Models are of central importance in many scientific contexts. The centrality of models such as inflationary models in cosmology, general-circulation models of the global climate, the double-helix model of DNA, evolutionary models in biology, agent-based models in the social sciences, and general-equilibrium models of markets in their respective domains is a case in point (the Other Internet Resources section at the end of this entry contains links to online resources that discuss these models). Scientists spend significant amounts of time building, (...) testing, comparing, and revising models, and much journal space is dedicated to interpreting and discussing the implications of models. In short, models are one of the principal instruments of modern science. (shrink)

Most scientific models are not physical objects, and this raises important questions. What sort of entity are models, what is truth in a model, and how do we learn about models? In this paper I argue that models share important aspects in common with literary fiction, and that therefore theories of fiction can be brought to bear on these questions. In particular, I argue that the pretence theory as developed by Walton (1990, Mimesis as make-believe: on the foundations of the (...) representational arts. Harvard University Press, Cambridge/MA) has the resources to answer these questions. I introduce this account, outline the answers that it offers, and develop a general picture of scientific modelling based on it. (shrink)

This monograph offers a critical introduction to current theories of how scientific models represent their target systems. Representation is important because it allows scientists to study a model to discover features of reality. The authors provide a map of the conceptual landscape surrounding the issue of scientific representation, arguing that it consists of multiple intertwined problems. They provide an encyclopaedic overview of existing attempts to answer these questions, and they assess their strengths and weaknesses. The book also presents a comprehensive (...) statement of their alternative proposal, the DEKI account of representation, which they have developed over the last few years. They show how the account works in the case of material as well as non-material models; how it accommodates the use of mathematics in scientific modelling; and how it sheds light on the relation between representation in science and art. The issue of representation has generated a sizeable literature, which has been growing fast in particular over the last decade. This makes it hard for novices to get a handle on the topic because so far there is no book-length introduction that would guide them through the discussion. Likewise, researchers may require a comprehensive review that they can refer to for critical evaluations. This book meets the needs of both groups. (shrink)

Scientific discourse is rife with passages that appear to be ordinary descriptions of systems of interest in a particular discipline. Equally, the pages of textbooks and journals are filled with discussions of the properties and the behavior of those systems. Students of mechanics investigate at length the dynamical properties of a system consisting of two or three spinning spheres with homogenous mass distributions gravitationally interacting only with each other. Population biologists study the evolution of one species procreating at a constant (...) rate in an isolated ecosystem. And when studying the exchange of goods, economists consider a situation in which there are only two goods, two perfectly rational agents, no restrictions on available information, no transaction costs, no money, and dealings are done immediately. Their surface structure notwithstanding, no competent scientist would mistake descriptions of such systems as descriptions of an actual system: we know very well that there are no such systems. These descriptions are descriptions of a model-system, and scientists use model-systems to represent parts or aspects of the world they are interested in. Following common practice, I refer to those parts or aspects as target-systems. What are we to make of this? Is discourse about such models merely a picturesque and ultimately dispensable façon de parler? This was the view of some early twentieth century philosophers. Duhem (1906) famously guarded against confusing model building with scientific theorizing and argued that model building has no real place in science, beyond a minor heuristic role. The aim of science was, instead, to construct theories, with theories understood as classificatory or representative structures systematically presented and formulated in precise symbolic.. (shrink)

In this paper we explore the constraints that our preferred account of scientific representation places on the ontology of scientific models. Pace the Direct Representation view associated with Arnon Levy and Adam Toon we argue that scientific models should be thought of as imagined systems, and clarify the relationship between imagination and representation.

It is now part and parcel of the official philosophical wisdom that models are essential to the acquisition and organisation of scientific knowledge. It is also generally accepted that most models represent their target systems in one way or another. But what does it mean for a model to represent its target system? I begin by introducing three conundrums that a theory of scientific representation has to come to terms with and then address the question of whether the semantic view (...) of theories, which is the currently most widely accepted account of theories and models, provides us with adequate answers to these questions. After having argued in some detail that it does not, I conclude by pointing out in what direction a tenable account of scientific representation might be sought. (shrink)

