Philosophy Idealizations in Science
by
Ashley Graham Kennedy
  • LAST REVIEWED: 10 November 2022
  • LAST MODIFIED: 29 May 2014
  • DOI: 10.1093/obo/9780195396577-0193

Introduction

Idealization, or the intentional misrepresentation of the empirical system that is being studied, is ubiquitous within the practice of science. Much of contemporary science proceeds via the use of models, and all models, including those used in biology, physics, economics, chemistry, and geology, contain idealizations. Idealizations are used by scientists for many purposes. Most often they are used to simplify scientific models for representational or explanatory uses or to make them computationally tractable. Idealizations come in different forms, including abstractions, approximations, Galilean idealizations, and fictions. Because of the widespread use of idealization across the scientific disciplines, philosophers of science have recently become interested in understanding their role in scientific practice. Of particular interest are the questions of the role of idealizations in scientific representation and explanation and of whether or not idealized models can be considered realistic.

Early Works

Nowak 1980, Cartwright 1983, McMullin 1985, Wimsatt 1987, and Giere 1988 are some of the most important early works that address the use of idealization in science.

  • Cartwright, Nancy. How the Laws of Physics Lie. Oxford: Oxford University Press, 1983.

    DOI: 10.1093/0198247044.001.0001Save Citation »Export Citation » Share Citation »

    NNNThis well-known collection of essays discusses idealization in the context of arguments for causal entity realism.

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  • Giere, Ronald. Explaining Science: A Cognitive Approach. Chicago: University of Chicago Press, 1988.

    DOI: 10.7208/chicago/9780226292038.001.0001Save Citation »Export Citation » Share Citation »

    NNNA discussion of the role of models in science, including an argument for idealized models as realistic representations of empirical systems.

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  • McMullin, Ernan. “Galilean Idealization.” Studies in History and Philosophy of Science 16.3 (1985): 247–273.

    DOI: 10.1016/0039-3681(85)90003-2Save Citation »Export Citation » Share Citation »

    NNNA canonical article that uses historical examples to explore the epistemic implications of the scientific practice of incorporating Galilean idealizations within models.

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  • Nowak, Leszek. The Structure of Idealization. Dordrecht, The Netherlands: D. Reidel, 1980.

    DOI: 10.1007/978-94-015-7651-2Save Citation »Export Citation » Share Citation »

    NNNThis article discusses the role of idealization in economics. Nowak argues that while idealized models do enable understanding, removing idealizations from a model and replacing them with true structures would enhance the model’s explanatory power. In other words, he argues that idealized models provide only “approximate explanations.”

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  • Wimsatt, William. “False Models as Means to Truer Theories.” In Neutral Models in Biology. Edited by M. Nitecki and A. Hoffman, 23–55. New York: Oxford University Press, 1987.

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    NNNArgues that one of the main values of false, or idealized, models is that they can be used as stepping-stones to more realistic models, which in turn can reveal truths about the empirical world.

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Reference Work

Jones and Cartwright 2005 is a comprehensive volume dedicated to the topic of idealization in science.

  • Jones, Martin R., and Nancy Cartwright, eds. Idealization XII: Correcting the Model: Idealization and Abstraction in the Sciences. Poznán Studies in the Philosophy of the Sciences and Humanities. Amsterdam and New York: Rodopi, 2005.

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    NNNA collection of eleven papers on idealization that cover a range of topics including idealization in economics and physics as well as a discussion of the implications of idealization for scientific realism.

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Types of Idealization

An idealization can be understood as a deliberate misrepresentation or an intentional distortion within a scientific theory or model of a part of the target system being described. There are many kinds of idealizations, and included in the following subsections are citations that discuss four of them: Abstraction, Approximation, Galilean Idealization, and Fiction. Although there is a lack of agreement in the current literature on exactly how to characterize these different types of idealizations, there is at least a generalized agreement that the types are in fact distinct from one another. Weisberg 2007 is the first article that comprehensively addresses the distinctions between differing types of idealization in scientific modeling.

  • Weisberg, Michael. “Three Kinds of Idealization.” Journal of Philosophy 104.12 (2007): 639–659.

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    NNNThis is an informative (and often cited) paper that discusses three types of idealization (Galilean idealization, minimalist idealization, and multiple-models idealization) and the various roles that they play in the practice of scientific modeling.

