We generalize the Bolzano-Weierstrass theorem on ideal convergence. We show examples of ideals with and without the Bolzano-Weierstrass property, and give characterizations of BW property in terms of submeasures and extendability to a maximal P-ideal. We show applications to Rudin-Keisler and Rudin-Blass orderings of ideals and quotient Boolean algebras. In particular we show that an ideal does not have BW property if and only if its quotient Boolean algebra has a countably splitting family.

We show that in the presence of the torsion tensor \, the quantum commutation relation for the four-momentum, traced over spinor indices, is given by \. In the Einstein–Cartan theory of gravity, in which torsion is coupled to spin of fermions, this relation in a coordinate frame reduces to a commutation relation of noncommutative momentum space, \, where U is a constant on the order of the squared inverse of the Planck mass. We propose that this relation replaces the integration (...) in the momentum space in Feynman diagrams with the summation over the discrete momentum eigenvalues. We derive a prescription for this summation that agrees with convergent integrals: \^s}\rightarrow 4\pi U^{s-2}\sum _{l=1}^\infty \int _0^{\pi /2} d\phi \frac{\sin ^4\phi \,n^{s-3}}{[\sin \phi +U\varDelta n]^s}\), where \}\) and \ does not depend on p. We show that this prescription regularizes ultraviolet-divergent integrals in loop diagrams. We extend this prescription to tensor integrals. We derive a finite, gauge-invariant vacuum polarization tensor and a finite running coupling. Including loops from all charged fermions, we find a finite value for the bare electric charge of an electron: \. This torsional regularization may therefore provide a realistic, physical mechanism for eliminating infinities in quantum field theory and making renormalization finite. (shrink)

Autor stawia w centrum rozważań koncepcję historii Cieszkowskiego i Hessa. "Prolegomena…" Cieszkowskiego wywarły silne wrażenie na Hessie. Autor "Heiligen Geschichte" przejął koncepcję filozofii czynu Cieszkowskiego, która nie ograniczała się do spekulacji, lecz przenosiła nas do sfery społecznej praktyki.

The authors present the main ideas of the computer-assisted proof of Mischaikow and Mrozek that chaos is really present in the Lorenz equations. Methodological consequences of this proof are examined. It is shown that numerical calculations can constitute an essential part of mathematical proof not only in the discrete mathematics but also in the mathematics of continua.

Jak i dlaczego powstał Wszechświat? Problem z naukowym wyjaśnieniem istnienia Wszechświata polega na tym, że zakłada ono pewną fizyczną przyczynę jego istnienia. Ale jakakolwiek fizyczna przyczyna Wszechświata musi być częścią Wszechświata, którego zaistnienie ma wyjaśnić. Z tego powodu każde czysto naukowe wyjaśnienie istnienia Wszechświata jest skazane na zapętlenie. Być może żadna teoria naukowa nie może przerzucić mostu pomiędzy absolutną nicością a istniejącym już Wszechświatem.Okazuje się jednak, że gdy metafizyczne pytanie typu: dlaczego istnieje Wszechświat? zamienimy na „bardziej naukowe”: w jaki sposób (...) powstał Wszechświat?, to mamy szansę na gruncie fizyki przedstawić współczesną wersję „historii” powstania Wszechświata. Kosmolog Lawrence M. Krauss twierdzi, że w tym celu wystarczy porzucić mętne – z punktu widzenia fizyki – pojęcie absolutnej nicości i za punkt wyjścia uznać fizyczną próżnię. Ponieważ – jak wynika z mechaniki kwantowej – kwantowa próżnia to dalece nie to samo co nicość metafizyczna, możliwe jest – w świetle naszej współczesnej wiedzy – powstanie Wszechświata z „niczego”. (shrink)

The author presents Einstein's viewpoint on the issue of the relation between mathematics and the world. Mathematics, as Einstein seems to suggest, cannot model the structure of the world in an absolutely adequate way since, if mathematical theorems are certain, they don't apply to the reality. However from the fact that something cannot be done in an adequate way, it doesn't follow that it can't be done at all. Mathematics can and should be applied to desrcibe the reality, but in (...) such a case its theorems are not certain. Mathematics is a formal science. To be able to state something about the world it must be filled with real meaning - which for Einstein means that mathematical asertions, after a suitable interpretation, must be linked through a network of experimental procedures with the world of nature. Einstein, as it appears, applied these general suggestions to approach the problem of geometry of real space. (shrink)

