Boolean connexive logic is an extension of Boolean logic that is closed under Modus Ponens and contains Aristotle’s and Boethius’ theses. According to these theses a sentence cannot imply its negation and the negation of a sentence cannot imply the sentence; and if the antecedent implies the consequent, then the antecedent cannot imply the negation of the consequent and if the antecedent implies the negation of the consequent, then the antecedent cannot imply the consequent. Such a logic was first introduced (...) by Jarmużek and Malinowski, by means of so-called relating semantics and tableau systems. Subsequently its modal extension was determined by means of the combination of possible-worlds semantics and relating semantics. In the following article we present axiomatic systems of some basic and modal Boolean connexive logics. Proofs of completeness will be carried out using canonical models defined with respect to maximal consistent sets. (shrink)

One of the logic defined by Richard Epstein in a context of an analysis of subject matter relationship is Symmetric Relatedness Logic S. In the monograph [2] we can find some open problems concerning relatedness logic, a Post-style completeness theorem for logic S is one of them. Our paper introduces a solution of this metalogical issue.

Standard deontic logic (SDL) is defined on the basis of possible world semantics and is a logic of alethic-deontic modalities rather than deontic modalities alone. The interpretation of the concepts of obligation and permission comes down exclusively to the logical value that a sentence adopts for the accessible deontic alternatives. Here, we set forth a different approach, this being a logic which additionally takes into consideration whether sentences stand in relation to the normative system or to the system of values (...) under which we predicate the deontic qualifications. By taking this aspect into account, we arrive at a logical system which preserves laws proper to a deontic logic but where the standard paradoxes of deontic logic do not arise. It is a logic of strictly-deontic modalities DR. (shrink)

We present here some Boolean connexive logics (BCLs) that are intended to be connexive counterparts of selected Epstein’s content relationship logics (CRLs). The main motivation for analyzing such logics is to explain the notion of connexivity by means of the notion of content relationship. The article consists of two parts. In the first one, we focus on the syntactic analysis by means of axiomatic systems. The starting point for our syntactic considerations will be the smallest BCL and the smallest CRL. (...) In the first part, we also identify axioms of Epstein’s logics that, together with the connexive principles, lead to contradiction. Moreover, we present some principles that will be equivalent to the connexive theses, but not to the content connexive theses we will propose. In the second part, we focus on the semantic analysis provided by relating- and set-assignment models. We define sound and complete relating semantics for all tested systems. We also indicate alternative relating models for the smallest BCL, which are not alternative models of the connexive counterparts of the considered CRLs. We provide a set-assignment semantics for some BCLs, giving thus a natural formalization of the content relationship understood either as content sharing or as content inclusion. (shrink)

In this paper, we apply relating semantics to the widely discussed problem of free choice between permitted actions or situations in normative systems. Leaving aside contexts in which the free choice principle is obviously unacceptable or uncontroversially valid, we concentrate on free choice for explicit permissions. In order to construct a formal representation of explicit permissions, we introduce a special constant, $\texttt {permit}$, which is analogous to the constant $\texttt {violation}$ used in the Andersonian–Kangerian approach to deontic logic with respect (...) to prohibition and obligation. Consequently, we define a permission operator on the basis of the $\texttt {permit}$ constant and a relation of legitimization. The general idea is that $P \varphi $ is true if and only if $\texttt {permit}$ is true, which means that a permission is actually issued and $\varphi $ is legitimized by $\texttt {permit}$. The intuitive notion of legitimization is formally represented by an operator of relating implication: a non-classical implication that is semantically defined by adding a constraint to the classical meaning of implication to the effect that arguments are related by a special relation. The properties of this relation are based on an informal, intuitive meaning of legitimization and determine the properties of the permission operator. We show that the resulting permission operator possesses the free choice property and avoids certain unwanted consequences that follow from alternative approaches. (shrink)

