We study the variety generated by the three-element equivalential algebra with conjunction on the dense elements. We prove the representation theorem which let us construct the free algebras in this variety.

We construct free algebras in the variety generated by the equivalential algebra with conjunction on dense elements and compute the formula for the free spectrum of this variety. Moreover, we describe the decomposition of free algebras into directly indecomposable factors.

In this paper, we complement proximate or ‘how’ explanations for the origins of language, broadening our perspective to include fitness-consequences explanations, i.e. ultimate, or ‘why’ explanations. We identify the platform of trust as a fundamental prerequisite for the development of a language-like system of symbolic communication. The platform of trust is a social niche in which cheap but honest communication with non-kin is possible, because messages tend to be trusted as a default. We briefly consider the place of the platform (...) of trust on the road map as laid out in the Mirror System Hypothesis. We then turn to recent research on turn-taking in primates, which has been proposed as a precursor of the cooperative structuring of conversation in humans. We suggest, instead, that human turn-taking, in its full richness that makes it an interesting explanatory target, may only appear in a communicative system that is already founded on a community-wide, cooperative platform of trust. (shrink)

The set of design features developed by Charles Hockett in the 1950s and 1960s remains probably the most influential means of juxtaposing animal communication with human language. However, the general theoretical perspective of Hockett is largely incompatible with that of modern language evolution research. Consequently, we argue that his classificatory system—while useful for some descriptive purposes—is of very limited use as a theoretical framework for evolutionary linguistics. We see this incompatibility as related to the ontology of language, i.e. deriving from (...) Hockett’s interest in language as a product rather than a suite of sensorimotor, cognitive and social abilities that enable the use but also acquisition of language by biological creatures. After a reconstruction of Hockett’s views on design features, we raise two criticisms: focus on the means at the expense of content and focus on the code itself rather than the cognitive abilities of its users. Finally, referring to empirical data, we illustrate some of the problems resulting from Hockett’s approach by addressing three specific points—namely arbitrariness and semanticity, cultural transmission, and displacement—and show how the change of perspective allows to overcome those difficulties. (shrink)

We study the structure of analytic ideals of subsets of the natural numbers. For example, we prove that for an analytic ideal I, either the ideal {X (Ω × Ω: En X ({0, 1,…,n} × Ω } is Rudin-Keisler below I, or I is very simply induced by a lower semicontinuous submeasure. Also, we show that the class of ideals induced in this manner by lsc submeasures coincides with Polishable ideals as well as analytic P-ideals. We study this class of (...) ideals and characterize, for example, when the ideals in it are Fσ or when they carry a locally compact group topology. We apply these results to Borel partial orders to rederive a theorem of Todorcevic and to Borel equivalence relations to answer a question of Kechris and Louveau. As another application we give a characterization of σ-ideals of μ-zero sets for Maharam submeasures μ on the Cantor set which is to a large extent analogous to a characterization of the meager ideal due to Kechris and the author. (shrink)

We applaud Heintz & Scott-Phillips's guiding metaphor of “unleashing leashed expression,” and we value the unified explanation for the emergence of not only language, but also other forms of unleashed expression, such as multimodal communication. We are more critical of the authors' discussion of the selection pressures acting towards unleashed expression, which are proposed to hinge on partner choice ecology.

The paper presents an analysis of the ethical, political and economic aspects of human work within two Polish historical periods – the years of the People’s Republic of Poland and after 1989. The starting point for the analysis was the assumption that every time period, each age, leaves a mark on man’s work. Analysis of the People's Republic of Poland period gives an opportunity to consider human work understood as a duty and right of every human guaranteed by the Constitution (...) of 1952. Questioning the principles ruling the labour market by the ideologists of the People’s Republic of Poland and, as a consequence, the politicization of labour, resulted in the collapse of the work ethic. Work, as it was at that time a commonly available good, lost its value, regarded as the source of life satisfaction, and thus became ridiculed. After 1989, in relation to the de-politicization of the Polish labour market, the employee became active in searching for a job. The phenomenon of unemployment resulted in competition on the labour market and the employer was thus given the opportunity to freely select a group of employees. As a result, the employer became a distributor of a ‘rare commodity.’ That, in turn, led to the situation where the approach of employers towards employees turned into the employer's diktat. It is the employer who determines the conditions of employment, standards of work and place of work. A lack of alternative that many employees face often makes them accept the dictated conditions of work. What is more, in Poland we deal with the insufficiently developed participation of employees in managing the enterprises, which is an effect of breaking off the bilateral dependency of employee and employer. (shrink)

The aim of this paper is to outline the general oversight of the concept of law in Leon Petrażycki’s legal theory. On the example of the principles of law, an attempt was made to answer the question, what Petrażycki’s theory proposes to modern science. In the first part of the presentation, the Author presented the current state of theoretical knowledge in the field of principles of law. The attention was paid to the problem of various characteristics of legal principles. In (...) further considerations, an attempt was made to answer the question about adoption of models proposed by Petrażycki in the contemporary theoretical discourse. The summary presents general conclusions of the paper. (shrink)

Livio Rossetti, Le dialogue socratique, Éditions Les Belles Lettres, Paris 2011, ss. 296.

