Porovnáním významu slovesa vykořisťovat v 19. a 20. století odhalíme jeho dramatickou proměnu: z pojmu neutrálního se stává pojem silně záporný a objevuje se v okolí nových slov jako kapitalista, měšťák, proletář. Tento průnik Marxova idiolektu do češtiny (a do jiných jazyků) s sebou nese několik otázek: proč vnímá Marx tyto pojmy tak vyhraněně? Z jaké pozice, když odmítá morálku jako buržoazní přežitek, odsuzuje vykořisťování? Jeho eschatologicko-dějinný rámec umožňuje čistě negativní polaritu slovesa vykořisťovat a také, bohužel, zakládá jeho autogenocidní potenciál. (...) When comparing the meaning of the verb to exploit between the nineteenth and twentieth century we discover a dramatic transformation: from a neutral term it becomes a purely negative one and collocates with new words such as capitalist, bourgeoisie, proletarian. This penetration of the idiolect of Marx into Czech (as well as other languages) raises several questions: why does Marx use these words in such a categorical way? From what position, having rejected morality as a bourgeois prejudice, does he condemn exploitation? We find that it is his apocalyptic historical frame which enables the purely negative polarity of the verb to exploit as well as its autogenocidal potential. (shrink)

One of the best known approaches to the logic of agency are the ‘stit’ logics. Often, it is not the actions of an individual agent that bring about a certain outcome but the joint actions of a set of agents, collectively. Collective agency has received comparatively little attention in ‘stit’. The paper maps out several different forms, several different senses in which a particular set of agents, collectively, can be said to bring about a certain outcome, and examines how these (...) forms can be expressed in ‘stit’ and stit-like logics. The outcome that is brought about may be unintentional, and perhaps even accidental; the account deliberately ignores aspects such as joint intention, communication between agents, awareness of other agents’ intentions and capabilities, even the awareness of another agent’s existence. The aim is to investigate what can be said about collective agency when all such considerations are ignored, besides mere consequences of joint actions. The account will be related to the ‘strictly stit’ of Belnap and Perloff, 25–48 1993) and their suggestions concerning ‘inessential members’ and ‘mere bystanders’. We will adjust some of those conjectures and distinguish further between ‘potentially contributing bystanders’ and ‘impotent bystanders’. (shrink)

The author of the article deals with the causes of anti-naturalism in culture today from the point view of both a philosophical conception of evolutionary ontology, and the psychology of environmental problems. He highlights the real potential for a biophilic transformation of culture in the context of current knowledge on cognitive psychology, where emphasis is placed on the limits to the phenomena of cognitive dissonance. The author of the article seeks certain options to repress these limits in Gestalt theory, which (...) on some aspects corresponds substantially to the insights and goals of evolutionary psychology. (shrink)

Local hidden-variable model of singlet-state correlations discussed in Czachor (Acta Phys Polon A 139:70, 2021a) is shown to be a particular case of an infinite hierarchy of local hidden-variable models based on an infinite hierarchy of calculi. Violation of Bell-type inequalities can be interpreted as a ‘confusion of languages’ problem, a result of mixing different but neighboring levels of the hierarchy. Mixing of non-neighboring levels results in violations beyond the Tsirelson bounds.

Die Beiträge dieses Bandes aus verschiedenen Disziplinen, Philosophie, Literaturgeschichte und Kunstgeschichte schließen sich zum Bild einer Epoche zusammen, die einen Höhepunkt des deutschen Geisteslebens darstellt. Dabei treten bestimmte Züge heraus, welche die Genese dieser Kultur in relativ eng umgrenzten Kommunikationszentren zeigen: Königsberg - Düsseldorf - Jena - Weimar - freilich mit Ausstrahlung auf das übrige Deutschland. So etwa: die Stilisierung der Geselligkeit über den literarischen Dialog bis zur philosophischen Interpersonalitätslehre Fichtes und einer dem entsprechenden Dialektik des Dialogs; einer Staats- und (...) Gesellschaftsauffassung, die zwar noch in der klassischen Naturrechtslehre der Aufklärung gründete, aber den Rechtsbegriff so in sich zu gliedern wußte, daß er Implikationen verbindlich auch für das politische Handeln hergeben konnte und so aus dem Rechtsbegriff erstmals die Umsetzung des Völkerfriedens politisch fordern konnte. Es zeigt sich hier ein Grundmodell, das aller pragmatisch ausmachbaren Verallgemeinerungsfähigkeit überlegen ist, da die sittliche Person auch schon im Recht eine individuelle Aufforderung erhält, soll politisches Handeln von der öffentlichen Meinung anerkannt werden. Schließlich tritt eine neue Religiosität auf, die ein Naturverständnis einbezog, das ästhetischer Herkunft war, und die vielleicht deswegen ihren überzeugendsten Ausdruck in der Malerei fand. In allen diesen Bereichen aber werden Natur und Kunst im Lichte der neuentdeckten Freiheit des autonomen Individuums wiederbelebt. (shrink)

