The purpose of this paper is to compare the notion of a Grzegorczyk point introduced in [19] (and thoroughly investigated in [3, 14, 16, 18]) to the standard notions of a filter in Boolean algebras and round filter in Boolean contact algebras. In particular, we compare Grzegorczyk points to filters and ultrafilters of atomic and atomless algebras. We also prove how a certain extra axiom influences topological spaces for Grzegorczyk contact algebras. Last but not least, we do not refrain from (...) a philosophical interpretation of the results from the paper. (shrink)

This is the first, out of two papers, devoted to Andrzej Grzegorczyk’s point-free system of topology from Grzegorczyk :228–235, 1960. https://doi.org/10.1007/BF00485101). His system was one of the very first fully fledged axiomatizations of topology based on the notions of region, parthood and separation. Its peculiar and interesting feature is the definition of point, whose intention is to grasp our geometrical intuitions of points as systems of shrinking regions of space. In this part we analyze separation structures and Grzegorczyk structures, and (...) establish their properties which will be useful in the sequel. We prove that in the class of Urysohn spaces with countable chain condition, to every topologically interpreted representative of a point in the sense of Grzegorczyk’s corresponds exactly one point of a space. We also demonstrate that Tychonoff first-countable spaces give rise to complete Grzegorczyk structures. The results established below will be used in the second part devoted to points and topological spaces. (shrink)

Legal probabilism is the view that juridical fact-finding should be modeled using Bayesian methods. One of the alternatives to it is the narration view, according to which instead we should conceptualize the process in terms of competing narrations of what happened. The goal of this paper is to develop a reconciliatory account, on which the narration view is construed from the Bayesian perspective within the framework of formal Bayesian epistemology.

This article proposes a mereological approach to the dao-you relation in the Daodejing. It is claimed here that dao and you can be conceived of as two integrated subregions, defined in terms of rules of composition and their persistence through time. It is shown that dao is an atemporal object (a fourdimensional unrestricted composition), whereas you is a temporal object (a three-dimensional restricted composition). This particular approach can provide a new understanding of essential issues in Daoist metaphysics.

As it is indicated in the title, this paper is devoted to the problem of defining mereological (collective) sets. Starting from basic properties of sets in mathematics and differences between them and so called conglomerates in Section 1, we go on to explicate informally in Section 2 what it means to join many objects into a single entity from point of view of mereology, the theory of part of (parthood) relation. In Section 3 we present and motivate basic axioms for (...) part of relation and we point to their most fundamental consequences. Next three sections are devoted to formal explication of the notion of mereological set (collective set) in terms of sums, fusions and aggregates. We do not give proofs of all theorems. Some of them are complicated and their presentation would divert the reader’s attention from the main topic of the paper. In such cases we indicate where the proofs can be found and analyzed by those who are interested. (shrink)

Provability logics are, roughly speaking, modal logics meant to capture the formal principles of various provability operators or predicates.

The first installment of a paper comparing the standard slingshot argument with the doxastic version.

One of the streams in the early development of set theory was an attempt to use mereology, a formal theory of parthood, as a foundational tool. The first such attempt is due to a Polish logician, Stanisław Leśniewski . The attempt failed, but there is another, prima facie more promising attempt by Jerzy Słupecki , who employed his generalized mereology to build mereological foundations for type theory. In this paper I situate Leśniewski's attempt in the development of set theory, describe (...) and evaluate Leśniewski's approach, describe Słupecki's strategy without unnecessary technical details, and evaluate it with a rather negative outcome. The issues discussed go beyond merely historical interests due to the current popularity of mereology and because they are related to nominalistic attempts to understand mathematics in general. The introduction describes very briefly the situation in which mereology entered the scene of foundations of mathematics — it can be safely sk.. (shrink)

