We generalize the notion of analytic/Borel equivalence relations, orbit equivalence relations, and Borel reductions between them to their continuous and quantitative counterparts: analytic/Borel pseudometrics, orbit pseudometrics, and Borel reductions between them. We motivate these concepts on examples and we set some basic general theory. We illustrate the new notion of reduction by showing that the Gromov–Hausdorff distance maintains the same complexity if it is defined on the class of all Polish metric spaces, spaces bounded from below, from above, and from (...) both below and above. Then we show that [Formula: see text] is not reducible to equivalences induced by orbit pseudometrics, generalizing the seminal result of Kechris and Louveau. We answer in negative a question of Ben Yaacov, Doucha, Nies, and Tsankov on whether balls in the Gromov–Hausdorff and Kadets distances are Borel. In appendix, we provide new methods using games showing that the distance-zero classes in certain pseudometrics are Borel, extending the results of Ben Yaacov, Doucha, Nies, and Tsankov. There is a complementary paper of the authors where reductions between the most common pseudometrics from functional analysis and metric geometry are provided. (shrink)

Descriptions of bodies within the literature of the enactive approach to cognitive science exhibit an interesting dialectical tension. On the one hand, a body is considered to be a unity which instantiates an identity, forming an intrinsic basis for value. On the other, a living body is in a reciprocally defining relationship with the environment, and is therefore immersed and entangled with, rather than distinct from, its environment. In this paper I examine this tension, and its implications for the enactive (...) approach, particularly the enactive conceptions of life and bodies. Following the lead of others, I argue that enactive cognitive science can benefit from a deeper reading and integration with extant work on the complexity and multiplicity of the living body within feminist philosophy and feminist science studies. (shrink)

The free association method is often employed in marketing research to investigate perceptions of a particular product or brand in different socio-cultural groups of customers. In our research, international and domestic students produced free associations in response to photographs of outdoor billboards from two different locations in one city (city centre and outskirts). The results indicate that free associations can depict qualitative aspects of outdoor billboards like poor quality (relating to the categories of amateurish and fake), problematic content (relating to (...) female stereotypes, gender stereotypes and cultural differences), and that they have the potential to capture the general atmosphere of the neighbourhood (categories of decay, depression, danger and past). (shrink)

Can we see the expressiveness of other people's gestures, hear the intentions in their voice, see the emotions in their posture? Traditional theories of social cognition still say we cannot because intentions and emotions for them are hidden away inside and we do not have direct access to them. Enactive theories still have no idea because they have so far mainly focused on perception of our physical world. We surmise, however, that the latter hold promise since, in trying to understand (...) cognition, enactive theory focuses on the embodied engagements of a cognizer with his world. In this paper, we attempt an answer for the question What is social perception in an enactive account? In enaction, perception is conceived as a skill, crucially involving action, an ability to work successfully within the set of regularities, or contingencies that characterize a given domain. If this is the case, then social perception should be a social skill. Having thus transformed the question of what social perception is into that of what social skill is, we examine the concept of social contingencies and the manner in which social skills structure—both constrain and empower— social interaction. Some of the implications of our account for how social and physical perception differ, the role of embodiment in social interaction and the distinction between our approach and other social contingency theories are also addressed. (shrink)

Die Beiträge zur Altertumskunde enthalten Monographien, Sammelbände, Editionen, Übersetzungen und Kommentare zu Themen aus den Bereichen Klassische, Mittel- und Neulateinische Philologie, Alte Geschichte, Archäologie, Antike Philosophie sowie Nachwirken der Antike bis in die Neuzeit. Dadurch leistet die Reihe einen umfassenden Beitrag zur Erschließung klassischer Literatur und zur Forschung im gesamten Gebiet der Altertumswissenschaften.

