarily associated with the contradictory character of the sensual world, in the paper it is argued that the philosophical basis of antilogic should be sought in the presentation of the views attributed to Protagoras and "adherents of flux" in Plato's dialogue Theaetetus. (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)

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.

Jednym z elementów współczesnej kultury są seriale telewizyjne, w przeważającej mierze charakteryzujące się brakiem jakichkolwiek wartości artystycznych oraz intelektualnych. Do nielicznych pod tym względem należy serial pt. Dr House. Centralną kwestią w tym serialu jest postawa moralna głównego bohatera. Krytycy dostrzegli w niej wiele analogii do moralności Nietzscheańskiego nadczłowieka. W artykule podjęto próbę ukazania, że w moralności dr House'a odzwierciedla się Nietzscheański model estetyzacji moralności, polegający na tym, że kryterium etycznej słuszności czynów jest wolność jednostki i jej autonomiczność w kształtowaniu (...) swego życia jako dzieła sztuki. (shrink)

This is the translation and interpretation of the Gorgias' speech from Plato's dialogue Gorgias (456A1-457C3). In the commentary it is argued that the Gorgias' speech in the dialogue is based on the philosophical and rhetorical motives which can be found both in Gorgias' epideictic speeches ("Helen" and "Palamedes") and doxographical accounts.