Everything you always wanted to know about structural realism but were afraid to ask Content Type Journal Article Pages 227-276 DOI 10.1007/s13194-011-0025-7 Authors Roman Frigg, Department of Philosophy, Logic and Scientific Method, London School of Economics and Political Science, Houghton Street, London, WC2A 2AE UK Ioannis Votsis, Philosophisches Institut, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, Geb. 23.21/04.86, 40225 Düsseldorf, Germany Journal European Journal for Philosophy of Science Online ISSN 1879-4920 Print ISSN 1879-4912 Journal Volume Volume 1 Journal Issue Volume 1, Number (...) 2. (shrink)

Computer simulations are an exciting tool that plays important roles in many scientific disciplines. This has attracted the attention of a number of philosophers of science. The main tenor in this literature is that computer simulations not only constitute interesting and powerful new science , but that they also raise a host of new philosophical issues. The protagonists in this debate claim no less than that simulations call into question our philosophical understanding of scientific ontology, the epistemology and semantics of (...) models and theories, and the relation between experimentation and theorising, and submit that simulations demand a fundamentally new philosophy of science in many respects. The aim of this paper is to critically evaluate these claims. Our conclusion will be sober. We argue that these claims are overblown and that simulations, far from demanding a new metaphysics, epistemology, semantics and methodology, raise few if any new philosophical problems. The philosophical problems that do come up in connection with simulations are not specific to simulations and most of them are variants of problems that have been discussed in other contexts before. (shrink)

Science provides us with representations of atoms, elementary particles, polymers, populations, genetic trees, economies, rational decisions, aeroplanes, earthquakes, forest fires, irrigation systems, and the world’s climate. It's through these representations that we learn about the world. This entry explores various different accounts of scientific representation, with a particular focus on how scientific models represent their target systems. As philosophers of science are increasingly acknowledging the importance, if not the primacy, of scientific models as representational units of science, it's important to (...) stress that how they represent plays a fundamental role in how we are to answer other questions in the philosophy of science. This entry begins by disentangling ‘the’ problem of scientific representation, before critically evaluating the current options available in the literature. (shrink)

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.

This is an extensive review of recent work on the foundations of statistical mechanics.

Research on sequence effects on learning visual categories has shown that interleaving (i.e., studying the categories in a mixed manner) facilitates category induction as compared to blocking (i.e., studying the categories one by one), but learners are unaware of the interleaving effect and prefer blocking. However, little attention has been paid to sequence effects in perceptual learning across further sensory modalities. The present (preregistered) research addresses this shortcoming by using auditory (birdcalls), olfactory (tealeaves), gustatory (ingredient mixtures), and tactile (stones) stimuli (...) across four analog experiments. The number of participants per experiment was determined based on a medium effect size of interleaving. Participants studied six categories (with six exemplars, respectively) either interleaved or blocked. No single experiment showed a significant effect of interleaving. We ran a comprehensive meta‐analysis based on the data from all experiments, which revealed a significant small effect of interleaving, demonstrating its applicability to perceptual learning across all sensory modalities. Learners in the interleaved condition underestimated their classification performance. Overall, learners did not rate interleaving as less effective than blocking, which is at odds with previous studies that consistently demonstrated a metacognitive preference of blocking. Our findings suggest that learners rely less on conventional beliefs about the effectivity of study sequence when dealing with unfamiliar (blindfolded) perceptual learning tasks. (shrink)

Filozoficko-antropologické dědictví Viktora E. Frankla zůstává dosud nedoceněnou oblastí v jeho široké tvůrčí činnosti, která zahrnuje také neurologické, psychiatrické, psychoterapeutické a axiologicko-etické bádání. Franklovým dílem však prolíná svébytná multidimenzionální koncepce člověka, která je v následujícím příspěvku úzce spojena s Franklovou primární profesní orientací - péčí o zdraví a snahou o uzdravení nemocných - a s jednou z dominant Franklovy tragické triády - utrpením.

