We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already, we significantly broaden this framework by developing the corresponding technique for countably closed models of size continuum. The applications range from various theorems on paradoxical decompositions of the plane, to coloring sparse set systems, results on graph chromatic number and constructions from point-set topology. Our main (...) purpose is to demonstrate the ease and wide applicability of this method in a form accessible to anyone with a basic background in set theory and logic. (shrink)

2 Popper's Logical Definition of Verisimilitude. 3 Popper's Probabilistic Definition of Verisimilitude. 4 Conclusion.

Of two false theories, One can be, Intuitively, Closer to the truth than the other. The purpose of the article is to propose a rigorous explication of this intuitive notion.

Chapter One: Constructions. Entities, constructions, and functions When one travels from Los Angeles to New York, going, say, by way of St. Louis, Chicago, ...

The article analyzes the aesthetic content of the concept of realism in stylistic, genre and ideological aspects. Guided by the comparative method and a comprehensive approach to the study of the problem, the author declares the a priori avant-garde nature of art and, as a result, the groundlessness of confrontation between realists and avant-gardists. The catharsis achieved by the realism of expressive means should be real. Thus, the author's vision of realism presupposes not so much the harmony of art with (...) the displayed epoch, but rather participation, confession of enduring values, which elevates art above the historical and social context. В статье анализируется эстетическое содержание понятия реализма в стилевом, жанровом и мировоззренческом аспектах. Руководствуясь компаративным методом и комплексным подходом к изучению проблемы, автор декларирует априорную авангардность искусства и, как следствие, беспочвенность конфронтации реалистов и авангардистов. Реальным должен быть катарсис, достигаемый реализмом выразительных средств. Таким образом, авторское ви́дение реализма предполагает не столько созвучие искусства отображаемой эпохе, сколько сопричастность, исповедание непреходящих ценностей, что возвышает искусство над историко-социальным контекстом. (shrink)

To mitigate the potentially devastating effects of the COVID-19 pandemic, it is vital to identify psychosocial and moral resources. The care, preservation, protection, and well-being of social communities are attributes of prosocial behavior that can be such a resource. The purpose of the study is to identify the features of prosocial orientation of Russian youth during the COVID-19 pandemic, as well as to identify strategies for prosocial behavior during the COVID-19 pandemic. The sample consisted of 447 people. The study was (...) conducted in May 2020 in the form of an online survey of subjects using Google Forms (“Moral Foundations Questionnaire method” and “Portrait Values Questionnaire”). The research made it possible to establish that Russians were dominated by norms of care, fairness, purity; values of benevolence-universalism, security, and self-direction. During the COVID-19 pandemic, the prosocial orientation of Russians may manifest itself in the following behavioral strategies: proactive prosocial strategy of “caring for others” (true altruism, expressed in forms of volunteering, helping a stranger, and charity despite the risk of contracting a coronavirus infection); egoistic strategy of prosocial behavior “self-care through caring for others” (volunteering based on self-development; helping a stranger to improve your own psychological well-being); conventional prosocial strategy “self-care” (self-isolation and preventive behavior). In the long run, it is necessary to identify personal and environmental resources that allowed people to effectively implement a prosocial self-isolation strategy during the COVID-19 pandemic, as well as various forms of volunteerism. (shrink)

This volume of the Logica Yearbook series brings together articles presented at the annual international symposium Logica 2017, Hejnice, the Czech Republic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.

Risk and crisis communication (RCC) is a complex constellation of multiple actors, platforms, and voices. It involves institutional actors but also laypeople. Participation by social media users can both facilitate and obstruct effective RCC. The present study draws on in-depth interviews with Swedish Facebook users, and explores motivational factors for lay participation in RCC in the context of vaccination utilizing Peter Dahlgren’s (2011) model. The contributions of this study are threefold. First, it identifies three dominant clusters of participation motivations: personal (...) interest, information brokerage, and persuasion. Second, the results show that Facebook sociality is characterized by asynchronous communication, loops, and widespread hostility. Third, degrees of content visibility set up “zones of peace” (backstage, safe communication spaces) and “zones of fight” (frontstage, open sub-arenas where various views on vaccination are debated). Moreover, the study finds that these forms of sociality and levels of visibility can both strengthen and undermine user motivations. (shrink)

