Chciałem Go pożegnać. Kilkakrotnie próbowałem napisać choć parę słów. O Nim samym. Okazało się, że nie potrafię. Udało mi się tylko przedstawić Jego poglądy na reizm Tadeusza Kotarbińskiego, ale uczyniłem to gdzie indziej. Muszę tu poprzestać na ofiarowaniu Mu tego, co napisałem na Jego dziewięćdziesiąte urodziny, w osiemdziesięciolecie naszej przyjaźni.

The formalist point of view maintains that formal derivations underlying proofs, although usually not carried out in practice, contribute to the confidence in mathematical theorems. Opposing this opinion, the main claim of the present paper is that such a gain of confidence obtained from any link between proofs and formal derivations is, even in principle, impossible in the present state of knowledge. Our argument is based on considerations concerning length of formal derivations. Thanks to Jody Azzouni for enlightening discussions concerning (...) the subject of this paper and to anonymous referees whose important remarks permitted us to correct the arguments and improve presentation. The remaining flaws remain, of course, solely the responsibility of the author. This research was partially supported by NSERC discovery grant and by the Research Chair in Distributed Computing at the Université du Québec en Outaouais. CiteULike Connotea Del.icio.us What's this? (shrink)

This book makes a significant contribution to the standard decision theory, that is, the theory of choice built around the principle of maximizing expected utility, both to its causal version and to the more traditional noncausal approach. The author’s success in clarifying the foundations of the standard decision theory in general, and causal decision theory in particular, also makes the book uniquely suitable for a person whose research in philosophy has led her to want to learn about contemporary decision theory. (...) The book presupposes some mathematical sophistication, and it contains more philosophical and mathematical argumentation per page than may be suitable for an undergraduate level course; but it stands out as an ideal textbook for a graduate-level course focused on the foundations of the standard decision theory. (shrink)

We examine the notion of primitive satisfaction in logical matrices. Theorem II. 1, being the matrix counterpart of Baker's well-known result for congruently distributive varieties of algebras (cf [1], Thm. 1.5), links the notions of primitive and standard satisfaction. As a corollary we give the matrix version of Jónsson's Lemma, proved earlier in [4]. Then we investigate propositional logics with disjunction. The main result, Theorem III. 2, states a necessary and sufficient condition for such logics to be finitely based.

This book is both suitable for logically and algebraically minded graduate and advanced graduate students of mathematics, computer science and philosophy, and ...

CONTENTS:--Reichenbach, H. Elementy logiki formalnej (fragmenty).--Wybrane studia z semiotyki logicznej.

In this paper, confronted are two radical currents of thought about the film image. In a first step, demonstrated is how some Marxist theorists define the film image as ontologically grounded in alienation and the destruction of non-mediated presence due to its technical origin, as well as its effects. In a second step, I try to show how André Bazin, influenced by phenomenology and taking up identical premises as the Marxists, came to diametrically opposite conclusions: it isn’t but the film (...) image that discloses the real. Drawing on the work of Jacques Rancière, Jean-Luc Nancy and Giorgio Agamben, in a third step I establish a certain synthesis between these two currents and examine how spectacle is guarded, but also re-evaluated within the regime of film images. Through this re-evaluation, one gets a glimpse at the contours of an exigent aesthetic program that in some respects conforms to, while also deviating from eminent ideas on cinematic postmodernism. (shrink)

Any finite support iteration of posets with precalibre ℵ 1 which has the length of cofinality greater than ω 1 yields a model for the dual Borel conjecture in which the real line is covered by ℵ 1 strong measure zero sets.

Peter Millican and Branden Thornhill-Miller have recently argued that contradictions between different religious belief systems, in conjunction with the host of defeaters based on empirical research concerning alleged sources of evidence for ‘perceived supernatural agency’, render all ‘first-order’, that is actual, religious traditions positively irrational, and a source of discord on a global scale. However, since the authors recognise that the ‘secularisation thesis’ appears to be incorrect, and that empirical research provides evidence that religious belief also has beneficial individual and (...) social effects, they put forward a hypothesis of a ‘second-order religious belief ’, with Universalist overtones and thus free of intergroup conflict, and free of irrationality, since supported (solely) by the Fine-Tuning Argument. While granting most of their arguments based on empirical research and embracing the new paradigm of the atheism/religion debate implicit in their paper, I contend that Millican’s and Thornhill-Miller’s proposal is unlikely to appeal to religious believers, because it misconstrues the nature and grounds of religious belief. I suggest that their hypothesis may be refined by taking into account a view of axiologically grounded religious belief that I refer to as ‘agatheism’, since it identifies God or the Ultimate Reality with the ultimate good (to agathon). (shrink)