The world of Jedi is very different from our own, that their awareness of the universe is more encompassing, richer. The Jedi call that mystical aspect of reality they perceive the Force. Jedi younglings and padawans must put their body to new uses, perform new tasks, and learn new skills in physical activities that have profound effects on the way they see the world around them. What the Jedi say more than anything else about the Force is that it flows. (...) Jedi who are able to coordinate their actions with that flow can work with the full potency of the universal relationship between all things. Jedi do not need a special Force‐organ to perceive the Force. The Force is not something Jedi just see, or hear, or taste, or touch, but rather it is something they experience on its own terms, probably using their whole body to do it. (shrink)

Enactive and ecological approaches to cognitive science both claim a “mutuality” between agents and their environments – that they have a complementary nature and should be addressed as a single whole system. Despite this apparent agreement, each offers criticisms of the other on precisely this point – enactivists claiming that ecological psychologists over-emphasise the environment, while the complementary criticism, of agent-centred constructivism, is levelled by ecological psychologists at enactivists. In this paper I suggest that underlying the confusion between the two (...) approaches is the complexity of agency, which comes in different forms, at different scales or levels of analysis. Cognitive science has not theorised the relationship between these different forms in a sufficiently disciplined manner, and a task therefore remains of finding a way to map the complex territory of agency. (shrink)

We extend results of Elekes and Máthé on monotone Borel hulls to an abstract setting of measurable space with negligibles. This scheme yields the respective theorems in the case of category and in the cases associated with the Mendez σ-ideals on the plane. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

In this paper we show that if the real line \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\Bbb R}$\end{document} is not a union of less than continuum many of its meager subsets then there exists an almost continuous Sierpiński–Zygmund function having a perfect road at each point. We also prove that it is consistent with ZFC that every Darboux function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $f\colon{\Bbb R}\to{\Bbb R}$\end{document} is continuous on some set (...) of cardinality continuum. In particular, both these results imply that the existence of a Sierpiński–Zygmund function which is either Darboux or almost continuous is independent of ZFC axioms. This gives a complete solution of a problem of Darji [4]. The paper contains also a construction (in ZFC) of an additive Sierpiński–Zygmund function with a perfect road at each point. (shrink)

ABSTRACT The Gödel–Dummett logic and Łukasiewicz one are two main many-valued logics used by the fuzzy logic community. Our goal is a quantitative comparison of these two. In this paper, we will mostly consider the 3-valued Gödel–Dummett logic as well as the 3-valued Łukasiewicz one. We shall concentrate on their implicational-negation fragments which are limited to formulas formed with a fixed finite number of variables. First, we investigate the proportion of the number of true formulas of a certain length n (...) to the number of all formulas of such length built with exactly one variable. Then, we investigate such proportion for satisfiable formulas. Second, we generalise our investigation on formulas written with $ k\ge 1 $ k ≥ 1 variables. The primary goal of the paper is the research on the asymptotic behaviour of these fractions when the length n tends to infinity. If such limits exists, they are real numbers between 0 and 1, which are called the density of truth or the density of SAT. To compare the density of truth and the density of satisfiable formulas for both fragments of 3-valued Gödel–Dummett's and Łukasiewicz's logics we use the powerful theory of analytic combinatorics. This paper is a natural continuation of the previous brief conference note by Kostrzycka and Zaionc (2020) as well as enriched with some previous results from Kostrzycka and Zaionc (2003). In the conference note we computed analytically the density of truth and the density of SAT (with a determined precision) for 3-valued Łukasiewicz's logic restricted to a language with only one variable. In Kostrzycka and Zaionc (2003) we computed the same values for exactly the same fragment of the 3-valued Gödel–Dummett logic. This paper answers the more general questions of the existence of density of truth and density of SAT for both many-valued logics with an arbitrary finite number of variables. Therefore this paper gives an an interesting picture of two main families of finite-valued fuzzy logics problems treated quantitatively. This picture is taken from the perspective of classical logic. It shows that unexpectedly there is quantitatively a little distance between these two approaches. (shrink)

The subject of the book is a reconsideration of the internalistic model of composition of the Platonic type, and its application in the ontology of quantum theory. Nonseparability is at the centre of quantum ontology. Quantum wholes are atemporal wholes governed by internalistic logic, requiring a relativization of fundamental notions of mechanics.