L'étude de la communication peut offrir une perspective sur le contexte de la théologie, un examen de sa structure, et une reflexion sur son contenu. La communication est primordiale pour la société contemporaine, affectant la façon dont les gens utilisent leur temps, façonnant les informations qu'ils reçoivent, influençant la manière dont ils pensent , et les rendant plus soupçonneux vis à vis de l'autorité. L'histoire de la théologie montre les effets des formes de communication, reflétant la narration, la rhétorique, et (...) les structures polémiques des cultures orales, aussi bien que les instruments analytiques de l'écriture et l'imprimerie. Finalement, l'étude de la communication suggère une façon différente de considérer des sujets théologiques traditionnels. Le salut divin, par exemple, peut se concentrer sur la communication en interprètant l'histoire du salut comme une histoire de l'auto-communication de Dieu et la restauration de la communication humaine. (shrink)

The article offers a rigorous explication of the intuitive notion of verisimilitude, I.E., Of the distance of a theory from the truth. The proposal is defended against charges of material inadequacy made by popper, Niniluoto, And miller.

We give proofs of the effective monotone interpolation property for the system of modal logic K, and others, and the system IL of intuitionistic propositional logic. Hence we obtain exponential lower bounds on the number of proof-lines in those systems. The main results have been given in [P. Hrubeš, Lower bounds for modal logics, Journal of Symbolic Logic 72 941–958; P. Hrubeš, A lower bound for intuitionistic logic, Annals of Pure and Applied Logic 146 72–90]; here, we give considerably simplified (...) proofs, as well as some generalisations. (shrink)

Intensions feature prominently among the entities we talk about.

In lieu of an abstract, here is a brief excerpt of the content:Thomas G. Pavel INCOMPLETE WORLDS, RITUAL EMOTIONS' IN recent years, the notion of "fictional world" has enjoyed a considerable rise in fortune. The expression, however, is not entirely new. To refer to the world of a literary work, of a novel or of a play, has always been a favorite way of speaking for literary critics and aestheticians. In most cases, these were informal worlds. A discussion of (...) the world of Balzac, Dostoyevsky, HenryJames, or Proust often amounts to a description of each author's preferences in die selection and rearrangement of his material. Such discussion primarily fits authors who purposefully attempt to build comprehensive representational artifacts. One speaks quite naturally about l'univers balzacien, or about the universe of Musil. But is one entitled to refer with equal ease to the world ofBenjamin Constant, meagerly perceptible in his Adolphe, a short novel built in the spirit of economy, displaying just a few characters and a minimum of worldly information? Perhaps density and comprehensiveness are not indispensable characteristics of literary worlds. Aestheticians and narratologists using the "fictional worlds" terminology seem to believe mat any kind of artistic text projects a world, be it rich or poor. Such worlds are imagined in the fashion of modern philosophy of logic as states of affairs, more or less comprehensive. Some writers believe that the states of affairs comprised in fictional worlds must be fairly sizable, since diey should include "not only what the author indicates, but also whatever is required (entailed) by that which he indicates." 1 The laws of nature which are not specifically contradicted by the text would belong to its world. Thus, a few notorious cases aside, there is no reason to doubt that every child born in fiction has been engendered by a human fadier as long as the text does not report an exception. And if it does? Then, assuming that the laws of logic still govern if not fiction itself at least our understanding of it, we may appeal to what "possible world" philosophers have called "small miracles." * Editor's note: This article, as well as the contributions by Gerald Prince, Peter van Inwagen, and Kendall Walton which follow it, grew out ofa symposium on "Styles ofFictionality," organized by Professor Pavel and held at Harvard University in 1981. The Fall, 1983 issue of PHILOSOPHY AND LITERATURE will contain additional papers presented at the symposium. 48 Thomas G. Pavel49 Imagine, for instance, the world in which Notre Dame de Paris would be covered with blue paint. While everything else would preserve the properties it possesses in the actual world, with the laws of nature and the caused chains maintained, a small local change, somewhat miraculous, would modify only the color of the venerable building. Similarly, the world of Balzac may be understood as the world of early and mid-nineteenth-century France, slightly modified by the addition of a few hundred imagined characters. That diese conform surprisingly well to the general laws of French society of the time is so much the goal of Balzac's successful project, that for the sociologically-minded reader die' actual nonexistence of Rastignac, Rubempré, Vautrin, or Birotteau may appear a mere accident. These characters, one may surmise, display every trait that actual counterparts of theirs would possess, except existence. Hence, why would Rastignac's or Vautrin's emergence in a world omerwise identical to nineteenth-century France amount to anydiing more than a "small miracle"? On the other hand, Balzac's world being blessed wim hundreds of such miracles, the very magnitude of the project vindicates the attribute of "visionary," ascribed to Balzac by Béguin, or, if metaphorically undercut, mat of"God the Father" given him by Thibaudet. For, would not such magnitude entail more than just local changes in an otherwise faithful representation of the "actual" nineteenthcentury France? Similarly, would we interpret a fictional world in which a child has been engendered not by a human father, but by a divinity, as identical in all respects to the actual world, except for the limited modification attributed to a small miracle? 2 If we grant for a moment the improbable assumption that nineteenth-century France was a given and that Balzac... (shrink)

