We introduce the subject of modal model theory, where one studies a mathematical structure within a class of similar structures under an extension concept that gives rise to mathematically natural notions of possibility and necessity. A statement φ is possible in a structure (written φ) if φ is true in some extension of that structure, and φ is necessary (written φ) if it is true in all extensions of the structure. A principal case for us will be the class Mod(T) (...) of all models of a given theory T—all graphs, all groups, all fields, or what have you—considered under the substructure relation. In this article, we aim to develop the resulting modal model theory. The class of all graphs is a particularly insightful case illustrating the remarkable power of the modal vocabulary, for the modal language of graph theory can express connectedness, k-colorability, finiteness, countability, size continuum, size ℵ1, ℵ2, ℵω, ℶω, first ℶ-fixed point, first ℶ-hyper-fixed point, and much more. A graph obeys the maximality principle φ(a)→φ(a) with parameters if and only if it satisfies the theory of the countable random graph, and it satisfies the maximality principle for sentences if and only if it is universal for finite graphs. (shrink)

When people talk about anarchism, what they have in mind is typically political anarchism, that is, the view that there should be no state. As the philosopher and anarchism scholar David Miller observes, however, anarchism itself is a more general view, namely the view that there should be no rulers. Miller writes that “although the state is the most distinctive object of anarchist attack, it is by no means the only object. Any institution which, like the state, appears to anarchists (...) coercive, punitive, exploitative or destructive is condemned in the same way”—including, for example, religious institutions, schools, or economic systems (Miller 1984: 8). In this sense, one can be an anarchist about different things. Relationship anarchy is anarchism about personal relationships. -/- Several thinkers in the anarchist tradition have held views on personal relationships (e.g., Godwin 1793; Bakunin 1866; Goldman 1910). In what follows, however, our focus is not on the general issue of anarchist views on relationships, but on the ideas of the contemporary movement of self-identifying relationship anarchists. -/- The ideas of relationship anarchy in this sense—hereafter RA—have been developed in queer and countercultural communities over the last two decades. Rather than focusing primarily on mechanisms of political power, RA theorists have been concerned with understanding and challenging the power dynamics at play in close personal relationships. Andie Nordgren, the movement’s central, founding theorist, describes RA as a radical commitment “to avoid defining relationships by attempts to exercise power over each other” (Nordgren 2018). -/- Our aim is to give a concise presentation and defense of RA. We will approach RA as a theory in applied ethics—in particular, as a theory in sexual ethics and relationship ethics—and relate it to ongoing debates in these areas. We, the authors, are both queer men with a background in countercultures where RA is widely practiced and discussed. One of us is an activist working on trans- and sex workers’ rights (Sørlie), the other is a philosophy professor (Moen). Although we make several claims about the scope, content, and justification of RA, we do not claim to speak with any special authority on the issue. Moreover, many of the points that we make here, while not attributable to a specific source, are not original to us, but are the result of several years of fruitful discussion with others in the RA community. -/- We start by considering the cases where, from an RA perspective, current mainstream relationship norms are too restrictive. Then we turn to the cases where current norms are too permissive. Our views on what counts as “mainstream” relationship norms are, no doubt, influenced by the fact that we are writing from a Scandinavian perspective. -/- We then proceed to consider the relationship between RA and polyamory. We argue that RA is compatible with some, but not all, forms of polyamorous practice. We also argue that, from an RA perspective, the increasingly popular term “consensual non-monogamy” is a misleading term that should be avoided. In the conclusion, we explain how RA, as a position in applied ethics, can be justified within consequentialist, deontological, and virtue ethical frameworks alike. -/- We have restricted our scope, in what follows, to chosen relationships between adults. Thus, we are not dealing with, for example, kinship relationships into which one is born, nor relationships between adults and minors. Although many issues and arguments deserve to be explored in greater depth than we can do here, we hope, nevertheless, to be able to convey the main nature and thrust of RA. (shrink)

In response to the fall of Constantinople in 1453, Nicholas of Cusa wrote De pace fidei defending a commitment to religious tolerance on the basis of the notion that all diverse rites are but manifestations of one true religion. Drawing on a discussion of why Nicholas of Cusa is unable to square the two objectives of arguing for pluralistic tolerance and explaining the contents of the one true faith, we outline why theological pluralism is compromised by its own meta-exclusivism.

We discuss the philosophical problems attendant to the justice of eternal punishments in Hell, particularly those portrayed in Dante’s Inferno. We conclude that, under Dante’s description, a unique version of the problem of Hell (and Heaven) can be posed.

