What sort of claims do scientific models make and how do these claims then underwrite empirical successes such as explanations and reliable policy interventions? In this paper I propose answers to these questions for the class of models used throughout the social and biological sciences, namely idealized deductive ones with a causal interpretation. I argue that the two main existing accounts misrepresent how these models are actually used, and propose a new account. *Received July 2006; revised August 2008. †To contact (...) the author, please write to: Department of Philosophy, University of Missouri, St. Louis, 599 Lucas Hall (MC 73), One University Blvd., St. Louis, MO 63121-4400; e-mail: alexandrovaa@umsl.edu. (shrink)

: This paper contains the analysis of nine interviews with UK scientists on the topic of scientific models. Scientific models are an important, very controversially discussed topic in philosophy of science. A reasonable expectation is that philosophical conceptions of models ought to be in agreement with scientific practice. Questioning practicing scientists on their use of and views on models provides material against which philosophical positions can be measured.

Cellular Automata (CA) based simulations are widely used in a great variety of domains, fromstatistical physics to social science. They allow for spectacular displays and numerical predictions. Are they forall that a revolutionary modeling tool, allowing for “direct simulation”, or for the simulation of “the phenomenon itself”? Or are they merely models "of a phenomenological nature rather than of a fundamental one”? How do they compareto other modeling techniques? In order to answer these questions, we present a systematic exploration of (...) CA’s various uses. (shrink)

This paper examines contemporary attempts to explicate the explanatory role of mathematics in the physical sciences. Most such approaches involve developing so-called mapping accounts of the relationships between the physical world and mathematical structures. The paper argues that the use of idealizations in physical theorizing poses serious difficulties for such mapping accounts. A new approach to the applicability of mathematics is proposed. Introduction Mathematical Explanations I: Entities Mathematical Explanations II: Operations Mapping Accounts: Strengths Mapping Accounts: Idealizations 5.1 Pincock and matching (...) models 5.2 Bueno, Colyvan, and the inferential conception Mapping Accounts: Limitations Suggestions for a New Approach Conclusion CiteULike Connotea Del.icio.us What's this? (shrink)

This paper examines the role of mathematical idealization in describing and explaining various features of the world. It examines two cases: first, briefly, the modeling of shock formation using the idealization of the continuum. Second, and in more detail, the breaking of droplets from the points of view of both analytic fluid mechanics and molecular dynamical simulations at the nano-level. It argues that the continuum idealizations are explanatorily ineliminable and that a full understanding of certain physical phenomena cannot be obtained (...) through completely detailed, nonidealized representations. (shrink)

A traditional view of mathematical modeling holds, roughly, that the more details of the phenomenon being modeled that are represented in the model, the better the model is. This paper argues that often times this ‘details is better’ approach is misguided. One ought, in certain circumstances, to search for an exactly solvable minimal model—one which is, essentially, a caricature of the physics of the phenomenon in question.

Webb distinguishes two endeavors she calls animal modeling and animat modeling and advocates for the former. I share her preference and point to additional virtues of modeling actual biological mechanisms (animal modeling). As Webb argues, animat modeling should be regarded as modeling of specific, but madeup, biological mechanisms. I contend that modeling made-up mechanisms in situations in which we have some knowledge of the actual mechanisms involved is modeling with one hand—the good one—tied behind one’s back.1 The hand that is (...) used in animat modeling is constructing and evaluating models by whether they behave in the right way—do they exhibit the particular phenomenon one is trying to understand? The good hand that is disavowed seeks to use evidence about the mechanism employed in real living systems both for inspiration in designing the model and for evaluating the model. Denying oneself use of one’s good hand both limits one’s access to valuable evidence for evaluating a model and denies oneself access to a potent discovery strategy. Webb draws attention to one reason to employ the good hand—if models are to be relevant to biology (and not just characterize hypothetical mechanisms), then the component parts and operations specified in the model must in some way map onto those in actual biological organisms. Especially if one accepts the possibility of multiple realizations, then if one only uses behavior to evaluate the model one may well have described an alternative realization than that found in real organisms. To determine that one has modeled the actual realization, it is necessary to compare the proposed mechanism with the actual mechanism—does it.. (shrink)

Scientific models invariably involve some degree of idealization, abstraction, or fictionalization of their target system. Nonetheless, I argue that there are circumstances under which such false models can offer genuine scientific explanations. After reviewing three different proposals in the literature for how models can explain, I shall introduce a more general account of what I call model explanations , which specify the conditions under which models can be counted as explanatory. I shall illustrate this new framework by applying it to (...) the case of Bohr’s model of the atom, and conclude by drawing some distinctions between phenomenological models, explanatory models, and fictional models. (shrink)

In this paper the topic of the relations between scientific theories and scientific models is tackled by considering the former as hypothetical scientific representations and the latter as fictive scientific representations. A classification of the models is also proposed.

