Classical statistical mechanics posits probabilities for various events to occur, and these probabilities seem to be objective chances. This does not seem to sit well with the fact that the theory’s time evolution is deterministic. We argue that the tension between the two is only apparent. We present a theory of Humean objective chance and show that chances thus understood are compatible with underlying determinism and provide an interpretation of the probabilities we find in Boltzmannian statistical mechanics.

The sensitive dependence on initial conditions (SDIC) associated with nonlinear models imposes limitations on the models’ predictive power. We draw attention to an additional limitation than has been underappreciated, namely, structural model error (SME). A model has SME if the model dynamics differ from the dynamics in the target system. If a nonlinear model has only the slightest SME, then its ability to generate decision-relevant predictions is compromised. Given a perfect model, we can take the effects of SDIC into account (...) by substituting probabilistic predictions for point predictions. This route is foreclosed in the case of SME, which puts us in a worse epistemic situation than SDIC. (shrink)

Entropy is ubiquitous in physics, and it plays important roles in numerous other disciplines ranging from logic and statistics to biology and economics. However, a closer look reveals a complicated picture: entropy is defined differently in different contexts, and even within the same domain different notions of entropy are at work. Some of these are defined in terms of probabilities, others are not. The aim of this chapter is to arrive at an understanding of some of the most important notions (...) of entropy and to clarify the relations between them, After setting the stage by introducing the thermodynamic entropy, we discuss notions of entropy in information theory, statistical mechanics, dynamical systems theory and fractal geometry. (shrink)

The United Kingdom Climate Impacts Program’s UKCP09 project makes high-resolution forecasts of climate during the 21st century using state of the art global climate models. The aim of this paper is to introduce and analyze the methodology used and then urge some caution. Given the acknowledged systematic errors in all current climate models, treating model outputs as decision relevant probabilistic forecasts can be seriously misleading. This casts doubt on our ability, today, to make trustworthy, high-resolution predictions out to the end (...) of this century. (shrink)

Determinism and chance seem to be irreconcilable opposites: either something is chancy or it is deterministic but not both. Yet there are processes which appear to square the circle by being chancy and deterministic at once, and the appearance is backed by well-confirmed scientific theories such as statistical mechanics which also seem to provide us with chances for deterministic processes. Is this possible, and if so how? In this essay I discuss this question for probabilities as they occur in the (...) empirical sciences, setting aside metaphysical questions in connection with free will, divine intervention and determinism in history. (shrink)

Consider a gas confined to the left half of a container. Then remove the wall separating the two parts. The gas will start spreading and soon be evenly distributed over the entire available space. The gas has approached equilibrium. Why does the gas behave in this way? The canonical answer to this question, originally proffered by Boltzmann, is that the system has to be ergodic for the approach to equilibrium to take place. This answer has been criticised on different grounds (...) and is now widely regarded as flawed. In this paper we argue that these criticisms have dismissed Boltzmann’s answer too quickly and that something almost like Boltzmann’s answer is true: the approach to equilibrium takes place if the system is epsilon-ergodic, i.e. ergodic on the entire accessible phase space except for a small region of measure epsilon. We introduce epsilon-ergodicity and argue that relevant systems in statistical mechanics are indeed espsilon-ergodic. (shrink)

Consider a gas that is adiabatically isolated from its environment and confined to the left half of a container. Then remove the wall separating the two parts. The gas will immediately start spreading and soon be evenly distributed over the entire available space. The gas has approached equilibrium. Thermodynamics (TD) characterizes this process in terms of an increase of thermodynamic entropy, which attains its maximum value at equilibrium. The second law of thermodynamics captures the irreversibility of this process by positing (...) that in an isolated system such as the gas entropy cannot decrease. The aim of statistical mechanics (SM) is to explain the behavior of the gas and, in particular, its conformity with the second law in terms of the dynamical laws governing the individual molecules of which the gas is made up. In what follows these laws are assumed to be the ones of Hamiltonian classical mechanics. We should not, however, ask for an explanation of the second law literally construed. This law is a universal law and as such cannot be explained by a statistical theory. But this is not a problem because we.. (shrink)

The present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of mathematics from their beginnings till today. The reference point of the considerations is the introducing of the reals in the 19th century that marked an epochal turn in the foundations of mathematics. In the book problems (...) connected with the concept of a number, with the infinity, the continuum and the infinitely small, with the applicability of mathematics as well as with sets, logic, provability and truth and with the axiomatic approach to mathematics are considered. In Chapter 6 the meaning of infinitesimals to mathematics and to the elements of analysis is presented. The authors of the present book are mathematicians. Their aim is to introduce mathematicians and teachers of mathematics as well as students into the philosophy of mathematics. The book is suitable also for professional philosophers as well as for students of philosophy, just because it approaches philosophy from the side of mathematics. The knowledge of mathematics needed to understand the text is elementary. Reports on historical conceptions. Thinking about today‘s mathematical doing and thinking. Recent developments. Based on the third, revised German edition. For mathematicians - students, teachers, researchers and lecturers - and readersinterested in mathematics and philosophy. Contents On the way to the reals On the history of the philosophy of mathematics On fundamental questions of the philosophy of mathematics Sets and set theories Axiomatic approach and logic Thinking and calculating infinitesimally – First nonstandard steps Retrospection. (shrink)