Time perspective theory provides a robust conceptual framework for analyzing human behavior in the context of time. So far, the concept has been studied and applied in multiple life domains, such as education, health, social relationships, environmental behavior, or financial behavior; however its explanatory potential has been completely neglected within the domain of sport. In the present paper we provide a deepened theoretical analysis of the potential role of temporal framing of human experience for sport-related attitudes, emotions, and athletic performance. (...) We propose a conceptual model in which time perspectives influence psychological functioning and performance of athletes via three major mechanisms: 1) magnitude and persistence of sport motivation and resulting athlete engagement, 2) regulation of affective states during sport performance, and 3) appraisal of one’s performance and coping with resulting emotions. We support the theoretical considerations based on the major assumptions of time perspective theory with research findings regarding the regulatory role of time perspectives in other life domains. We also highlight potential research paths that would allow us to empirically test the present model and determine the actual role of temporal perspectives in shaping crucial aspects of athletes’ psychological functioning, as well as levels of their sport performance. (shrink)

Moral thinking plays an important role in philosophy of Leszek Kołakowski. The paper examines his ethical position as it was presented in Kołakowski’s writings dealing directly with this subject, against the background of those stances that he opposed. In the scope of the author’s interest is the problem of the persistence of some elements and the development of the position in question. Both Kołakowski’s ethical and metaethical reflection is taken into account. In conclusion, Kołakowski’s position is ascribed to the anti-theoretic (...) current in ethics. (shrink)

Epistemicism associates vagueness with ignorance produced by semantic plasticity: the shiftiness of intensions in our language resulting from small changes in usage. The recent literature (Caie 2012; Magidor 2018; Yli-Vakkuri 2016) points to a missing piece in the epistemicist theory of vagueness, namely a clear account of the semantics of the definiteness operator Δ. The fundamentals of the epistemicist theory are well understood. However, the technical work of defining the definiteness operator has proven difficult. There are several desiderata that we (...) would like Δ to satisfy. For instance, we would like the epistemicist notion of ‘definiteness’ to interact well with modal operators and validate intuitive principles like ‘necessarily, if φ is definitely true, then φ is true’. Providing an account that would meet all such desiderata has eluded the epistemicists so far. In this paper, I present a novel version of a multidimensional model inspired by the work of Robert Stalnaker and David Kaplan. Using this model, I provide an account of epistemicist definiteness that meets our desiderata. (shrink)

The epistemicist theory aims to explain ignorance due to vagueness by semantic plasticity: the shiftiness of intensions across close possible worlds resulting from shiftiness in usage. This explanation is challenged by the Omniscient Speaker Puzzle (Sennet in Philos Stud 161(2):273–285, 2012). Suppose that an omniscient speaker, Barney, who knows all the facts about usage and how these facts determine the intensions of expressions, cooks up a scheme to stabilise the intension of a normally semantically plastic term like ‘rich’. It seems (...) that ‘rich’ would display all the phenomena associated with vagueness without being semantically plastic, thus making the epistemicist explanation of ignorance due to vagueness insufficient. In this paper, I present a few choice points for epistemicism that arise as a result of the puzzle. (shrink)

Polskie przepisy prawne formułujące warunki dopuszczalności eksperymentu medycznego, a więc ipso facto wyznaczające jego granice, można różnorako interpretować, zwłaszcza w tym zakresie, w jakim określają wymagany dla przeprowadzenia eksperymentu bilans związanych z nim możliwych korzyści i szkód. W artykułach prawniczych komentujących te przepisy w zasadzie jednak brak prób systematycznego i (na tyle, na ile pozwala na to sam przedmiot analizy) ścisłego wyróżnienia tych interpretacji w języku tzw. teorii racjonalnego wyboru (rational choice theory), teorii szczególnie przydatnej w tym kontekście z uwagi (...) na jej rozbudowany aparat pojęciowy pozwalający badać różnorakie konfiguracje relacji między costs i benefits. Artykuł próbuje wypełnić tę lukę: wyróżnione w nim zostały różne interpretacje przepisów prawnych określających warunki dopuszczalności eksperymentu medycznego; interpretacje te zostały również poddane ocenie. (shrink)