In this paper a unified theory of models and thought experiments is proposed by considering them as fictions, la Vaihinger. In order to reach this aim, the Hertzian and Botzmannian interpretation of theories as Bilder is reconsidered.

I extract some philosophical morals from some aspects of Lagrangian mechanics. (A companion paper will present similar morals from Hamiltonian mechanics and Hamilton-Jacobi theory.) One main moral concerns methodology: Lagrangian mechanics provides a level of description of phenomena which has been largely ignored by philosophers, since it falls between their accustomed levels---``laws of nature'' and ``models''. Another main moral concerns ontology: the ontology of Lagrangian mechanics is both more subtle and more problematic than philosophers often realize. The treatment of Lagrangian (...) mechanics provides an introduction to the subject for philosophers, and is technically elementary. In particular, it is confined to systems with a finite number of degrees of freedom, and for the most part eschews modern geometry. (shrink)

This paper argues that even when simple analogue models picture parallel worlds, they generally still serve as isolating tools. But there are serious obstacles that often stop them isolating in just the right way. These are obstacles that face any model that functions as a thought-experiment but they are especially pressing for economic models because of the paucity of economic principles. Because of the paucity of basic principles, economic models are rich in structural assumptions. Without these no interesting conclusions can (...) be drawn. This, however, makes trouble when it comes to exporting conclusions from the model to the world. One uncontroversial constraint on induction from special cases is to beware of extending conclusions to situations that we know are different in relevant respects. In the case of economic models it is clear by inspection that the unrealistic structural assumptions of the model are intensely relevant to the conclusion. Any inductive leap to a real situation seems a bad bet. (shrink)

In this paper the claim that laws of nature are to be understood as claims about what necessarily or reliably happens is disputed. Laws can characterize what happens in a reliable way, but they do not do this easily. We do not have laws for everything occurring in the world, but only for those situations where what happens in nature is represented by a model: models are blueprints for nomological machines, which in turn give rise to laws. An example from (...) economics shows, in particular, how we use--and how we need to use--models to get probabilistic laws. (shrink)

Metaphors and models involve correspondences between events in separate domains. They differ in the form and precision of how the correspondences are expressed. Examples include correspondences between phylogenic and ontogenic selection, and wave and particle metaphors of the mathematics of quantum physics. An implication is that the target article's metaphors of resistance to change may have heuristic advantages over those of momentum.

The semantic view of theoriesis one according to which theoriesare construed as models of their linguisticformulations. The implications of thisview for scientific realism have been little discussed. Contraryto the suggestion of various champions of the semantic view,it is argued that this approach does not makesupport for a plausible scientific realism anyless problematic than it might otherwise be.Though a degree of independence of theory fromlanguage may ensure safety frompitfalls associated with logical empiricism, realism cannot be entertained unless models or (abstractedand/or idealized) (...) aspects thereof are spelled out in terms of linguistic formulations (such as mathematical equations),which can be interpreted in terms of correspondencewith the world. The putative advantage of thesemantic approach – its linguistic independence – isthus of no help to the realist. I consider recent treatmentsof the model-theoretic view (Suppe, Giere, Smith), and find that although some of these accounts harbour the promiseof realism, this promise is deceptive. (shrink)

In this paper, I show how some of the fundamental problems that face a structuralist conception of representation can be solved by (a) distinguishing between three relevant senses of ‘representation’ (i.e. denotation, epistemic representation, and faithful epistemic representation), (b) claiming that, properly understood, the structural conception of representation aims at providing us with an account of faithful epistemic representation not of epistemic representation simpliciter, and (c) adopting an interpretational conception of epistemic representation.

In this paper, I distinguish scientific models in three kinds on the basis of their ontological status—material models, mathematical models and fictional models, and develop and defend an account of fictional models as fictional objects—i.e. abstract objects that stand for possible concrete objects.

In this paper, I develop Mauricio Suárez’s distinction between denotation, epistemic representation, and faithful epistemic representation. I then outline an interpretational account of epistemic representation, according to which a vehicle represents a target for a certain user if and only if the user adopts an interpretation of the vehicle in terms of the target, which would allow them to perform valid (but not necessarily sound) surrogative inferences from the model to the system. The main difference between the interpretational conception I (...) defend here and Suárez’s inferential conception is that the interpretational account is a substantial account—interpretation is not just a “symptom” of representation; it is what makes something an epistemic representation of a something else. (shrink)

In this paper, I consider how different versions of the similarity account of scientific representation might apply to a simple case of scientific representation, in which a model is used to predict the behaviour of a system. I will argue that the similarity account is potentially susceptible to the problem of accidental similarities between the model and the system and that, if it is to avoid this problem, one has to specify which similarities have to hold between a model and (...) a system for the model to be a faithful representation of that system. The sort of similarity that needs to hold between the model and the system, I argue, is a “second-order” similarity rather than simply a “first-order” similarity. This will not only avoid the problem but hopefully will contribute to dispelling the impression that an account of representation based on similarity is hopelessly vague. (shrink)

