We apply Benacerraf’s distinction between mathematical ontology and mathematical practice to examine contrasting interpretations of infinitesimal mathematics of the seventeenth and eighteenth century, in the work of Bos, Ferraro, Laugwitz, and others. We detect Weierstrass’s ghost behind some of the received historiography on Euler’s infinitesimal mathematics, as when Ferraro proposes to understand Euler in terms of a Weierstrassian notion of limit and Fraser declares classical analysis to be a “primary point of reference for understanding the eighteenth-century theories.” Meanwhile, scholars like (...) Bos and Laugwitz seek to explore Eulerian methodology, practice, and procedures in a way more faithful to Euler’s own. Euler’s use of infinite integers and the associated infinite products are analyzed in the context of his infinite product decomposition for the sine function. Euler’s principle of cancellation is compared to the Leibnizian transcendental law of homogeneity. The Leibnizian law of continuity similarly finds echoes in Euler. We argue that Ferraro’s assumption that Euler worked with a classical notion of quantity is symptomatic of a post-Weierstrassian placement of Euler in the Archimedean track for the development of analysis, as well as a blurring of the distinction between the dual tracks noted by Bos. Interpreting Euler in an Archimedean conceptual framework obscures important aspects of Euler’s work. Such a framework is profitably replaced by a syntactically more versatile modern infinitesimal framework that provides better proxies for his inferential moves. (shrink)

ABSTRACT The following text is a large fragment of the lectures on heresy that Leszek Kołakowski (1927–2009) gave between November 1982 and February 1983 on the Polish radio station Radio Free Europe. These lectures have never been published in English. They were only published under the title ‘Herezja’ in Poland after the author’s death in 2010 by the publishing company Znak. Kołakowski raises the universal and timeless issues of tolerance, ideological struggles, protection of doctrine by religious institutions and the changing (...) attitude of the Catholic Church towards heretical challenges (tackling them and attempting to annex and colonize certain ideas). The concept of heresy is an opportunity to describe the history of ideological conflicts, show how they arise and how they can be resolved. The story of struggle between dogmatists and heretics is an endless story of changing social order and giving new shapes to the reality created by people and their ideas. Kołakowski points out that any doctrinal, political or ideological system must allow for criticism and otherness. Nearly 40 years after these lectures were given, they retain a special freshness in the context of the political, ideological and social crisis that Europe is experiencing in the early twenty-first century. (shrink)

As shown in (Łukowski, Gensler, 2013), the paradox of the stone is a failed attempt to show that “omnipotence” is a contradictory concept. An element of the argument presented there is that God, while unable to lift the stone, can nevertheless annihilate it. This work considers the amplification of the paradox of the stone to the form generated by the question: can God create a stone which He will not be able to lift, nor, once created, will He be able (...) to destroy. (shrink)

This interdisciplinary study introduces readers to Friedrich Schleiermacher’s diverse pathways of reflection and creative practice that are related to the field of translation. By drawing attention to Schleiermacher’s various writings on a range of subjects (including philology, criticism, hermeneutics, dialectics, rhetoric and religion), the author makes it clear that the frequently cited lecture Über die verschiedenen Methoden des Übersetzens (On the Different Methods of Translating) represents but a fraction of Schleiermacher’s contributions to modern-day insights into translation. The analysis of Schleiermacher’s (...) various pathways of reflection on translation presented in this book leads to the conclusion that translation is part of the essence of the world, as it is a fundamental tool of our cognition and a foundation of our existence. In Schleiermacher’s works, transfer, translation, mediation, and communication underpin our very existence in the world and our self-awareness. At the same time, they represent fundamental categories for a project that focuses on the consolidation and assimilation – through translation – of that which is foreign, different, diverse. (shrink)

An attempt at moral interpretation of Hegelian 'struggle for recognition'. The Author shows how the Hegelian figures of 'Lord' and 'Bondsman' can be used to explain social role and importance of the idea of tolerance in the context of group moralities and the universal morality. The text is built of three parts: the author sketches the connection of the traditional idea of tolerance and sociological understanding of morality on the basis of Hegel's understanding of recognition. In the second step, he (...) gives an outline of Hegelian two accounts of mutual recognition, finally the author shows the moral dimension of recognition, as referred to the idea of tolerance and universalistic morality. (shrink)