Pietruszczak (Bull Sect Log 38(3/4):163–171, 2009) proved that the normal logics K45 , KB4 (=KB5), KD45 are determined by suitable classes of simplified Kripke frames of the form ⟨W,A⟩ , where A⊆W. In this paper, we extend this result. Firstly, we show that a modal logic is determined by a class composed of simplified frames if and only if it is a normal extension of K45. Furthermore, a modal logic is a normal extension of K45 (resp. KD45; KB4; S5) if (...) and only if it is determined by a set consisting of finite simplified frames (resp. such frames with A≠∅; such frames with A=W or A=∅; such frames with A=W). Secondly, for all normal extensions of K45, KB4, KD45 and S5, in particular for extensions obtained by adding the so-called “verum” axiom, Segerberg’s formulas and/or their T-versions, we prove certain versions of Nagle’s Fact (J Symbol Log 46(2):319–328, 1981) (which concerned normal extensions of K5). Thirdly, we show that these extensions are determined by certain classes of finite simplified frames generated by finite subsets of the set N of natural numbers. In the case of extensions with Segerberg’s formulas and/or their T-versions these classes are generated by certain finite subsets of N. (shrink)

In the paper, we examine tableau systems for R. Epstein’s logics of content relationship: D (Dependence Logic), DD (Dual Dependence Logic), Eq (Logic of Equality of Content), S (Symmetric Relatedness Logic) and R (Nonsymmetric Relatedness Logic) (cf. Epstein in Philos Stud 36:137–173, 1979, Epstein in Rep. Math. Logic 21:19–34, 1987, Klonowski in Logic Log Philos 30(4):579–629, 2021, Krajewski in J Non Class Logic 8:7–33, 1991). The first tableau systems for those logics were defined by Carnielli. However, his approach has (...) some limitations, for example, it requires a proof of functional completeness and axiomatization. Notwithstanding the first two constraints, it does not include all Epstein logics, e.g., logic Eq. Unlike Carnielli’s approach, here we use set-assignment semantics to determine those logics. Since syntax and semantics of a given logic usually determine a minimal syntax and structure of a tableau system for the logic along with other properties, we propose a uniform tableau framework for the logics determined by set-assignment semantics. What distinguishes our tableau systems is that they combine the features of tableaux for propositional logics and syllogistic logics when the problem of content of propositions is analysed in tableau proofs. To denote the content of propositions in the proofs, we use generalised labels (see Jarmużek and Goré in Landscapes in Logic, College Publications, London, 2021). (shrink)

The goal of the article is twofold. The first one is to provide logics based on positional semantics which will be suitable for the analysis of epistemic modalities such as ‘agent... knows/beliefs that...’. The second one is to define tableau systemsfor such logics. Firstly, we present the minimal positional logic MR. Then, we change the notion of formulas and semantics in order to consider iterations of the operator of realization and “free” classical formulas. After that, we move on to weaker (...) logics in order to avoid the well known problem of logical omniscience. At the same time, we keep the positional counterparts of modal axioms, and. For all of the considered logics we present sound and complete tableau systems. (shrink)

In the paper a generalised method for obtaining an adequate axiomatic system for any relating logic expressed in the language with Boolean connectives and relating implication, determined by the limited positive relational properties is studied. The method of defining axiomatic systems for logics of a given type is called an algorithm since the analysis allows for any logic determined by the limited positive relational properties to define the adequate axiomatic system automatically, step-by-step. We prove in the paper that the algorithm (...) really works and we show how it can be applied to BLRI. (shrink)

We define and investigate from a logical point of view a family of consequence relations defined in probabilistic terms. We call them relations of supporting, and write: |≈w where w is a probability function on a Boolean language. A |≈w B iff the fact that A is the case does not decrease a probability of being B the case. Finally, we examine the intersection of |≈w, for all w, and give some formal properties of it.

In this paper, we indicate how Jan Woleński’s non-linguistic concept of the norm allows us to clarify the deontic relationship between sentences and the given normative system. A relationship of this kind constitutes a component of the metalogic of relating deontic logic, which subjects the logical value of the deontic sentence to the logical value of the constituent sentence and its relationship with a given normative system in the accessible possible worlds.