The main aim of this paper is to disentangle three senses in which we can say that a model represents a system—denotation epistemic representation, and successful epistemic representation--and to individuate what questions arise from each sense of the notion of representation as used in this context. Also, I argue that a model is an epistemic representation of a system only if a user adopts a general interpretation of the model in terms of a system. In the process, I hope to (...) clarify where those who, following Craig Callander and Jonathan Cohen, claim that there is no special problem about scientific representation go wrong. In the terminology adopted here, even if scientific representation is only an instance of epistemic representation, scientific representation should not be confounded with denotation. (shrink)

Not all models are explanatory. Some models are data summaries. Some models sketch explanations but leave crucial details unspecified or hidden behind filler terms. Some models are used to conjecture a how-possibly explanation without regard to whether it is a how-actually explanation. I use the Hodgkin and Huxley model of the action potential to illustrate these ways that models can be useful without explaining. I then use the subsequent development of the explanation of the action potential to show what is (...) required of an adequate mechanistic model. Mechanistic models are explanatory. (shrink)

Several prominent philosophers of science, most notably Ron Giere, propose that scientific theories are collections of models and that models represent the objects of scientific study. Some, including Giere, argue that models represent in the same way that pictures represent. Aestheticians have brought the picturing relation under intense scrutiny and presented important arguments against the tenability of particular accounts of picturing. Many of these arguments from aesthetics can be used against accounts of representation in philosophy of science. I rely on (...) Dominic Lopes’ recent summary of arguments against various views of picturing and reformulate some of them to fit the philosophy of science context. My specific targets here are Giere and Steven French. I go on to argue that assuming all scientific models and images represent in the same way is not the best guide to understanding scientific practice. (shrink)

The semantic view on theories has been much in vogue over four decades as the successor of the syntactic view. In the present paper, I take issue with this approach by arguing that theories and models must be separated and that a theory should be considered to be a linguistic systems consisting of a vocabulary and a set of rules for the use of that vocabulary.

Stein once urged us not to confuse the means of representation with that which is being represented. Yet that is precisely what philosophers of science appear to have done at the meta-level when it comes to representing the practice of science. Proponents of the so-called ‘syntactic’ view identify theories as logically closed sets of sentences or propositions and models as idealised interpretations, or ‘theoruncula, as Braithwaite called them. Adherents of the ‘semantic’ approach, on the other hand, are typically characterised as (...) taking them to be families of models that are set-theoretic, according to Suppes and others, or abstract, as Giere has argued. da Costa and French (Science and Partial Truth. OUP, Oxford, 2003) suggested that we should refrain from ontological speculation as to the nature of scientific theories and models and focus on their appropriate representation for various purposes within the philosophy of science. Such an approach allows both linguistic and non-linguistic resources to play their appropriate role (see also French and Saatsi, Philosophy of Science, Proceedings of the 2004 PSA Meeting, 78:548–559, 2006) and can be supported by recent case studies illustrating the heterogeneity of scientific practice. My aim in this paper is to further develop this ‘quietist’ view, and to indicate how it offers a fruitful way forward for the philosophy of science. (shrink)

In its most common use, the term ‘model’ refers to a simplified and stylised version of the socalled target system, the part or aspect of the world that we are interested in. For instance, in order to determine the orbit of a planet moving around the sun we model the planet and the sun as perfect homogenous spheres that gravitationally interact with each other but nothing else in the universe, and then apply Newtonian mechanics to this system, which reveals that (...) the planet moves on an elliptical orbit. Views diverge about what sort of entity such a model is. Those focussing on the formal aspects of models regard them either as equations or settheoretical structures, while those opposed to such an approach take them to be descriptions or abstract (yet non-mathematical) entities. A further question concerns the relation of models and theories. In some cases models can be derived from theory simply by specifying the relevant determinables in a theory’s general equations. But many models cannot be obtained from theory in this straightforward way, and some even involve assumptions that contradict the fundamental theory. The relation of models to their respective target systems is equally complex and fraught with controversy. Two influential proposals take the relation between a model and its target to be isomorphism or similarity, respectively. This, however, has been criticised as too restrictive as many models do not seem to fit this mould. (shrink)

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)

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)

Models are of central importance in many scientific contexts. The centrality of models such as the billiard ball model of a gas, the Bohr model of the atom, the MIT bag model of the nucleon, the Gaussian-chain model of a polymer, the Lorenz model of the atmosphere, the Lotka-Volterra model of predator-prey interaction, the double helix model of DNA, agent-based and evolutionary models in the social sciences, or general equilibrium models of markets in their respective domains are cases in point. (...) Scientists spend a great deal of time building, testing, comparing and revising models, and much journal space is dedicated to introducing, applying and interpreting these valuable tools. In short, models are one of the principal instruments of modern science. (shrink)

