'The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite.' David Hilbert (1862-1943). This interdisciplinary study of infinity explores the concept through the prism of mathematics and then offers more expansive investigations in areas beyond mathematical boundaries to reflect the broader, deeper implications of infinity for human intellectual thought. More than a dozen (...) world-renowned researchers in the fields of mathematics, physics, cosmology, philosophy, and theology offer a rich intellectual exchange among various current viewpoints, rather than a static picture of accepted views on infinity. The book starts with a historical examination of the transformation of infinity from a philosophical and theological study to one dominated by mathematics. It then offers technical discussions on the understanding of mathematical infinity. Following this, the book considers the perspectives of physics and cosmology: Can infinity be found in the real universe? Finally, the book returns to questions of philosophical and theological aspects of infinity"--Provided by publisher. (shrink)

This article presents a new model aimed at predicting behavior in games involving a randomized allocation procedure. It is designed to capture the relative importance and interaction between procedural justice (defined crudely in terms of the difference between one’s expected payoff and average expected payoff in the group) and distributive justice (difference between own and average actual payoffs). The model is applied to experimental games, including “randomized” variations of simple sequential bargaining games, and delivers qualitatively correct predictions. In view of (...) the model redistribution of income can be seen as a substitute for vertical social mobility. This contributes to the explanation of greater demand for redistribution in European countries vis-a-vis the United States. I conclude with suggestions for further verification of the model and possible extensions. (shrink)

De Dreu and Gross (D&G) seem to have disregarded some relevant experimental literature on games of conflict, most notably variations on “matching pennies” games. While in such games, “attacker” and “defender” are typically not explicitly labelled, players’ differentiated roles yield naturally to such notions. These studies partly validate some of D&G's findings and interpretations.

Apart from the Treaty of human nature, political philosophy of David Hume's not systematic. This fact is probably associated with Hume's skepticism, disbelief in the philosophical, abstract synthesis, which necessarily reduces the complexity of the world to just one aspect. Most distinct evidence of this belief are philosophical essays, often recognized for popularizing some of the ideas contained in the Treaty. Popularization of the former no doubt, but there were also more than that. Hume They analyzed human reason and morality (...) in a very broad historical context. Essays are full of details taken from the history of culture, politics and the economy in both England and the ancient peoples. Greeks and Romans had for special esteem for Hume, and ancient historians considered it his pattern, moreover, does not mean that he was against them uncritically. (shrink)

This article is a short presentation of the problem of individual liberty – as we understand it today – in the context of the problematic of Goodness in Plato’s philosophy of politics as presented in his two main political dialogues: the Republic and the Laws. The crucial distinction is for me dichotomy: negative vs. positive liberty as defined by Isaiah Berlin following Benjamin Constant. In this article I also consider to what extent justifiable is liberal critique of Plato as a (...) totalitarian. At the end of the text I suggest that the best interpretation of Plato’s vision would be its treatment not so much as a strictly political one but rather as a program of education of the soul based on specific understanding of politics derived from Plato’s anthropology. (shrink)

Celem przeprowadzonych badań jest próba oceny sposobu funkcjonowania Uniwersytetu Trzeciego Wieku działającego na Uniwersytecie Rolniczym w Krakowie w latach 2019–2022 w kontekście wykorzystania w procesie kształcenia narzędzi cyfrowych. Na podstawie zebranych danych i przeprowadzonej analizy podjęto próbę uzyskania odpowiedzi na następujące pytania badawcze: Jaka formuła została wówczas przyjęta, jeśli chodzi o sposób prowadzenia wykładów, organizowania uroczystości akademickich i innych wydarzeń naukowych oraz kulturalnych w okresie obowiązujących restrykcji sanitarnych spowodowanych pandemią SARS-CoV-2? Jaka była aktywność słuchaczy podczas zastosowania nowych metod i technik (...) kształcenia? Czy narzędzia cyfrowe, wdrożone wówczas w celu realizacji zadań, znalazły zastosowanie po zniesieniu obowiązkowych restrykcji sanitarnych? (shrink)