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Abstraction

Abstraction, which some characterize as a type of idealization, and others as something distinct from it, involves leaving out, in the theory or model, something that is considered to be irrelevant to what is being studied in the target system in question. This is done in order to focus on the target property or entity of interest exclusively. The process of abstraction is commonly used across the scientific disciplines. Included here are a few representative articles on the nature and use of abstraction in science. Chakravartty 2010, Godfrey-Smith 2009, and Jones 2005 discuss the relationship and differences between abstraction and idealization in various contexts in scientific research.

  • Chakravartty, Anjan. “Truth and Representation in science: Two inspirations from art.” In Beyond Mimesis and Convention: Representation in Art and Science. Edited by Roman Frigg and Matthew C. Hunter, 33–50. Dordrect, The Netherlands, and London: Springer, 2010.

    DOI: 10.1007/978-90-481-3851-7Save Citation »Export Citation » Share Citation »

    NNNA paper originally presented at the conference “Beyond Mimesis and Convention: Representation in Art and Science” held in London in 2006. Discusses the differing relationships of the processes of abstraction and idealization to the notion of approximate truth. Includes a discussion of analogies between scientific models and works of art.

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  • Godfrey-Smith, Peter. “Abstractions, Idealizations, and Evolutionary Biology.” In Mapping the Future of Biology: Evolving Concepts and Theories. Edited by Anouk Barberousse, Michel Morange, and Thomas Pradeu, 47–56. Dordrect, The Netherlands: Springer, 2009.

    DOI: 10.1007/978-1-4020-9636-5Save Citation »Export Citation » Share Citation »

    NNNThis article discusses the relationship between idealization and abstraction in the context of evolutionary theory. Godfrey-Smith characterizes idealization as treating things as having features they do not have and abstraction as leaving things out.

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  • Jones, Martin R. “Idealization and Abstraction: A Framework.” In Idealization XII: Correcting the Model: Idealization and Abstraction in the Sciences. Edited by Martin R. Jones and Nancy Cartwright, 3. Amsterdam: Rodopi, 2005.

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    NNNA discussion that distinguishes between idealization as misrepresentation or “assertion of a falsehood” and abstraction as “omission of a truth.”

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Approximation

Those that separate the notions of approximation and idealization generally argue that approximations can be analyzed in terms of distance from the facts or truth, while idealizations are not necessarily amenable to this kind of comparative analysis. Beyond this initial distinction, however, there are many ways to break down the differences and relations between these two epistemic tools. The following citations illustrate four of these ways. Laymon 1990 discusses the use of approximation in computer simulation, Liu 1999 analyzes approximation as a comparative concept, Niiniluoto 1986 addresses the use of approximation in scientific theory, and Norton 2012 argues that idealization and approximation are different, and that this difference has scientific importance.

  • Laymon, Ronald. “Computer Simulations, Idealizations and Approximations.” PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 2 (1990): 519–534.

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    NNNAs the title suggests, this article gives an analysis of idealization (which Laymon defines as something that ignores a causally relevant factor) and calculational approximation, and the relations between the two, within the context of computer simulations.

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  • Liu, Chang. “Approximation, Idealization, and Laws of Nature.” Synthese 118.2 (1999): 229–256.

    DOI: 10.1023/A:1005186322310Save Citation »Export Citation » Share Citation »

    NNNAn interesting discussion in which Liu defines approximation as a purely comparative notion of closeness to the truth, while analyzing idealizations, on the other hand, as counterfactual claims.

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  • Niiniluoto, Ilkka. “Theories, Approximations and Idealizations.” In Logic, Methodology and Philosophy of Science VII: Proceedings of the Seventh International Congress of Logic, Methodology, and Philosophy of Science, Salzberg 1983. Edited by Ruth Barcan Marcus, Georg Dorn, and Paul Weingartner, 255–289. Amsterdam: North Holland, 1986.

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    NNNIn this article Niiniluoto discusses the use of idealization in scientific theories. He argues that in this context the use of idealization can yield approximately true theories. This article is helpful for those who want to understand the role of scientific idealization in theories.

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  • Norton, John D. “Approximations and Idealization: Why the Difference Matters.” Philosophy of Science 79.2 (April 2012): 207–232.

