We give a few results concerning the notions of causal completability and causal closedness of classical probability spaces . We prove that any classical probability space has a causally closed extension; any finite classical probability space with positive rational probabilities on the atoms of the event algebra can be extended to a causally up-to-three-closed finite space; and any classical probability space can be extended to a space in which all correlations between events that are logically independent modulo measure zero event (...) have a countably infinite common-cause system. Collectively, these results show that it is surprisingly easy to find Reichenbach-style ‘explanations' for correlations, underlining doubts as to whether this approach can yield a philosophically relevant account of causality. 1 Introduction2 Basic Definitions and Results in the Literature3 Causal Completability the Easy Way: ‘Splitting the Atom’4 Causal Completability of Classical Probability Spaces: The General Case5 Infinite Statistical Common-Cause Systems for Arbitrary Pairs6 ConclusionAppendix A. (shrink)

In this article, we address the case of self-tracking as a practice in which two meaningful backgrounds play an important role as the spatial dimension of human practices. Using a phenomenological approach, we show how quantification multiplies backgrounds, while at the same time generating data about the user. As a result, we can no longer speak of a unified background of human activity, but of multiple dimensions of this background, which, additionally, is perceived as having no pivotal role in the (...) process, often being hidden, situated beyond human consciousness, or taken for granted. Consequently, the phenomenological experience of the background turns into a hermeneutic practice focused on the interpretation of representations and descriptions. By adopting a phenomenological approach, we show the problems and limitations of quantification of human activities occurring in self-tracking and the theoretical problems associated with the scheme of human-technology relations. (shrink)

Let ΩΩ be the semigroup of all mappings of a countably infinite set Ω. If U and V are subsemigroups of ΩΩ, then we write U≈V if there exists a finite subset F of ΩΩ such that the subsemigroup generated by U and F equals that generated by V and F. The relative rank of U in ΩΩ is the least cardinality of a subset A of ΩΩ such that the union of U and A generates ΩΩ. In this paper (...) we study the notions of relative rank and the equivalence ≈ for semigroups of endomorphisms of binary relations on Ω.The semigroups of endomorphisms of preorders, bipartite graphs, and tolerances on Ω are shown to lie in two equivalence classes under ≈. Moreover such semigroups have relative rank 0, 1, 2, or in ΩΩ where is the minimum cardinality of a dominating family for . We give examples of preorders, bipartite graphs, and tolerances on Ω where the relative ranks of their endomorphism semigroups in ΩΩ are 0, 1, 2, and .We show that the endomorphism semigroups of graphs, in general, fall into at least four classes under ≈ and that there exist graphs where the relative rank of the endomorphism semigroup is 20. (shrink)

A history of logic -- Patterns of reasoning -- A language and its meaning -- A symbolic language -- 1850-1950 mathematical logic -- Modern symbolic logic -- Elements of set theory -- Sets, functions, relations -- Induction -- Turning machines -- Computability and decidability -- Propositional logic -- Syntax and proof systems -- Semantics of PL -- Soundness and completeness -- First order logic -- Syntax and proof systems of FOL -- Semantics of FOL -- More semantics -- Soundness and (...) completeness -- Why is first order logic "First Order"? (shrink)

This article utilises feminist technoscience studies’ notions of bodily ‘materialisation’ and ‘ontological choreographies’, offering a cyborg feminist account of ‘bioavailability’ as embodied becomings, rather than a fixed ontological state of being. Drawn from 2 years’ ethnographic study in in vitro fertilisation clinics in Spain with migrant women who provided eggs to the cross-border in vitro fertilisation industry, this work explores how global understandings of race and inequalities, clinical practices and women’s own emotional and physical labours collectively produce bioavailability. Through examples (...) from observations and interviews in in vitro fertilisation clinics, we examined women’s embodied stories to understand the ways in which bioavailability becomes. The article demonstrates a novel way in which to think about ‘bioavailability’, a concept which has already been of enormous use to the social sciences since its introduction by Lawrence Cohen. We examine recent configurations of bodily extraction in the reproduction–migration nexus that help us rethink the concept of bioavailability. (shrink)

In this article, we address the case of self-tracking as a practice in which two meaningful backgrounds (physical world and technological infrastructure) play an important role as the spatial dimension of human practices. Using a (post)phenomenological approach, we show how quantification multiplies backgrounds, while at the same time generating data about the user. As a result, we can no longer speak of a unified background of human activity, but of multiple dimensions of this background, which, additionally, is perceived as having (...) no pivotal role in the process, often being hidden, situated beyond human consciousness, or taken for granted. Consequently, the phenomenological experience of the background turns into a hermeneutic practice focused on the interpretation of representations and descriptions. By adopting a (post)phenomenological approach, we show the problems and limitations of quantification of human activities occurring in self-tracking and the theoretical problems associated with the scheme of human-technology relations. (shrink)

The text presents the results of a qualitative study focused on the issue of using nanomaterials in the extraordinary circumstances linked to the COVID-19 pandemic, particularly referring to the “Roušky s TULkou” initiative. Within several weeks, this initiative managed to launch the production of highly efficient nanofiber filters using the original AC Electrospinning technology on an industrial scale. The goal of the research was to analyse both the regional experience and the value-based challenges, conflicts and ethical dilemmas posed by an (...) emergency situation. The theoretical starting points of the research were the Turnerian understanding of liminality, communitas and antistructure and Stenner’s concept of liminal spaces. The results of the research show that the pandemic situation contributed to the emergence of an unexpected potential of the new technology and that the realisation of the activity was influenced not only by know-how and the university’s technical facilities, but particularly by social capital, thus uncovering the potential of the anti-structural character of the initiative and the temporary suspension of hierarchically established university structures. (shrink)