We discuss circumscription, a logical formalization of non-monotonic reasoning, introduced by John McCarthy and Vladimir Lifschitz. First section contains presentation of assumptions of logic-based artificial intelligence, problem of non-monotonicity in commonsense reasoning and informal formulation of circumscription. In section two, a formal definition of circumscription is given. The idea of circumscription is discussed from syntactic and semantic point of view. Theoretical investigations are supplemented with examples. In section three, methods of computing circumscription are discussed. Section four contains exemplary circumscription-based formalization (...) of simple non-monotonic reasoning. Finally, not only a comment about the role of logic in artificial intelligence is made but a piece of information about implementation of circumscription is given as well. (shrink)

Akademickie rozważania dotyczące twórczości i statusu twórcy w XXI wieku nie mogą ominąć tak istotnego pola rozważań, jak internet i pokrewne mu nowe technologie. Celem niniejszego artykułu jest prześledzenie przemian społecznych w zakresie twórczości, przyczyn i przejawów tych przemian. Autorzy przywołują najnowsze koncepcje teoretyczne związane z twórczością, wskazując na ich podstawie nowe formacje społeczne korzystające z (re)demokratyzacji procesu twórczego dzięki upowszechnieniu dostępu do Internetu. W pracy omówione zostały takie zagadnienia, jak demokratyzacja twórczości w sieci, twórczość oddolna i partycypacyjna nierówność. Autorzy (...) wskazują, dlaczego sieciowi twórcy – elita użytkowników Internetu, nazywana digitariuszami, prosumentami bądź netokratami – są grupą o specjalnym znaczeniu i godną szczególnej uwagi. (shrink)

Internal audit provides an independent and objective opinion to the Board on risk management, control and governance, by measuring and evaluating their effectiveness in achieving an organisation’s agreed objectives. It also provides an independent and objective consultancy service to help line management improve the organisation’s processes. Internal auditors should respect in their work some ethical rules, especially these included in the Code of Ethics formed by the IIA. This code is intended to clarify the standard of conduct expected from all (...) members of the internal audit unit. The main four principles that should be observed are as follows: integrity, objectivity, competency and confidentiality Being ethical in internal audit is necessary in order to win the trust of the environment in which auditors work. However, declaring one’s readiness to respect the Code of Ethics is not enough. Much more important is to implement and comply with given rules in carrying out audit duties. (shrink)

The main purpose of the article is to compare the originally Greek, Plato\'s concept of dialogue and its function in the procedure of philosophying to the one developed by the 20-century \"philosophy of dialogue\" (F. Rosenzweig, M. Buber, F. Ebner, E. Levinas). It seems quite astounding that philosophy of dialogue, a trend which consistently and persistently defends the privileged position of dialogue in the structure of reality and uses it as an essential factor in the understanding of the relation between (...) God and Man, has not developed any solid methodological perspective. What is even worse, it failed to observe its presence in the very core of philosophical thinking, i.e. in Plato\'s thought. We are capable of reconstructing Plato\'s modus philosophandi with its essential conditions: the philosopher must not only \'see\' the truth (the noetical function), but must also tell it to the others, choose the partners of the dialogue and defend his logos if necessary (the apophantical function). The article consists of two complementary analyses: the first one is devoted to the presentation of the dialogical factor in Plato\'s noetics and apophantics, and the second one focuses on Rosenzweig\'s criticism of the whole European philosophy. The author tries to indicate its doubtful moments by -putting forward the question whether Plato\'s philosophy may be justly ascribed to the tradition under Rosenzweig\'s criticism, and if so, to what extent. (shrink)