    DOI: 10.1086/664746Save Citation »Export Citation » Share Citation »

    NNNIn this article Norton uses the term approximation to mean an “inexact description of a target system” and the term idealization to denote “another system whose properties also provide an inexact description of the target system.” What makes his ensuing discussion particularly interesting is that Norton conceives of an “idealization” in the way that many conceive of a “model.”

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Galilean Idealization

Galilean idealization is the simplification, within a model, of a complicated entity, property, or process in a target, with the objective of increasing model tractability. Galilean idealizations are distinct from fictions in that they can be removed from a model via processes of de-idealization. McMullin 1985 was the first to introduce the idea of Galilean idealization into the philosophy of science. Weisberg 2007 expands upon McMullin’s ideas about Galilean idealization, while distinguishing them from other types of idealizations in science.

  • McMullin, Ernan. “Galilean Idealization.” Studies in History and Philosophy of Science 16.3 (1985): 247–273.

    DOI: 10.1016/0039-3681(85)90003-2Save Citation »Export Citation » Share Citation »

    NNNA canonical article that uses historical examples to explore the epistemic implications of the scientific practice of incorporating Galilean idealizations into models.

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  • Weisberg, Michael. “Three Kinds of Idealization.” Journal of Philosophy 104.12 (2007): 639–659.

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    NNNThis often-cited paper discusses three types of idealization, including Galilean idealization, and the various roles that they play in the practice of scientific modeling.

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Fiction

Some sources, such as Godfrey-Smith 2009 and Frigg 2010, use the terms idealization and fiction interchangeably. These terms are used to indicate any false component within a scientific model. Others, such as Kennedy 2012 and Bokulich 2009, distinguish between idealizations and fictions. Kennedy 2012 argues that idealizations have correlates in the target system but that fictions do not, while Bokulich 2009 argues that fictions are representations of entities that are not present within the target.

  • Bokulich, Alisa. “Explanatory Fictions.” In Fictions in Science: Philosophical Essays on Modeling and Idealization. Edited by Mauricio Suárez, 91–109. New York: Routledge, 2009.

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    NNNIn this chapter Bokulich argues that fictional models can, in some cases, provide better explanations than models that are approximately true.

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  • Frigg, Roman. “Models and Fiction.” Synthese 172 (2010): 251–268.

    DOI: 10.1007/s11229-009-9505-0Save Citation »Export Citation » Share Citation »

    NNNTreats models as a whole as “fictional” and gives an account of scientific models as analogous to literary works of fiction.

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  • Godfrey-Smith, Peter. “Models and Fictions in Science.” Philosophical Studies 143 (2009): 101–116.

    DOI: 10.1007/s11098-008-9313-2Save Citation »Export Citation » Share Citation »

    NNNIn this article Godfrey-Smith argues that the use of fictions in science allows scientists to compare the properties of models with the properties of their targets.

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  • Kennedy, Ashley. “Models, Idealization and Scientific Explanation.” PhD diss., University of Virginia, 2012.

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    NNNChapter 3 gives an account of the difference between idealizations (false model components that have correlates in the target system that is being modeled) and fictions (false model components that have no correlates in the target).

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Idealization and Scientific Representation

There is a sizable literature on the topic of idealization in scientific representation. Very generally, this literature can be divided into accounts of scientific representation of two types: mapping accounts (see for instance Bueno and French 2012, cited under Idealization and Mathematical Application, and French and Ladyman 1999 and Pincock 2012, cited under Mapping Accounts), which say that scientific representation can be analyzed as a mathematical relation (usually partial isomorphism) between the model and the target being modeled, and user-based accounts (such as van Frassen 2008 and Giere 2010, cited under User-Based Accounts), which say that no two-place mathematical relation is sufficient to describe the representational relationship between a model and its target, but that the user (and often his or her intentions) also enter into the representational relationship. Weisberg 2013 (cited under Mapping Accounts) gives an alternative account of representation in terms of a mathematical notion of similarity. Downes 2011 gives an overview of the various representational accounts in the current literature, while Humphreys and Imbert 2011 includes several papers that discuss the role of representation in scientific models and simulations.

Mapping Accounts

Mapping (sometimes also called “structuralist”) accounts of scientific representation analyze the relationship between a model and its target mathematically, usually as some sort of isomorphism. Bueno and Colyvan 2011, da Costa and French 2003, French and Ladyman 1999, Frigg 2006, Pincock 2005, and Pincock 2012 give good overviews of the structuralist account. Weisberg 2013 provides an alternative to the mapping account via a mathematical analysis of the similarity relation between a model and its target.