The article begins from a consideration of the relationships between ethics and method, dignity and trustworthiness of the scholar in his normal activity. Then the views of Stanisław Ossowski are presented concerning the conditions of the permanence and development of the normal academic life, and his commandments for the academic professions are quoted safeguarding the normal academic life. A discussion of the question of freedom and responsibility in academic research is combined with Ossowski’s conception of philosophy of science. Ossowski had (...) a conception of the historical mission and function of science. With it was connected a notion of indispensable freedom of the scientists which they must possess to be able to perform their professional tasks normally. Ossowski also had a conception of the duties and professional responsibility of the scientists. The article ends with a review of threats to the normal functioning of science and of the countermeasures that should be used, according to Ossowski, in order to ensure growth of science and unencumbered performance of scholarly tasks. (shrink)

Książka ta jest obszerną pracą o ścisłe historyczno-naukowym charakterze, przedstawiającą życie Stanisława Wydry, jezuity, profesora matematyki na Uniwersytecie w Pradze. Składa się ona z Wprowadzenia i rozdziałów poświęconych: oświeceniu i odrodzeniu narodowemu w Czechach; sytuacji uniwersytetu w Pradze, a w szczególności - Wydziału Filozoficznego; następnie – podręcznikom do matematyki na osiemnastowiecznym uniwersytecie w Pradze; życiu Stanisława Wydry oraz jego pracom naukowym - w tym kilku w szczególności, i wreszcie - jego oddziaływaniu na matematykę i kulturę Czech. Po Dodatku umieszczono wykaz (...) literatury oraz szereg skorowidzów. (shrink)

An ideal I defined on a group G is called idempotent if for every $A \in I, \{g \in G: Ag^{-1} \not\in I\} \in I$ . We show that a countably complete idempotent ideal on an abelian group cannot be prime but may have strong saturation properties.

Gdyby nastał zwyczaj umieszczania słów kluczowych w życiorysach, Jej osobę i życie mogłyby określić: „buntownicza niezależność”, „bojowość”, „odwaga”, „zracjonalizowany radykalizm” i „lakonizm”. Klemens Szaniawski żartował, że Barbara pisze wyłącznie zwięzłe streszczenia swych własnych rozpraw: traktowała to jako komplement; i słusznie. Wspominała te słowa z nie ukrywaną satysfakcją. Niekiedy zwięzłość Jej wypowiedzi działa nieomal hipnotycznie...

Discursive (or discussive) logic, D₂, introduced by Jaśkowski, is widely recognized as a first formal approach to paraconsistency. Jaśkowski applied a quite extraordinary technique at that time to describe his logic. He neither gave a set of the axiom schemata nor presented a direct semantics for D₂ but used a translation function to express his philosophical and logical intuitions. Discursive logic was defined by an interpretation in the language of S₅ of Lewis. The aim of this paper is to present (...) a modified system of the discursive logic that allows some of the weaker versions of Duns Scotus's thesis to be valid. The initial idea is to consider a different characteristic of the connective of negation. We introduce both a direct semantics and an axiomatization of the new system, prove the key metatheorems, and describe labeled tableaux for the system. (shrink)

We propose a new schema for the deduction theorem and prove that the deductive system S of a prepositional logic L fulfills the proposed schema if and only if there exists a finite set A(p, q) of propositional formulae involving only prepositional letters p and q such that A(p, p) L and p, A(p, q) s q.

The paper is conceived as a first study on the Suszko operator. The purpose of this paper is to indicate the existence of close relations holding between the properties of the Suszko operator and the structural properties of the model class for various sentential logics. The emphasis is put on generality both of the results and methods of tackling the problems that arise in the theory of this operator. The attempt is made here to develop the theory for non-protoalgebraic logics.