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)

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)

In the paper we analyse the problem of axiomatizing the minimal variant of discussive logic denoted as $$ {\textsf {D}}_{\textsf {0}}$$ D 0. Our aim is to give its axiomatization that would correspond to a known axiomatization of the original discussive logic $$ {\textsf {D}}_{\textsf {2}}$$ D 2. The considered system is minimal in a class of discussive logics. It is defined similarly, as Jaśkowski’s logic $$ {\textsf {D}}_{\textsf {2}}$$ D 2 but with the help of the deontic normal logic (...) $$\textbf{D}$$ D. Although we focus on the smallest discussive logic and its correspondence to $$ {\textsf {D}}_{\textsf {2}}$$ D 2, we analyse to some extent also its formal aspects, in particular its behaviour with respect to rules that hold for classical logic. In the paper we propose a deductive system for the above recalled discussive logic. While formulating this system, we apply a method of Newton da Costa and Lech Dubikajtis—a modified version of Jerzy Kotas’s method used to axiomatize $$ {\textsf {D}}_{\textsf {2}}$$ D 2. Basically the difference manifests in the result—in the case of da Costa and Dubikajtis, the resulting axiomatization is pure modus ponens-style. In the case of $$ {\textsf {D}}_{\textsf {0}}$$ D 0, we have to use some rules, but they are mostly needed to express some aspects of positive logic. $$ {\textsf {D}}_{\textsf {0}}$$ D 0 understood as a set of theses is contained in $$ {\textsf {D}}_{\textsf {2}}$$ D 2. Additionally, any non-trivial discussive logic expressed by means of Jaśkowski’s model of discussion, applied to any regular modal logic of discussion, contains $$ {\textsf {D}}_{\textsf {0}}$$ D 0. (shrink)

In this paper we present a comparison of certain inconsistencyadaptive logics and Jaśkowski’s logic.

In this paper I would like to argue that Stoic logic is a kind ofrelevant logic rather than the classical logic. To realize this purpose I willtry to keep as close as possible to Stoic calculus as expressed with the helpof their arguments.

In Béziau a logic \ was defined with the help of the modal logic \. In it, the negation operator is understood as meaning ‘it is not necessary that’. The strong soundness–completeness result for \ with respect to a version of Kripke semantics was also given there. Following the formulation of \ we can talk about \-like logics or Beziau-style logics if we consider other modal logics instead of \—such a possibility has been mentioned in [1]. The correspondence result between (...) modal logics and respective Beziau-style logics has been generalised for the case of normal logics naturally leading to soundness–completeness results [see Marcos :279–300, 2005) and Mruczek-Nasieniewska and Nasieniewski :229–248, 2005)]. In Mruczek-Nasieniewska and Nasieniewski :185–196, 2008), :189–203, 2009) some partial results for non-normal cases are given. In the present paper we try to give similar but more general correspondence results for the non-normal-worlds case. To achieve this aim we have to enrich original Beziau’s language with an additional negation operator understood as ‘it is necessary that not’. (shrink)

In [1] J. Perzanowski formulated, among others, an ontology expressed in the relational language. He presented some interesting connections which hold between these relations. In the present paper we focus on further analysis of these relations.

In the context of modal logics one standardly considers two modal operators: possibility ) and necessity ) [see for example Chellas ]. If the classical negation is present these operators can be treated as inter-definable. However, negative modalities ) and ) are also considered in the literature [see for example Béziau ; Došen :3–14, 1984); Gödel, in: Feferman, Collected works, vol 1, Publications 1929–1936, Oxford University Press, New York, 1986, p. 300; Lewis and Langford ]. Both of them can be (...) treated as negations. In Béziau a logic \ has been defined on the basis of the modal logic \. \ is proposed as a solution of so-called Jaśkowski’s problem [see also Jaśkowski ]. The only negation considered in the language of \ is ‘it is not necessary’. It appears that logic \ and \ inter-definable. This initial correspondence result between \ and \ has been generalised for the case of normal logics, in particular soundness-completeness results were obtained [see Marcos :279–300, 2005); Mruczek-Nasieniewska and Nasieniewski :229–248, 2005)]. In Mruczek-Nasieniewska and Nasieniewski it has been proved that there is a correspondence between \-like logics and regular extensions of the smallest deontic logic. To obtain this result both negative modalities were used. This result has been strengthened in Mruczek-Nasieniewska and Nasieniewski :261–280, 2017) since on the basis of classical positive logic it is enough to solely use \ to equivalently express both positive modalities and negation. Here we strengthen results given in Mruczek-Nasieniewska and Nasieniewski by showing correspondence for the smallest regular logic. In particular we give a syntactic formulation of a logic that corresponds to the smallest regular logic. As a result we characterise all logics that arise from regular logics. From this follows via respective translations a characterisation of a class of logics corresponding to some quasi-regular logics where \ is the smallest element. Moreover, if a given quasi-regular logic is characterised by some class of models, the same class can be used to semantically characterise the logic obtained by our translation. (shrink)