  • Bueno, Otavio, and Mark Colyvan. “An Inferential Conception of the Application of Mathematics.” Nous 45.2 (2011): 345–374.

    DOI: 10.1111/j.1468-0068.2010.00772.xSave Citation »Export Citation » Share Citation »

    NNNArgues that the mapping account has certain shortcomings that can be overcome by extending that account into an inferential conception of scientific representation.

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  • da Costa, Newton C. A., and Steven French. Science and Partial Truth: A Unitary Approach to Models and Scientific Reasoning. Oxford: Oxford University Press, 2003.

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    NNNA comprehensive and often-cited account of the structuralist (or mapping) view of scientific representation.

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  • French, Steven, and James Ladyman. “Reinflating the Semantic Approach.” International Studies in the Philosophy of Science 13 (1999): 103–121.

    DOI: 10.1080/02698599908573612Save Citation »Export Citation » Share Citation »

    NNNA defense of the “partial structures” approach to scientific representation set within the context of the debate between the semantic vs. the syntactic view of theories.

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  • Frigg, Roman. “Scientific Representation and the Semantic View of Theories.” Theoria 55 (2006): 49–65.

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    NNNArgues that the semantic view is inadequate as an account of scientific representation, in part because, according to Frigg, it cannot account for misrepresentation (idealization) in scientific modeling.

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  • Pincock, Christopher. “Overextending Partial Structures: Idealization and Abstraction.” Philosophy of Science 72.5 (December 2005): 1248–1259.

    DOI: 10.1086/508123Save Citation »Export Citation » Share Citation »

    NNNPincock argues in this article that the partial structures account (daCosta and French) of scientific representation cannot account for idealization in all cases.

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  • Pincock, Christopher. Mathematics and Scientific Representation. Oxford: Oxford University Press, 2012.

    DOI: 10.1093/acprof:oso/9780199757107.001.0001Save Citation »Export Citation » Share Citation »

    NNNAn impressive work that, beginning with the assumption of a structuralist, or mapping, account of scientific representation, uses many detailed examples (mostly from physics) to outline the epistemic contribution of mathematics to science.

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  • Weisberg, Michael. Simulation and Similarity: Using Models to Understand the World. Oxford: Oxford University Press, 2013.

    DOI: 10.1093/acprof:oso/9780199933662.001.0001Save Citation »Export Citation » Share Citation »

    NNNDiscusses the role of idealization in scientific models and simulations. Argues against fictional accounts of scientific representation and gives a mathematical analysis of the similarity relation between a model and its target.

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User-Based Accounts

User-based accounts of scientific representation reject the idea that the relationship of a model to its target can be accurately specified via a two-place mathematical relationship. Instead, it is argued that the role of the user must be taken into account if the representational relationship is to be appropriately characterized and understood. Knuuttila 2011, Giere 2010, van Frassen 2008, and Suárez 2005 provide alternatives to the structuralist account of scientific representation by highlighting the importance of the user and his or her intentions in the practice of scientific modeling.

  • Giere, Ronald N. “An Agent-Based Conception of Models and Scientific Representation.” Synthese 172.2 (2010): 269–281.

    DOI: 10.1007/s11229-009-9506-zSave Citation »Export Citation » Share Citation »

    NNNAn excellent article that argues that a two-place relation between a model and a target is not enough for scientific representation. Instead, in Giere’s view, an adequate conception of representation in science requires bringing “scientific agents and their intentions into the picture.”

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  • Knuuttila, Tarja. “Modelling and Representing: An Artefactual Approach to Model-Based Representation.” Studies in History and Philosophy of Science 42.2 (2011): 262–271.

    DOI: 10.1016/j.shpsa.2010.11.034Save Citation »Export Citation » Share Citation »

    NNNGives a novel, non-representationalist account of models as epistemic tools. Knuuttila argues that scientists learn from models by manipulating them.

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  • Suárez, Mauricio. “An Inferential Conception of Scientific Representation.” Philosophy of Science 71.5 (December 2005): 767–779.