Today, there are several problems in the field of criminal law caused both by the emergence of new types of legal relations and by the imperfection of legislation. Due to the emergence of new challenges in the field of criminal law, many of them require theoretical understanding. Some of these challenges, generated in the light of the armed aggression of the Russian Federation against Ukraine, revealed several reasons for discussion in the Ukrainian and international legal community. The purpose of the (...) study involves consideration of certain aspects of modern challenges in the field of criminal-legal relations, which arose against the background of the military aggression of the Russian Federation in Ukraine. The first part of the study is devoted to the question of the qualification of war crimes committed by the Russian Federation in Ukraine as acts of genocide. The second part of the work is devoted to the issue of using existing international legal mechanisms to hold the Russian Federation accountable for war crimes. There are convincing reasons to say that the actions of the Russian Federation during the war in Ukraine have signs of the crime of genocide. Even though Ukraine is not a party to the Rome Statute, the Ukrainian government can use another tool to bring the subjects of war crimes to justice, by creating a certain mixed investigative mechanism or a criminal tribunal that could deal directly with the crime of aggression. (shrink)

Many scientific models are representations. Building on Goodman and Elgin’s notion of representation-as we analyse what this claim involves by providing a general definition of what makes something a scientific model, and formulating a novel account of how they represent. We call the result the DEKI account of representation, which offers a complex kind of representation involving an interplay of, denotation, exemplification, keying up of properties, and imputation. Throughout we focus on material models, and we illustrate our claims with the (...) Phillips-Newlyn machine. In the conclusion we suggest that, mutatis mutandis, the DEKI account can be carried over to other kinds of models, notably fictional and mathematical models. (shrink)

Обґрунтовано стратегію високочастотної біржової торгівлі (high-frequency trading) акціями. Для цього досліджено особливості та обмеження біржової високочастотної торгівлі, визначено верхню межу прибутку агресивного «шкідливого» високочастотного трейдера, обґрунтовано оптимальну частоту стратегії біржової високочастотної торгівлі акціями, розглянуто емпіричне підтвердження прогнозованості біржових курсів акцій на надкоротких горизонтах інвестування.

Understanding scientific modelling can be divided into two sub-projects: analysing what model-systems are, and understanding how they are used to represent something beyond themselves. The first is a prerequisite for the second: we can only start analysing how representation works once we understand the intrinsic character of the vehicle that does the representing. Coming to terms with this issue is the project of the first half of this chapter. My central contention is that models are akin to places and characters (...) of literary fictions, and that therefore theories of fiction play an essential role in explaining the nature of model-systems. This sets the agenda. Section 2 provides a statement of this view, which I label the fiction view of model-systems, and argues for its prima facie plausibility. Section 3 presents a defence of this view against its main rival, the structuralist conception of models. In Section 4 I develop an account of model-systems as imagined objects on the basis of the so-called pretence theory of fiction. This theory needs to be discussed in great detail for two reasons. First, developing an acceptable account of imagined objects is mandatory to make the fiction view acceptable, and I will show that the pretence theory has the resources to achieve this goal. Second, the term ‘representation’ is ambiguous; in fact, there are two very different relations that are commonly called ‘representation’ and a conflation between the two is the root of some of the problems that beset scientific representation. Pretence theory provides us with the conceptual resources to articulate these two different forms of representation, which I call p-representation and t-representation respectively. Putting these elements together provides us with a coherent overall picture of scientific modelling, which I develop in Section 5. (shrink)

Williams’s famous argument against immortality rests on the idea that immortality cannot be desirable, at least for human beings, and his contention has spawned a cottage industry of responses. As I will intend to show, the arguments over his view rest on both a difference of temperament and a difference in the sense of desire being used. The former concerns a difference in whether one takes a forward-looking or a backward-looking perspective on personal identity; the latter a distinction between our (...) normal desire to continue living and the kind of desire implied in desiring immortality. Showing that there is some sense of identity and desire that support Williams’s conclusion goes some way toward providing support for his argument, if not a full-fledged defense of it. (shrink)

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)

On the face of it ‘deterministic chance’ is an oxymoron: either an event is chancy or deterministic, but not both. Nevertheless, the world is rife with events that seem to be exactly that: chancy and deterministic at once. Simple gambling devices like coins and dice are cases in point. On the one hand they are governed by deterministic laws – the laws of classical mechanics – and hence given the initial condition of, say, a coin toss it is determined whether (...) it will land heads or tails.2 On the other hand, we commonly assign probabilities to the different outcomes a coin toss, and doing so has proven successful in guiding our actions. The same dilemma also emerges in less mundane contexts. Classical statistical mechanics (which is still an important part of modern physics) assigns probabilities to the occurrence of certain events – for instance to the spreading of a gas that is originally confined to the left half of a container – but at the same time assumes that the relevant systems are deterministic. How can this apparent conflict be resolved? (shrink)