In this paper we present a tableau system for deontic logics with the operator of explicit permission. By means of this system the decidability of the considered logics can be proved. We will sketch how these logics are semantically defined by means of relating semantics and how they provide a simple solution to the free choice permission problem. In short, these logics employ relating implication and a certain propositional constant. These two are in turn used to define deontic operators similarly (...) as in Andersonian-Kangerian reduction, which uses different intensional implications and constants. (shrink)

In the paper we examine the problem of logical systems that are extensions of Classical Propositional Logic with new, intensional connectives of agency: monadic and dyadic _bringing it about that_. These systems are usually studied within the neighbourhood semantics. Here we propose a different strategy. We study all of the accepted laws and rules of logic of agency and define a translation of the agency operators into connectives interpreted in relating semantics. After this translation we can make a reduction to (...) more basic semantic properties that are required by the particular groups of laws and axioms. Finally, we define proper semantic structures and prove that they are complete with respect to all possible logical systems determined by the combinations of the axioms and rules. (shrink)

In this paper we discuss whether the relation between formulas in the relating model can be directly introduced into the language of relating logic, and present some stances on that problem. Other questions in the vicinity, such as what kind of functor would be the incorporated relation, or whether the direct incorporation of the relation into the language of relating logic is really needed, will also be addressed.

Fantastyka naukowa (ang. science fiction, w skrócie - SF) jest często przedstawianajako gatunek literacki dobrze przystosowany do spekulacji filozoficznej. SF i filozofia dzielą zainteresowanie kwestią nieśmiertelności, a ich ujęcia tego tematu można zestawić i porównać. Proponujemy tutaj zarys taksonomii różnych modeli czy wizji nieśmiertelności oferowanych przez filozofów i autorów fantastyki naukowej. Po wskazaniu istotnych rozbieżności między tymi modelami przedstawiamy sugestię, że pewne problemy oraz wątpliwości wysuwane przez pisarzy SF i filozofów wynikają z pomieszania różnych modeli. Mamy nadzieję, że te porównania (...) pokażą wstępnie, w jakim sensie można powiedzieć, że fantastyka naukowa funkcjonuje jako dyskurs filozoficzny. (shrink)

This study offers an experiential and practical way of understanding Plotinus' thought and philosophy through a focus on the act of contemplation. Mateusz Stróżyński argues that contemplation, or direct seeing of the principles of reality, is not merely a part of Plotinus' thought, but rather a significant dimension of it.

The paper addresses the question how descriptive language is used to express legal norms. Sentences we find in legislative acts, i.e. statutes, constitutions and regulations, express legal norms. Linguistically speaking, there are various grammatical and lexical ways of expressing norms, such as imperative mood, modal verbs, deontic verbs, etc. However, norms may also be expressed by descriptive sentences, namely sentences in present or future tense and indicative (declarative) mood (i.e. _The minister determines the tax rate_). In many civil law countries (...) (including Poland), this is a very common, if not the default, form of expressing norms in legislative texts. Often presented as a legal peculiarity, this phenomenon has yet to draw much academic attention. The normative meaning of descriptive sentences is usually attributed to purely pragmatic factors stemming from our shared assumptions about the legal system. However, a closer look reveals that similar grammatical constructions are ubiquitous in everyday communication and in different languages. We tend to utter various sorts of directives using descriptive sentences (_Now we add a spoon of salt to the sauce_; _credit cards are not accepted_). This suggests the possibility for a linguistic (as opposed to exclusively legal) explanation. This paper aims to offer such an explanation. Rather than resorting to formal semantics, so prevalent in legal theory, it borrows from Cognitive Linguistics to reveal the cognitive underpinnings of our surprising tendency to express normativity in descriptive terms. This involves four different, yet complementary, theories. Firstly, the theory of conceptual metaphor by George Lakoff and Mark Johnson which explains the phenomenon in question in terms of the metaphor “ ought is is ”; with “ ought ” as the more abstract target domain and “ is ” as the more concrete, cognitively simpler source domain. Secondly, the theory of speech act metonymy by Panther and Thornburg which presents descriptive legal sentences as referring to various components of the underlying cognitive scenario of obligation. Thirdly, Ronald Langacker’s notion of the virtuality of language as the explanation for non-present, including future, perpetual and directive, uses of the present tense. Fourtly, the notion of normative generics which points to the nominal, as opposed to verbal, structure of descriptive legal sentences as the source of their normativity. (shrink)