Celem niniejszego artykułu jest przedstawienie estetycznej wrażliwości karolińskiego mnicha i erudyty Walahfrida Strabona. Podstawą analiz stał się spisany przez Strabona botaniczny poemat De cultura hortorum. Kontemplacyjne rozważania wczesnośredniowiecznego poety dowodzą, w jak ścisłym zespoleniu trwały dwa odległe, a jednocześnie jednak tak bardzo bliźniacze światy - antyczny i chrześcijański. Wyznacznikiem tej koincydencji był nie tylko uniwersalizm języka łacińskiego, ale także stopniowo przyswajana, uświadamiana i konwertowana sztuka i filozofia. Walahfrid zajmuje bardzo ważne miejsce w procesie kształtowania myśli estetycznej. Jest ogniwem łączącym Alkuina, (...) przepowiadającego ideę ładu, z Janem Szkotem Eriugeną, który wspomniany ład odważył się spektakularnie zdefiniować jako chrześcijańską estetykę opartą na myśli Greków i Rzymian. (shrink)

In [5] we study Nonassociative Lambek Calculus augmented with De Morgan negation, satisfying the double negation and contraposition laws. This logic, introduced by de Grooté and Lamarche [10], is called Classical Non-Associative Lambek Calculus. Here we study a weaker logic InNL, i.e. NL with two involutive negations. We present a one-sided sequent system for InNL, admitting cut elimination. We also prove that InNL is PTIME.

a This is an outline of a coherence theory of law. Its basic ideas are: reasonable support and weighing of reasons. All the rest is commentary.a (TM) These words at the beginning of the preface of this book perfectly indicate what On Law and Reason is about. It is a theory about the nature of the law which emphasises the role of reason in the law and which refuses to limit the role of reason to the application of deductive logic. (...) In 1989, when the first edition of On Law and Reason appeared, this book was ground breaking for several reasons. It provided a rationalistic theory of the law in the language of analytic philosophy and based on a thorough understanding of the results, including technical ones, of analytic philosophy. That was not an obvious combination at the time of the booka (TM)s first appearance and still is not. The result is an analytical rigor that is usually associated with positivist theories of the law, combined with a philosophical position that is not natural law in a strict sense, but which shares with it the emphasis on the role of reason in determining what the law is. If only for this rare combination, On Law and Reason still deserves careful study. On Law and Reason also foreshadowed and influenced a development in the field of Legal Logic that would take place in the nineties of the 20th century, namely the development of non-monotonic (a defeasiblea (TM)) logics for the analysis of legal reasoning. In the new Introduction to this second edition, this aspect is explored in some more detail. (shrink)

Magdalena Jaworska-Wołoszyn On the Pantheon of Plethon’s LawsOf all the surviving fragments of Plethon’s Laws there emerges a holistic vision – that of a truly original philosophy. The last of Plethon’s works consists of many issues analyzed from different perspectives. The main purpose of this article is the presentation of Plethon’s hierarchy of gods. In the light of Plethon’s philosophy, the pantheon itself is the foundation of an original and controversial metaphysics. Indeed, knowing the divine order determines the cognition (...) of the structural elements of the whole reality. Keywords: the pantheon of Plethon’s Laws, metaphysical nature of gods. (shrink)

Le Maitre de Claville należy do tradycji moralistycznej klasycyzmu francuskiego i stara się podołać niebagatelnemu zadaniu stworzenia portretu człowieka godnego, honnete homme’a. Usiłując zdefiniować pojęcie cnoty, odwołuje się do własnego smaku estetycznego, subiektywnych emocji radości, zachwytu i rozkoszy wynikających z obcowania z pięknem. Z dużą dowolnością wybiera to, co sam uważa za najdoskonalsze z antyku, Biblii i w najnowszych prądach myślowych swego czasu: m.in. racjonalizmu. Połączenie tych trzech elementow nie jest łatwe. W jego rozważaniach ujawnia się wysiłek moralisty starającego się (...) nadać swej koncepcji kształt logicznie uporządkowanej doktryny, z elementow swobodnie wybranych, nie zawsze ze sobą zgodnych. (shrink)

It is proved that the following conditions are equivalent: (a) there exists a complete, atomless, σ-centered Boolean algebra, which does not contain any regular, atomless, countable subalgebra, (b) there exists a nowhere dense ultrafilter on ω. Therefore, the existence of such algebras is undecidable in ZFC. In "forcing language" condition (a) says that there exists a non-trivial σ-centered forcing not adding Cohen reals.

