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)

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)

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)

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)

Regions-based theories of space aim—among others—to define points in a geometrically appealing way. The most famous definition of this kind is probably due to Whitehead. However, to conclude that the objects defined are points indeed, one should show that they are points of a geometrical or a topological space constructed in a specific way. This paper intends to show how the development of mathematical tools allows showing that Whitehead’s method of extensive abstraction provides a construction of objects that are fundamental (...) building blocks of specific topological spaces. (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)

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)

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.

According to contrastivism in epistemology - advocated chiefly by Jonathan Schaffer - the knowledge relation is not binary (s knows that p) but ternary (s knows that p rather than q). Thus knowledge ascriptions are contrast-sensitive. The aim of this paper is to portray, investigate and assess the details of this view. In the first three sections I focus mainly on arguments for contrastivism. Section fourth is devoted to the contrastivist solution to the skeptical puzzle. In the last three sections (...) I present several problems for contrastivism as well as three main binary explanations for contrast-sensitivity. (shrink)

Two fundamental features of a liberal political community are usually identified in contemporary deliberations: there is an inevitable pluralism of visions of good and worthy life, blended into a wide range of religious, philosophical and ethical positions; those who are in power are under an obligation to set public matters in such a way as to avoid discrimination of any class of the ruled. In respect of and, it is presumed that the process of enacting, implementing and executing public law (...) shall be separated from any perfectionist moral position, because being impartial when making political decisions is a prerequisite for non-discriminatory politics. This kind of politics looks for proper, convincing and comprehensible reasons to establish a new legal standard of behaviour in the ‘public reason’ – a set of moral statements and political values commonly shared in an open, pluralistic and tolerant society, which does not provide decisive answers to any questions about the meaning of life and does not bring us closer to discover its ideal. This article tries to reproduce the main notions and ideas of leading, contemporary liberal philosophers – John Rawls and Charles Larmore – that deal with the very nature of impartiality of a liberal state and the ability of policymakers to be impartial. It also presents the critical views of Stephen Macedo and Nicholas Wolterstorff, who question the possibility of building a neutral state. (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 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.

The goal is to sketch a nominalist approach to mathematics which just like neologicism employs abstraction principles, but unlike neologicism is not committed to the idea that mathematical objects exist and does not insist that abstraction principles establish the reference of abstract terms. It is well-known that neologicism runs into certain philosophical problems and faces the technical difficulty of finding appropriate acceptability criteria for abstraction principles. I will argue that a modal and iterative nominalist approach to abstraction principles circumvents those (...) difficulties while still being able to put abstraction principles to a foundational use. (shrink)

One of the standard axioms for Boolean contact algebras says that if a region __x__ is in contact with the join of __y__ and __z__, then __x__ is in contact with at least one of the two regions. Our intention is to examine a stronger version of this axiom according to which if __x__ is in contact with the supremum of some family __S__ of regions, then there is a __y__ in __S__ that is in contact with __x__. We study (...) a modal possibility operator which is definable in complete algebras in the presence of the aforementioned axiom, and we prove that the class of complete algebras satisfying the axiom is closely related to the class of modal KTB-algebras. We also demonstrate that in the class of complete extensional contact algebras the axiom is equivalent to the statement: _every region is isolated_. Finally, we present an interpretation of the modal operator in the class of the so-called _resolution contact algebras_. (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)

This is a spin-off paper to [3, 4] in which we carried out an extensive analysis of Andrzej Grzegorczyk’s point-free topology from [5]. In [1] Loredana Biacino and Giangiacomo Gerla presented an axiomatization which was inspired by the Grzegorczyk’s system, and which is its variation. Our aim is to compare the two approaches and show that they are slightly different. Except for pointing to dissimilarities, we also demonstrate that the theories coincide in presence of axiom stipulating non-existence of atoms.

A family $$\mathcal {I}$$ I of subsets of a set X is an ideal on X if it is closed under taking subsets and finite unions of its elements. An ideal $$\mathcal {I}$$ I on X is below an ideal $$\mathcal {J}$$ J on Y in the Katětov order if there is a function $$f{: }Y\rightarrow X$$ f : Y → X such that $$f^{-1}[A]\in \mathcal {J}$$ f - 1 [ A ] ∈ J for every $$A\in \mathcal {I}$$ A (...) ∈ I. We show that the Hindman ideal, the Ramsey ideal and the summable ideal are pairwise incomparable in the Katětov order, where The Ramsey ideal consists of those sets of pairs of natural numbers which do not contain a set of all pairs of any infinite set (equivalently do not contain, in a sense, any infinite complete subgraph), The Hindman ideal consists of those sets of natural numbers which do not contain any infinite set together with all finite sums of its members (equivalently do not contain IP-sets that are considered in Ergodic Ramsey theory), The summable ideal consists of those sets of natural numbers such that the series of the reciprocals of its members is convergent. (shrink)

The author of the article reconstructs the aesthetic motives in Arnold Gehlen’s project of philosophical anthropology. The first part of the essay presents the process of emerging of artistic creativity from ritual-presenting actions. In the second part author elaborates the conception of abstract art, which Gehlen treats as a specific laboratory in which artists explore the possibilities of deep, previously undiscovered layers of human perception.