    DOI: 10.1086/421415Save Citation »Export Citation » Share Citation »

    NNNArgues against the mapping account and in favor of a deflationary view of scientific representation in terms of inference. In this view a model is a representation of a target if the user intends it to be, and if he or she is able to make valid inferences from it.

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  • van Frassen, Bas. Scientific Representations: Paradoxes of Perspective. Oxford: Oxford University Press, 2008.

    DOI: 10.1093/acprof:oso/9780199278220.001.0001Save Citation »Export Citation » Share Citation »

    NNNHere van Frassen argues that a two-place relation between a model and a target is not enough for representation. His view is that what is needed for representation is something that is not found in either the model or the target: the user.

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Idealization in Scientific Explanation

All scientific models contain idealizations, or deliberate misrepresentations, of the target system, of some form or another. But idealized models are often taken by the scientists who create them to be explanatory. What, then, is the role of idealization in scientific explanation? The answer to this question divides into two types in the literature. The first type is sometimes called the “causal isolationist” account of model explanation. This type of account proposes that the idealized components in scientific models are those that do not play a direct role in the model explanation. That is, the function of idealization in this kind of account is to section off the explanatorily relevant model components (the non idealized parts) from the explanatorily irrelevant (the idealized) components. The other account of the role of idealization in scientific explanation that can be found in the literature allows for an active participation of the idealized components of a scientific model in the explanatory process. Proponents of this view argue that in some cases model explanations depend upon the idealized components of the models.

Causal Isolationist Accounts

Causal isolationist accounts of model explanation argue that idealizations serve to mark off the parts of a model that are not explanatory. Strevens 2007, Mäki 1994, and Laymon 1980 provide the best introductions to the causal isolationist view of model explanation. Mizrahi 2012 provides an alternative way of understanding the role of false model components. Reiss 2013 is a good overview of the various ways in which false model components can contribute to model explanations.

  • Laymon, Ronald. “Idealization, Explanation, and Confirmation.” PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1 (1980): 336–350.

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    NNNAn argument that idealizations in scientific explanations are acceptable only if they can be removed or improved.

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  • Mäki, Uskali. “Isolation, Idealization and Truth in Economics.” In Idealization VI: Idealization in Economics. Edited by Bert Hamminga and Neil B. De Marchi, 147–168. Poznan Studies in the Philosophy of the Sciences and the Humanities 38. Amsterdam: Rodopi, 1994.

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    NNNFrom a conference held at Tilburg University, 1–3 July 1991. Argues, via examples from economics, that idealizations allow scientists to isolate causally and explanatorily relevant model components. In this view idealizations are not, in themselves, explanatory.

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  • Mizrahi, Moti. “Idealizations and Scientific Understanding.” Philosophical Studies 160.2 (2012): 237–252.

    DOI: 10.1007/s11098-011-9716-3Save Citation »Export Citation » Share Citation »

    NNNAn interesting article that sidesteps the worries about false idealization and explanation by arguing that idealizations have a role in (quasi-factive) understanding.

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  • Reiss, Julian. “Models, Idealisation, Explanation.” In Philosophy of Economics: A Contemporary Introduction. By Julian Reiss, 119–141. New York: Routledge, 2013.

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    NNNA helpful overview of different views on the role that idealization plays in explanation and on various ways to answer the question of whether or not false models can be explanatory.

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  • Strevens, Michael. “Why Explanations Lie: Idealization in Explanation.” Self published, 2007.

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    NNNRecommended as a first introduction to the causal isolationist view of model explanation. Strevens argues that the idealizations within scientific models serve to tell scientists what is not causally relevant to the behavior of the modeled phenomenon.

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Active Participant Accounts

Active participant accounts of model explanation argue that idealizations, in many cases, actively contribute to model explanations. Batterman 2002 argues that certain model explanations depend upon idealizations, Bokulich 2008 and Bokulich 2011 argue that fictional model components can have an explanatory role, Kennedy 2012 and Wayne 2011 argue for an active role of idealization in models in astrophysics and physics, and Grüne-Yanoff 2013 argues that certain non representational models can confer scientific knowledge.

  • Batterman, Robert. “Asymptotics and the Role of Minimal Models.” British Journal for the Philosophy of Science 53 (2002): 21–38.