§1. Introduction. Ideals and filters of subsets of natural numbers have been studied by set theorists and topologists for a long time. There is a vast literature concerning various kinds of ultrafilters. There is also a substantial interest in nicely definable ideals—these by old results of Sierpiński are very far from being maximal— and the structure of such ideals will concern us in this announcement. In addition to being interesting in their own right, Borel and analytic ideals occur naturally in (...) the investigations of compact subsets of the space of all Baire class 1 functions on a Polish space, see [12, 18]. Also, certain objects associated with such ideals are of considerable interest and were quite extensively studied by several authors. Let us list here three examples; in all three of them I stands for an analytic or Borel ideal.1. The partial order induced by I on P: X ≥I Y iff X \ Y ϵ I and the partial order.2. Boolean algebras of the form P/I and their automorphisms.3. The equivalence relation associated with I: XEI Y iff X Δ ϵ I.In Section 4, we will have an opportunity to state some consequences of our results for equivalence relations as in 3. (shrink)

A new approach to semantics, based on ordered Banach spaces, is proposed. The Banach spaces semantics arises as a generalization of the four particular cases: the Giles' approach to belief structures, its generalization to the non-Boolean case, and fuzzy extensions of Boolean as well as of non-Boolean semantics.

The paper describes in detail the procedure of identification of the inner language and an inner logico of a physical theory. The procedure is a generalization of the original ideas of J. von Neuman and G. Birkhoff about quantum logic.

John Searle’s Chinese Room Argument purports to demonstrate that syntax is not sufficient for semantics, and, hence, because computation cannot yield understanding, the computational theory of mind, which equates the mind to an information processing system based on formal computations, fails. In this paper, we use the CRA, and the debate that emerged from it, to develop a philosophical critique of recent advances in robotics and neuroscience. We describe results from a body of work that contributes to blurring the divide (...) between biological and artificial systems; so-called animats, autonomous robots that are controlled by biological neural tissue and what may be described as remote-controlled rodents, living animals endowed with augmented abilities provided by external controllers. We argue that, even though at first sight, these chimeric systems may seem to escape the CRA, on closer analysis, they do not. We conclude by discussing the role of the body–brain dynamics in the processes that give rise to genuine understanding of the world, in line with recent proposals from enactive cognitive science. (shrink)

We prove that for every family I of closed subsets of a Polish space each Σ 1 1 set can be covered by countably many members of I or else contains a nonempty Π 0 2 set which cannot be covered by countably many members of I. We prove an analogous result for κ-Souslin sets and show that if A ♯ exists for any $A \subset \omega^\omega$ , then the above result is true for Σ 1 2 sets. A theorem (...) of Martin is included stating that this result is also true for weakly homogeneously Souslin sets. As an application of our results we derive from them a general form of Hurewicz's theorem due to Kechris, Louveau, and Woodin and a theorem of Feng on the open covering axiom. Also some well-known theorems on finding "big" closed sets inside of "big" Σ 1 1 and Σ 1 2 sets are consequences of our results. (shrink)

We prove that every analytic set in ω ω × ω ω with σ-bounded sections has a not σ-bounded closed free set. We show that this result is sharp. There exists a closed set with bounded sections which has no dominating analytic free set, and there exists a closed set with non-dominating sections which does not have a not σ-bounded analytic free set. Under projective determinacy analytic can be replaced in the above results by projective.

