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)

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)

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)

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.

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)

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 ...

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 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.

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)

Polish medical law does not explicitly regulate the possibility of off-label use of medicines. Such procedures therefore raise doubts in medical practice, where medicines are often prescribed beyond the Characteristic of Medicinal Product. This phenomenon particularly affects the treatment of children, as there is a lack of registered medicines in this age group, but they are registered for use in adults. Since such treatment goes beyond the scope of registration, a dilemma arises as to whether it is permissible and, if (...) so, under what conditions and whether sanctions are imposed on the medical professional using the off-label medicine. These issues are addressed in an article by Dr Maria Gutowska-Ibbs, entitled 'Off label - practical consequences of unclear legislation". The present study complements these considerations and is in part an ad vocem statement. The article attempts to differentiate between the use of off-label medicines and medical experiments, following the criterion of the purpose for which a given medical action is performed. The limits of admissibility of such actions under criminal law are also discussed in more detail. Off-label treatment is considered through the prism of the required precautionary rules, compliance with which is the antithesis of inadvertence. It is assumed that if the drug was administered in accordance with current medical knowledge and the treatment is adequate to the patient's condition, there is no violation of these rules, which excludes the imputation of inadvertence. An extensive section of the study is devoted to the issue of the patient's consent to treatment outside the indications. Above all, it emphasises the need to explain in detail to the patient the circumstances of prescribing such a drug and, on this basis, to obtain informed consent. It also stresses the importance of the written form of consent, which can have a significant evidentiary impact in potential litigation. (shrink)

In some cases one is provided with inconsistent information and has to reason about various consistent scenarios contained within that information. Our goal is to argue that filtered paraconsistent logics are not the right tool to handle such cases and that the problems generalise to a large class of paraconsistent logics. A wide class of paraconsistent logics is obtained by filtration: adding conditions to the classical consequence operation . We start by surveying the most promising candidates and comparing their strengths. (...) Then we discuss the mainstream views on how non-classical logics should be chosen for an application and argue that none of these allows us to choose any of the filtered logics for action-guiding reasoning with inconsistent information, because such reasoning has to start with the selection of possible scenarios – and such a.. (shrink)

I focus on the monastery life in Europe and its predomination of vita contemplativa upon vita activa. It is not hard to distinguish within Christianity its Manichaean component whose characteristic feature is a grudge against matter, body and sexuality. This complexity of ideas brought about the contempt of vital elements of human existence, so that its animal past, still present in Zivilisationsprozess. An alternative anthropology inspired by an evolutionism should based on the presumption that only through the appreciation of an (...) animal dimension of us—instead of monastic desire of becoming an angel—will it be possible to create new perspectives for renegotiation of the human–animal boundaries. (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 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.

One of the standard views on plural quantification is that its use commits one to the existence of abstract objects–sets. On this view claims like ‘some logicians admire only each other’ involve ineliminable quantification over subsets of a salient domain. The main motivation for this view is that plural quantification has to be given some sort of semantics, and among the two main candidates—substitutional and set-theoretic—only the latter can provide the language of plurals with the desired expressive power (given that (...) the nominalist seems committed to the assumption that there can be at most countably many names). To counter this approach I develop a modal-substitutional semantics of plural quantification (on which plural variables, roughly speaking, range over ways names could be) and argue for its nominalistic acceptability. (shrink)

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)

Philosophy of religion has been the object of penetrating critiques concerning its continued near-complete blindness to all but a single religion. The need for philosophy of religion to open up so as to include more than merely occasional and tokenistic treatments of ‘Other’ religions is clearly evident from the slew of recently published titles concerned with diversifying the field. In this light, a book such as Victoria Harrison’s Eastern Philosophy of Religion should surely come as a welcome addition. And yet, (...) unfortunately, this book turns out to be a case study in how not to diversify philosophy of religion in the twenty-first century. (shrink)

Main task of the paper is to recall sociologist and philosopher – Zygmunt Bauman’s observations and concepts on the fears, anxieties, and uncertainties that appear in the modern world. Main focus was directed to Europe as Bauman was particularly concerned about its future and its role in the global society. The paper is illustrated using current examples from political, social, and economic life to confirm and/or negate Bauman’s concepts. We ask: are fears stable or changeable? Are they stronger or weaker? (...) Are they constant, coming to an end, or are they replaced by new ones? Additionally, we confront Bauman’s concepts with the ideas of other sociologists who applied the interpretative perspective. We define fear following Bauman’s various proposals, and we distinguish many kinds of fears, giving examples from Western societies and socio-economic realities during the time of globalization. We refer to a few relevant sociological concepts to understand Bauman’s view better, e.g. the strategy of detour or the term of generalized other. In conclusions, we state that most fears remain the same (especially ontological ones). However, in the 21st century, we can observe the emergence of new ones (also artificial ones). (shrink)