In this paper, we focus on the development of geometric cognition. We argue that to understand how geometric cognition has been constituted, one must appreciate not only individual cognitive factors, such as phylogenetically ancient and ontogenetically early core cognitive systems, but also the social history of the spread and use of cognitive artifacts. In particular, we show that the development of Greek mathematics, enshrined in Euclid’s Elements, was driven by the use of two tightly intertwined cognitive artifacts: the use of (...) lettered diagrams; and the creation of linguistic formulae. Together, these artifacts formed the professional language of geometry. In this respect, the case of Greek geometry clearly shows that explanations of geometric reasoning have to go beyond the confines of methodological individualism to account for how the distributed practice of artifact use has stabilized over time. This practice, as we suggest, has also contributed heavily to the understanding of what mathematical proof is; classically, it has been assumed that proofs are not merely deductively correct but also remain invariant over various individuals sharing the same cognitive practice. Cognitive artifacts in Greek geometry constrained the repertoire of admissible inferential operations, which made these proofs inter-subjectively testable and compelling. By focusing on the cognitive operations on artifacts, we also stress that mental mechanisms that contribute to these operations are still poorly understood, in contrast to those mechanisms which drive symbolic logical inference. (shrink)

The cognitive foundations of geometry have puzzled academics for a long time, and even today are mostly unknown to many scholars, including mathematical cognition researchers. -/- Foundations of Geometric Cognition shows that basic geometric skills are deeply hardwired in the visuospatial cognitive capacities of our brains, namely spatial navigation and object recognition. These capacities, shared with non-human animals and appearing in early stages of the human ontogeny, cannot, however, fully explain a uniquely human form of geometric cognition. In the book, (...) Hohol argues that Euclidean geometry would not be possible without the human capacity to create and use abstract concepts, demonstrating how language and diagrams provide cognitive scaffolding for abstract geometric thinking, within a context of a Euclidean system of thought. -/- Taking an interdisciplinary approach and drawing on research from diverse fields including psychology, cognitive science, and mathematics, this book is a must-read for cognitive psychologists and cognitive scientists of mathematics, alongside anyone interested in mathematical education or the philosophical and historical aspects of geometry. (shrink)

Celem artykułu jest prezentacja i krytyczna analiza koncepcji uczuć egzystencjalnych, autorstwa współczesnego filozofa psychiatrii o orientacji fenomenologicznej — Matthew Ratcliffe’a. Uczucia egzystencjalne są specjalną klasą stanów afektywnych, nadającą emocjonalnego zabarwienia subiektywnemu doświadczeniu rzeczywistości. Mają one charakter przedrefleksyjny i stanowią niejawne tło świadomości fenomenalnej, które w potocznym doświadczeniu pozostaje poza polem uwagi. Uczucia te mają ścisły związek z emocjami, determinując typy przedmiotów intencjonalnych zawartych w stanach emocjonalnych i wyznaczając repertuar możliwych do doświadczenia emocji. Najważniejsze uczucia egzystencjalne, które wyróżnia Ratcliffe, to: (1) (...) poczucie rzeczywistości, czyli przedrefleksyjne i fenomenalne wrażenie o realnym istnieniu świata jako takiego; (2) poczucie przynależności, czyli przedrefleksyjne i fenomenalne wrażenie własnego istnienia i osadzenia w świecie pośród osób i rzeczy. Te dwie kategorie stanowią fundamentalne składowe pierwszoosobowego doświadczenia podmiotu, wyznaczając tym samym jego relację do innych ludzi oraz rzeczywistości w jej najbardziej ogólnym sensie. W artykule przedstawiam główne cechy i typy uczuć egzystencjalnych. Zwracam także uwagę na szczególną rolę psychopatologii w analizie i uzasadnianiu istnienia tego zjawiska. W związku z tym, za Ratcliffem, opisuję w jaki sposób określone aspekty uczuć egzystencjalnych ulegają dezintegracji w przebiegu epizodów zaburzeń psychicznych, takich jak depresja czy schizofrenia. Pokazuję także różnicę pomiędzy fenomenologicznym i poznawczo-behoawioralnym podejściem do zaburzeń psychicznych. Powołując się na badania neurobiologiczne staram się wskazać potencjalne neuronalne korelaty uczuć egzystencjalnych. Tekst wieńczą krytyczne uwagi na temat koncepcji uczuć egzystencjalnych w ujęciu Matthew Ratcliffe’a. Rozwiązanie zidentyfikowanych wad i niedociągnięć tej teorii filozoficznej zarazem nakreśla przyszłe perspektywy jej rozwoju. (shrink)