In the paper there are presented two proposals of the interpretations of the applications of mathematics in the natural sciences - realistic and instrumentalistic. The realistic conception, in accordance with the successes of science, maintains that there exists some kind of correspondence between the mathematical structures and the internal structure of the world. It is expressed in the thesis of the mathematicality of nature. The instrumentalistic approach separates the cognitive content of the scientific theory from the mathematical means of expression (...) of the content. In this approach the mathematical categories do not represent any aspect of the modelled reality. In the final part of the paper the author undertakes such an attempt of approaching the applications of mathematics which, while combining the advantages of the above discussed conceptions, would be devoid of their disadvantages. (shrink)

The paper is an attempt to present the cognitive functions of mathematics in relation to empirical sciences. Firstly - mathematics is a 'generator' of mathematical categories used in natural sciences. In this sense mathematics is a science about the tools of cognition which it creates or perfects. Secondly - mathematics plays the role of 'prism' through which we view the world because some phenomena e.g. from the micro- and macro-world can only be seen through the prism of mathematical structures and (...) notions. And thirdly - mathematics is also a 'selector' of cognitive content. It eliminates from the cognitive field these phenomena which presently can't be grasped by the existing mathematical structures. It is worth noticing that the functions of mathematics: 'selector' and 'prism' are complementary in some sense; although they are opposites ('prism' lets you 'see' something, and 'selector' restricts this 'seeing'), they don't exclude each other. (shrink)

This paper is an attempt to review the historically existing types of demonstration of mathematical theorems. The author shows how the notion of mathematical proof has changed through the time from the moment when mathematicians realised (thanks to the philosophical method) the necessity to justify their theses until a precise notion of proof has appeared in the framework of the formal method. Next, the author considers the possibility of modifying the notion of mathematical proof under the influence of the development (...) of computer sciences. (shrink)

The aim of this paper is a presentation, specification and criticism of the thesis proclaiming the mathematicality of nature. The author distinguishes between the structural and the functional aspects of this thesis. With such an interpretation this thesis has a strong methaphysical interpretation. However such thesis is linked with some problems, concerning the issue of its verification. Therefore the author proposes to consider a neutral thesis proclaiming that nature is amathematical. Then we avoid strong assumptions concerning the structure of the (...) world and better understand not only the successes but also failures of mathematical methods. Besides we gain a new view of the issue of efficacy of mathematical methods in natural sciences. (shrink)

Ostatnie osiągnięcia w kosmologii i fizyce cząstek prowadzą do zaskakujących wniosków. Sugerują istnienie wielu odmiennych – od naszego – wszechświatów. Hipoteza multiwszechświata pojawia się jako wynik rozważań przeprowadzanych zarówno w największej skali na gruncie tzw. teorii wiecznej, chaotycznej inflacji jak i w skali najmniejszej z możliwych – jako wniosek płynący z teorii superstrun, wyartykułowany jako propozycja tzw. kosmicznego „krajobrazu”. Koncepcja multiwszechświata mogłaby w racjonalny sposób wyjaśnić pochodzenie naszego Wszechświata, sposób jego zaistnienia a także szczegóły jego funkcjonowania, w szczególności kwestię jego (...) „dostrojenia” dla rozwoju życia. Ale czy spekulacje na temat wszechświatów, których nigdy nie będziemy mogli zobaczyć oparte na teoriach, które być może nigdy nie będą testowalne empirycznie są jeszcze nauką czy już filozofią? (shrink)