This article surveys briefly the main concepts of the nation and nationalism, and notes the wide range of interpretations. A distinction is drawn between Liberal and integral nationalism, the use of the Polish term nacjonalizm, and the alleged basic difference between nationalism in Western and Eastern Europe.The second part of this article is devoted to Walicki’s theses and contributions. They are characterized by a rejection of the concept of the artificiality of the nation, of “constructivism” and the “imagined community” model. (...) He does it not only on purely theoretical grounds but on the basis of an examination of the origins and development of Polish nationalism and patriotism which the above-cited writers have ignored. He concludes that only a profound knowledge of Polish history—sadly lacking in Western literature—would permit a more nuanced presentation of the general phenomena of nation and nationalism in Europe. (shrink)

As far as existence of enduring subjects of change is concerned, Roman Ingarden's substance ontology stands in direct opposition to Whitehead's process metaphysics. However, with regard to domain of necessary relations, both systems are deeply platonic. Thus in this paper I pursue towards revealing some parallels and differences between both systems regarding views on ideal entities, necessary relations and pure possibilities. I examine whether having assumed contrary concepts of reality (substantial/procesual) both philosophers are forced to accept diverse conclusions in respect (...) to ideal entities domain. I also point out some crucial problems that are to be found in both systems: what is the ground of necessary relations – is it a nature of so called ideal qualities, or is it content of ideas (Ingarden); is it an individual or a relational essence of eternal objects, so called "primordial nature of God", or evolving actuality (Whitehead). Finally I investigate whether points of convergence between both concepts could serve as a basis for some modifications to overcome relevant problems. (shrink)

ABSTRACTThe author traces the impact of Abramowski's ideas on the recent history of Poland. His concepts were not only popular in the Polish Socialist Party and the syndicalist movement in the interwar period, but they also exerted a profound influence on the cooperative movement and democratic left-wing opposition in the 1970s and 1980s. The leaders of the Workers’ Defence Committee were much influenced by Abramowski's ideas and, according to some researchers, the Solidarity movement from 1980 to 1981 in Poland was (...) the culmination of his concepts. Today's anti-systemic movements in Poland are also inspired by Abramowski. The author also draws attention to certain similarities between Abramowski's ideas, Kropotkin's idea, Gramsci's concept of civil society and the thought of the young Marx. The author also outlines Abramowski's social ideas in the context of ideas promoted by the main theoreticians of the Polish left in the late nineteenth and early twentieth centuries. (shrink)

Volume 17, Issue 5, November 2020, Page 566-588.

ABSTRACT The article analyses the language used by the Polish nationalist right in relation to LGBT communities and the right to abortion. The authors show links between the language of Church hierarchs and right-wing columnists as the ideological backbone of the governing right-wing populist right. According to the authors, the attack on gender is the same method of political mobilisation and power management as the campaign against refugees and the anti-immigrant hysteria. On the one hand, the anti-gender discourse may strengthen (...) the narrative against the ‘liberal EU’ and, on the other hand, it is used to show substitute ‘scapegoats’ in Poland. Moral panic makes it possible to release class tensions in the manner that is safe for the system through the artificially induced cultural and ideological conflict. However, the dispersed anti-gender discourse has a real impact on social attitudes – on the one hand, it polarises social sympathies and, on the other hand, it strengthens conservative attitudes. The analysis is based on right-wing press articles, Church hierarchs’ statements, videos on YouTube and a parliamentary debate about the right to abortion. (shrink)

Interpretations of logics with only truth-functional connectives create a number of problems regarding the understanding of interpreted sentences. A particular problem is caused by the understanding of a sentence that is the negation of another. What is the meaning of sentence ¬p, for a particular sentence p? Even when we know what the semantic correlate of the sentence p is, we still do not know how to understand the semantic correlate of the sentence ¬p. The standard algebraic approach does not (...) explain much. The problem is still open, because it is still unclear how to understand the element of algebra −v(p). The propositional logic with the connective of the content implication, as it is a non-Fregean logic, proposes a simple solution to this problem. The key to understanding the content of the sentence ¬p is to understand the content of the sentence p. Because, the content of the natural language sentence usually has a partial understanding, so it can be understood differently. Therefore, the negation ¬p is here understood adequately to the current and partial understanding of the sentence p. It seems that the proposed approach is consistent with our daily thinking. (shrink)

The ancient paradox of Protagoras had the opinion of an unsolved problem. The two solutions proposed in the 20th century by W. Lenzen and L. Aqvist are considered to be the best. In fact none of them may be treated as proper. In the paper we show that both of authors avoid contradiction solely by means of mere neglect. However quite a simple solution seems to be feasible when the paradox is approached as an amphibolic construction, thus an ambiguity.