In [1] J.-Y. Bèziau formulated a logic called Z. Bèziau’s idea was generalized independently in [6] and [7]. A family of logics to which Z belongs is denoted in [7] by K. In particular; it has been shown in [6] and [7] that there is a correspondence between normal modal logics and logics from the class K. Similar; but only partial results has been obtained also for regular logics. In a logic N has been investigated in the language with negation; (...) implication; conjunction and disjunction by axioms of positive intuitionistic logic; the right-to-left part of the second de Morgan law; and the rules of modus ponens and contraposition. From the semantical point of view the negation used by Došen is the modal operator of impossibility. It is known this operator is a characteristic of the modal interpretation of intuitionistic negation. In the present paper we consider an extension of N denoted by N+. We will prove that every extension of N+ that is closed under the same rules as N+; corresponds to a regular logic being an extension of the regular deontic logic D21. The proved correspondence allows to obtain from soundnesscompleteness result for any given regular logic containing D2, similar adequacy theorem for the respective extension of the logic N+. (shrink)

In Jaśkowski’s model of discussion, discussive connectives represent certain interactions that can hold between debaters. However, it is not possible within the model for participants to use explicit modal operators. In the paper we present a modal extension of the discussive logic $\textbf{D}_{\textbf{2}}$ that formally corresponds to an extended version of Jaśkowski’s model of discussion that permits such a use. This logic is denoted by $\textbf{m}\textbf{D}_{\textbf{2}}$. We present philosophical motivations for the formulation of this logic. We also give syntactic characterizations (...) of the logic and propose a comparison with certain other modal systems. In particular, we prove that $\textbf{m}\textbf{D}_{\textbf{2}}$ is neither normal nor regular. On the basis of the axiomatization of $\textbf{D}_{\textbf{2}}$, we give an axiomatization of $\textbf{m}\textbf{D}_{\textbf{2}}$. We also give another axiomatization which is not based on the axiomatization of $\textbf{D}_{\textbf{2}}$. Furthermore, we give a natural Kripke-style semantics for $\textbf{m}\textbf{D}_{\textbf{2}}$ and prove the respective adequacy theorems. (shrink)

The monograph is aimed at an analysis of the reasons for theory change in science. The writer develops a model of theory change according to which the origins of scientific revolutions lie not in a clash of fundamental theories with facts, but of ‘old’ fundamental theories with each other.

In the article I discuss functionalist interpretations of Husserlian phenomenology. The first one was coined in the discussion between Hubert Dreyfus and Ronald McIntyre. They argue that Husserl’s phenomenology shares similarities with computational functionalism, and the key similarity is between the concept of noema and the concept of mental representation. I show the weaknesses of that reading and argue that there is another available functionalist reading of Husserlian phenomenology. I propose to shift perspective and approach the relation between phenomenology and (...) functionalism from a methodological perspective, specifically taking into account the functionalist explanatory strategy called functional analysis. I discuss the notion of function in Husserl’s works and Husserl’s idea of functional phenomenology. The key argument I develop is that in functional phenomenology we can find an explanatory strategy which is analogous to the strategy of functional decomposition used in functional analysis. I conclude that the proposed functionalist reading of phenomenology opens a new approach to the integration of phenomenology with cognitive sciences. (shrink)

The paper is a contribution to the debate on the epistemological status of thought experiments. I deal with the epistemological uniqueness of experiments in the sense of their irreducibility to other sources of justification. In particular, I criticize an influential argument for the irreducibility of thought experiments to general arguments. First, I introduce the radical empiricist theory of eliminativism, which considers thought experiments to be rhetorically modified arguments, uninteresting from the epistemological point of view. Second, I present objections to the (...) theory, focusing on the critique of eliminativism by Tamar Szabó Gendler based on the reconstruction of famous Galileo's Pisa experiment. I show that her reconstruction is simplistic and that more elaborate reconstruction is needed for an appropriate assessment of the epistemic power of general argument. I propose such a reconstruction and demonstrate that general version of Pisa experiment is epistemically equal to the particular one. Thus, from an epistemological perspective, Galileo's thought experiment is reducible to a straightforward argument without particular premises. (shrink)