In consequence of significant social, political, economic, and demographic changes several wildlife species are currently growing in numbers and recolonizing Europe. While this is rightly hailed as a success of the environmental movement, the return of wildlife brings its own issues. As the animals arrive in the places we inhabit, we are learning anew that life with wild nature is not easy, especially when the accumulated cultural knowledge and experience pertaining to such coexistence have been all but lost. This book (...) provides a hermeneutic study of the ways we come to understand the troubling impacts of wildlife by exploring and critically discussing the meanings of 'ecological discomforts'. Thus, it begins the work of rebuilding the culture of coexistence. The cases presented in this book range from crocodile attacks to mice infestations, and their analysis consequently builds up an ethics that sees wildlife as active participants in the shaping of human moral and existential reality. This book is of interest not only to environmental philosophers, who will find here an original contribution to the established ethical discussions, but also to wildlife managers, and even to those members of the public who themselves struggle to make sense of encounters with their new wild neighbors. (shrink)

We introduce a principle of local collection for compositional truth predicates and show that it is arithmetically conservative over the classically compositional theory of truth. This axiom states that upon restriction to formulae of any syntactic complexity, the resulting predicate satisfies full collection. In particular, arguments using collection for the truth predicate applied to sentences occurring in any given (code of a) proof do not suffice to show that the conclusion of that proof is true, in stark contrast to the (...) case of the induction scheme. We analyse various further results concerning end-extensions of models of compositional truth and the collection scheme for the compositional truth predicate. (shrink)

In this article we investigate the relationship between legal translation and legal interpretation. The common wisdom is that these activities are closely related, but the nature of that relationship remains disputable. We adopt the perspective of legal theory—as opposed to the perspective of translation studies—which seems to be underrepresented in the literature of the subject. We start with distinguishing between the two notions of legal interpretation: the wide sense and the narrow sense. We argue that the relationship between legal translation (...) and legal interpretation changes significantly depending on the notion of legal interpretation that is assumed. The wide sense is often assumed by translation scholars and it renders legal interpretation as a necessary prerequisite for legal translation. Jurists, on the other hand, usually assume the narrow sense which renders legal interpretation and legal translation as two distinct activities with some shared features. We then focus on four issues of legal interpretation in the narrow sense: the types of legal interpretive problems, the creation of legal interpretive problems, the methods of legal interpretation, the resolution of legal interpretive problems. We conclude with a detailed comparison of legal translation and legal interpretation in the context of those four issues. (shrink)

Idea słowiańska” jest terminem ogólnym, odnoszącym się do wielu politycznych, historiozoficznych i kulturowych wątków, dla których inspiracją było językowe i kulturowe pokrewieństwo między narodami słowiańskimi. Takie ruchy jak słowianofilstwo i panslawizm miały na celu kulturalne i polityczne zjednoczenie Słowian. Idea ta wywarła silny wpływ na muzykę krajów środkowej i wschodniej Europy w XIX i XX wieku. Pod jej wpływem powstała znaczna liczba utworów muzycznych. Można utwory te podzielić na kilka grup. W jednych „słowiańskość” podkreślana była poprzez tytuł. Kompozytorzy używali również (...) typowo słowiańskich gatunków tanecznych i pieśniowych, jak polski mazurek i ukraińska dumka. Innym sposobem realizacji idei słowiańskiej były muzyczne kontakty między twórcami. Idea muzyki słowiańskiej pojawia się również w komentarzach muzykologicznych: słowiański „charakter” muzyczny bywał najczęściej łączony ze specyficznymi kategoriami emocjonalnymi, takimi jak smutek, tęsknota, szczególnie zaś żal, które to określenie stosowano do opisu przemożnego nastroju panującego w dziełach Chopina. (shrink)