In the framework of Stewart Shapiro, computations are performed directly on strings of symbols (numerals) whose abstract numerical interpretation is determined by a notation. Shapiro showed that a total unary function (unary relation) on natural numbers is computable in every injective notation if and only if it is almost constant or almost identity function (finite or co-finite set). We obtain a syntactic generalization of this theorem, in terms of quantifier-free definability, for functions and relations relatively intrinsically computable on certain types (...) of equivalence structures. We also characterize the class of relations and partial functions of arbitrary finite arities which are computable in every notation (be it injective or not). We consider the same question for notations in which certain equivalence relations are assumed to be computable. Finally, we discuss connections with a theorem by Ash, Knight, Manasse and Slaman which allow us to deduce some (but not all) of our results, based on quantifier elimination. (shrink)

The paper contains a comment on the criticism of the author's book Początek jest wszędzie (Prószynski i S-ka, 2002) by Marek Lagosz ("Przegląd Filozoficzny - Nowa Seria, 14, 2005, 121-133). The comment focuses on the following issues: (1) the conception of philosophy of physics; (2) some methodological questions, especially the role of models in physics; (3) some explanations concerning the model proposed by the present author and his coworkers. A few "ideological remarks" are also made.

Physics is inseparably connected with western philosophy. From the seventieth century, physics began to play the role similar to that of ontology. Moreover, many notions and problems moved from philosophy to physics. That way it came into being something that is now called „philosophy in physics”. It means that some traditional philosophical questions, like for example the problem of individualization, emerge in physics in a new, exact and mathematical form. Therefore, physics will in the future become gradually philosophy.

Space, time and probabilities not only form the arena of many physical theories, but also the arena of our everyday life. Therefore, the problem of their ontological status becomes even more interesting. It seems that this problem cannot be solved before we have the final physical theory ("theory of everything"). However, various methods of looking for such a theory lead to converging results, and are able to elucidate the problem in question. We analyze noncommutative algebraic methods, and show that, when (...) applied to model the fundamental level, they suggest a nonlocal regime in which there is no space and no time, in their usual sense, and which is essentially probabilistic (in a generalized sense). In the noncommutative approach there are many probabilistic measures (not just one "probability" as in macroscopic physics), and none of them seems to be distinguished in any way. The tentative conclusion is that space, time and probability are not "absolute categories", but rather aspects of the world structure emergent from the fundamental level. One should expect that the ultimate theory will be well off our traditional philosophical categories. This shows that our mind has a peculiar property allowing it to reach far beyond its usual limitations. (shrink)

Zygmunt Zawirski, a member of the Lwow-Warsaw Philosophical School, in 1927-28 published an extensive paper (in three parts) devoted to the critical examination of the eternal return hypothesis - the idea that the history of the universe is fundamentally a cyclic process. After presenting the development of this idea throughout the ages Zawirski discusses arguments on its behalf coming mainly from the second law of thermodynamics and from the Poincaré recurrence theorem. Zawirski's criticism is confronted with the present state of (...) art. in this domain. Three new theoretical inputs are taken into account: first, our present knowledge of the global structure of space-time geometries with closed timelike curves; second, some results of relativistic thermodynamics; third, Tipler's no-return theorem (relativistic counterpart of the Poincaré theorem). Our knowledge regarding the eternal return, although not less hypothetical, is more „formalized” and more sophisticated than it was in Zawirski's time. (shrink)

In the previous paper (Filozofia Nauki No 3-4, 1994, pp. 7-17) we have shown how the initial and final singularities in the closed Friedman world model can be analysed in terms of the structured spaces in spite of the fact that these singularities constitute the single point in the b-boundary of space-time. In the present paper we generalize our approach by using methods of noncommutative geometry. We construct a noncommutative algebra in terms of which geometry of space-time with singularities can (...) be developed. This algebra admits a representation in the space of operators on a Hilbert space, and the initial and final singularities in the closed Friedman model are given by its two distinct representations. The striking feature of this approach is its analogy with the mathematical formalism of quantum mechanics. (shrink)

How to define space-time singularities is a serious problem in general relativity. Schmidt's b-boundary construction was commonly regarded as leading to the best (and very elegant) definition of singularities: space-time is said to be singular if it contains at least one b-incomplete curve. Unfortunately, Bosshard (1976) and Johnson (1977) demonstrated that the b-boundary of the closed Friedman universe consists of the single point. This means that the initial and final singularieties (i.e., the beginning and the end of the Friedman world) (...) coincide. So far no remedy to cure this disaster was known. In the present paper, the author reviews the results obtained by himself and W. Sasin (1994) which clarify the problem. The closed Friedman space-time together with its singularities is not smooth manifold but it turns out to be a structured space which is a strong generalization of the manifold concept. Consequently, if the problem is considered within the correct category, i.e. the category of structured spaces, the patologies dissapear. If one remains within the space-time everything is all right. It is only if one attempts to „touch” the singularity (to extend the differential structure from the inside of space-time to the singularity) when the beginning and the end of the universe coalesce. From the perspective of the Demiurg creating the closed Friedman universe the cosmic history is but a single point. The methodological significance of this result is briefly discussed. (shrink)

Essay delivered at 4th Embassy of Poland Annual Lecture, University of Ottawa, on November 6, 2002. It renders main studies on Janusz Korczak published in special issues of Dialogue and Universalism (nos. 9-10/1997, 9-10/2001), putting emphasis on the philosophical dimensions of Korczak’s vision of society.