This book, provides a critical approach to all major logical paradoxes: from ancient to contemporary ones. There are four key aims of the book: 1. Providing systematic and historical survey of different approaches – solutions of the most prominent paradoxes discussed in the logical and philosophical literature. 2. Introducing original solutions of major paradoxes like: Liar paradox, Protagoras paradox, an unexpected examination paradox, stone paradox, crocodile, Newcomb paradox. 3. Explaining the far-reaching significance of paradoxes of vagueness and change for philosophy (...) and ontology. 4. Proposing a novel, well justified and, as it seems, natural classification of paradoxes. (shrink)

ABSTRACT How can we understand the term ‘utopia’ and does the adjective ‘utopian’ discredit the social thought to which it refers? The author discusses the role of utopia in the emergence of social sciences and alludes to Immanuel Wallerstein and his analysis of utopistics. He also defends the hypothesis that in the times of political, economic and ecological crisis which is sweeping through Europe and the world in the first decades of the twenty-first century, utopian thinking may be reborn not (...) only as a way of showing possible social alternatives, but also as a means of democratizing public debate and the existing status quo. In this perspective, utopianism can be invigorating not only for democracy, but also for independent and critical social thought. Social utopias, which contributed to the rise of the mass workers’ movement in the nineteenth century, today may become a force mobilizing human imagination and sensitivity to the struggles for a more emancipatory and democratic social order. (shrink)

The 20 th Cracow Methodological Conference took place on May 30-31, 2016, at the Polish Academy of Arts and Sciences in Kraków. The meeting brought together physicists, cosmologists, mathematicians and philosophers interested in research program called philosophy in science started and popularized by Michał Heller. It is worth noting that the 20 th Cracow Methodological Conference was dedicated to Professor Heller and can be considered as a contribution to the celebration of the 80 th anniversary of his birthday.

This Research Topic addresses the first Sustainable Development Goal, which is to “end poverty in all its forms everywhere.” Progress toward this goal is measured by a number of individual targets and indicators. As highlighted in the UN’s most recent SDG progress report, the slowdown in poverty reduction since 2015 has been greatly exacerbated by the coronavirus pandemic. In 2020, for example, around 120 million people were pushed back into extreme poverty, representing the first increase in extreme poverty in over (...) 20 years. Along with workers in the informal economy, the pandemic has also disproportionately impacted young and female workers. At present, the goal of eradicating poverty by 2030 is not on course to be met, with around 600 million people expected to be living in extreme poverty in 2030. Against the backdrop of the growing climate crisis, significant efforts are therefore needed to bring the 2030 target within reach. * This Research Topic will address the first Sustainable Development Goal from a sociology-specific perspective. It will enquire about the framing and elaboration of the goal, its adaptation to particular geographical contexts, stakeholder involvement in it, and influence and impact of social mobility and social stratification studies on it. Given the setbacks to poverty reduction across the world resulting from the coronavirus pandemic, this year’s edition of the Research Topic will focus particularly on the challenges and complexities of poverty reduction in the wake of the COVID-19 crisis. (shrink)

The aim of the paper is to sketch an idea—seen from the point of view of a cognitive scientist—of cognitive semiotics as a discipline. Consequently, the article presents aspects of the relationship between the two disciplines: semiotics and cognitive science. The main assumption of the argumentation is that at least some semiotic processes are also cognitive processes. At the methodological level, this claim allows for application of cognitive models as explanations of selected semiotic processes. In particular, the processes of embedded (...) interpretation are considered: belief revision, dynamic organization of meaning and metaknowledge. The explanations are formulated in terms of artificial cognitive agents of the GLAIR/SNePS cognitive architecture. Finally, it is suggested that even if someone rejects the idea of artificial cognitive systems as simulations of semiotic processes, they may acknowledge the usefulness of cognitive modeling in analysis of semiotic processes in virtual, simulated worlds and in the area of “new media”. (shrink)

