Roman Frigg

How does mathematics apply to something non-mathematical? We distinguish between a general application problem and a special application problem. A critical examination of the answer that structural mapping accounts offer to the former problem leads us to identify a lacuna in these accounts: they have to presuppose that target systems are structured and yet leave this presupposition unexplained. We propose to fill this gap with an account that attributes structures to targets through structure generating descriptions. These descriptions are physical descriptions and so there is no such thing as a solely mathematical account of a target system.

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.

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.

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.

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

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

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].

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.

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.

The last decade and a half has seen an ardent development of self-organised criticality, a new approach to complex systems, which has become important in many domains of natural as well as social science, such as geology, biology, astronomy, and economics, to mention just a few. This has led many to adopt a generalist stance towards SOC, which is now repeatedly claimed to be a universal theory of complex behaviour. The aim of this paper is twofold. First, I provide a brief and non-technical introduction to SOC. Second, I critically discuss the various bold claims that have been made in connection with it. Throughout, I will adopt a rather sober attitude and argue that some people have been too readily carried away by fancy contentions. My overall conclusion will be that none of these bold claims can be maintained. Nevertheless, stripped of exaggerated expectations and daring assertions, many SOC models are interesting vehicles for promising scientific research.Author Keywords: Self-organised criticality; Scaling law; Models; Formal analogy.

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.

The roles models play in science have long been recognised and sparked rich and varied philosophical debates. In recent years attention has also been paid to the computational techniques used in the sciences, and the question arose what the implications were of the use of computer simulations for our understanding of scientific modelling, and science more generally. This was the subject of the conference “Models and Simulations”, which took place at the IHPST in Paris in June 2006. Selected papers of that conference appeared in a special issue of this journal (Synthese 169(3) (2009)). After the conference there was a general feeling that there still was much ground to cover, and so we decided to organize a follow up a year later. “Models and Simulations 2” took place in October 2007 at the Tilburg Center for Logic and Philosophy of Science (TiLPS) in the Netherlands. The conference was made possible due to generous financial support from IHPST (Paris, CNRS), Universitat de Barcelona, TiLPS (Tilburg Center for Logic and Philosophy of Science) and the Evert Willem Beth Foundation. The papers in this special issue were presented at the conference and selected after a double-blind review process. We would like to thank the authors and referees of the papers for their work, and Vincent Hendricks and John Symons for their support of the project of another special issue on models and simulations.

The aim of this article is twofold. Recently, Lewis has presented an argument, now known as the "counting anomaly", that the spontaneous localization approach to quantum mechanics, suggested by Ghirardi, Rimini, and Weber, implies that arithmetic does not apply to ordinary macroscopic objects. I will take this argument as the starting point for a discussion of the property structure of realist collapse interpretations of quantum mechanics in general. At the end of this I present a proof of the fact that the composition principle, which holds true in standard quantum mechanics, fails in all realist collapse interpretations. On the basis of this result I reconsider the counting anomaly and show that what lies at the heart of the anomaly is the failure to appreciate the peculiarities of the property structure of such interpretations. Once this flaw is uncovered, the anomaly vanishes.

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.

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.

On an influential account, chaos is explained in terms of random behaviour; and random behaviour in turn is explained in terms of having positive Kolmogorov-Sinai entropy (KSE). Though intuitively plausible, the association of the KSE with random behaviour needs justification since the definition of the KSE does not make reference to any notion that is connected to randomness. I provide this justification for the case of Hamiltonian systems by proving that the KSE is equivalent to a generalized version of Shannon's communication-theoretic entropy under certain plausible assumptions. I then discuss consequences of this equivalence for randomness in chaotic dynamical systems. Introduction Elements of dynamical systems theory Entropy in communication theory Entropy in dynamical systems theory Comparison with other accounts Product versus process randomness.

The formalism of quantum mechanics provides us with the probabilities for certain events to occur—this much is uncontroversial. But how are we to understand these probabilities? The essays in this special issue approach this question from different angles. The first three contributions take as their point of departure the philosophy of probability and discuss what the two main outlooks—objective and subjective interpretations of probability—have to offer in the context of quantum mechanics. The following five papers explore the question of how probabilities in particular interpretations of quantum mechanics—modal interpretations, relative state interpretations, Bohmian mechanics, and GRW theory—can be interpreted. The last three essays address specific issues: non-standard probability and algebraic quantum field theory, quantum propensities, and the relation between decoherence and the interpretation of probability.

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..

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

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

Computer simulations have changed the face of many scientific disciplines. This has attracted the attention of a number of philosophers of science, who have started discussing the philosophical implications of the use of computational methods in science. It was the aim of the conference Models and Simulations that took place at the IHPST in Paris, France, on 12 and 13 June 2006 to bring researchers working in this field together and provide a platform to discuss these issues in a focused way. The papers in this special issue were presented at this conference. We would like to thank the IHPST and the CNRS (département SHS, ATIP “Physique et Calcul”) for generous financial support of the conference. We also would like to thank the authors and referees of the papers for their work, and Vincent Hendricks and John Symons for their support of the project of a special issue of this journal to the topic of the conference.