The aim of this book is to present and analyze philosophical conceptions concerning mathematics and logic as formulated by Polish logicians, mathematicians and philosophers in the 1920s and 1930s. It was a remarkable period in the history of Polish science, in particular in the history of Polish logic and mathematics. Therefore, it is justified to ask whether and to what extent the development of logic and mathematics was accompanied by a philosophical reflection. We try to answer those questions by analyzing (...) both works of Polish logicians and mathematicians who have a philosophical temperament as well as their research practice. Works and philosophical views of the following Polish scientists will be analyzed: Wacław Sierpiński, Zygmunt Janiszewski, Stefan Mazurkiewicz, Stefan Banach Hugo Steinhaus, Eustachy Żylińsk and Leon Chwistek, Jan Łukasiewicz, Zygmunt Zawirski, Stanisław Leśniewski, Tadeusz Kotarbiński, Kazimierz Ajdukiewicz, Alfred Tarski, Andrzej Mostowski and Henryk Mehlberg, Jan Sleszyński, Stanisław Zaremba and Witold Wilkosz. To indicate the background of scientists being active in the 1920s and 1930s we consider in Chapter 1 some predecessors, in particular: Jan Śniadecki, Józef Maria Hoene-Wroński, Samuel Dickstein and Edward Stamm. (shrink)

The word «history» can always be understood in two different meanings: as what happened in the past and as a story about the past. One and the same past can be described in different ways. The gap between historical events and representations of these events determines the diversity of historical discourses. Shifting the focus of the philosophy of history from identifying the con- ditions for the possibility of historical knowledge to the analysis of the process of historiography reflects an understanding (...) of the fundamental nature of historical discourses for the formation of pictures of the past. But the fascination with the subject of historical representation often overshadows what makes it possible in principle. Historical discourse is a modern narrative of the past. Thus, the condition for the possibility of historical discursiveness is the mediation of the horizons of the present and the past, which is a fundamental feature of the historicity of human existence. This article explains the discourses of memory and oppositional critical scientific history. Discourses of memory are considered as modern forms of manifestation of the historicity of human existence, because it is in them that the constant mediation of time horizons of the past and present becomes thematic. Critical history declaratively opposes the discourses of memory, but reveals the dependence of its methodological foundations on predetermined forms of under- standing the past presented in memory. The opposition between the discourses of memory and critical history structurally repeats the opposition of tradition and scientific history revealed in hermeneutics. The conceptual shift from tradition to memory reflects the fundamental changes in the modern understanding of historicity associated with the further detraditionalization and globalization of the world. Me- mory appears as a new form of understanding the past, associated with the fear of losing it, as well as understanding the distances and gaps in relation to it. Based on the differentiation of collective memory types, the corresponding types of dis- courses are distinguished. It is argued that historical discourses of identity cannot be identified with historical discourses of power, and historical-didactic and historical-aesthetic discourses are independent forms of modern attitude to the past. In an effort to separate critical reconstruc- tion from memory, scientific discourses become counterfactual to the taken for granted past, represented in the narratives of collective memory. (shrink)

Two crucial concepts of the methodology and philosophy of mathematics are considered: proof and truth. We distinguish between informal proofs constructed by mathematicians in their research practice and formal proofs as defined in the foundations of mathematics (in metamathematics). Their role, features and interconnections are discussed. They are confronted with the concept of truth in mathematics. Relations between proofs and truth are analysed.

To the question of the methodology of the study of modern nationalisms Anderson’s radical change in the perspective of the studies of nations allow to consider them beyond traditional subjectivation and objectification as imagined communities, standing on the same level as the worldviews of world religions. The article is devoted to clarifying the conditions of such comparison of nations and religions. Anderson himself explained this correlation with the concepts like “cultural artefacts” and “wide cultural systems”. These concepts, however, are not (...) very clear and are not provided with an appropriate methodology. The article argues that the juxtaposition of religious and national communities is methodologically grounded through the application of the phenomenological concept of symbolic universes to them. The latter are understood as the comprehensive horizons of meanings that legitimize local lifeworlds. The crite- rion for defining of the symbolic universe is the presence of legitimation of death as the man’s most marginalized experience. The application of the concept of symbolic universes to contem- porary communities reveals the ultimate forms of collective identity, the competition between which defines the outlines of actual world politics. (shrink)

