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)

This is the first book on the role of cognition in the aesthetic theory of Li Zehou (1930–2021), one of China's most important and influential contemporary philosophers. The cognitive dimension and its integration with practice is discussed by examining one of Li's pivotal concepts: "subjectality," a human subject shaped by the world in which they live, including beauty and aesthetic experience. Li's theory is also contextualized in the threefold inspiration coming from Confucian, Kantian, and Marxist philosophies, which differently conceptualize the (...) aesthetic and cognitive dimensions in humans. By referring to different aesthetic theories and interdisciplinary approaches to cognition, the book aims to show how Li's cognitively oriented project can contribute to contemporary research into aesthetics. Although primarily written for philosophers working in aesthetics, Chinese, and comparative philosophy, the book is also addressed to anyone interested in contemporary Chinese thought. (shrink)

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)

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)

This paper offers a critical reconstruction of the motivations that led to the development of mereology as we know it today, along with a brief description of some problems that define current research in the field.

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)

In this article, I discuss parthood status in mereologi- cally interpreted Daoist metaphysics, based on the Daodejing. I depart from the dao and you interrela- tion, which mereologically overlap by sharing parts. I consider the case of a complete overlap, which (a) challenges proper parthood, according to which a part cannot be identical with the whole that it com- poses, and (b) entails the question of identity that, while complying with classical mereology, cannot be consis- tent with Daoist metaphysics. The (...) discussion leads to abandoning proper parthood and antisymmetry axiom from classical axiomatics. It also shows a plausible fur- ther direction for mereological reconstruction. (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)

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)

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)

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)

Advances in analytical understanding of the biosphere’s biogeochemical cycles have spawned concepts of Gaia and noosphere. Earlier in this century, in concert with the Jesuit paleontologist Pierre Teilhard de Chardin, the natural scientist Vladimir Vernadsky developed the notion of noosphere-an evolving collective human consciousness on Earth exerting an ever increasing intluence on biogeochemical processes. More recently, the chemist James Lovelock postulated the Earth to be a self-regulating system made up of biota and their environment with the capacity to maintain a (...) planetary steady state favorable to life. This is the Gaia hypothesis. To many, Gaia and noosphere represent contradictory interpretations of humanity’s relation to planetary ecology. Noosphere emphasizes a free will and obligation to shape the destiny of humanity on Earth through technology and new kinds of social relations. In contrast, Gaia invokes mysterious mechanisms of planetary evolution that lie beyond human control and understanding. I argue that if brought together, noosphere and Gaia can provide a useful symbol for guiding human interventions in global ecology because the contradictions of a nature-centered view of Gaia and a human-centered view of noosphere are coming to be irrelevant with the emergence of an analytical science of the biosphere. (shrink)

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.

Graham Priest claims that Asian philosophy is going to constitute one of the most important aspects in 21st-century philosophical research. Assuming that this statement is true, it leads to a methodological question whether the dominant comparative and contrastive approaches will be supplanted by a more unifying methodology that works across different philosophical traditions. In this article, I concentrate on the use of empirical evidence from nonphilosophical disciplines, which enjoys popularity among many Western philosophers, and examine the application of this approach (...) to early Chinese philosophy. I specifically focus on Confucian ethics and the study of altruism in experimental psychology. (shrink)

Name der Zeitschrift: Nietzscheforschung Jahrgang: 23 Heft: 1 Seiten: 314-318.

The article presents research into borrowings from German to the Polish language. That research was initiated in the 19th century. German lexical borrowings were linked to other linguistic issues, such as morphology, syntax, phonology or semantic field theory. The most important researcher of German borrowings in Polish were Aleksander Bruckner, Leszek Moszyński, Ludwik Zabrocki, Wilhelm Kästner, Alicja Karszniewicz-Mazur etc. The article is a critical analysis of the most significant publications on this subject.