After several decades during which diagrams were neglected as a reliable source of mathematical knowledge, in recent years we have witnessed a revival of interest in the role of diagrams in mathematical cognition. In the paper, I consider how those investigations relate to the concept of spatial intuition and its role in mathematical cognition. It is argued that some characteristics of mathematical cognition that involve the use of diagrams are analogous with characteristics usually attributed to intuitive knowledge, above all the (...) immediacy of access to the analyzed object that in-tuition is said to deliver. First of all, this is due to the special characteristics of dia-grams, such as their structural similarity to the mathematical object represented and their ability to convey a lot of information. However, it is argued that the immediacy of mathematical cognition related to diagrams should not cancel the necessity to use concepts or reasoning, which are in fact indispensable in mathematical practice. Sev-eral other possible ways of using the concept of “intuition” are then indicated. One of them is connected with the common distinction between “intuition that” and “intuition of”. Visual “intuition that” is a mathematical belief that appears in us as a result of a visual contact with a diagram, and visual “intuition of” a mathematical object may appear when we have a tendency to visualize this object while thinking or reasoning with it (this may be the case with objects like a triangle, graph, lattice, as well as number line). Finally, it is stressed that many analyses of the use of diagrams and visualization in mathematics completely dispense with the use of the term “intuition”. (shrink)

Niniejszy tekst podejmuje kwestię bogów i bohaterów mitów greckich, odnosząc ją do obecnej w psychologii głębi koncepcji archetypów i nieświadomości zbiorowej. Główny cel badań sprowadza się tym samym do bacznego przyjrzenia się potencjalnej korelacji pomiędzy zewnętrznymi w rozumieniu starożytnego Greka postaciami bogów i bogiń, a wewnętrznymi przejawami nieświadomości zbiorowej, które mogą stanowić – według Carla Gustava Junga – istotę antycznych bóstw. Ponadto został poddany namysłowi problem wpływu „wewnętrznych bogów” na sposób myślenia, odczuwania i działania jednostki, wpływu zarówno pozytywnego, jak i (...) negatywnego. Wynikająca z przeprowadzonych badań konkluzja zwraca uwagę na wartość sfery irracjonalnej – źródła pochodzenia zapomnianych, politeistycznych bogów, zamieszkujących psychikę współczesnego człowieka. ---------------------- Zgłoszono: 14/04/2022. Zrecenzowano: 11/05/2022. Zaakceptowano do publikacji: 30/05/2022. (shrink)

The subject of responsibility has lately become very important in the context of the economic crisis. In economy, it took the form of social responsibility. It concerns activities additionally undertaken by organizations in order to establish correct relations with their employees and society, as well as with regard to the natural environment. Therefore, a very important role is played by the ethos of the undertaken socially responsible actions. To a large extent it is reflected in the ethical dimension. Thus, in (...) enterprises, codes of ethics have become a base of axiology in building of the organization cultures. Unfortunately, Polish companies – as shown in the paper – still attach a minor role to the ethical dimension of business. (shrink)

Officials in a democratic state should be its society's loyal servants, bound to respect the law. They are also bound to be loyal for the supervisors, and obedient to their orders. The Author analyzes legal regulation concerning conflicts which arise from that „double loyalty” of the officials, especially when the orders they are given contradict legal regulation or principles of ethic they find binding.

‘FORGIVING’ IN DERRIDA’S PHILOSOPHY OF MEETING, OR ON ETHICS AS AN FUNCTION OF LANGUAGE Ethics, which became a central point of the late works by Jacques Derrida, is a peculiar project within works of this scholar. Even an observation that the ‘deconstruction’ was solely an initial epistemological procedure, whose aim was to force its way through tissue of appropriating discourses, in order to make it available for ethics to exist from the beginning, once again, does not exhaust the risen issue. (...) Ethics, as interpreted by Derrida, is based on the categories of the philosophy of meeting – first of all in the Levinas’ version – but is in no way exhausted within its classical interpretations. A reason for such a situation is a high status given to a language by the author of the ‘Margins of Philosophy’. The philosophy of meeting, according to him, takes place in words, gestures and events, which dialoging is an introduction to construction of a fundamental ethic situation, i.e. the moment of meeting. One of such keywords is ‘forgiving’ – that becomes not only a signal of openness to accept the other, but also a communicative slogan, creating a horizon of ethics. It turns out that an ability of ‘forgiving’ is a basic condition. Through meeting it we can give each other a hand, and overcome the surrounding walls and entanglements. This is the feature of ‘forgiving’, where Derrida sees a basic chance for survival of the most precious values of our culture. (shrink)