The aim of the article is to analyze the relationship between Singapore and the People’s Republic of China in the light of the current policy of the President of the United States Donald Trump. The point of reference for the presented analysis is the foreign policy of the former President Barack Obama, based on the strategy known as “pivot to Asia” – the strategic turnabout of the United States to the Asia-Pacific region. One of its main objectives was the signing (...) of a multilateral agreement on the establishment of a free trade zone, the Trans-Pacific Partnership (TPP), bringing together 12 countries. The main subject of the present analysis is to examine the impact of Donald Trump’s decision of January 2017 to withdraw from the TPP trade agreement on the relations between the remaining signatories of the agreement, as well as to examine Beijing’s actions, which may seek to increase its sphere of influence in Asia through the breakdown of TPP. The main part of the research is focused on the triangle politics concept in international politics, which will include China, Singapore and the United States. Besides the two largest economic powers, Singapore is included because of its membership in the TPP and ASEAN, and due to its strong economy and its population (predominantly) of Chinese origin it can be viewed as the “fifth column” or may otherwise play a role in the Greater China concept. (shrink)

Aphasia is an acquired impairment of language functions resulting from a brain lesion. It is usually accompanied by deficits in non-linguistic cognitive processes. This study aimed to investigate in patients with aphasia the complex interrelationships between selected cognitive functions: auditory speech comprehension, working memory, and temporal information processing in the millisecond time range. Thirty right-handed subjects aged from 27 to 82 years suffering from post-stroke aphasia participated in the study. Verbal working memory and spatial working memory were assessed with: a (...) receptive verbal test and the Corsi Block-Tapping Test, respectively. Both these WM tests used the forward tasks and backward tasks. Auditory comprehension was assessed by receptive language tests, and TIP efficiency was assessed by auditory perception of temporal order in the millisecond time range. We observed better performance of forward WM tasks than backward ones, independently of the type of material used. Furthermore, the severity of auditory comprehension impairment correlated with the efficiency on both forward and backward VWM tasks and the backward SWM task. Further analysis revealed that TIP plays a crucial role only in the latter task. These results indicate the divergent pattern of interactions between WM and TIP depending on the type of WM tasks. Level of verbal competency appeared to play an important role in both VWM tasks, whereas TIP appeared to be important for SWM, but only on the backward task. (shrink)

Artykuł jest próbą analizy koncepcji minimalistycznej neurofilozofii autorstwa Henrika Waltera w kontekście dyskusji dotyczącej problemu psychofizycznego. Bezpośrednio związana z ową koncepcją teoria o „zróżnicowanej metafizyce” została w tekście powiązana z ideą pluralizmu eksplanacyjnego i ukazana jako metodologiczna alternatywa dla poszukiwania fundamentalnych teorii świadomości. Jednocześnie poza ewentualnymi zaletami metafilozoficznej refleksji podejmowanej w ramach minimalistycznej neurofilozofii zarysowane zostały jej podstawowe ograniczenia i problemy związane m.in. z uznaniem superweniencji za punkt łączący różnorodne stanowiska neurofilozoficzne.

This paper is a follow-up to [4], in which a mistake in [6] was corrected. We give a strenghtening of the main result on the semantical nonconservativity of the theory of PT−with internal induction for total formulae${$, denoted by PT−in [9]). We show that if to PT−the axiom of internal induction forallarithmetical formulae is added, then this theory is semantically stronger than${\rm{P}}{{\rm{T}}^ - } + {\rm{INT}}\left$. In particular the latter is not relatively truth definable in the former. Last but not (...) least, we provide an axiomatic theory of truth which meets the requirements put forward by Fischer and Horsten in [9]. The truth theory we define is based on Weak Kleene Logic instead of the Strong one. (shrink)