In [Laurence, Margolis 2003] the authors try - within their polemics against F.Jackson’s views in [Jackson 1998] - to decide the question whether concepts are a priori (in their formulation “to be defined a priori”). Their discussion suffers - as a number of similar articles - from a typical drawback: some problem whose solution requires an exact notion of concept is handled as if the latter were quite clear. The consequence of this ‘conceptual laxity’ is that a) the topic of (...) the discussion is not very clear (what does the phrase ‘concepts must be defined a priori’ mean?); b) the relevance of the Quinean criticism of the “second dogma of empiricism”, i.e., of Quine’s claim that “science sometimes overturns our most cherished beliefs” and therefore there is no sharp boundary between analytic and synthetic is uncritically accepted; c) no distinction is made between the question whether the relation between an expression and its meaning is a priori and the question whether the relation between a concept and the object identified by the concept is a priori. The present article intends to elucidate and then to answer the questions that can be asked when we say something like “concepts are a priori ”. (shrink)

[A Note on Peregrin‘s Critique of Cmorej‘s Conception. of Linguistic Expression].

Ultimately everything returns to its own place. And our life, like a river that had overflowed its banks, is again returning to its former bed. We are now assimilating long-hidden treasures, understanding forgotten truths, and regaining our sight and seeing what we were unable to see when we were blinded.

The paper deals with the semantics of mathematical notation. In arithmetic, for example, the syntactic shape of a formula represents a particular way of specifying, arriving at, or constructing an arithmetical object (that is, a number, a function, or a truth value). A general definition of this sense of "construction" is proposed and compared with related notions, in particular with Frege's concept of "function" and Carnap's concept of "intensional isomorphism." It is argued that constructions constitute the proper subject matter of (...) both logic and mathematics, and that a coherent semantic account of mathematical formulas cannot be given without assuming that they serve as names of constructions. (shrink)

We give an exponential lower bound on number of proof-lines in the proof system K of modal logic, i.e., we give an example of K-tautologies ψ₁, ψ₂,... s.t. every K-proof of ψi must have a number of proof-lines exponential in terms of the size of ψi. The result extends, for the same sequence of K-tautologies, to the systems K4, Gödel—Löb's logic, S and S4. We also determine some speed-up relations between different systems of modal logic on formulas of modal-depth one.

European Journal of Philosophy, EarlyView.

Logical pluralism from historical perspective -The plurality of logics is understood as a challenge to seek a deeper understanding of the na- ture and import of logic. Two basic approaches to demarcation of logic are considered, the model-theoretic and the proof-theoretic one. Investigation of the history which led to these two appraoches identifies the postion of logic in Kant's epistemology as crucial for the devel- opment. An analogical development from Kant's conception of geometry to the plurality of geometric theories leads (...) to a holistic view both of geometry and of logic. It furthermore proves essential to understand the pragmatic import of logic. Given the problems tied to the attempts to demarcate logic, inferentialism and logical expressivism are arrived at as jointly provid- ing the most appropriate account. These approaches are developed into a conception which stresses, in line with the historical perspective of the work, the ability of logic to develop. (shrink)

A new approach to defining complexity of propositional formulas and proofs is suggested. Instead of measuring the size of these syntactical structures in the propositional language, the article suggests to define the complexity by the size of external descriptions of such constructions. The main result is a lower bound on proof complexity with respect to this new definition of complexity.