Článek reaguje na monografii Homo Natura: Nietzsche, Philosophical Anthropology and Biopolitics (2020) současné akademičky Vanessy Lemmové zabývající se Nietzschovým úkolem „přesadit člověka zpět do přírody“, tzn. chápat jej jako bytost veskrze imanentní přírodě. Reakce směřuje především na jednu z hlavních tezí knihy, podle níž tato Nietzschova snaha otevírá možnost nového, postantropocentrického pohledu na člověka a jeho vztahu k přírodě – pohledu, v jehož centru zájmu již nestojí člověk, nýbrž život sám, resp. kontinuum života, jež se ztělesňuje v lidském druhu a (...) jehož je lidský druh rovnocennou součástí po boku ostatních organismů. Nietzschova myšlenka o homo natura podle Lemmové předznamenává myšlení současného posthumanismu vyznačujícího se právě snahou vytvořit takový pohled na člověka a jeho vztah k přírodě, který bybyl vhodným teoretickým rámcem pro sebepojetí člověka v epoše antropocénu. Článek tuto tezi doplňuje o Heideggerovu interpretaci Nietzschovy myšlenky nadčlověka podanou v sérii přednášek Co znamená myslet?, v níž je nadčlověk chápán jako ekologický ideál lidstva schopného zodpovědně převzít moc plynoucí z technického přetváření země. Cílem článku je ukázat, že, v souladu s interpretacemi Lemmové a Heideggera, u Nietzscheho lze nalézt způsob, jak by se lidstvo mohlo produktivně vyrovnat s realitou antropocénu, a to skrze přechod od „posledního člověka“ k „nadčlověku“, kde přechod k „nadčlověku“ je chápán jako idea nastolení nového vztahu mezi lidmi a přírodou, resp. mezi lidmi a zemí. (shrink)

History provides us with instances of various societal and economic changes that with a hindsight are interpreted as either indicating progressive or regressive trends. The present paper attempts to define what represents progress and regress by applying psychological constructs to evaluation of the psychosocial changes. Seven principles of progress are applied as criteria for interpreting various historic events. The primary condition for progress is courage to face adversity or, in the cognitive domain, ambiguity, controversy and “unknown”. An overall model of (...) Challenge-Resilience-Resourcefulness is described as the process through which progress can be achieved. (shrink)

Philosophical work on the concept of consent in the past few decades has got to grips with it as a rich notion. We are increasingly sensitive to consent not as a momentary, atomic, transactional thing, but as a complex idea admitting of various qualities and dimensions. In this paper we note that the recognition of this complexity demands a theoretical framework quite different to those presently extant, and we suggest that the enactive approach is one which offers significant value in (...) this regard. In consonance with arguments made by Laurie Penny about how consent is a continuous and dynamic process, we outline how an enactive approach identifies consent as temporally extended (rather than momentarily transactional), and as affected by the skilfulness of the agents involved, the fitness of community provided resources to negotiate the consensual relationship over time, and the unfolding of circumstances in the situation in which the joint action is taking place. We argue that the value of an enactive perspective on consent is in highlighting these complexities, and providing resources to articulate and theorise them in ways that are not open to other current approaches. (shrink)

A flurry of recent publications have challenged consensus views on the tempo and mode of plastid (chloroplast) evolution in eukaryotes and, more generally, the impact of endosymbiosis in the evolution of the nuclear genome. Endosymbiont‐to‐nucleus gene transfer is an essential component of the transition from endosymbiont to organelle, but the sheer diversity of algal‐derived genes in photosynthetic organisms such as diatoms, as well as the existence of genes of putative plastid ancestry in the nuclear genomes of plastid‐lacking eukaryotes such as (...) ciliates and choanoflagellates, defy simple explanation. Collectively, these papers underscore the power of comparative genomics and, at the same time, reveal how little we know with certainty about the earliest stages of the evolution of photosynthetic eukaryotes. Editor's suggested further reading in BioEssaysEarly steps in plastid evolution: current ideas and controversies AbstractDinoflagellate mitochondrial genomes: stretching the rules of molecular biology Abstract. (shrink)