Celem artykułu jest przedstawienie nauczania Kościoła jako wykraczającego poza błędny i rozłączny podział etyki na deontologię i teleologię. Autor przypomina szerokie tło przemian kulturowych, które towarzyszyły kontrowersjom wokół encykliki bł. Pawła VI "Humanae vitae". Teologiczna kontestacja nauczania Magisterium była powodem napisania przez św. Jana Pawła II encykliki "Veritatis splendor". Papież rozwiewa doktrynalne wątpliwości zasiane przez proporcjonalistów, przedstawiając im niezwykle przemyślaną i tradycyjną koncepcję źródeł moralności. Wychodząc od priorytetu celowości ludzkiego działania Papież podkreślił wagę przedmiotu czynu. Dla moralnego dobra ludzkiego czynu (...) konieczne jest jego podwójne właściwe odniesienie: wertykalnie do celu ostatecznego, czyli Boga, oraz horyzontalnie wobec człowieka poprzez przedmiotową zgodność działania z ludzkim dobrem. Papieskie rozważania zostają uzupełnione komentarzem do "Summy Teologii" św. Tomasza, który w analogiczny sposób przedstawia źródła moralności ludzkiego czynu. Rozróżniając wewnętrzny i zewnętrzny akt woli, św. Tomasz pokazuje właściwe źródła moralności każdego z tych aktów. W pierwszym przypadku jest to właściwy przedmiot woli, który jest tożsamy z dobrem; natomiast w drugim – konieczny jest ponadto właściwy przedmiot innych władz. Właściwa antropologia przywraca fundament pod adekwatne rozumienie zarówno prawa naturalnego, jak i potrzebę etyki cnót, która okazuje się wielką praktyczną pomocą dla człowieka w drodze do właściwej mu doskonałości. Przedstawione podstawowe prawdy nauczane od lat przez Magisterium o tyle domagają się przypomnienia, że współczesna dominująca kultura wytrwale dekonstruuje racjonalny porządek tego nauczania czyniąc zeń karykaturę. Papieskie analizy pozwalają oczyścić etyczne kryteria rozeznawania dobra i zła, przypominając o zaproszeniu do piękna teologalnego życia w Chrystusie. Umożliwia ono zdrowy krytyczny osąd konkretnych sytuacji, jak również możliwość uniknięcia rozpowszechnionych współcześnie błędów i wynikającego z nich kryzysu tożsamości. (shrink)

BackgroundThere has been no in-depth research of public attitudes on withholding or withdrawing life-prolonging treatment, euthanasia, assisted suicide and physician assisted suicide in Croatia. The aim of this study was to examine these attitudes and their correlation with sociodemographic characteristics, religion, political orientation, tolerance of personal choice, trust in physicians, health status, experiences with death and caring for the seriously ill, and attitudes towards death and dying. MethodsA cross-sectional study was conducted on a three-stage random sample of adult citizens of (...) the Republic of Croatia, stratified by regions, counties, and locations within those counties. In addition to descriptive statistics, ANOVA and Chi-square tests were used to determine differences, and factor analysis, correlation analysis and multiple regression analysis for data analysis.Results38.1% of the respondents agree with granting the wishes of dying people experiencing extreme and unbearable suffering, and withholding life-prolonging treatment, and 37.8% agree with respecting the wishes of such people, and withdrawing life-prolonging treatment. 77% of respondents think that withholding and withdrawing procedures should be regulated by law because of the fear of abuse. Opinions about the practice and regulation of euthanasia are divided. Those who are younger and middle-aged, with higher levels of education, living in big cities, and who have a more liberal worldview are more open to euthanasia. Assisted suicide is not considered to be an acceptable practice, with only 18.6% of respondents agreeing with it. However, 40.1% think that physician assisted suicide should be legalised. 51.6% would support the dying person’s autonomous decisions regarding end-of-life procedures.ConclusionsThe study found low levels of acceptance of withholding or withdrawing life-prolonging treatment, euthanasia, assisted suicide and physician assisted suicide in Croatia. In addition, it found evidence that age, level of education, political orientation, and place of residence have an impact on people’s views on euthanasia. There is a need for further research into attitudes on different end-of-life practices in Croatia. (shrink)