Expression of physical motion (e.g., man runs by) shows systematic variability not only between language types (i.e., inter-typological) but also within a language type (i.e., intra-typological). In this study, we asked whether the patterns of variability extend to metaphorical motion events (e.g., time runs by). Our analysis of randomly selected 450 physical motion (150/language) and 450 metaphorical motion (150/language) event descriptions from written texts originally produced by German, Polish, and Spanish authors showed strong inter-typological differences in the expression of both (...) event types. German and Polish speakers differed from Spanish speakers in how they packaged manner and path components of a motion event; they also differed in how extensively they expressed each component in their lexicalization of motion. The strong inter-typological differences were accompanied by more modest intra-typological variability: Polish and German writers differed in their packaging and lexicalization of manner and path components of metaphorical—but not physical—motion events. Our results provide evidence for robust inter-typological differences evident in the expression of both physical and metaphorical motion, along with less robust intra-typological differences, largely evident in the expression of metaphorical motion. Our study thus highlights event type as an important factor in determining crosslinguistic variation in motion expression. (shrink)

The introduction of the concept of the field of rationality and its correlates (the field of potentiality and the formal field) by Józef Życiński and Michał (Michael) Heller opened up space for the philosophical explanation of the unreasonable effectiveness of mathematics in capturing regularities built into the physical reality. The presented study is a response to the clear incentive of these authors towards the development of the understanding and applicability of these concepts. It is argued that identifying symmetries within the (...) field of rationality not only helps to articulate the fundamental role of symmetries in physics but also provides a better grasp on the issue of potentialities for the emergence of complexity in the Universe. Additionally, some global properties of this field can be more deeply comprehended. By indicating the drawbacks and limitations of this approach, perspectives for further inquiry into the meaning and usefulness are suggested. (shrink)

Involutive Nonassociative Lambek Calculus is a nonassociative version of Noncommutative Multiplicative Linear Logic, but the multiplicative constants are not admitted. InNL adds two linear negations to Nonassociative Lambek Calculus ; it is a strongly conservative extension of NL Logical aspects of computational linguistics. LNCS, vol 10054. Springer, Berlin, pp 68–84, 2016). Here we also add unary modalities satisfying the residuation law and De Morgan laws. For the resulting logic InNLm, we define and study phase spaces. We use them to prove (...) the cut elimination theorem for a one-sided sequent system for InNLm, introduced here. Phase spaces are also employed in studying auxiliary systems InNLm, assuming the k-cyclic law for negation. The latter behave similarly as Classical Nonassociative Lambek Calculus, studied in de Groote and Lamarche :355–388, 2002) and Buszkowski. We reduce the provability in InNLm to that in InNLm. This yields the equivalence of type grammars based on InNLm with -free) context-free grammars and the PTIME complexity of InNLm. (shrink)

Procrastination as putting off until tomorrow what one had intended to do today is well-known tendency in everyday life. In an attempt to understand the character of procrastination in different life-domains, a large body of research has been accumulated over the last decades. This article was aimed to evaluate a specific decisional procrastination of school-to-work transition that is treated as maturity postponement. Two studies are reported examining SWT procrastination defined as career indecision among Polish students graduating universities. In Study 1, (...) attitudinal and identity statuses were analyzed as correlates of career procrastination. A path analysis conducted for the model, which was aimed to explain the influence of career self-efficacy and occupational commitment on career indecision, revealed its very good fitness. Those two independent variables explain 10% of career indecision variance. Stepwise multiple regression analyses conducted to ascertain relationship of five identity statuses to procrastination measure showed that Commitment Making and Ruminative Exploration are strongest predictor variables. In study 2, the stepwise multiple regression analyses conducted to ascertain the independent relationship of each of Big Five personality factor revealed that Neuroticism and Extraversion accounts of the most of explained variance of school-to-work transition procrastination. (shrink)

This article presents the results of lead isotope analysis of ten Byzantine seals from the sigillographic collection of Robert Feind. The report is preceded by an overview of pre-existing studies on lead use in the Byzantine Empire and a presentation of the investigated seals datable to the Early Byzantine, Middle Byzantine and Late Byzantine period. Three seals are of imperial issue. The results of the analysis of lead are compared against the results of isotope analysis of other silver and lead (...) artefacts from Late Antiquity and the Late Byzantine period. The isotop analysis leads to the following conclusions: Many of the seals have isotope ratios consistent with Aegean-Bulgaria-Western Turkey sources; Reused lead was also employed in the manufacture of seals; There appear to be significant chronological and regional differences in the lead used for casting blanks in the eastern Mediterranean. The number of lead seals subjected here to analysis is admittedly too small for the results to be fully representative; still, they provide a starting point for more similar studies which will preferably include excavation finds with known and secure provenance. (shrink)

Traditional martial arts continue to be interesting and inspiring to many people around the globe. Some of their contemporary adaptations attract enthusiasts for whom they are especially important. In this article, the author bases his observations on his own long-term participation. The analysis takes into account the influence of the perspectives of Jigoro Kano and several other creators of modern varieties of Japanese budo. It can be concluded that regular, even daily, practice—cultivating martial arts and internalizing its values—co-creates the lifestyle (...) of instructors and advanced students. (shrink)