Some subfamilies of κ, for κ regular, κ λ, called -semimorasses are investigated. For λ = κ+, they constitute weak versions of Velleman's simplified -morasses, and for λ > κ+, they provide a combinatorial framework which in some cases has similar applications to the application of -morasses with this difference that the obtained objects are of size λ κ+, and not only of size κ+ as in the case of morasses. New consistency results involve existence of nonreflecting objects of singular (...) sizes of uncountable cofinality such as a nonreflecting stationary set in κ, a nonreflecting nonmetrizable space of size λ, a nonreflecting nonspecial tree of size λ. We also characterize possible minimal sizes of nonspecial trees without uncountable branches. (shrink)

The aim of the paper is to point out the modelling choices that lead to different systems of deontic action logic. A kind of a roadmap is presented. On the one hand it can help the reader to find the deontic logic appropriate for an intended application relying on the information considering the way in which a deontic logic represents actions and how it characterises deontic properties in relation to (the representation of) actions. On the other hand it is a (...) guideline how to build a deontic action logic which satisfies the desired properties. (shrink)

We study a strengthening of the notion of a perfectly meager set. We say that a subset A of a perfect Polish space X is countably perfectly meager in X, if for every sequence of perfect subsets $\{P_n: n \in \mathbb N\}$ of X, there exists an $F_\sigma $ -set F in X such that $A \subseteq F$ and $F\cap P_n$ is meager in $P_n$ for each n. We give various characterizations and examples of countably perfectly meager sets. We prove (...) that not every universally meager set is countably perfectly meager correcting an earlier result of Bartoszyński. (shrink)

A calculus of names is a logical theory describing relations between names. By a pure calculus of names we mean a quantifier-free formulation of such a theory, based on classical propositional calculus. An axiomatisation of a pure calculus of names is presented and its completeness is discussed. It is shown that the axiomatisation is complete in three different ways: with respect to a set theoretical model, with respect to Leśniewski's Ontology and in a sense defined with the use of axiomatic (...) rejection. The independence of axioms is proved. A decision procedure based on syntactic transformations and models defined in the domain of only two members is defined. (shrink)

In the paper we examine the method of axiomatic rejection used to describe the set of nonvalid formulae of Aristotle's syllogistic. First we show that the condition which the system of syllogistic has to fulfil to be ompletely axiomatised, is identical to the condition for any first order theory to be used as a logic program. Than we study the connection between models used or refutation in a first order theory and rejected axioms for that theory. We show that any (...) formula of syllogistic enriched with classical connectives is decidable using models in the domain with three members. (shrink)

It is our intention to re-investigate only a few of the innumerable epistemological problems concerning Paley's argumentation for the existence of God. Nowadays this argumentation is commonly considered as invalid. Modern philosophers believe that the Humean Dialogs on Natural Religion and the Darwinian theory of evolution deprived Paley's reasoning of any cognitive validity. This judgment seems to us unjustified. We shall try to demonstrate that the very meaning and the logical structure of Paley's argumentation are continuously misunderstood, and that critics (...) have attacked rather a false image of Paley's cognitive pathway. Furthermore, we will show that Paley actually argues for the existence of a single agent producing biological organs. Indeed Paley demonstrates, that a biological organ is a kind of objective whole, and by necessity one produced by a single agent. However, Paley's form of argumentation is not sufficient to indicate whether this agent might be identified with a divine Creator, or Aristotelian "soul" building and commanding biological organs, or the recently discovered, described and deciphered deoxynucleotide polymer present in the reproductive biological cell. (shrink)

We consider the existence of coherent families of finite-to-one functions on countable subsets of an uncountable cardinal κ. The existence of such families for κ implies the existence of a winning 2-tactic for player TWO in the countable-finite game on κ. We prove that coherent families exist on κ = ωn, where n ∈ ω, and that they consistently exist for every cardinal κ. We also prove that iterations of Axiom A forcings with countable supports are Axiom A.