The video game producers are currently in spotlight of market information services. Successes and huge budgets of such companies attract many readers. However, scientific studies related to this sector do not share the same popularity. A reflection on the source of value in this sector shows that what generates revenues is not disclosed in the report. Great examples are customers’ relationships or the value of employees creating the game code and story of the game. Video games producers sector presents a (...) good combination of business and culture that allows reflection on financial characteristics of knowledge based companies. Prior studies show that market’s valuation takes into account unrecognised assets but capital-intensive character of a production and intangibility of a product and its assets causes problems with exact valuation. In this paper the author asks about the impact of the characteristics on the assessment of a financial condition. The research question in this paper is whether it is possible to use and interpret correctly popular discriminant analysis model for knowledge based entities on the example of video game companies. Results are applicable by analysts and managers of this sector and help to determine the usefulness of this method, but it still depends on assumptions and accounting policies. The reflection presented also broadens the discussion on financialisation because analysed companies can oppose this trend in a specific way. (shrink)

With material on his early philosophical views, his contributions to set theory and his work on nominalism and higher-order quantification, this book offers a uniquely expansive critical commentary on one of analytical philosophy’s great ...

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)

Let $\mathcal {I}$ be an ideal on $\omega $. For $f,\,g\in \omega ^{\omega }$ we write $f \leq _{\mathcal {I}} g$ if $f(n) \leq g(n)$ for all $n\in \omega \setminus A$ with some $A\in \mathcal {I}$. Moreover, we denote $\mathcal {D}_{\mathcal {I}}=\{f\in \omega ^{\omega }: f^{-1}[\{n\}]\in \mathcal {I} \text { for every } n\in \omega \}$ (in particular, $\mathcal {D}_{\mathrm {Fin}}$ denotes the family of all finite-to-one functions).We examine cardinal numbers $\mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathcal {I}} \times \mathcal {D}_{\mathcal (...) {I}}))$ and $\mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathrm {Fin}}\times \mathcal {D}_{\mathrm {Fin}}))$ describing the smallest sizes of unbounded from below with respect to the order $\leq _{\mathcal {I}}$ sets in $\mathcal {D}_{\mathrm {Fin}}$ and $\mathcal {D}_{\mathcal {I}}$, respectively. For a maximal ideal $\mathcal {I}$, these cardinals were investigated by M. Canjar in connection with coinitial and cofinal subsets of the ultrapowers.We show that $\mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathrm {Fin}} \times \mathcal {D}_{\mathrm {Fin}})) =\mathfrak {b}$ for all ideals $\mathcal {I}$ with the Baire property and that $\aleph _1 \leq \mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathcal {I}} \times \mathcal {D}_{\mathcal {I}})) \leq \mathfrak {b}$ for all coanalytic weak P-ideals (this class contains all $\bf {\Pi ^0_4}$ ideals). What is more, we give examples of Borel (even $\bf {\Sigma ^0_2}$ ) ideals $\mathcal {I}$ with $\mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathcal {I}} \times \mathcal {D}_{\mathcal {I}}))=\mathfrak {b}$ as well as with $\mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathcal {I}} \times \mathcal {D}_{\mathcal {I}})) =\aleph _1$.We also study cardinals $\mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathcal {J}} \times \mathcal {D}_{\mathcal {K}}))$ describing the smallest sizes of sets in $\mathcal {D}_{\mathcal {K}}$ not bounded from below with respect to the preorder $\leq _{\mathcal {I}}$ by any member of $\mathcal {D}_{\mathcal {J}}\!$. Our research is partially motivated by the study of ideal-QN-spaces: those cardinals describe the smallest size of a space which is not ideal-QN. (shrink)

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)

This article is devoted to the problem of ontological foundations of three-dimensional Euclidean geometry. Starting from Bertrand Russell’s intuitions concerning the sensual world we try to show that it is possible to build a foundation for pure geometry by means of the so called regions of space. It is not our intention to present mathematically developed theory, but rather demonstrate basic assumptions, tools and techniques that are used in construction of systems of point-free geometry and topology by means of mereology (...) and Whitehead-like connection structures. We list and briefly analyze axioms for mereological structures, as well as those for connection structures. We argue that mereology is a good tool to model so called spatial relations. We also try to justify our choice of axioms for connection relation. Finally, we briefly discuss two theories: Grzegorczyk’s point-free topology and Tarski’s geometry of solids. (shrink)