The aim of this article is to identify the main challenges for global ethics as an academic discipline. This article assesses the moral and practical justifications for common global principles. Individual and institutional responsibility on the supranational level is connected with the standard of human rights and the relational aspects of the globalised world. It also points out two separate problems which global ethics should aim to solve. The first is metatheoretical and methodological and concerns the discipline's lack of self-reflexiveness. (...) The second is essential and concerns the clash of values . Regarding the second problem, the main future challenge of global ethics is to construct a measurement to bring political decisions closer to morality and more strongly connect rights with responsibilities. (shrink)

In the second installment to Gruszczyński and Pietruszczak we carry out an analysis of spaces of points of Grzegorczyk structures. At the outset we introduce notions of a concentric and \-concentric topological space and we recollect some facts proven in the first part which are important for the sequel. Theorem 2.9 is a strengthening of Theorem 5.13, as we obtain stronger conclusion weakening Tychonoff separation axiom to mere regularity. This leads to a stronger version of Theorem 6.10. Further, we show (...) that Grzegorczyk points are maximal contracting filters in the sense of De Vries, but the converse inclusion is not necessarily true. We also compare the notions of a Grzegorczyk point and an ultrafilter, and establish several properties of topological spaces based on Grzegorczyk structures. The main results of the paper are representation and completion theorems for G-structures. We prove both set-theoretical and topological representation theorems for various classes of G-structures. We also present topological object duality theorem for the class of complete G-structures and the class of concentric spaces, both restricted to structures which satisfy countable chain condition. We conclude the paper with proving equivalence of the original Grzegorczyk axiom with the one accepted by us as axiom. (shrink)

Safety and care for the natural environment are two of the most important values that drive scientific enterprise in twentieth century. Researchers and innovators often develop new technologies aimed at pollution reduction, and therefore satisfy the strive for fulfilment of these values. This work is often incentivized by policy makers. According to EU directive 2006/40/EC on mobile air conditioning since 2013 all newly approved vehicles have to be filled with refrigerant with low global warming potential. Extensive and expensive research financed (...) by leading car manufacturers led to invention of R-1234yf refrigerant with GWP < 1, which was huge improvement. For the proper understanding of this case it will be useful to refer it to the idea of responsible innovation, which is now being developed and quickly attracts attention. I proceed in the following order. Firstly, I present the relevant properties of R-1234yf and discuss the controversy associated with its marketing. Secondly, I examine framework for responsible innovation. In greater detail I discuss the notions of care for future generations and collective responsibility. Thirdly, I apply the offered framework to the case study at hand. Finally, I draw some conclusions which go in two directions: one is to make some suggestions for improving the framework of RI, and the second is to identify missed opportunities for developing truly responsible refrigerant. (shrink)

The paper is devoted to the analysis of two seminal definitions of points within the region-based framework: one by Whitehead (1929) and the other by Grzegorczyk (Synthese, 12(2-3), 228-235 1960). Relying on the work of Biacino & Gerla (Notre Dame Journal of Formal Logic, 37(3), 431-439 1996), we improve their results, solve some open problems concerning the mutual relationship between Whitehead and Grzegorczyk points, and put forward open problems for future investigation.

This article investigates the structures of an identifiably Buddhist philosophy of religion, understood as the philosophical exposition and exploration of Buddhist religiosity. I thus theorize what forms a philosophy of religion structured according to Buddhist principles and paradigms might take, address various theoretical and methodological considerations, and survey a range of candidate schemas, which latter are arranged under textual, sectarian, and doctrinal rubrics. Overall, this project is undertaken on the understanding that the study of Buddhism, among other global traditions, need (...) not and should not replicate conceptual structures imposed upon it from without, and that philosophy of religion is enriched by attention to the resolutely plural philosophies of religions worldwide. (shrink)