The current paper studies the formal properties of the Global Reflection Principle, to wit the assertion “All theorems of$\mathrm {Th}$are true,” where$\mathrm {Th}$is a theory in the language of arithmetic and the truth predicate satisfies the usual Tarskian inductive conditions for formulae in the language of arithmetic. We fix the gap in Kotlarski’s proof from [15], showing that the Global Reflection Principle for Peano Arithmetic is provable in the theory of compositional truth with bounded induction only ($\mathrm {CT}_0$). Furthermore, we (...) extend the above result showing that$\Sigma _1$-uniform reflection over a theory of uniform Tarski biconditionals ($\mathrm {UTB}^-$) is provable in$\mathrm {CT}_0$, thus answering the question of Beklemishev and Pakhomov [2]. Finally, we introduce the notion of a prolongable satisfaction class and use it to study the structure of models of$\mathrm {CT}_0$. In particular, we provide a new model-theoretical characterization of theories of finite iterations of uniform reflection and present a new proof characterizing the arithmetical consequences of$\mathrm {CT}_0$. (shrink)

In the following paper we propose a model-theoretical way of comparing the “strength” of various truth theories which are conservative over PA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ PA $$\end{document}. Let Th\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak {Th}}$$\end{document} denote the class of models of PA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ PA $$\end{document} which admit an expansion to a model of theory Th\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} (...) \begin{document}$${ Th}$$\end{document}. We show that PA⊃TB⊃RS⊃UTB⊇CT-,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} {{\mathfrak {PA}}}\supset {\mathfrak {TB}}\supset {{\mathfrak {RS}}}\supset {\mathfrak {UTB}}\supseteq \mathfrak {CT^-}, \end{aligned}$$\end{document}where PA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak {PA}}$$\end{document} denotes simply the class of all models of PA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ PA $$\end{document} and RS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak {RS}}$$\end{document} denotes the class of recursively saturated models of PA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ PA $$\end{document}. Our main original result is that every model of PA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ PA $$\end{document} which admits an expansion to a model of CT-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ CT ^-$$\end{document}, admits also an expansion to a model of UTB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ UTB $$\end{document}. Moreover, as a corollary to one of the results we conclude that UTB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ UTB $$\end{document} is not relatively interpretable in TB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ TB $$\end{document}, thus answering the question from Fujimoto. (shrink)

The aim of the paper is to discuss the idea of dialogue with nature. Even though the idea of dialogue with animals, plants – even objects of inanimate nature – is well known, it has usually been treated as an expression of a naive or folk view. Yet, it has recently gained in importance as an idea that is used to describe an ecological approach to natural environment and tends to be treated as a foundation for an ecological culture. A (...) noteworthy contribution to the reconsideration of the concept of human-nature dialogue has also been given by a number of contemporary philosophers who have offered an environmental reinterpretation of phenomenology and hermeneutics based on, among other things, Martin Buber’s concept of the I-You relationship. The paper will focus on two aspects of the concept of dialogue, namely on its epistemological and ethical implications. Following Erazim Kohák’s theory, which will be presented as a key figure of a particular manner of speaking about nature, one that leads to ecological personalism. (shrink)

The notion of implicit commitment has played a prominent role in recent works in logic and philosophy of mathematics. Although implicit commitment is often associated with highly technical studies, it remains an elusive notion. In particular, it is often claimed that the acceptance of a mathematical theory implicitly commits one to the acceptance of a Uniform Reflection Principle for it. However, philosophers agree that a satisfactory analysis of the transition from a theory to its reflection principle is still lacking. We (...) provide an axiomatization of the minimal commitments implicit in the acceptance of a mathematical theory. The theory entails that the Uniform Reflection Principle is part of one’s implicit commitments, and sheds light on why this is so. We argue that the theory has significant epistemological consequences in that it explains how justified belief in the axioms of a theory can be preserved to the corresponding reflection principle. The theory also improves on recent analyses of implicit commitment based on truth or epistemic notions. (shrink)

AbstraktPEŁNY TEKST: PDF References Heidegger Martin, Bycie i czas, przeł. B. Baran, PWN, Warszawa 1994. Hoły-Łuczaj Magdalena, Kształtowalność. Postheideggerowskie pytanie o inny wymiar bycia, Copernicus Center Press, Kraków 2022. Hoły-Łuczaj Magdalena, Radykalny nonantropocentryzm. Martin Heidegger i ekologia głęboka, Wydawnictwa Uniwersytetu Warszawskiego, Warszawa–Rzeszów 2018.