Clinical Ethics Consultations are an important tool for physicians in solving difficult cases. They are extremely common in North America and to a lesser extent also present in Europe. However, there is little data on this practice in Poland. We present results of a survey of 521 physicians practising in Poland concerning their opinion on CECs and related practices. We analysed the data looking at such issues as CECs’ perceived availability, use of CECs, and perceived usefulness of such support. Physicians (...) in our study generally encounter hard ethics cases, even—surprisingly—those who do not work in hospitals. Most physicians have no CEC access, and those that do still do not employ CECs. However, physicians perceive this form of support as useful—even more so among actual users of CECs. We compared these findings with similar studies from other European countries and the North America. We point out peculiarities of our results as compared to those in other countries, with some possible explanations. We hope the results may encourage regulatory debate on the need to formally introduce CECs into the Polish healthcare system. (shrink)

Bell’s theorem cannot be proved if complementary measurements have to be represented by random variables which cannot be added or multiplied. One such case occurs if their domains are not identical. The case more directly related to the Einstein–Rosen–Podolsky argument occurs if there exists an ‘element of reality’ but nevertheless addition of complementary results is impossible because they are represented by elements from different arithmetics. A naive mixing of arithmetics leads to contradictions at a much more elementary level than the (...) Clauser–Horne–Shimony–Holt inequality. (shrink)

Newtonian physics is based on Newtonian calculus applied to Newtonian dynamics. New paradigms such as ‘modified Newtonian dynamics’ change the dynamics, but do not alter the calculus. However, calculus is dependent on arithmetic, that is the ways we add and multiply numbers. For example, in special relativity we add and subtract velocities by means of addition β1⊕β2=tanh+tanh-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _1\oplus \beta _2=\tanh \big +\tanh ^{-1}\big )$$\end{document}, although multiplication β1⊙β2=tanh·tanh-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} (...) \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _1\odot \beta _2=\tanh \big \cdot \tanh ^{-1}\big )$$\end{document}, and division β1⊘β2=tanh/tanh-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _1\oslash \beta _2=\tanh \big /\tanh ^{-1}\big )$$\end{document} do not seem to appear in the literature. The map fX=tanh-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_{\mathbb{X}}=\tanh ^{-1}$$\end{document} defines an isomorphism of the arithmetic in X=\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}=$$\end{document} with the standard one in R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}}$$\end{document}. The new arithmetic is projective and non-Diophantine in the sense of Burgin, 1977), while ultrarelativistic velocities are super-large in the sense of Kolmogorov, 1961). Velocity of light plays a role of non-Diophantine infinity. The new arithmetic allows us to define the corresponding derivative and integral, and thus a new calculus which is non-Newtonian in the sense of Grossman and Katz. Treating the above example as a paradigm, we ask what can be said about the set X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}$$\end{document} of ‘real numbers’, and the isomorphism fX:X→R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_{{\mathbb{X}}}:{\mathbb{X}}\rightarrow {\mathbb{R}}$$\end{document}, if we assume the standard form of Newtonian mechanics and general relativity but demand agreement with astrophysical observations. It turns out that the observable accelerated expansion of the Universe can be reconstructed with zero cosmological constant if fX≈0.8sinh/\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_{\mathbb{X}}\approx 0.8\sinh /$$\end{document}. The resulting non-Newtonian model is exactly equivalent to the standard Newtonian one with ΩΛ=0.7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega _\Lambda =0.7$$\end{document}, ΩM=0.3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega _M=0.3$$\end{document}. Asymptotically flat rotation curves are obtained if ‘zero’, the neutral element 0X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0_{{\mathbb{X}}}$$\end{document} of addition, is nonzero from the point of view of the standard arithmetic of R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}}$$\end{document}. This implies fX-1=0X>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f^{-1}_{{\mathbb{X}}}=0_{{\mathbb{X}}}>0$$\end{document}. The opposition Diophantine versus non-Diophantine, or Newtonian versus non-Newtonian, is an arithmetic analogue of Euclidean versus non-Euclidean in geometry. We do not yet know if the proposed generalization ultimately removes any need of dark matter, but it will certainly change estimates of its parameters. Physics of the dark universe seems to be both geometry and arithmetic. (shrink)