Nagarjuna (c. 150-250), founder of the Madhyamaka or Middle Way school of Buddhist philosophy and the most influential of all Buddhist thinkers aside from the Buddha himself, concludes his masterpiece, Fundamental Verses on the Middle Way, with these baffling verses: -/- For the abandonment of all views He taught the true teaching By means of compassion I salute him, Gautama -/- But how could anyone possibly abandon all views? In Buddhism between Religion and Philosophy, Rafal K. Stepien shows not only (...) how Nagarjuna's radical teaching of no-view or “abelief” makes sense within his Buddhist philosophy, but also how it stands at the summit of his religious mission to care for all living beings. Rather than treating any one aspect of Nagarjuna's ideas in isolation, here his metaphysics, epistemology, and ethics emerge as a single coherent and convincing philosophical-religious system of thought and practice. -/- Grounded in meticulous study of original texts from classical India and China but innovating on the theories and methods underpinning contemporary scholarship East and West, this study shows how profoundly important voices from the diverse religious and philosophical traditions of the world have until now been diminished, distorted, and silenced. In opening up truly global horizons of existing and co-existing in the world, this work challenges the very ways in which we think about religion and philosophy. (shrink)

This article departs from a mereological conceptualization of the Daoist metaphysi- cal system in the Daodejing 道德經. I discuss what parthood status applies to dao 道. Whereas it is quite intuitive that you 有—the region of concrete objects—has parthood relationships and compositions (entities made from parts), the other, undif- ferentiated region, dao, poses a considerable problem. This problem can be charac- terized in the following way: (a) dao cannot be characterized as a particular com- position, which entails that it does (...) not include parts. However, (b) dao underpins compositions in you, which entails that it contains compositions or at least parts that make compositions in you. This generates a problem of how compositions are possi- ble with an undifferentiated ontological foundation. I focus on one possible approach to this problem––mereological nihilism, according to which no composition is pos- sible. Assuming nihilism entails dao composed of mereological simples––funda- mental entities, which are not parts. (shrink)

The present paper puts forward a first outline of a possible agonistic theory of adjudication, conceived of as an extension of Chantal Mouffe’s agonistic theory of democracy onto the domain of the juridical, and specifically, judicial decision-making. Mouffe’s concept of the political as the dimension of inherent and unalienable conflicts (antagonisms) which, nonetheless, need to be tamed for a pluralist democracy to function, creates an excellent vantage point for a critical theory of adjudication. The paper argues for perceiving all judicial (...) decisions as having a double nature—juridical and political. Cloaked in legal form, judgments nonetheless decide on individual instances of on-going collective conflicts, opposing workers to employers, consumers to traders, tenants to landlords, moral progressives to traditionalists, minorities to majorities and so forth. Judges, when handing down judgments, enjoy a ‘relative sovereignty’, being always already inscribed into the institutional imperatives of the juridical, on one hand, and ideological influences, on the other, but at the same time called upon to decide in the terrain of the undecidable and contingent (after all, law does not ‘apply itself’ on its own). Indeed the determinacy of legal decisions is only relative: in many cases judges can, by performing a sufficient amount of legal interpretive work, reach a conclusion which will be different from theprima facieinterpretation. The collective conflicts of a various nature (economic, ideological, socio-political), once they are juridified, become the object of judicial decisions which, in light of Mouffe’s theory, can be seen as temporary hegemonic fixations. The goal of critical legal scholarship is to destabilise such hegemonies in the name of justice. This can be done not only through an external critique of the law, but also through an internal one. The methodological approach advanced in the latter part of the paper emphasises the need for a critique of judicial decisions based on the consideration of all possible alternative decisions a court could have reached, and their evaluation in the light of conflicting interests and ideologies. (shrink)

Author: Michalski Rafał Title: IN SEARCH OF PARADISIAC NAMES – PHILOSOPHICAL ANTHROPOLOGY AND THE PROBLEM OF ORIGIN OF LANGUAGE (W poszukiwaniu „rajskich imion” – antropologia filozoficzna wobec problemu genezy języka) Source: Filo-Sofija year: 2006, vol:.6, number: 2006/1, pages: 101-117 Keywords: WALTER BENJAMIN, HERDER, GEHLEN, ORIGINS LANGUAGE Discipline: PHILOSOPHY Language: POLISH Document type: ARTICLE Publication order reference (Primary author’s office address): E-mail: www:The article deals with the problem of origin of an individual, particular speech and its relation to the language (...) of intersubjective communication. Paradisiac names – the term used by Walter Benjamin – are words which release suppresed semantic potentiality originated in the early phase of childhood. The author of the article shows the way J.G. Herder and A. Gehlen make clear this phaenomen in their conceptions of anthropology. (shrink)