An important contemporary version of Boltzmannian statistical mechanics explains the approach to equilibrium in terms of typicality. The problem with this approach is that it comes in different versions, which are, however, not recognized as such and not clearly distinguished. This article identifies three different versions of typicality‐based explanations of thermodynamic‐like behavior and evaluates their respective successes. The conclusion is that the first two are unsuccessful because they fail to take the system's dynamics into account. The third, however, is promising. (...) I give a precise formulation of the proposal and present an argument in support of its central contention. †To contact the author, please write to: Department of Philosophy, Logic, and Scientific Method, London School of Economics, Houghton Street, London WC2A 2AE, England; e‐mail: [email protected]. (shrink)

Gases reach equilibrium when left to themselves. Why do they behave in this way? The canonical answer to this question, originally proffered by Boltzmann, is that the systems have to be ergodic. This answer has been criticised on different grounds and is now widely regarded as flawed. In this paper we argue that some of the main arguments against Boltzmann's answer, in particular, arguments based on the KAM-theorem and the Markus-Meyer theorem, are beside the point. We then argue that something (...) close to Boltzmann's original proposal is true for gases: gases behave thermodynamic-like if they are epsilon-ergodic, i.e., ergodic on the entire accessible phase space except for a small region of measure epsilon. This answer is promising because there are good reasons to believe that relevant systems in statistical mechanics are epsilon-ergodic. (shrink)

GRW Theory postulates a stochastic mechanism assuring that every so often the wave function of a quantum system is `hit', which leaves it in a localised state. How are we to interpret the probabilities built into this mechanism? GRW theory is a firmly realist proposal and it is therefore clear that these probabilities are objective probabilities (i.e. chances). A discussion of the major theories of chance leads us to the conclusion that GRW probabilities can be understood only as either single (...) case propensities or Humean objective chances. Although single case propensities have some intuitive appeal in the context of GRW theory, on balance it seems that Humean objective chances are preferable on conceptual grounds because single case propensities suffer from various well know problems such as unlimited frequency tolerance and lack of a rationalisation of the principal principle. (shrink)

Computer simulations are an exciting tool that plays important roles in many scientific disciplines. This has attracted the attention of a number of philosophers of science. The main tenor in this literature is that computer simulations not only constitute interesting and powerful new science, but that they also raise a host of new philosophical issues. The protagonists in this debate claim no less than that simulations call into question our philosophical understanding of scientific ontology, the epistemology and semantics of models (...) and theories, and the relation between experimentation and theorising, and submit that simulations demand a fundamentally new philosophy of science in many respects. The aim of this paper is to critically evaluate these claims. Our conclusion will be sober. We argue that these claims are overblown and that simulations, far from demanding a new metaphysics, epistemology, semantics and methodology, raise few if any new philosophical problems. The philosophical problems that do come up in connection with simulations are not specific to simulations and most of them are variants of problems that have been discussed in other contexts before. (shrink)

Veritism, the position that truth is necessary for epistemic acceptability, seems to be in tension with the observation that much of our best science is not, strictly speaking, true when interpreted literally. This generates a paradox: truth is necessary for epistemic acceptability; the claims of science have to be taken literally; much of what science produces is not literally true and yet it is acceptable. We frame Elgin’s project in True Enough as being motivated by, and offering a particular resolution (...) to, this paradox. We discuss the paradox with a focus on scientific models and argue that there is another resolution available which is compatible with retaining veritism: rejecting the idea that scientific models should be interpreted literally. (shrink)

There are two theoretical approaches in statistical mechanics, one associated with Boltzmann and the other with Gibbs. The theoretical apparatus of the two approaches offer distinct descriptions of the same physical system with no obvious way to translate the concepts of one formalism into those of the other. This raises the question of the status of one approach vis-à-vis the other. We answer this question by arguing that the Boltzmannian approach is a fundamental theory while Gibbsian statistical mechanics is an (...) effective theory, and we describe circumstances under which Gibbsian calculations coincide with the Boltzmannian results. We then point out that regarding GSM as an effective theory has important repercussions for a number of projects, in particular attempts to turn GSM into a nonequilibrium theory. (shrink)