Extending the ideas from (Hofer-Szabó and Rédei [2006]), we introduce the notion of causal up-to-n-closedness of probability spaces. A probability space is said to be causally up-to-n-closed with respect to a relation of independence R_ind iff for any pair of correlated events belonging to R_ind the space provides a common cause or a common cause system of size at most n. We prove that a finite classical probability space is causally up-to-3-closed w.r.t. the relation of logical independence iff its probability (...) measure is constant on the set of atoms of non-0 probability. (The latter condition is a weakening of the notion of measure uniformity.) Other independence relations are also considered. (shrink)

Współcześni tomiści usiłują wykazać zgodność metafizyki arystotelesowsko-tomistycznej z teorią makroewolucji biologicznej. W ostatnim czasie stanowisko takie poparł Dr Mariusz Tabaczek. Jednak przyznaje on, że naukę Tomasza należy zmodyfikować w istotny sposób, aby można ją było pogodzić z teistycznym ewolucjonizmem. W jego ujęciu główny punkt takiej modyfikacji stanowi kwestia tego, czy stworzenie się zakończyło, czy nadal powstają nowe gatunki. W istocie ewolucyjny postulat powstawania nowych gatunków uderza nie tylko w naukę Tomasza, ale klasyczne chrześcijańskie rozumienie stworzenia. Tomistyczni ewolucjoniści nie potrafią wyjaśnić (...) pochodzenia nowych form substancjalnych. Odwołują się do zmian przypadłościowych, takich jak przypadkowe mutacje genetyczne, których kumulacja miałaby prowadzić do powstania nowych gatunków. To jednak nie jest możliwe w świetle metafizyki tomistycznej, ponieważ zmiana przypadłościowa nie tworzy nowej substancji. Dodatkowo koncepcja tomistycznych ewolucjonistów nie harmonizuje z wieloma faktami odkrywanymi przez współczesną biologię. Tomistyczni ewolucjoniści muszą porzucić fundamentalne pojęcia filozofii św. Tomasza, takie jak złożenie bytowe substancja-przypadłości czy umiarkowany realizm. Nie da się więc pogodzić makroewolucji biologicznej z nauką Akwinaty. (shrink)

This article discusses the question of the presence of the category of the family in the media, which most often operate as commercial enterprises these days. At the same time the influence of media communication on the family is underlined. The analysis results in distinguishing between two ways of presenting and treating the family in media broadcasting. The first – objective – resembles the authentic nature and character of this basic social group, while the second – subjective – distorts the (...) image and uses the category of the family as merely material for an producing media offer of any kind. Among other issues, stress is put on the business model of media enterprises, which seriously influences the social communication character of mass media, which results, for example, in the transformation of information into a commodity and the media public into customers. (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)

We present a short account of the early history of the Center for Interdisciplinary Research in Cracow. These beginnings go back to the inter-war period when the tradition was established of close interactions between philosophers and scientists, especially physicists (Smoluchowski, Natanson). In the post-war period, under the communist regime, this tradition was continued at the Theological Institute (later the Pontifical Academy of Theology) in Cracow, erected by Cardinal Wojtyła, the then archbishop of Cracow, after the Theological Faculty had been removed (...) from the Jagiellonian University by the communists. The collaboration of the Cracow Center with the Catholic University of Lublin and with the Warsaw Academy of Theology is briefly described, and the style of philosophy in Cracow presented. (shrink)