The central core of this article aims to theorise about the process of theatrical transitions, specifically based on the part dedicated to the “transitions” of Polish theatre in Latin America. The development of the theory begins with a fundamental question: how did and does Polish theatre influence and influence Latin American theatre, and at the same time, what were its points of departure, its routes, its journeys? In this work, the category of “transition” raises several problems. It is defined in (...) two ways, it is both an episteme and a category. Consequently, this research framework will offer to analyse, present and show which are the axes of transition that have marked the perspective of sense and meaning in Latin American theatricality from the 1960s onwards, taking as the object of study for this purpose the influences of Grotowski, Kantor and Mrożek. If so, these broad time frames would predict an “ultimate destiny” that remains to be discovered and that will “allow” us to cover long periods of time in the context of the proposed study. It is necessary to mention that the article will work on two categories of research, namely 1.- The axis present in Genealogy (Foucault): The pass, the transfers, the mechanisms of translation; 2.- On the axis of the theatrical epistemes that organise, reinterpret, distribute the discourses in their respective fields of action. Finally applying the Theory of Transitions, it will be possible to observe and study in detail the starting points, the “scenic routes” that these three creators had on the continent. (shrink)

This article focusses on the meta-literary thread in the correspondence exchanged between Sławomir Mrożek and Wojciech Skalmowski. The latter, wondering about the actual reason why writers create literature, provocatively reduced the metaphysical dimension of a work of art to learn about its contemporary actual value; whether it is was only trade-based. Baudelaire’s work as interpreted by Walter Benjamin became a major context indicating the diversity in the perception of the analysed problem depending on historical time. The article discusses how (...) during his exchange with Skalmowski Mrożek tried to answer the title question about the reason why he created literature, and, which is the most important, how he started focussing on elements which he previously missed or marginalised. (shrink)

The first two sections of the paper draw attention to some incompletely interpreted issues within two Romantic dramas: the unclear status of the protagonist in Dziady, Part IV (on the one hand, representing the indefinability of man and, on the other, constituting the illustration of how lightly one may lose consistency and identity), and the ambiguous relationship between Goplana and Grabiec in Balladyna (which can be perceived in terms of the complex relations between ‘the angelic soul and the bluff head’ (...) (dusza anielska i czerep rubaszny). The third section of notes is an encouragement to discuss two topics: ‘From Zygmunt Krasiński’s Leonard to Jerzy Andrzejewski’s Diego de Manente’; ‘From Pierścień Wielkiej-Damy, czyli: Ex-machina-Durejko by Cyprian Norwid to Tango by Sławomir Mrożek’. (shrink)

Les écrivains montrent leurs expériences, liées avec la lecture, dans: les cours sur la littérature, les traductions de la classique littéraire, les analyses des textes, les notes sur les lectures et les modifications des œuvres. Cet article presente de différents exemples de l’art de la compréhension des textes, des lectures étant la création et la production de tels auteurs, comme: A. Libera, P. Huelle, O. Tokarczuk, S. Mrożek, S. Chwin, K. Lars, V. Nabokov, W. Bąk, J. P. Davidts, J. (...) Updike. (shrink)

The first two sections of the paper draw attention to some incompletely interpreted issues within two Romantic dramas: the unclear status of the protagonist in "Dziady, Part IV", and the ambiguous relationship between Goplana and Grabiec in "Balladyna". The third section of notes is an encouragement to discuss two topics: ‘From Zygmunt Krasiński’s Leonard to Jerzy Andrzejewski’s Diego de Manente’; ‘From "Pierścień Wielkiej-Damy, czyli: Ex-machina-Durejko" by Cyprian Norwid to "Tango" by Sławomir Mrożek’.

On manipulating the meaning of words: the strategy of distorting the meaning of concepts in order to redirect people’s attitudes has been put in practice by ideologists and politicians for years. the paper focuses on the refections of selected thinkers and men of letters on this phenomenon. intellectual contributions of isaiah Berlin, Friedrich a. Hayek, leszek Kołakowski and charles l. stevenson on the one hand, and the considerations of george orwell, aldous Huxley, ayn Rand, sławomir mrożek and małgorzata musierowicz (...) on the other hand are analysed. some recent incarnations of the tactics of perverting the meaning of words in recent political discourse in poland are critically examined. special attention is given to the manipulating the meaning of “paedophilia” in the context of the nationwide discussion on child sexual abuse in the catholic church. it is concluded that the dishonourable practice of verbal misrepresentation used under communism is at work again, this time in even more sophisticated form. (shrink)