Jaśkowski’s discussive logic D2 was formulated with the help of the modal logic S5 as follows (see [7, 8]): \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A \in {D_{2}}}$$\end{document} iff \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\ulcorner\diamond{{A}^{\bullet}}\urcorner \in {\rm S}5}$$\end{document}, where (–)• is a translation of discussive formulae from Ford into the modal language. We say that a modal logic L defines D2 iff \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm D}_{2} = (...) \{A \in {\rm For^{\rm d}} : \ulcorner\diamond{{A}^{\bullet}}\urcorner \in {\it L}\}}$$\end{document}. In [14] and [10] were respectively presented the weakest normal and the weakest regular logic which (†): have the same theses beginning with ‘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\diamond}$$\end{document}’ as S5. Of course, all logics fulfilling the above condition, define D2. In [10] it was prowed that in the cases of logics closed under congruence the following holds: defining D2 is equivalent to having the property (†). In this paper we show that this equivalence holds also for all modal logics which are closed under replacement of tautological equivalents (rte-logics).We give a general method which, for any class of modal logics determined by a set of joint axioms and rules, generates in the given class the weakest logic having the property (†). Thus, for the class of all modal logics we obtain the weakest modal logic which owns this property. On the other hand, applying the method to various classes of modal logics: rte-logics, congruential, monotonic, regular and normal, we obtain the weakest in a given class logic defining D2. (shrink)

Perceptual modalities have been traditionally considered the product of dedicated biological systems producing information for higher cognitive processing. Psychological and neuropsychological evidence is offered which undermines this point of view and an alternative account of modality from the enactive approach to understanding cognition is suggested. Under this view, a perceptual modality is a stable form of perception which is structured not just by the biological sensitivities of the agent, but by their goals and the set of skills or expertise which (...) they are deploying at a given time. Such a view suggests that there is no such thing as an experience that is purely visual, auditory, or otherwise modal and that our attempts to understand consciousness and the mind must be conducted within a framework that provides an account of embodied, goal-directed adaptive coping with the world. (shrink)

Dotyczy: przestrzeń, czas, ciało, kognitywistyka, fenomenologia.

The book deals with distorted humanities and social sciences and examines alternatives. The topic is analysed in a way that is ground-breaking in its global comparison of research in Central Europe, Latin America, China, Russia, Africa and India.

Artykuł przedstawia polskie regulacje prawne z lat 1998-2007 będące podstawą lustracji. Analizuje szereg aktów prawnych prezentując zakładane cele lustracji, jej zakres, procedury i przewidywane sankcje karne. Celem autora jest identyfikacja aksjologicznych podstaw regulacji prawnych dotyczących lustracji. W trakcie analiz wskazuje on m. in. na brak proporcji między sankcjami karnymi a winą jednostek, zwłaszcza w niektórych przypadkach penalizacji oświadczeń lustracyjnych niezgodnych z prawdą lub penalizacji niezłożenia oświadczeń. Autor argumentuje także, że analizowane rozwiązania zakładały – wbrew deklarowanym celom – przeniesienie odpowiedzialności za (...) zło systemu politycznego z jego aktywnych twórców na jednostki wbrew woli poddane działaniu tego systemu. Ponadto argumentuje, że lustracja oparta na przeprowadzanym przez państwo „teście moralności” radykalnie ingeruje w wewnętrzną sferę moralności jednostki i stąd zakłada elementy typowe dla aksjologii systemów totalitarnych; państwo nakazuje dokonać działania, które bezpośrednio i wprost zmierza do realizacji ściśle wewnętrznej wartości moralnej opartej na zgodności oświadczenia z przekonaniami, i jednocześnie państwo ustanawia siebie nie tylko obserwatorem i sędzią realizacji tej wartości, ale także autorem wzorca przekonań, z którymi oświadczenie ma być zgodne. (shrink)