Wittgenstein’s philosophy endeavored to define the role of language as communicative. Language became an original “code” of multifarious meanings and designations but it is also a code which entails emotions and different sorts of internal and external reactions of an individual. The mechanism of penalty and the notion of penalty have invariably raised emotions and meaningful reactions. The analysis focuses on a short derivation of the notion of penalty. It considers its functions, basic tasks and external impact—a short word revealing (...) so many actions and social behaviors. (shrink)

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)

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)

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)

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)

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)

David Lewis has formulated a well-known challenge to his Best System account of lawhood: the content of any system whatever can be formulated very simply if one allows for perverse choices of primitive vocabulary. We show that the challenge is not that dangerous, and that to account for it one need not invoke natural properties or relativized versions of the Best System account. This way, we help to move towards an even better Best System account. We discuss extensions of our (...) strategy to the discussions about the indexicality of the notion of laws of nature, and to another trivialization argument. (shrink)

Karol Wojtyła—the future pope John Paul II—chose the human being, especially in its personalistic dimension, as the main point of his philosophical research. Inaccordance with the metaphysical rule agere sequitur esse, he investigated the dynamisms proper to a human being: the reactive dynamism of the human body, the emotive dynamism of the human psyche, and the personalistic dynamism associated with free choice of the will. These allowed him to experience and understand the human being as a complex yet integrated entity. (...) The personal structure of the human being is manifest in terms of selfpossession, self-determination, and self-governance. Thanks to self-possession, human beings experience freedom of the will, which expresses itself in each free act. Being endowed with a free will, the human being is able to grow in freedom but can also lose his freedom. Wojtyła’s philosophical investigations are innovative by way of the use that he made of the philosophy of being according to Thomas Aquinas and the philosophy of consciousness articulated by Husserl. He not only pointed out man’s structure but also presented man as an objective entity in an objective world. Each human being is constituted by his or her inner self, which is absolutely exceptional because it is completely irreducible to anything else in the world. (shrink)

Abstract:This article is concerned with the role of Buddhist philosophy, and more broadly of non-Western philosophies, within the discipline of philosophy as this is professed and practiced today. I begin by deliberately engaging in a game of definitions to demonstrate that, whichever of the definitions standardly employed to deny non-Western philosophy the prestigious moniker, Buddhism nevertheless wins: it does count as philosophy. Having made that point, however, I go on to effectively undermine it by pointing out that anyone can win (...) the game if they get to make up the rules. Given that the score is arbitrary, then, I show up the game itself as absurd. On this basis, I ultimately cry foul at the perpetuation of a game still so plainly played on fields far from level, and therefore argue against excusing philosophers engaged in it of the charge of racism. (shrink)

In 2021, there was a significant amendment to the legislation on medical experimentation. In particular, Chapter 4 of the Law of December 5, 1996 on the Profession of Physician and Dentist (Journal of Laws 2023, item 1516) was amended, in which the prerequisites of legally relevant consent given by the participant in the experiment or by other entities that express a position on their behalf were specified. In addition, procedures related to the opinion of the research project by the so-called (...) bioethics committee were described. Its members were obliged to maintain confidentiality with regard to information obtained in connection with the fulfilled function. These norms became protected by criminal sanctions, set forth in the amended Article 58 of the law. New generic types of criminal acts were introduced, primarily aimed at protecting the participant's right to self-determination, the voluntariness of participation in the experiment, and the confidentiality of data submitted by the experimenters in their proposals to bioethics committees. These norms fill in the gaps that have existed so far in the criminal law protection of these values. The article systematically discusses the generic types of criminal acts that have been penalized in Article 58 (4) to (6) of the referenced law. Their object of protection, object side, subject, subject side, punishability and potential confluence with other regulations are presented. The historical-dogmatic justification for the introduction of these regulations is also shown. (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 proposes a minimalist concept of autonomy that is consistent with determinism, but negates fatalism. Drawing on Nicolai Hartmann’s stratified ontology, it argues that autonomy is achieved not by suspending physical laws, but by introducing new, higher-level determinations unique to individual entities. The tension between general laws and individual autonomy is resolved by emphasizing the unique properties and individual laws that apply to each entity. The article also explains how this minimal autonomy makes sense of setting goals and attempting (...) to achieve them, demonstrating that even within a deterministic framework, individuals can have meaningful influence over their actions and outcomes. (shrink)