The aim of this article is to introduce the work of Leopold Blaustein — philosopher and psychologist, who studied under Kazimierz Twardowski in Lvov and under Husserl in Freiburg im Breisgau. In his short academic career Blaustein developed an original philosophy that drew upon both phenomenology and Twardowski’s analytical approach. One of his main publications concerns Husserl’s early theory of intentional act and object, introduced in Logische Untersuchungen. In the first part of the article I briefly present Blaustein’s biography and (...) some general features of his philosophy. The second part provides an overview of Blaustein’s dissertation concerning Husserl’s early phenomenology. In the third and final part I summarize Blaustein’s research, including the critical remarks of Roman Ingarden. (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)

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.

Introduction: A Theory of Democracy and Justice.

The Law of Peoples and Global Justice: Beyond the Liberal Nationalism of John Rawls The paper deals with the relation of a theory of international justice, specifically John Rawls's philosophy of the law of peoples, and a theory of global justice. In the first part, the paper outlines Rawls's main theses on the international conception of the law of peoples. The second part concerns a problem found in segments of Rawls's theory, specifically his concept of a social contract—contractualism. This problem (...) inadequately approaches the relationship between the individual and the community. The third part deals with the inconsistent points in Rawls's theory contained in part two, i.e. his principles of justice selected with the aid of social contract. In the fourth part, the paper concentrates on the consequences of these limitations for a socially distributive dimension of justice or as an approach for dealing with disproportionate global inequalities. The last part formulates the causes of the limitations of Rawls's theory of international justice and points out the need for a global justice which is socially and inter-culturally considerate. (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 fact of religious diversity is vital for the philosopher of religion but also, to some extent, for the believer of a given faith. It takes place in such a dimension in which the views of a given believer or the meaning of the practice of a given religion presupposes the truthfulness of specific claims concerning a given religion or the beliefs included in it. If now on the part of the philosopher of religion or the followers of another religion, (...) there is a direct or indirect challenge to such a key proposition, religious disagreement with epistemic dimension is involved. At the same time, it is not the case that any religious diversity is a case of epistemically significant religious dissent. The paper, by distinguishing different aspects of religions and functions performed by religion, tries to show in which situations religious diversification leads to religious disagreement. Both the follower of religion and the philosopher of religion can and should seek the truth in matters of crucial importance to religion. The difference is that the follower of a given religion is more interested in the salvific and practical functions of religion, along with the associated sense of value and meaningfulness of life and, to a lesser degree, the theoretical certainty that her religion is correct at crucial points. On the other hand, the achievement of ‘the soteriological’ purpose of religion based on false belief is impossible, just as the meaningfulness of life 'based on the sand and not on the rock’. It is because the false foundation is devoid of higher value. That is why there is a community of a philosopher of religion and a follower of a given religion to search for the truth of it. (shrink)

Local hidden-variable model of singlet-state correlations discussed in Czachor 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.

The paper links higher education reforms and welfare states reforms in postcommunist Central European countries. It links current higher education debates (and reform pressures) and public sector debates (and reform pressures), stressing the importance of communist-era legacies in both areas. It refers to existing typologies of both higher education governance and welfare state regimes and concludes that the lack of the inclusion of Central Europe in any of them is a serious theoretical drawback in comparative social research. The region should (...) still, after more than two decades of transition and heavy international policy advising, be viewed as a “laboratory of social experimentation”. It is still too risky to suggest generalizations about how Central European higher education and welfare systems fit existing typologies. Consequently, the “transition” period is by no means over: it is over in terms of politics and economics but not in terms of social arrangements. Both higher education and welfare states should be viewed as “work in progress”: permanently under reform pressures, and with unclear future. (shrink)

According to recent discussion, cross-explanatory integration in cognitive science might proceed by constraints on mechanistic and dynamic-mechanistic models provided by different research fields. However, not much attention has been given to constraints that could be provided by the study of first-person experience, which in the case of multifaceted mental phenomena are of key importance. In this paper, we fill this gap and consider the question whether information about first-person experience can constrain dynamic-mechanistic models and what the character of this relation (...) is. We discuss two cases of such explanatory models in neuroscience, namely that of migraine and of epilepsy. We argue that, in these cases, first-person insights about the target phenomena significantly contributed to explanatory models by shaping explanatory hypotheses and by indicating the dynamical properties that the explanatory models of these phenomena should account for, and thus directly constraining the space of possible explanations. (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)

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)

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)

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)

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)