    DOI: 10.1093/bjps/53.1.21Save Citation »Export Citation » Share Citation »

    NNNAn important article for anyone who is interested in the topic of idealization in explanation. Batterman argues that in some asymptotic cases model explanations depend upon their idealizations.

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  • Bokulich, Alisa. “Can Classical Structures Explain Quantum Phenomena?” British Journal for the Philosophy of Science 59.2 (2008): 217–235.

    DOI: 10.1093/bjps/axn004Save Citation »Export Citation » Share Citation »

    NNNArgues, via an example from quantum physics, that fictional components in models often have an explanatory role and that, further, in some cases, fictional models provide better explanations than their more realistic counterparts.

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  • Bokulich, Alisa. “How Scientific Models Can Explain.” Synthese 180.1 (May 2011): 33–45.

    DOI: 10.1007/s11229-009-9565-1Save Citation »Export Citation » Share Citation »

    NNNA novel account of model explanation that leaves room for fictions to play an active role in the explanatory process.

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  • Grüne-Yanoff, Till. “Appraising Models Nonrepresentationally.” Philosophy of Science 80.5 (December 2013): 850–861.

    DOI: 10.1086/673893Save Citation »Export Citation » Share Citation »

    NNNArgues that “non-representational” models, or models that depict possible, but not necessarily actual, processes or situations can confer scientific knowledge. Gives six interesting and detailed examples from different branches of the sciences.

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  • Kennedy, Ashley. “A Non Representationalist View of Model Explanation.” Studies in History and Philosophy of Science 43.2 (2012): 326–332.

    DOI: 10.1016/j.shpsa.2011.12.029Save Citation »Export Citation » Share Citation »

    NNNArgues, via the use of two examples from contemporary astrophysics, that models often explain in virtue of their idealized components, rather than in spite of them.

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  • Wayne, Andrew. “Expanding the Scope of Explanatory Idealization.” Philosophy of Science 78.5 (December 2011): 830–841.

    DOI: 10.1086/662277Save Citation »Export Citation » Share Citation »

    NNNArgues that certain “non-harmless” idealizations in physics can yet have an explanatory role.

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Idealization in Scientific Modeling and Experimentation

The use of idealization in scientific modeling and experimentation is not haphazard, but rather idealizations are used strategically to meet various epistemic goals. Idealizations are incorporated into scientific models and experiments with the various aims of exploring, explaining, and understanding the physical world. Elgin 2009, Levins 1966, Morrison and Morgan 1999, and Muldoon and Weisberg 2011 discuss the use of idealization as a model building strategy. Laymon 1985 discusses the experimental testing of idealization limits, and Teller 2001 discusses context-dependent modeling.

  • Elgin, Catherine. “Exemplification, Idealization, and Understanding.” In Fictions in Science: Essays on Idealization and Modeling. Edited by Mauricio Suarez, 77–90. London: Routledge, 2009.

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    NNNArgues that idealizations, even though false, can be used to confer genuine scientific understanding.

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  • Laymon, Ronald. “Idealizations and the Testing of Theories by Experimentation.” In Observation Experiment and Hypothesis in Modern Physical Science. Edited by Peter Achinstein and Owen Hannaway, 147–173. Cambridge, MA: MIT Press, 1985.

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    NNNA classic paper that characterizes idealizations as ideal limits that can be tested experimentally.

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  • Levins, R. “The Strategy of Model Building in Population Biology.” American Science 54 (1966): 421–431.

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    NNNA classic paper that discusses the ways scientific idealizations are used strategically in the aim for (and trade-offs between) realism, precision, and generality.

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  • Morrison, Margaret, and Mary S. Morgan. “Models as Mediating Instruments.” In Models as Mediators. Edited by Mary S. Morgan and Margaret Morrison, 10–37. Cambridge, UK: Cambridge University Press, 1999.

    DOI: 10.1017/CBO9780511660108Save Citation »Export Citation » Share Citation »

    NNNThis is an excellent chapter that illustrates how idealizations can be used instrumentally in the practice of scientific modeling.

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  • Muldoon, Ryan, and Michael Weisberg. “Robustness and Idealization in Models of Cognitive Labor.” Synthese 183 (2011): 161–174.

    DOI: 10.1007/s11229-010-9757-8Save Citation »Export Citation » Share Citation »

    NNNAn interesting discussion of some of the strategic ways idealizations are used in scientific modeling. Argues that idealizations can be used to simplify models so that the models can confer understanding, but also argues that idealizations should not be so extreme as to sacrifice realism.