Computer simulations are an exciting tool that plays important roles in many scientific disciplines. This has attracted the attention of a number of philosophers of science. The main tenor in this literature is that computer simulations not only constitute interesting and powerful new science, but that they also raise a host of new philosophical issues. The protagonists in this debate claim no less than that simulations call into question our philosophical understanding of scientific ontology, the epistemology and semantics of models (...) and theories, and the relation between experimentation and theorising, and submit that simulations demand a fundamentally new philosophy of science in many respects. The aim of this paper is to critically evaluate these claims. Our conclusion will be sober. We argue that these claims are overblown and that simulations, far from demanding a new metaphysics, epistemology, semantics and methodology, raise few if any new philosophical problems. The philosophical problems that do come up in connection with simulations are not specific to simulations and most of them are variants of problems that have been discussed in other contexts before. (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)

Summary of the talk given to the 22nd Conference on the History of Logic, Cracow (Poland), July 5–9, 1976.

Models occupy a central role in the scientific endeavour. Among the many purposes they serve, representation is of great importance. Many models are representations of something else; they stand for, depict, or imitate a selected part of the external world (often referred to as target system, parent system, original, or prototype). Well-known examples include the model of the solar system, the billiard ball model of a gas, the Bohr model of the atom, the Gaussian-chain model of a polymer, the MIT (...) bag model of quark confinement, the Lorenz model of the atmosphere, the Lotka-Volterra model of the predator-prey interaction, or the hydraulic model of an economy, to mention just a few. All these models represent their target systems (or selected parts of them) in one way or another. (shrink)

This study examines whether corporate social responsibility performance is associated with corporate tax avoidance. Employing a matched sample of 434 firm-year observations from the Kinder, Lydenberg, and Domini database over the period 2003–2009, our logit regression results show that the higher the level of CSR performance of a firm, the lower the likelihood of tax avoidance. Our results indicate that more socially responsible firms are likely to display less tax avoidance. Finally, the results from our additional analysis show that the (...) CSR categories community relations and diversity represent particularly important elements of CSR performance that reduce tax avoidance. (shrink)

BackgroundThe theory and practice of ethics consultations (ECs) in health care are still characterized by many controversies, including, for example, the practice of giving recommendations. These controversies are complicated by an astonishing lack of evidence in the whole field. It is not clear how often a recommendation is issued in ethics consultations and when and why this step is taken. Especially in a facilitation model in which giving recommendations is optional, more data would be helpful to evaluate daily practice, ensure (...) that this practice is in line with the overarching goals of this approach and support the development of standards.MethodsWe analyzed all consultations requested from an EC service working under a facilitation approach at a maximum-care university hospital in Germany over a period of more than 10 years. Our aim was to better understand why—and under what circumstances—some consultation requests result in a recommendation, whereas others can be sufficiently addressed solely by facilitated meetings. We especially wanted to know when and why clients felt the need for clear advice from the EC service while in other cases they did not. We compared ethics consultations in terms of the differences between cases with and without recommendations issued by the ethics consultants using χ2 difference tests and Welch’s t-test.ResultsA total of 243 ECs were carried out between September 2008 and December 2019. In approximately half of the cases, a recommendation was given. All recommendations were issued upon the request of clients. When physicians asked for an EC, the consultation was significantly more likely to result in a recommendation than when the EC was requested by any other party. ECs in cases on wards with ethics rounds resulted in comparably fewer recommendations than those in wards without ethics rounds. When interpersonal conflicts were part of the problem or relatives were present in the meeting, clients less frequently asked for a recommendation.ConclusionFrom the client’s point of view, there does not seem to be only one “right” way to provide ethics consultations, but rather several. While facilitated meetings are obviously appreciated by clients, there also seem to be situations in which a recommendation is desired (especially by physicians). Further empirical and theoretical research is needed to validate our single-center results and re-evaluate the role of recommendations in ethics consultations. (shrink)

