The article discusses the concept of progressive and degressive proportionality of the distribution of parliamentary seats. In the first part are presented axiological sources of the principles of proportionality and progressive and degressive proportionality and the history of degressively proportional apportionments of seats in the European Parliament. The main part of the article is devoted to the formulation of proposals for strict formal definition of degressive and progressive proportionality, and a description of the method of apportionment of seats in the (...) European Parliament based on the strict definition of degressive proportionality and maintaining maximum compatibility with former apportionments adopted in multilateral negotiations. The last part of the article consists of a discussion of the possibilities of adopting the concept of progressive proportionality in the analysis of the functioning of parliamentary electoral systems. (shrink)

Jacek Urbaniec: Platonism in the philosophy of mathematics does not necessarily imply that there are links between the temporal physical world and the eternal world of mathematics..

The purpose of the paper is to rethink the role of actuality in the branching model of possibilities. We investigate the idea that the model should be enriched with an additional factor—the so-called Thin Red Line—which is supposed to represent the single possible course of events that gets actualized in time. We believe that this idea was often misconceived which prompted some unfortunate reactions. On the one hand, it suggested problematic semantic models of future tense and and on the other, (...) it provoked questionable lines of criticism. We reassess the debate and point to potential pitfalls, focusing on the semantic dimension of the Thin Red Line theory. Our agenda transcends the semantics, however. We conclude that semantic considerations do not threaten the Thin Red Line theory and that the proper debate should be carried in the domain of metaphysics. (shrink)

In this paper we present a characterization of hyper-connexivity by means of a relating semantics for Boolean connexive logics. We also show that the minimal Boolean connexive logic is Abelardian, strongly consistent, Kapsner strong and antiparadox. We give an example showing that the minimal Boolean connexive logic is not simplificative. This shows that the minimal Boolean connexive logic is not totally connexive.

We prove that no logic (i.e. consequence operation) determined by any class of orthomodular lattices admits the deduction theorem (Theorem 2.7). We extend those results to some broader class of logics determined by ortholattices (Corollary 2.6).

The papers in this issue were first assembled for the American Academy of Religion conference in 2022 to consider Søren Kierkegaard's analysis of the media environment of his day and the relevance of his perspective to both traditional and new media today. Each author takes a different approach to Kierkegaard's ethics of mass communication, but all agree that his ideas still retain a great deal of applicability in a vastly different media environment.

Let J be any proper ideal of subsets of the real line R which contains all finite subsets of R. We define an ideal J * ∣B as follows: X ∈ J * ∣B if there exists a Borel set $B \subset R \times R$ such that $X \subset B$ and for any x ∈ R we have $\{y \in R: \langle x,y\rangle \in B\} \in \mathscr{J}$ . We show that there exists a family $\mathscr{A} \subset \mathscr{J}^\ast\mid\mathscr{B}$ of power ω (...) 1 such that $\bigcup\mathscr{A} \not\in \mathscr{J}^\ast\mid\mathscr{B}$ . In the last section we investigate properties of ideals of Lebesgue measure zero sets and meager sets in Cohen extensions of models of set theory. (shrink)

The aim of this note is to give an example of application of model theory to the theory of logical matrices. . More precisely, we show that Wojtylak's representation theorem is an immediate consequence of a result due to Mal'cev . Throughout the present note we assume that matrices, and classes of matrices under consideration are of the same xed similarity type. Suppose that K is an arbitrary class of matrices, and M is a matrix . We say that M1 (...) 2 K is called a replica of M in the class K i there is a homomorphism h of M onto M1 such that for every homomorphism g of M into arbitrary N 2 K there exists a homomorphism f of M1 into N such that g = f h. (shrink)

The present paper is to be considered as a sequel to [1], [2]. It is known that Johansson's minimal logic is not uniform, i.e. there is no single matrix which determines this logic. Moreover, the logic C J is 2-uniform. It means that there are two uniform logics C 1, C 2 (each of them is determined by a single matrix) such that the infimum of C 1 and C 2 is C J. The aim of this paper is to (...) give a detailed description of the logics C 1 and C 2. It is performed in a lattice-theoretical language. (shrink)

The aim of this book is to present essays centered upon the subjects of Formal Ontology and Logical Philosophy. The idea of investigating philosophical problems by means of logical methods was intensively promoted in Torun by the Department of Logic of Nicolaus Copernicus University during last decade. Another aim of this book is to present to the philosophical and logical audience the activities of the Torunian Department of Logic during this decade. The papers in this volume contain the results concerning (...) Logic and Logical Philosophy, obtained within the confines of the projects initiated by the Department of Logic and other research projects in which the Torunian Department of Logic took part. (shrink)

t. 1. Etyka ogólna -- t. 2, cz. 1-2 Etyka szczegółowa.