Nowadays, computers are in common use, both in experimental and theoretical research. It is worth considering if the implementation of a new, universal research tool has significantly changed the science of the end of 20th century. The crucial question which I will try to answer is if computers have revolutionized the scientific research. In order to find the answer, I will describe modern digitally aided science, taking into consideration the research conducted in the greatest elementary physics laboratory. Subsequently, I will (...) refer to the classic concept of scientific revolution proposed by Thomas S. Kuhn. Finally, I will answer the question related to digital revolution in science. (shrink)

Nowadays, computers are in common use, both in experimental and theoretical research. It is worth considering if the implementation of a new, universal research tool has significantly changed the science of the end of 20th century. The crucial question which I will try to answer is if computers have revolutionized the scientific research. In order to find the answer, I will describe modern digitally aided science, taking into consideration the research conducted in the greatest elementary physics laboratory. Subsequently, I will (...) refer to the classic concept of scientific revolution proposed by Thomas S. Kuhn. Finally, I will answer the question related to digital revolution in science. (shrink)

Informatycy zajmujący się problematyką algorytmów ewolucyjnych twierdzą, że miał miejsce transfer idei z biologii do informatyki, tzn. że ustalenia biologii ewolucyjnej stały się inspiracją do powstania tych algorytmów i że działają one analogicznie do procesów ewolucyjnych zachodzących w świecie przyrody. Jeśli jest tak faktycznie, to warto odpowiedzieć na pytanie, w jakim zakresie następuje przeniesienie ustaleń z biologii ewolucyjnej do działu informatyki zajmującego się algorytmami ewolucyjnymi. Zadanie to stanie się możliwe po uprzednim zreferowaniu sposobu działania algorytmów ewolucyjnych.

Wobec postępującego od lat procesu dyferencjacji nauk warto zadać pytanie o ich możliwą integrację. Problem ten przedstawiony zostanie na przykładzie kosmologii antropicznej. W pierwszej części artykułu opisane zostaną dwa podstawowe ujęcia kosmologii antropicznej, to znaczy mocna i słaba kosmologia antropiczna (kosmologia inflacyjna oraz kosmologia kwantowa). Następnie zostanie ona ukazana jako przykład projektu integracji nauk ewolucyjnych. W ostatniej części artykułu podjęta zostanie próba wykazania, że kosmologia antropiczna (w znaczeniu szerszym niż wcześniej opisana słaba i mocna kosmologia antropiczna) może stanowić paradygmatyczny przykład (...) nauki ewolucyjnej o najszerszym zakresie badawczym i spójnej metodzie badawczej, wspólnej dla wszystkich nauk ewolucyjnych. Będzie to zatem opis projektu badawczego, który jednoczy wszystkie nauki ewolucyjne. ------------------------- Zgłoszono: 18/04/2023. Zrecenzowano: 20/09/2023. Zaakceptowano do publikacji: 15/11/2023. (shrink)

Deceased in January this year, the Polish-British sociologist Zygmunt Bauman has left an extremely rich scholarly legacy. In one of his last academic interviews, he refers to the key issues which had been the subject of his in-depth analysis for many years. Bauman starts with reflections on the gap between political authority and power. Next, given his long-standing research into ‘liquid modernity’, he focuses on the vitality of capitalism, which has now adopted a lighter, consumer form. Another thread of the (...) interview is Bauman’s own research attitude, which he refers to as ‘sociological hermeneutics’. It is characterized by his reluctance to use any ‘-isms’ and a profound mistrust of all particular schools of research which could limit creative freedom. In the final part of the interview, Bauman highlights the problem of the social entanglement of intellectuals. (shrink)

This paper explores the integration of machine learning into economics and social sciences, assessing its potential impact and limitations. It introduces fundamental machine learning concepts and principles, highlighting the differences between the two disciplines, particularly the focus on causal inference in economics and prediction in machine learning. The paper discusses diverse applications of machine learning, from extracting insights from unstructured data to creating novel indicators and improving predictive accuracy, while also addressing challenges related to data quality, computational efficiency, and data (...) ownership. It emphasizes the importance of standardization, transparency, and ethical considerations in prediction tasks, recognizing that machine learning is a powerful tool but cannot replace economic theory. Ultimately, researchers remain optimistic about the transformative potential of machine learning in re-shaping research methodologies and generating new insights in economics and social sciences. (shrink)

Let us consider multimodal logics and. We assume that is characterised by a class of connected frames, and there exists an -frame with a so-called -starting point. Similarly, the logic is characterised by a class of connected frames, and there exists an -frame with a -starting point. Using isomorphic copies of the frames and, we construct a connected frame which characterises the fusion. The frame thus obtained has some useful properties. Among others, is countable if both and are countable, and (...) there is a special world of the frame such that any formula is valid in the frame if and only if it is valid at the point. We also describe a similar construction where we assume the existence of two classes consisting of rooted frames only. Using those classes and frames with so-called -roots, we construct a rooted frame adequate for the fusion of modal logics characterised by the classes under consideration. Both constructions can be used interchangeably. The selection of the construction depends on... (shrink)