$(X_\alpha: \alpha is a strong chain in ℘(ω 1 )/Fin if and only if X β - X α is finite and X α - X β is uncountable for each $\beta . We show that it is consistent that a strong chain in ℘(ω 1 ) exists. On the other hand we show that it is consistent that there is a strongly almost-disjoint family in ℘(ω 1 ) but no strong chain exists: □ ω 1 is used to construct (...) a c.c.c forcing that adds a strong chain and Chang's Conjecture to prove that there is no strong chain. (shrink)

By pure calculus of names we mean a quantifier-free theory, based on the classical propositional calculus, which defines predicates known from Aristotle’s syllogistic and Leśniewski’s Ontology. For a large fragment of the theory decision procedures, defined by a combination of simple syntactic operations and models in two-membered domains, can be used. We compare the system which employs `ε’ as the only specific term with the system enriched with functors of Syllogistic. In the former, we do not need an empty name (...) in the model, so we are able to construct a 3-valued matrix, while for the latter, for which an empty name is necessary, the respective matrices are 4-valued. (shrink)

In the paper, several data reduction techniques for machine learning from big datasets are discussed and evaluated. The discussed approach focuses on combining several techniques including stacking, rotation, and data reduction aimed at improving the performance of the machine classification. Stacking is seen as the technique allowing to take advantage of the multiple classification models. The rotation-based techniques are used to increase the heterogeneity of the stacking ensembles. Data reduction makes it possible to classify instances belonging to big datasets. We (...) propose to use an agent-based population learning algorithm for data reduction in the feature and instance dimensions. For diversification of the classifier ensembles within the rotation also, alternatively, principal component analysis and independent component analysis are used. The research question addressed in the paper is formulated as follows: does the performance of a classifier using the reduced dataset be improved by integrating the data reduction mechanism with the rotation-based technique and the stacking? (shrink)

We give geometric axioms for existentially closed Hasse fields. We prove a quantifier elimination result for existentially closed n-truncated Hasse fields and characterize them as reducts of existentially closed Hasse fields.

We investigate a speci c model of knowledge and beliefs and their dynamics. The model is inspired by public announcement logic and the approach to puzzles concerning knowledge using that logic. In the model epistemic considerations are based on ontology. The main notion that constitutes a bridge between these two disciplines is the notion of epistemic capacities. Within the model we study scenarios in which agents can receive false announcements and can have incomplete or improper views about other agent's epistemic (...) capacities. Moreover, we try to express the description of problem speci cation using the tools from applied ontology { RDF format for information and the Protege editor. (shrink)

Trivalence is quite natural for deontic action logic, where actions are treated as good, neutral or bad.We present the ideas of trivalent deontic logic after J. Kalinowski and its realisation in a 3-valued logic of M. Fisher and two systems designed by the authors of the paper: a 4-valued logic inspired by N. Belnap’s logic of truth and information and a 3-valued logic based on nondeterministic matrices. Moreover, we combine Kalinowski’s idea of trivalence with deontic action logic based on boolean (...) algebra. (shrink)

In the paper we provide an overview of issues related to the models used in the research on the logic of norms and actions. We present two models of the variability of the world: temporal (acyclic) and atemporal (cyclic). In the first one the past is always clearly defined, and the future is potentially “branched”. The second type of model allows for a return to the situation that took place. Next we describe different approaches towards agency modeling. We present the (...) most important paradigms, including the logic of actions, where actions are interpreted as transitions between the situations and STIT logic, which states only the responsibility of the agent for particular states of affairs. We discuss questions of determinism and indeterminism of actions, identification of basic actions and operations and the issue of identity. The final part of the paper is devoted to deontic categories. In particular, the applicability of the concepts of strong and weak permission and prohibition in different situational contexts, and their relationship to the two concepts of obligation: abstract and derived. (shrink)

This article describes the slight impact of Lysenkoism upon Polish botany. I begin with an account of the development of plant genetics in Poland, as well as the attitude of scientists and the Polish intelligentsia toward Marxist philosophy prior to the World War II. Next I provide a short history of the introduction and demise of Lysenkoism in Polish science, with a focus on events in botany, in context with key events in Polish science from 1939 to 1958. The article (...) outlines the little effects of Lysenkoism upon botanists and their research, as well as how botanists for the most part rejected what was often termed the "new biology." My paper shows that though Lysenko's theories received political support, and were actively promoted by a small circle of scientists and Communist party activists, they were never accepted by most botanists. Once the political climate in Poland altered after the events of 1956, Lysenko's theories were immediately abandoned. (shrink)