The first part of the paper is a reminder of fundamental results connected with the adequacy problem for sentential logics with respect to matrix semantics. One of the main notions associated with the problem, namely that of the degree of complexity of a sentential logic, is elucidated by a couple of examples in the second part of the paper. E.g., it is shown that the minimal logic of Johansson and some of its extensions have degree of complexity 2. This is (...) the first example of an exact estimation of the degree of natural complex logics, i.e. logics whose deducibility relation cannot be represented by a single matrix. The remaining examples of complex logics are more artificial, having been constructed for the purpose of checking some theoretical possibilities. (shrink)

The objective of this paper is to discuss current reductive theories of the non-existent objects, specifically - contemporary deflationary theories of the fictional objects. By such theories I mean those denying that fictional objects have any ontological status at all. Theories, which claim that fictional proper names denote some sort of objects but deny that these names denote individual objects, are treated as the reductive theories of non-existent as well. In the discourse I present the following ideas: 1) Russell's theory (...) of description with the further remarks by W. V. O. Quine; 2) A. Plantinga's view that the fictional names have no denotation, which is realized in the framework of possible worlds semantics; 3) Theories by N. Wolterstorf and P. van Inwagen which can be seen as a link between strictly deflationary theories and meinongian theories; Wolterstorff claim that empty names denote general abstract objects and Inwagen identify fictional objects with theoretical objects of literal criticism; 4) Theories based on the speech acts theories; 5) Theories which identify fictional objects with mental objects. The conclusion of the argument is that the aforementioned theories are not adequate for the analysis of fiction (non-existent) and that more suitable for such a purpose are meinongian theories of non-existent objects. (shrink)

Punktem wyjścia rozważań są cztery hipotezy: dwie leksykalne, gramatyczna i historyczna: 1. Wyrażenie „rozumieć" jest polisemem i to podwójnie: a) wieloznacznością właściwą wielu predykatom mentalnym (tj. może mieć w szczególności sens aktualny, habitualny, sekwencyjny lub procesualny); b) wieloznacznością swoistą (tj. może w szczególności mieć sens intuicyjny, identyfikacyjny, indulgencyjny lub inskrypcyjny). 2. Wyrażenie „rozumieć” w sensie identyfikacyjnym występuje w kontekstach eliptycznych (może mieć wówczas sens esencjalny, strukturalny, funkcjonalny, kauzalny, kategorialny lub konceptualny). 3. Wszelkie (niemetaforyczne) konteksty i derywaty wyrażenia „rozumieć" dadzą się (...) sparafrazować za pomocą wprowadzonych rozróżnień. 4. Różnice zdań w sprawie rozumienia albo biorą się z pomieszania znaczeń, albo są empirycznie testowalne. Przedstawione hipotezy pozwalają usunąć nieporozumienia, dotyczące kolejno: argumentów relacji rozumienia, kategorii semantycznej „rozumienia", relacji między poszczególnymi pojęciami „rozumienia" oraz. między rozumieniem a innymi funkcjami mentalnymi, warunkami poprawności definicji „rozumienia konceptualnego", na koniec kryteriów kompetencji językowej. (shrink)

Review of the book: Człowiek na granicy istnienia. Dyskusje o śmierci mózgowej i innych aspektach umierania, Grzegorz Hołub, Piotr Duchliński, Akademia Ignatianum w Krakowie, Wydawnictwo WAM, Kraków 2017.

Niniejszy artykuł stanowi polemikę z esejem Saula Smilansky’ego pt. O wątpliwej warości moralnej pewnych rozpowszechnionych form modlitwy. Według Smilansky’ego niektóre modlitwy prośby, a zwłaszcza modlitwy o czyjeś dobra kosztem kogoś innego, są niemoralne. Zgadzam się, że nie każda modlitwa jest moralnie akceptowalna, lecz jednocześnie argumentuję, że jego uzasadnienie tej tezy zakłada lub zawiera fałszywe przesłanki. W szczególności formułuję cztery zastrzeżenia (lub zarzuty) wobec jego argumentu: (i) punktem wyjścia filozofii modlitwy powinny być nie prywatne przekonania filozofa, lecz (w przypadku braku empirycznej (...) wiedzy o modlących się ludziach) ortodoksja lub ortopraksja określonej religii (zastrzeżenie metodologiczne); (ii) modląca się osoba (zwłaszcza w trudnej sytuacji życiowej) nie rozważa konsekwencji wysłuchania swej modlitwy (zastrzeżenie psychologiczne); (iii) zgodnie z modelem biblijnym każda modlitwa prośby zawiera warunek ‘jeśli Bóg chce’ (zastrzeżenie teologiczne); (iv) pomimo (reprezentowanej przez Smilansky’ego) powszechnej opinii, modlitwa prośby nie jest działaniem w zwykłym znaczeniu tego słowa (zastrzeżenie ontologiczne). Tej ostatniej tezy bronię, posługując się rozróżnieniem Charlesa Taliaferro na Świat Omodlony i Świat Nieomo- dlony. Poza tym próbuję podać własne kryterium moralności modlitwy prośby: modlitwa taka jest moralnie dobra, jeśli buduje pozytywną relację z Bogiem lub innymi ludźmi oraz jest wypowiadana wraz z uzupełnieniem ‘Boże, bądź wola Twoja!’. (shrink)

Søren Kierkegaard and Walter Lippmann wrote in very different times and places but both characterized the public as a “phantom.” Importantly, each did so within the context of a broader analysis that linked the press with specific notions about the public and democracy. This paper highlights the specific characteristics of the press that each thinker believed were responsible for the construction of the phantom public and its effects. While taking seriously the differences between Kierkegaard and Lippmann, in both their respective (...) sociopolitical contexts and their formulations of the public and the press, this paper applies their critiques to a vastly different media terrain than either thinker could have envisioned. (shrink)