W artykule przedstawiono możliwość zastosowania Ricoeurowskich wzorców tożsamości osobowej: charakteru i dochowanego słowa do rozjaśnienia dialektyki bycia sobą samym oraz bycia kimś/czymś innym. W tym celu przedstawiono powiązania nowych wzorców z tradycyjnymi modelami tożsamości ujmowanymi jako bycie tym samym i bycie sobą. Ukazano zdolności bycia sobą do wykraczania poza wzorzec bycia tym samym, ujawniające się w analizach charakteru i dochowanego słowa oraz umożliwiające ukonstytuowanie „tego, który jest sobą samym”. Opisano również rolę inności, która wykraczając poza aspekty tożsamości „tego, który jest (...) sobą samym” umożliwia konstytucję „tego, który jest sobą samym, jak i kimś/czymś innym”. (shrink)

SUFFERING, ANUISH, DISTRESS: THE DESTRUCTIVE EROS IN THE WORK OF FYODOR DOSTOEVSKY My paper discusses the idea of destructive eroticism in the work of Fyodor Dostoevsky. Eros is posited here as manifesting in two, opposite forms: the Christian virtue of agape consisting in a humble service to a beloved person, and the Greek eros which in Dostoevsky is transformed into destructive love, one steeped in egoism and sadistic-masochistic impulses. I want to argue that destructive eroticism is for Dostoevsky of greatest (...) interest, while love conceived as agape serves in his work only as a minor, normative projection, a tribute paid to the Russian Orthodox worldview. In my analysis I refer to Georges Bataille’s philosophical thought to combine the pattern of unfulfilled and ruinous love in Dostoevsky with his conviction that irrational aspects of man, his penchant to evil and transgression can be seen as a measure of the intensity and authenticity of one’s spiritual life. Contrary to religious interpretations of Dostoevsky, I argue that the author of Crime and Punishment prefers to cast his protagonists into the limbo of suffering, anguish and distress and therefore he ultimately rejects the possibility that human beings can content themselves with a mediocre life in which existential complacency is bought at a price of resignation from dangerous passions of which one could say that were “worth a life”. (shrink)

A first impulse to write this article came from noticing, while reading Descartes' "Meditations", that author gives different meaning to the idea of "doubt" in each part of book. In First Meditation "doubt" has a function of a unique method of research, first step to build new, strictly rational and scientific knowledge – in contrast to the former collection of unjustified and un-proved or even false conceptions. Therefore "doubt" has positive value. So why does Descartes in his evidence of God's (...) existence in Third Meditation, talks about "doubt" as if it were imperfection and weakness of human nature? As if it were something worthless and part of "nothingness"? The only way to resolve this contradiction is to consider thoroughly what the role of "doubt" is in each part of "Meditations". Then, it will be clear that in Descartes' "Meditations" problem of knowledge is strictly attached to problem of existence, and how order of cognition changes without notice into cognition of Divine Order. (shrink)

The aim of this thesis is to describe contemporary cultural problems in Europe using the category of historiosophy developed by Feliks Koneczny. The author discusses the division of civilisations in Europe as described by Koneczny and his ‘historical laws’ which concern mutual relations between these civilisations. Nowadays, Europe is an area where five civilisations mix. One of them has appeared in Europe due to the mass migration of the Muslim population. According to Koneczny, there can be no synthesis between civilisations (...) and only a mixture of civilisations can emerge which will lead to an anti-civilisational status or a war. The current situation in Europe requires serious correction. The paper refers to a multi-civilisational phenomenon that was the Polish‑Lithuanian Commonwealth. Its two main pillars were a strong identity of the state and respect for civilisational minorities. The model of the Polish-Lithuanian Commonwealth seems to be the best solution for the present problems of the European Union. (shrink)