Artykuł podejmuje polemikę z obiegowym rozumieniem tolerancji. Autor podkreśla znaczenie podziału na tolerancję jako postawę i na dyskursy o tolerancji. Następnie, w nawiązaniu i częściowo w dyskusji z koncepcją tolerancji zaproponowaną przez Iję Lazari Pawłowską, przedstawione jest rozróżnienie trzech odmian tolerancji, a także rozróżnienie odpowiednich trzech odmian nietolerancji. Rozważane są również niektóre paradoksy związane z tolerancją oraz ze zwalczaniem nietolerancji.

According to UNESCO guidelines, one of the four forms of bioethics committees in medicine are the Hospital Ethics Committees. The purpose of this study was to evaluate how the above guidelines are implemented in real practice. There were 111 hospitals selected out of 176 Polish clinical hospitals and hospitals accredited by Center of Monitoring Quality in Health System. The study was conducted by the survey method. There were 56 hospitals that responded to the survey. The number of HECs members fluctuated (...) between 3 and 16 members, where usually 5 members were part of the board committee. The composition of the HECs for professions other than physicians was diverse and non-standardized. Only 55 % of HECs had a professional set of standards. 98 % of HECs had specific tasks. 62 % of HECs were asked for their expertise, and 55 % prepared <6.88 % of the opinions were related to interpersonal relations between hospital personnel, patients and their families with emphasis on the interactions between superiors and their inferiors or hospital staff and patients and their families. Only 12 % of the opinions were reported by the respondents as related to ethical dilemmas. In conclusion, few Polish hospitals have HECs, and the structure, services and workload are not always adequate. To ensure a reliable operation of HECs requires the development of relevant legislation, standard operating procedures and well trained members. (shrink)

Kuala Lumpur is a diverse city representing many different religions and nationalities. Recent government policy has actively promoted unity and cohesion throughout the city; and the country of Malaysia, with the implementation of a programme called 1Malaysia. In this book, the authors investigate the aims of this programme – predominantly to unify the Malaysian society – and how these objectives resonate in the daily spatial practices of the city’s residents. -/- This book argues that elements of urban infrastructure could work (...) as an essential mediator ‘beyond community’, allowing inclusive social structures to be built, despite cultural and religious tensions existing within the city. It builds on the premise of an empirical study which explores the ways in which different communities use the same spaces, supported through the implementation of a theoretical framework which looks at both Western and Islamic conceptualisations of the notion of community. Through the analysis of Kuala Lumpur, this book contributes towards the creation of more inclusive places in multi-ethnic, multi-cultural and multi-religious communities across the world. (shrink)

The production of renewable energy in agricultural biogas plants is being widely criticized because—among other things—most of the feedstock comes from purpose-grown crops like maize. These activities generate competitive pressure to other crops that are used for feeding or food production, worsening their affordability. Unique pretreatment technology that allows substitution of the purpose-grown crops by farming residues was built 6 years ago on a commercial basis in Pěčín under modest funding and without publicity. The design of the concept; financial assessment (...) and moral viewpoint were analyzed based on practical operating data. It showed that the apparatus improves economic, environmental and moral acceptance as well. However, according to the government’s view, public funding for this type of processing was shortened, “because waste materials represent a lower cost”. The impact of such governance was analyzed as well. (shrink)

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)

According to The Consensus Gentium Argument from the premise: “Everyone believes that God exists” one can conclude that God does exist. In my paper I analyze two ways of defending the claim that somebody’s belief in God is a prima facie reason to believe. Kelly takes the fact of the commonness of the belief in God as a datum to explain and argues that the best explanation has to indicate the truthfulness of the theistic belief. Trinkaus Zagzebski grounds her defence (...) on rationality of epistemic trust in others. In the paper I argue that the second line of reasoning is more promising and I propose its improved version. (shrink)

ABSTRACT:Microfinance is often assumed to be an ethically progressive industry, but in recent years it has been the target of much ethical criticism. Microfinance institutions have been accused of using exploitative lending techniques and charging usurious interest rates; and critics even question the ability of microfinance to alleviate poverty. This article reviews recent research on the microfinance sector that addresses these ethical issues. We show how this research is relevant to a number of theoretical issues, such as how to define (...) poverty, how to understand exploitation, and how to balance financial and social goals in commercial organizations. We conclude by identifying a critical agenda for future research. (shrink)

We obtain several game characterizations of Baire 1 functions between Polish spaces _X_, _Y_ which extends the recent result of V. Kiss. Then we propose similar characterizations for equi-Bare 1 families of functions. Also, using related ideas, we give game characterizations of Baire measurable and Lebesgue measurable functions.