This paper argues that a successful philosophical analysis of models and simulations must accommodate an account of mathematically rigorous results. Such rigorous results may be thought of as genuinely model-specific contributions, which can neither be deduced from fundamental theory nor inferred from empirical data. Rigorous results provide new indirect ways of assessing the success of models and simulations and are crucial to understanding the connections between different models. This is most obvious in cases where rigorous results map different models on (...) to one another. Not only does this put constraints on the extent to which performance in specific empirical contexts may be regarded as the main touchstone of success in scientific modelling, it also allows for the transfer of warrant across different models. Mathematically rigorous results can thus come to be seen as not only strengthening the cohesion between scientific strategies of modelling and simulation, but also as offering new ways of indirect confirmation. (shrink)

This paper argues that, for a prospective philosophical analysis of models and simulations to be successful, it must accommodate an account of mathematically rigorous results. Such rigorous results are best thought of as genuinely model-specific contributions, which can neither be deduced from fundamental theory nor inferred from empirical data. Rigorous results often provide new indirect ways of assessing the success of computer simulations of individual models. This is most obvious in cases where rigorous results map different models on to one (...) another. Not only does this allow for the transfer of warrant across different models, it also puts constraints on the extent to which performance in specific empirical contexts may be regarded as the main touchstone of success in scientific modelling. Rigorous results and relations can thus come to be seen as giving cohesion and stability to actual practices of scientific modelling. (shrink)

Recent work on the role of models in science has revealed a great many kinds of models performing many different roles. In this paper I suggest that one can find much unity among all this diversity by thinking of many models as being components of distributed cognitive systems. I begin by distinguishing the relevant notion of a distributed cognitive system and then give examples of different kinds of models that can be thought of as functioning as components of such systems. (...) These include both physical and abstract models. After considering several objections, I conclude by locating distributed cognition within larger movements in contemporary cognitive science. (shrink)

This paper constitutes my first attempt publicly to comment on Nancy Cartwright’s philosophy of science. That I have not done this earlier is primarily due to the great similarities in our views on topics where our interests overlap.2 But Cartwright’s work also covers topics I have never seriously considered, such as the use of linear models in economics and the measurement problem in quantum mechanics. Even the subject of probabilistic causation, to which I once contributed, is not one I now (...) feel confident in examining in any detail. I will concentrate, therefore, on her views regarding the nature of scientific theories, laws, models, and causality in general – topics at the forefront of my own current thinking. More specifically still, I will focus on the picture of classical mechanics she presents in The Dappled World (1999). (shrink)

There has recently been an increase in interest in the role of models in science, of which the Pavia workshop on model-based reasoning is a manifestation. One result of this increased attention has been a proliferation of views on what models are and how they are used in science. In this presentation I will develop a unified interpretation of the nature and role of models in science. Central to this interpretation is an understanding of the relationships between models and other (...) elements of an understanding of science, particularly theories, data, and analogy. My conclusion will be that models play a much larger role in science than even the most ardent enthusiasts for models have typically claimed. Modeling, on my view, is not at all ancillary to doing science, but central to constructing scientific accounts of the natural world. (shrink)

I argue for an intentional conception of representation in science that requires bringing scientific agents and their intentions into the picture. So the formula is: Agents (1) intend; (2) to use model, M; (3) to represent a part of the world, W; (4) for some purpose, P. This conception legitimates using similarity as the basic relationship between models and the world. Moreover, since just about anything can be used to represent anything else, there can be no unified ontology of models. (...) This whole approach is further supported by a brief exposition of some recent work in cognitive, or usage-based, linguistics. Finally, with all the above as background, I criticize the recently much discussed idea that claims involving scientific models are really fictions. (shrink)

The usual question, “Are models fictions?” is replaced by the question, “Should scientific models be regarded as works of fiction?” This makes it clear that the issue is not one of definition but of interpretation. First one must distinguish between the ontology of scientific models and their function in the practice of science. Theoretical models and works of fiction are ontologically on a par, their both being creations of human imagination. It is their differing functions in practice that makes it (...) inappropriate to regard scientific models as works of fiction. Three reasons for thinking scientific models should be regarded as works of fiction are rejected. First, scientists themselves sometimes invoke the idea of fictions in their discussions of specific models. Second, many scientific models are physically impossible to realize in the real world. Third, regarding scientific models as works of fiction supports a general fictionalist understanding of scientific theories. It is concluded that promoting the general idea that scientific models are works of fiction unnecessarily supports attacks on the legitimacy of science itself. (shrink)