The United Kingdom Climate Impacts Programme’s UKCP09 project makes high-resolution projections of the climate out to 2100 by post-processing the outputs of a large-scale global climate model. The aim of this paper is to describe and analyse the methodology used and then urge some caution. Given the acknowledged systematic, shared errors of all current climate models, treating model outputs as decision-relevant projections can be significantly misleading. In extrapolatory situations, such as projections of future climate change, there is little reason to (...) expect that post-processing of model outputs can correct for the consequences of such errors. This casts doubt on our ability, today, to make trustworthy probabilistic projections at high resolution out to the end of the century. (shrink)

John Fischer has recently argued that the value of acting freely is the value of self-expression. Drawing on David Velleman’s earlier work, Fischer holds that the value of a life is a narrative value and free will is valuable insofar as it allows us to shape the narrative structure of our lives. This account rests on Fischer’s distinction between regulative control and guidance control. While we lack the former kind of control, on Fischer’s view, the latter is all that is (...) needed for self-expression. I first develop Fischer’s narrative account, focusing on his reliance on temporal loops as giving us control over the value of our lives. Second, I argue that the narrative account grants us greater power over the past than Fischer would allow: since narrative allows not only for changes in how we feel about episodes in our past but what those episodes in fact were, it allows for a kind of retroactive self-constitution. Finally, I suggest that this modification of the narrative view opens the possibility of a conception of freedom far stronger than guidance control. It does not give us the libertarian control over whether to choose A or B in the present, but it does provide a measure of control over the sort of person an agent has been, and thus whether she is the sort of person who will choose A or B in the future. (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)

This long-awaited translation of Das literarische Kunstwerk makes available for the first time in English Roman Ingarden's influential study. Though it is inter-disciplinary in scope, situated as it is on the borderlines of ontology and logic, philosophy of literature and theory of language, Ingarden's work has a deliberately narrow focus: the literary work, its structure and mode of existence. The Literary Work of Art establishes the groundwork for a philosophy of literature, i.e., an ontology in terms of which the (...) basic general structure of all literary works can be determined. This "essential anatomy" makes basic tools and concepts available for rigorous and subtle aesthetic analysis. (shrink)

Roman Frigg and James Nguyen present a detailed statement and defense of the fiction view of scientific models, according to which they are akin to the characters and places of literary fiction. They argue that while some of the criticisms this view has attracted raise legitimate points, others are myths. In this chapter, they first identify and then rebut the following seven myths: that the fiction view regards products of science as falsehoods; that the fiction view holds that models (...) are data-free; that the fiction view is antithetical to representation; that the fiction view trivializes epistemology; that the fiction view cannot account for the use of mathematics in the modeling; that the fiction view misconstrues the function of models in the scientific process; and that the fiction view stands on the wrong side of politics. As a result, they conclude that the fiction view of models, suitably understood, remains a viable position. (shrink)

A gas prepared in a non-equilibrium state will approach equilibrium and stay there. An influential contemporary approach to Statistical Mechanics explains this behaviour in terms of typicality. However, this explanation has been criticised as mysterious as long as no connection with the dynamics of the system is established. We take this criticism as our point of departure. Our central claim is that Hamiltonians of gases which are epsilon-ergodic are typical with respect to the Whitney topology. Because equilibrium states are typical, (...) we argue that there follows the desired conclusion that typical initial conditions approach equilibrium and stay there. (shrink)

Why do systems prepared in a non-equilibrium state approach, and eventually reach, equilibrium? An important contemporary version of the Boltzmannian approach to statistical mechanics answers this question by an appeal to the notion of typicality. The problem with this approach is that it comes in different versions, which are, however, not recognised as such, much less clearly distinguished, and we often find different arguments pursued side by side. The aim of this paper is to disentangle different versions of typicality-based explanations (...) of thermodynamic behaviour and evaluate their respective success. My conclusion will be that the boldest version fails for technical reasons, while more prudent versions leave unanswered essential questions. (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)

The so-called ergodic hierarchy (EH) is a central part of ergodic theory. It is a hierarchy of properties that dynamical systems can possess. Its five levels are egrodicity, weak mixing, strong mixing, Kolomogorov, and Bernoulli. Although EH is a mathematical theory, its concepts have been widely used in the foundations of statistical physics, accounts of randomness, and discussions about the nature of chaos. We introduce EH and discuss how its applications in these fields.