The Polish equivalents of Research Ethics Committees are Bioethics Committees (BCs). A questionnaire study has been undertaken to determine their situation. The BC is usually comprised of 13 members. Nine of these are doctors and four are non-doctors. In 2006 BCs assessed an average of 27.3 ± 31.7 (range: 0–131) projects of clinical trials and 71.1 ± 139.8 (range: 0–638) projects of other types of medical research. During one BC meeting an average of 10.3 ± 14.7 (range: 0–71) projects of (...) medical research were assessed (2006). The amendment of Polish laws according with Directive 2001/20/EC caused a percentage increase in BCs which assessed less than 20 projects per year (16% vs. 33% or 42% in 2003 vs. 2005 or 2006 respectively, p < 0,05). The results confirm the usefulness of the current practice of creating BCs by medical universities, medical institutes and regional chambers of physicians and dentists but rationalization of the workload for individual BCs is necessary. (shrink)

Referring to basic Weberian notions of rationalization and secularization, I try to find a more accurate sense of the term “secularization”, intending to describe adequately the position of religion in modernity. The result of this query is—or at least should be—a new, original conceptualization of religion as one of finite provinces of meaning within one paramount reality of the life-world, as defined by Alfred Schutz. I proceed by exposing a well known, major oversimplification of the Weberian concept of secularization, very (...) well outlined in Peter Berger’s The sacred canopy, in order to point to the genuine, much more differentiated position of Max Weber in this matter (especially from the period of Foundations of social economic and Economy and society), and, consequently, to return to the roots of Berger’s thought: phenomenological sociology of Alfred Schutz, an attempt to assure the philosophical foundations of Weber’s sociological theory. At a closer glimpse, transformation of religion in the modern process of rationalization does not consist—according to Weber—in eliminating religion and thus depriving society of the religious source of meaning, but in parallel emancipation of many different domains of rationality, including religion itself. Using Schutz’s analysis of the social world as a complex structure of many different final provinces of meaning, I describe religion as such a province and show what does the process of rationalization of this province consist and what it should consist in: a complex, ongoing exchange of cognitive relevances and contents, combined with growing autonomy of many different sub-worlds. Schutz’s theory of symbol, rooted in Edmund Husserl’s description of constitution of complex objects in mono- and polythetic acts of consciousness, moves the analysis to the epistemological level, pointing to a chance of intensifying our cognitive relation to reality through increasing interpenetration of various sub-universes of meaning. (shrink)

Elekes proved that any infinite-fold cover of a σ-finite measure space by a sequence of measurable sets has a subsequence with the same property such that the set of indices of this subsequence has density zero. Applying this theorem he gave a new proof for the random-indestructibility of the density zero ideal. He asked about other variants of this theorem concerning I-almost everywhere infinite-fold covers of Polish spaces where I is a σ-ideal on the space and the set of indices (...) of the required subsequence should be in a fixed ideal ${{\mathcal{J}}}$ on ω. We introduce the notion of the ${{\mathcal{J}}}$ -covering property of a pair ${({\mathcal{A}}, I)}$ where ${{\mathcal{A}}}$ is a σ-algebra on a set X and ${{I \subseteq \mathcal{P}(X)}}$ is an ideal. We present some counterexamples, discuss the category case and the Fubini product of the null ideal ${\mathcal{N}}$ and the meager ideal ${\mathcal{M}}$ . We investigate connections between this property and forcing-indestructibility of ideals. We show that the family of all Borel ideals ${{\mathcal{J}}}$ on ω such that ${\mathcal{M}}$ has the ${{\mathcal{J}}}$ -covering property consists exactly of non weak Q-ideals. We also study the existence of smallest elements, with respect to Katětov–Blass order, in the family of those ideals ${\mathcal{J}}$ on ω such that ${\mathcal{N}}$ or ${\mathcal{M}}$ has the ${\mathcal{J}}$ -covering property. Furthermore, we prove a general result about the cases when the covering property “strongly” fails. (shrink)