The article concerns two axiom systems of Słupecki for the functionally complete three-valued propositional logic: W1–W6 and A1–A9. The article proves that both of them are inadequate—W1–W6 is semantically incomplete, on the other hand, A1–A9 governs a functionally incomplete calculus, and thus, it cannot be a semantically complete axiom system for the functionally complete three-valued logic.

A method of constructing Hilbert-type axiom systems for standard many-valued propositional logics was offered by Rosser and Turquette. Although this method is considered to be a solution of the problem of axiomatisability of a wide class of many-valued logics, the article demonstrates that it fails to produce adequate axiom systems. The article concerns finitely many-valued propositional logics of Łukasiewicz. It proves that if standard propositional connectives of the Rosser–Turquette axiom systems are definable in terms of the propositional connectives of Łukasiewicz’s (...) logics, and thus, they are normal ones, then every Rosser–Turquette axiom system for a finite-valued Łukasiewicz’s logic is semantically incomplete. (shrink)

Oikologia to nauka o domu rozumianym szeroko, w kontekście dialektyki zakorzenienia człowieka w świecie, jako relacja zachodząca między nim a otaczającą go rzeczywistością. Dotyka w swojej analizie m.in. pytań z zakresu etyki środowiska dotyczących ludzkiej ingerencji w strukturę świata i stara się wspierać refleksję i wynikającą z niej postawę pełną wrażliwości na związek człowieka ze środowiskiem. Ekofilozofia, jako dyscyplina podejmująca wieloaspektową problematykę ochrony środowiska z perspektywy filozoficznej refleksji, w centrum zainteresowania stawia również badanie samej relacji łączącej człowieka ze środowiskiem przyrodniczym. (...) Celem artykułu jest wskazanie, iż refleksja oikologiczna może okazać się pomocną perspektywą dla szeroko pojętej ekofilozofii, a więc właśnie dla rozważań skupiających się na odpowiednim ułożeniu wspomnianej interakcji. Przykładem praktycznego problemu, w którym tego typu spojrzenie zostanie zaprezentowane, jest kwestia przestrzeni miejskiej, a konkretniej jej rewitalizacji, ze szczególnym naciskiem na obszary poprzemysłowe, którą w omawianym kontekście ekofilozofii wiąże się przede wszystkim z ideą zrównoważonego rozwoju. (shrink)

The subject embodied in the designed environment. Analysis of the use of the affordance concept in architecture: James Gibson’s ecological psychology is considered as one of the research subtraditions within embodied cognition. Gibson emphasizes the nature of the agent-environment interaction through the development of the theory of affordances. According to this idea, affordances are relational properties of the environment that enable a specific action for the agent. Currently this concept is being applied in many different contexts. This paper considers the (...) application potential of affordance in architectural studies as a tool that analyses the agent’s interaction with the environment. In this context, the affordance category can be a tool that allows one to take into account the importance of space for the shaping of behavior and interactions between its users, without falling into architectural determinism. The main aim of this study is to analyze affordances as a category that, despite its diversity and vagueness, can play an important role in the embodied view of architecture. The first part of the article is an attempt to synthetically place affordances in the context of embodied cognition and to point out the basic philosophical interpretations and discussions related to Gibson’s concept. In the next part, we situate the concept of affordances in the context of design practice. We also present the pros and cons of applying affordances to this ground. The last section in presenting the concept of affordances is considered within the background of the embodied current in architecture. (shrink)

The paper explores the link between contemplation of the One and happiness in Plotinus and challenges the traditional interpretation according to which a contemplative or mystical experience of the One is by necessity brief and transitory, while the experience of Intellect can become a stable state in this life. Were it so, it would not serve as a ground for the good or happy life. In order to reconcile this point with Plotinus’s other claim about contemplation, his doctrine of the (...) double activity of Intellect is invoked. (shrink)