This paper aims to formalize Galileo’s argument against the Aristotelian view that the weight of free-falling bodies influences their speed. I obtain this via the application of concepts of parthood and of mereological sum, and via recognition of a principle which is not explicitly formulated by the Italian thinker but seems to be natural and helpful in understanding the logical mechanism behind Galileo’s train of thought. I also compare my reconstruction to one of those put forward by Atkinson and Peijnenburg (...) :115–136, 2004), and propose a formalization which is based on a principle introduced by them, which I shall call the speed is mediative principle. (shrink)

Legal institutions are created at a certain point in time, intended to be applied to ‘life’ as it is perceived at the specific moment when they are elaborated and cast into legal form. As a result, legal institutions always already refer, in their original design, to a certain normality, but between the moment of creation of a legal institution and its application to future situations there is always a certain time lag. Some legal institutions—referred to in the paper as “legal (...) survivals” –outlive the epoch in which they were created and continue their legal life long after the conditions which lead to their creation had, in the meantime, disappeared. The aim of this paper is to put forward an archaeologico–genealogical perspective on legal survivals not only as a method of studying continuity of law and the resilience of juridical form, but also as a line of enquiry capable of enriching our understanding of the juridical in its relation to the changing circumstances of life. The study of legal survivals allows to combine three aspects of legal continuity: firstly, the continued use of the same legal forms in different circumstances and for different purposes, whereby the same juridical form is filled with different socio-economic substance; secondly, the gradual adaptation of legal forms to new circumstances; thirdly, the emergence of new legal forms in close reference to old ones. The study of legal survivals allows to address the foundations of law’s claims to authority, based on stability and predictability of juridical forms. It also reveals the complex and multilayered nature of legal form which effectively has the structure of a palimpsest. (shrink)

The aim of this paper is to articulate dispositonal essentialism (DE) as a viable position in the discussions considering properties and laws of nature. In the first part of the article there are given several „must have” trades of properties in DE. They are followed by the conceptions themselves. The last part of the article brings a little insight about ceteris paribus laws in DE.

Niniejszy artykuł został poświęcony charakterystyce poglądów wybranych scholastyków i dekretalistów z XIII wieku dotyczących kwestii spożywania w poście słodkich wyrobów aptekarzy, zwanych po łacinie _electuaria_, w angielskiej literaturze przedmiotu znanych jako _electuary_. Autor omówił to zagadnienie, opierając się na analizie fragmentów dzieł autorstwa: Wilhelma z Auxerre (_Summa aurea_, znanym też jako _Summa in IV Sententiarum_), Aleksandra z Hales (_Summa teologii_), Tomasza z Akwinu (_Komentarz do czterech ksiąg Sentencji Piotra Lombarda_ (łac. _Scriptum super libros Sententiarum_) i _Summa teologii_), Innocentego IV (_Commentaria (...) super libros quinque decretalium_) oraz Henryka z Ostii (znanego jako Hostiensis, _Apparatus in Decretales_). Poglądy poszczególnych autorów niniejszej kwestii były zbieżne i sprowadzały się do stwierdzenia, że spożycie elekwarzy w poście jest dopuszczalne, o ile będą traktowane jako słodycze. Każdy z wymienionych autorów używał nieco odmiennych argumentów. I tak Wilhelm z Auxerre wskazał, że przyjmowanie powidełek leczniczych, choć prowadzi do złamania postu, nie skutkuje utratą zasługi, tj. nagrody do życia wiecznego. Aleksander z Hales dokonał analizy typologicznej produktów spożywczych i podzielił je na cztery kategorie, takie jak: lekarstwa, właściwa żywność, lekarstwa pokarmowe i żywność lecznicza. Elekwarze zostały zaliczone do grupy trzeciej i z tego względu mogły być spożywane w poście. Święty Tomasz z Akwinu podkreślił znaczenie czynnika ilościowego i roli walorów smakowych jako kryteriów oceny dopuszczalności spożywania elekwarzy w czasie postu. Zaś zarówno Innocenty IV, jak i Henryk z Suzy (Hostiensis) uwypuklili jedyny warunek spożycia powidełek leczniczych w czasie postu, jakim jest choroba. W konkluzji autor dochodzi do wniosku, że uwaga wybitnych przedstawicieli ówczesnej myśli teologicznej, jak i prawniczej, poświęcona zagadnieniu dopuszczalności spożywania w poście elekwarzy, czyli słodkich wyrobów aptekarskich, stanowiła odpowiedź na zmieniającą się wówczas rolę tego typu wyrobów aptekarskich. Traktowane uprzednio jako lekarstwa na różne dolegliwości (na ogół o podłożu gastrycznym), stawały się słodyczami jedzonymi dla przyjemności i w nadmiarze. Tym samym ich przyjmowanie w czasie postu, czyli umartwiania, rodziło istotny dylemat moralny. W zgodnej opinii zarówno scholastyków, jak i dekretalistów zostały one uznane jako medykamenty i jako takie mogły być przyjmowane w poście. W efekcie ten typ wyrobów aptekarskich, obok kontektów (łac. _confectes_), na trwałe wszedł do menu postnego u schyłku średniowiecza. Co więcej, postrzegane jako produkty postne, cieszyły się rosnącą popularnością, niezależnie od uwarunkowań ówczesnej medycyny, jak i poglądów myślicieli i dekretalistów z XIII wieku. (shrink)