It is said that Europe finds itself today in a post-christian situa-tion. Further, there are many who advocate abandoning monotheism in order to get back to prechristian polytheism in the hope that the plurality of gods would favour a democratic tolerance in a pluralistic world. In this article the author firstly asks if European Christians have not gone back to adoring idols and to attempting to distinguish between them in the new forms of devotion to possessiveness, to power and to (...) pleasure. He then goes on to ask about the possibilities of pro-claiming the God of Jesus Christ. The third and the fourth part of the article point out several forms of necessary witness to God in contemporary society, with special reference made to European society in the conclusion. (shrink)

Millions of animals are used every year in oftentimes extremely painful and distressing scientific procedures. Legislation of animal experimentation in modern societies is based on the supposition that this is ethically acceptable when certain more or less defined formal (e.g. logistical, technical) demands and ethical principles are met. The main parameters in this context correspond to the “3Rs” concept as defined by Russel and Burch in 1959, i.e. that all efforts to replace, reduce and refine experiments must be undertaken. The (...) licensing of animal experiments normally requires an ethical evaluation process, oftentimes undertaken by ethics committees. The serious problems in putting this idea into practice include inter alia unclear conditions and standards for ethical decisions, insufficient management of experiments undertaken for specific (e.g. regulatory) purposes, and conflicts of interest of ethics committees’ members. (shrink)

It is said that Europe finds itself today in a post-christian situa-tion. Further, there are many who advocate abandoning monotheism in order to get back to prechristian polytheism in the hope that the plurality of gods would favour a democratic tolerance in a pluralistic world. In this article the author firstly asks if European Christians have not gone back to adoring idols and to attempting to distinguish between them in the new forms of devotion to possessiveness, to power and to (...) pleasure. He then goes on to ask about the possibilities of pro-claiming the God of Jesus Christ. The third and the fourth part of the article point out several forms of necessary witness to God in contemporary society, with special reference made to European society in the conclusion. (shrink)

The potential to achieve dynamic, scalable and cost-effective marketplaces and eCommerce solutions has driven recent research efforts towards so-called Semantic Web Services that are enriching Web services with machine-processable semantics. To this end, the Web Service Modeling Ontology (WSMO) provides the conceptual underpinning and a formal language for semantically describing all relevant aspects of Web services in order to facilitate the automatization of discovering, combining and invoking electronic services over the Web. In this paper we describe the overall structure of (...) WSMO by its four main elements: ontologies, which provide the terminology used by other WSMO elements, Web services, which provide access to services that, in turn, provide some value in some domain, goals that represent user desires, and mediators, which deal with interoperability problems between different WSMO elements. Along with introducing the main elements of WSMO, we provide a logical language for defining formal statements in WSMO together with some motivating examples from practical use cases which shall demonstrate the benefits of Semantic Web Services. (shrink)

We define certain properties of subsets of models of arithmetic related to their codability in end extensions and elementary end extensions. We characterize these properties using some more familiar notions concerning cuts in models of arithmetic.

Angesichts aktueller Krisenzustände sucht man nach einer globalen Ethik. Im vorliegenden Artikel wird Albert Schweitzers Weltanschauung der Ehrfurcht vor dem Leben als möglicher Beitrag zur Entwicklung einer solchen Ethik untersucht. Mit seinem Entwurf wollte Schweitzer am Beginn des 20. Jahrhunderts die zerrüttete abendländische Kultur erneuern. Der Mensch müsse sich als „Leben inmitten von Leben“ erfahren. Da die biologische Natur für die Ethik keine Quelle sein kann, ist sie verwiesen auf den Willen zur Liebe, den der Mensch in sich selbst entdeckt (...) und der ihn nötigt, aus einer Haltung der Ehrfurcht alles Leben zu erhalten und zu fördern. Mit der tätigen Mystik der Ehrfurcht vor dem Leben wollte Schweitzer eine universale Grundlegung jeglicher Ethik entwickeln, was ihm aber nur unzureichend gelungen ist. Auch wenn seine Weltanschauung kaum – wie er sie darzulegen versucht – als „denknotwendig“ gelten kann, ist sie nach Auffassung des Autors aber dennoch für den heutigen Krisenzustand als Inspiration und Motivation hochaktuell.Regarding the current crisis conditions, we are looking for a global ethics. This paper investigates Albert Schweitzer’s reverence for life worldview as a possible contribution to the development of such ethics. With his project at the beginning of the 20th century, Schweitzer wanted to renew the devastated Western culture. Man must experience himself as “a life in the midst of life”. As biological nature cannot be the source for ethics, it is referred to the will to love which man discovers in himself and which, due to the attitude of reverence, obliges him for sustaining and promoting all life. With the active mysticism of reverence for life Schweitzer intended to develop a universal foundation of all ethics, but the intention was inadequate. In the author’s opinion, although his worldview can hardly be considered “logically necessary” – as he tries to demonstrate – it is still highly relevant as an inspiration and motivation in the contemporary crisis condition. (shrink)

The paper is devoted to the description of life and scientific achievements as well as the influence of Seweryna Łuszczewska-Romahnowa.