Recently predominant forms of anti-realism claim that all truths are knowable. We argue that in a logical explanation of the notion of knowability more attention should be paid to its epistemic part. Especially very useful in such explanation are notions of group knowledge. In this paper we examine mainly the notion of distributed knowability and show its effectiveness in the case of Fitch’s paradox. Proposed approach raised some philosophical questions to which we try to find responses. We also show how (...) we can combine our point of view on Fitch’s paradox with the others. Next we give an answer to the question: is distributed knowability factive? At the end, we present some details concerning a construction of anti-realist modal epistemic logic. (shrink)

The essay reviews references to Immanuel Kant’s transcendental philosophy in the work of Helmuth Plessner. First discussed is the Krisis der transzendentalen Wahrheit im Anfang, in which Plessner effects a critique of the transcendental method and shows that overcoming its crisis requires philosophy to rigorously restrict the applicability of theory to the experimental sphere and put it up for judgment by the tribunal of practical reason. Next under scrutiny is Plessner’s programmatic text in philosophical anthropology, in which he strives to (...) employ Kant’s deductive method for the construction of his own system of organic forms. (shrink)

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

The results of the linguistic interpretation should be verified through systemic and purposive methods of interpretation. That process is especially desirable in the cases where the result of the linguistic interpretation is not unequivocal. Whereas, as practice demonstrates, the quality of tax law is not the best, it is impossible to overestimate the role of the non-linguistic method of interpretation. The object of this paper was to present the role which the linguistic interpretation may play in interpreting the tax law. (...) However it was also important to: place the purposive interpretation among the methods of tax law interpretation and to present static and dynamic elements in tax law interpretation. Within the frames of this paper one can find out about historical interpretation of tax law, economic method of tax law interpretation and purposive interpretation directives. The above considerations allow for posit a thesis according to which purposive interpretation is an indispensable element of the process of interpreting a legal text. Its role in the scope of norms of tax law is, however, peculiar, since it serves only to verify the results of linguistic interpretation. However, it can be indicated that the growth in importance of purposive interpretation is direct proportional to the fall in the quality of tax law regulations. (shrink)

The first traces the production of numerous stone tools from the period of the Plio-Pleistocene represent a deep antiquity technical processes in the context of human evolution. Determining cognitive ability needed to convey the first hominids manufacture of stone tools is a challenge for the cognitive archaeology. Currently, thanks to archaeological discoveries and the development of cognitive science we can try to restore all the necessary treatments aimed at the production and use of stone tools along with a broad understanding (...) of their underlying cognitive processes. Analyses based on empirical data derived from Lokalalei – one of the oldest archaeological sites – indicate that the hominids comprehensive understanding of the principles of producing stone tools already at their very beginning. (shrink)

The paper describes the circumstances in which digital technology arises; the change is recognized in the literature as the basis of digital transformation. This transformation is understood as a deterministic economic process. However, the analysis of the deeper circumstances of this process shows that we are dealing with a vast change in the ways of understanding and describing the world, i.e. with an epistemological change. This change concerns, on the one hand, the method of creating general mathematical (including geometric) structures (...) that are the basis of models used to describe the world, and on the other hand—tools for its description, e.g. network theory, systems theory, complexity theory. Such a broadly understood change makes the deterministic description proposed by the digital transformation too simple and shallow. Instead, the concept of predigital transformation is proposed. It includes not only the omitted historical part but also creates better and richer conditions for understanding the digital transformation process, as well as for developing appropriate conceptual tools for its use. (shrink)

This article presents Slavic loanwords in the Austrian variant of the German language. Its aim is twofold: it discusses words of Polish, Slovakian, Czech, Serbo­-Croatian, and Slovenian origin in the Austrian variant of German, as well as stressing the multicultural history of Austria and its influence on vocabulary. The analysis will not only deal with the meaning and etymology of particular words, but will also scrutinize their description in the “Duden” dictionaries: “Deutsches Universalwörterbuch” and “Duden. Wie sagt man in Österreich?”.