A weakly o-minimal structure image expanding an ordered group is called nonvaluational iff for every cut left angle bracketC,Dright-pointing angle bracket of definable in image, we have that inf{y−x:xset membership, variantC,yset membership, variantD}=0. The study of nonvaluational weakly o-minimal expansions of real closed fields carried out in [D. Macpherson, D. Marker, C. Steinhorn,Weakly o-minimal structures and real closed fields, Trans. Amer. Math. Soc. 352 5435–5483. MR1781273 (2001i:03079] suggests that this class is very close to the class of o-minimal expansions of (...) real closed fields. Here we further develop this analogy. We establish an o-minimal style cell decomposition for weakly o-minimal non-valuational expansions of ordered groups. For structures enjoying such a strong cell decomposition we construct a canonical o-minimal extension. Finally, we make attempts towards generalizing the o-minimal Euler characteristic to the class of sets definable in weakly o-minimal structures with the strong cell decomposition property. (shrink)

The paper is aimed at studying the topological dimension for sets definable in weakly o-minimal structures in order to prepare background for further investigation of groups, group actions and fields definable in the weakly o-minimal context. We prove that the topological dimension of a set definable in a weakly o-minimal structure is invariant under definable injective maps, strengthening an analogous result from [2] for sets and functions definable in models of weakly o-minimal theories. We pay special attention to large subsets (...) of Cartesian products of definable sets, showing that if X, Y and S are non-empty definable sets and S is a large subset of X × Y, then for a large set of tuples $\langle \overline{a}_{1},\ldots,\overline{a}_{2^{k}}\rangle \in X^{2^{k}}$ , where k = dim(Y), the union of fibers $S_{\overline{a}_{1}}\cup \cdots \cup S_{\overline{a}_{2^{k}}}$ is large in Y. Finally, given a weakly o-minimal structure ������, we find various conditions equivalent to the fact that the topological dimension in ������ enjoys the addition property. (shrink)

Given a group , G⊆Mm, definable in a first-order structure equation image equipped with a dimension function and a topology satisfying certain natural conditions, we find a large open definable subset V⊆G and define a new topology τ on G with which becomes a topological group. Moreover, τ restricted to V coincides with the topology of V inherited from Mm. Likewise we topologize transitive group actions and fields definable in equation image. These results require a series of preparatory facts concerning (...) dimension functions, some of which might be of independent interest. (shrink)

We investigate small theories of Boolean ordered o-minimal structures. We prove that such theories are $\aleph_{0}-categorical$ . We give a complete characterization of their models up to bi-interpretability of the language. We investigate types over finite sets, formulas and the notions of definable and algebraic closure.

Let (M, ≤,...) denote a Boolean ordered o-minimal structure. We prove that a Boolean subalgebra of M determined by an algebraically closed subset contains no dense atoms. We show that Boolean algebras with finitely many atoms do not admit proper expansions with o-minimal theory. The proof involves decomposition of any definable set into finitely many pairwise disjoint cells, i.e., definable sets of an especially simple nature. This leads to the conclusion that Boolean ordered structures with o-minimal theories are essentially bidefinable (...) with Boolean algebras with finitely many atoms, expanded by naming constants. We also discuss the problem of existence of proper o-minimal expansions of Boolean algebras. (shrink)

Given an infinite Boolean algebra B, we find a natural class of equation image-definable equivalence relations equation image such that every imaginary element from Beq is interdefinable with an element from a sort determined by some equivalence relation from equation image. It follows that B together with the family of sorts determined by equation image admits elimination of imaginaries in a suitable multisorted language. The paper generalizes author's earlier results concerning definable equivalence relations and weak elimination of imaginaries for Boolean (...) algebras, obtained in 10. (shrink)

We give a complete characterization of Boolean algebras admitting weak elimination of imaginaries in terms of elementary invariants.

We prove weak elimination of imaginary elements for Boolean orderings with finitely many atoms. As a consequence we obtain equivalence of the two notions of o-minimality for Boolean ordered structures, introduced by C. Toffalori. We investigate atoms in Boolean algebras induced by algebraically closed subsets of Boolean ordered structures. We prove uniqueness of prime models in strongly o-minimal theories of Boolean ordered structures.

Machine ethics and robot rights are quickly becoming hot topics in artificial intelligence and robotics communities. We will argue that attempts to attribute moral agency and assign rights to all intelligent machines are misguided, whether applied to infrahuman or superhuman AIs, as are proposals to limit the negative effects of AIs by constraining their behavior. As an alternative, we propose a new science of safety engineering for intelligent artificial agents based on maximizing for what humans value. In particular, we challenge (...) the scientific community to develop intelligent systems that have human-friendly values that they provably retain, even under recursive self-improvement. (shrink)

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)

Our reply to Fabian Freyenhagen’s article “Was ist orthodoxe Kritische Theorie?” (DZPhil 65.3 [2017], 456-469) raises the question whether his proposal that Critical Theory only “be adequately and appropriately critical” without a program of justification spares the search for any general criteria. Answering negatively we conversely want to recall, particularly with regard to Horkheimers’s and Adornos’s Dialectic of Enlightment as well as Habermas‘s concept of an emancipatory interest, that such a criterion as a normative foundation of critique is crucial not (...) only for systematical purposes, but also recognised as necessary in this respect by Adorno, who Freyenhagen wants to play off against programs of justification. Critical Theory needs to be clear in this respect. Against this background we are questioning Freyenhagen‘s recourse to an “interest in abolishing social injustice” as the “only criterion for Critical Theory.” Because Freyenhagen ignores the fact that Critical Theory has been understood by its representatives in a twofold manner – as a theoretical program of justification for one and secondly as a cultural diagnosis – his plea for an orthodox Critical Theory is endangered by decisionism. (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)

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)

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)

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.

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.

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

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)

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)

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)

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)

This paper attempts to formalize and to address the ‘leakproofing’ of the Singularity problem presented by David Chalmers. The paper begins with the definition of the Artificial Intelligence Confinement Problem. After analysis of existing solutions and their shortcomings, a protocol is proposed aimed at making a more secure confinement environment which might delay potential negative effect from the technological singularity while allowing humanity to benefit from the superintelligence.

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)

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)

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)

The paper is devoted to the presentation and analysis of the philosophical views concerning logic and mathematics of the leading members of Cracow Circle, i.e., of Jan Salamucha, Jan Franciszek Drewnowski and Józef Maria Bocheński. Their views on the problem of possible applicability of logical tools in metaphysical and theological researches is also discussed.

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)

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)

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)

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)

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)

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)

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)