Le scepticisme de Montaigne a jusqu'à présent dominé le débat sur la portée philosophique des Essais. C'est pourtant le concept épicurien du plaisir qui oriente la pensée philosophique tout entière de Montaigne. En tant que force motrice principale régissant les actions humaines, le plaisir constitue en effet la seule mesure des choses, le tamis par lequel doit passer tout contenu existentiel, quelle que soit sa nature: religieuse, philosophique ou passionnelle.

This article presents German loanwords in the Polish language. Its aim is twofold: to discuss words of German origin in Polish, as well as to stress Polish-German language contacts and their influences on vocabulary. The analysis will not only deal with the meaning and etymology of particular words, but will also scrutinize their description in the dictionaries of Polish edited by Doroszewski and Sobol.

Working memory training has recently become one of the most debated issues in the field of cognitive psychology. Since working memory is considered a strong correlate of IQ, numerous researchers have been trying to increase the latter by training the former. Proven effectiveness of working memory training could lead to its application in the therapy of many cognitive impairments. WMT could be also used as a tool of improving cognitive functioning of healthy subjects. However, almost every publication claiming to provide (...) evidence for achieving one of above mentioned objectives has been criticised, mostly because of methodological shortcomings. The aim of my presentation is to extract potential sources of inconsistencies existing between the authors of meta-analysis and reviews of WMT research. For this reason I take a closer look at results and conclusions of several meta-analysis and reviews. As a result I point few indications that should be taken into consideration in future studies on WMT effectiveness. (shrink)

El artículo es una recensión del autor del libro Crimen Obicere: Retórica forense y correspondencia antidonatista de Agustín (2020), presentado cómo los elementos esenciales de la retórica que Cicerón había recogido en su obra De inventione marcaron no solo la formación sino también la obra de san Agustín. Se expone la teoría de los status así como los diferentes tipos de status o contitutiones que enuncia el mismo Cicerón. Posteriormente se aplica dicha teoría a las cartas antidonatistas de san Agustín (...) para demostrar cómo el Hiponate usó diversos status en su discusión con los donatistas y cómo el marco retórico es imprescindible para entender mejor la obra de los Padres de la Iglesia y en particular la de san Agustín. (shrink)

This is the third installment of a paper which deals with comparison and evaluation of the standard slingshot argument (for the claim that all true sentences, if they refer, refer to the same object) with the doxastic formulation.