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)

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)

The article presents and justifies the thesis that the way of understanding knowledge has changed significantly over the last century. This change consists in departing from the classic definition of knowledge formulated by Plato, and in particular in questioning the subjective role of man as the holder of knowledge and abandoning claims to the truthfulness of knowledge. This process was an intensive evolution; its elements are given and justified in the text. Its source was a deep reconstruction of the mode (...) of creating epistemic structures in mathematics and geometry, based on the abandonment of the principle of representation. Knowledge turned out to be determined by the social context, it became dispersed, decentralized, which led to the rejection of the condition of its truthfulness. The last phase of this evolution is knowledge as a phenomenon in the area of digital technologies, in particular artificial intelligence. This evolution has led to the emergence of many variants of knowledge that act as local knowledge, which justifies the use of the plural in this case. (shrink)

W artykule podjęto problem związków zachodzących między retoryką a współczesną antropologią filozoficzną. Głównym punktem odniesienia jest dzieło Hansa Blumenberga. Rekonstrukcja założeń antropologicznych odwołujących się wprost do tradycji retorycznej zostanie uzupełniona analizą jego programu metaforologii – dyscypliny badającej logikę poznania przedpojęciowego. Koncept człowieka jako istoty nacechowanej brakiem – zarówno biologicznymi deficytami, jak i przypadkowością egzystencji, prowadzi do interesującej zmiany paradygmatu rozumienia samej antropologii. Skoro homo defectus zdany jest na prowizoryczność wiedzy o świecie i o sobie samym, antropologia powinna zrezygnować z perfekcjonistycznych (...) roszczeń poznawczych i zwrócić się ku badaniu metaforycznych zasobów języka, które determinują zarówno dyskurs filozoficzny, jak i potoczny język. (shrink)

The question whether I am the same person at different moments has brought many difficulties for a long time. The problem with identity of things through time was already known in the ancient times especially when Plutarch asked whether a ship of Theseus with exchanged elements is still the same ship as before renovation. Today, we continue these considerations asking, for instance, if things, apart from their physical parts, also have temporal parts. The number of the proposed solutions to the (...) problem of identity and identity of persons at different times resembles wandering in a dark room with a scarf on your eyes. As a result, rather than coming closer to the light switch, we find concepts which suggest that personal identity is not important, or what is important is psychological continuity or identity which is only a matter of degree. So I can be the same person as I was in some part, in some degree. It sounds like a constitution person who likes darkness and does not need light anymore. Unfortunately, first of all, we still use successfully the concept of identity in an ordinary language, and what is more, the abandonment of the notion of personal identity results in a greater number of absurdities, so in consequence, we still do not have an idea how to treat personal identity. (shrink)

Inductive reasoning, initially identified with enumerative induction is nowadays commonly understood more widely as any reasoning based on only partial support that the premises give to the conclusion. This is a tad too sweeping, for this includes any inconclusive reasoning. A more moderate and perhaps more adequate characterization requires that inductive reasoning not only includes generalizations, but also any predictions or explanations obtained in absence of suitable deductive premises. Inductive logic is meant to provide guidance in choosing the most supported (...) from a given assembly of conjectures. (shrink)

The relation between indicative conditionals in natural language and material implication wasn’t a major topic in the Lvov-Warsaw school. However, a major defense of the claim that the truth conditions of these two are the same has been developed by Ajdukiewicz. The first major goal of this paper is to present, assess, and improve his strategy. It turns out that it is quite similar to the approach developed by Grice, so our second goal is to compare these two and to (...) argue that the accuracy of Ajdukiewicz’s explanation is less dependent on controversial properties of a systematic but convoluted general theory of cooperative communicative behavior. In Lvov-Warsaw school the relation between material implication and indicative conditionals was also discussed by Goł ąb :27–29, 1949) and Słupecki :32–35, 1949), so the third part of our paper is devoted to their discussion and relating it to Ajdukiewicz’s views. (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)

This article compares two philosophical traditions and their attitudes to war and violence within the context of international relations. The first refers to Hobbes’ political realism, the second to the Grotian idea of international community. Each of these traditions understands the role of violence and war at an international level differently. From the perspective of political realism, violence is part of anarchistic relations between states and a means for achieving their goals. From the perspective of international community, violence is a (...) factor that needs to be minimized via the mechanisms of peaceful international cooperation between states. Based on the analysis of these two approaches, it is claimed that the Hobbesian perspective can be partly included in the perspective of the English School, which is based on the Grotian tradition. (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 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.

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)

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.

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)

Tematem rozważań jest ludzka agresja. Czy agresja jest wrodzona? Jak sposób rozumienia tego, czym jest agresja, wpływa na sposoby radzenia sobie ze szkodliwymi skutkami zachowań agresywnych?

Ksenologie, ed. Ksenia Olkusz i Krzysztof M. Maj, 2018. Kraków: Ośrodek Badawczy.

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.

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)

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)

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)

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)

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)