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  • Teller, Paul. “Twilight of the Perfect Model Model.” Erkenntnis 55 (2001): 393–415.

    DOI: 10.1023/A:1013349314515Save Citation »Export Citation » Share Citation »

    NNNIn this classic article Teller argues that an evaluation of the similarity of an idealized model to an empirical system is context-dependent. He argues that in certain contexts one model may provide an appropriate similarity relation, while in other contexts another model might perform this function. Thus his view is that it is not necessary to have one generalized theory, because different contexts can be modeled differently.

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Idealization and Mathematical Application

There is debate in the philosophy of mathematics over the question of whether or not mathematics can explain physical phenomena. Those who argue that it can must then specify how it does so, and in attempts to do this there is often reference to the role that idealization plays in such explanations. Baker 2005 argues that mathematics can genuinely explain physical phenomena. Batterman 2009 argues that if there are mathematical explanations of the physical systems, these explanations depend upon idealization. Bueno and French 2012 and Pincock 2011 argue that Batterman’s examples can be accounted for in the structuralist view. Saatsi 2011 argues that mathematics plays a representational rather than an explanatory role in application to the empirical world.

  • Baker, Alan. “Are There Genuine Mathematical Explanations of Physical Phenomena?” Mind 114 (2005): 223–238.

    DOI: 10.1093/mind/fzi223Save Citation »Export Citation » Share Citation »

    NNNHelpful for those interested in mathematical explanation in science. Argues via two examples that mathematics does, at least in some cases, genuinely explain physical phenomena. Distinguishes between mathematical posits (which Baker thinks can be genuinely explanatory) and idealized descriptions (which he does not think explain).

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  • Batterman, Robert. “On the Explanatory Role of Mathematics in Empirical Science.” British Journal for the Philosophy of Science 61 (2009): 1–25.

    DOI: 10.1093/bjps/axp018Save Citation »Export Citation » Share Citation »

    NNNThis article begins by assuming that mathematics can explain the empirical and then focuses on the question of how it does so. Batterman argues that mathematical explanations of empirical systems sometimes depend upon model idealizations.

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  • Bueno, Otavio, and Steven French. “Can Mathematics Explain Physical Phenomena?” British Journal for the Philosophy of Science 63.1 (March 2012): 85–113.

    DOI: 10.1093/bjps/axr017Save Citation »Export Citation » Share Citation »

    NNNArgues that mathematics can explain physical phenomena just in case it allows for inferential reasoning. Defends the structuralist account of scientific representation against Batterman’s 2009 attacks.

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  • Pincock, Christopher. “On Batterman’s ‘On the Explanatory Role of Mathematics in Empirical Science.’” British Journal for the Philosophy of Science 62.1 (2011): 211–217.

    DOI: 10.1093/bjps/axq025Save Citation »Export Citation » Share Citation »

    NNNArgues that while idealization does have a role in mathematical explanations of empirical systems, this role can be accommodated on a mapping account of scientific representation.

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  • Saatsi, Juha. “The Enhanced Indispensability Argument: Representational versus Explanatory Role of Mathematics in Science.” British Journal for Philosophy of Science 62 (2011): 143–154.

    DOI: 10.1093/bjps/axq029Save Citation »Export Citation » Share Citation »

    NNNA very interesting paper that proposes a unique viewpoint on the debate over mathematical explanations of empirical phenomena. Saatsi argues that in many of the often-cited examples in the literature on this debate, mathematics is playing a representational, rather than an explanatory role.

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Idealization and Scientific Realism

Because idealizations are false, and because all scientific models, and many scientific theories, make use of them, the question of whether or not these idealized models and theories can give realistic explanations is of interest to many philosophers of science. While it might at first seem surprising, many philosophers of science, such as the authors of Wimsatt 1987, McMullin 1984, Hughes 1990, Levy 2012, Mäki 2011, Saatsi 2011, and Suarez 2010, argue that idealization is in fact compatible with scientific realism.

  • Hughes, R. I. G. “The Bohr Atom, Models and Realism.” Philosophical Topics 18 (1990): 71–84.

    DOI: 10.5840/philtopics19901824Save Citation »Export Citation » Share Citation »

    NNNUses the example of the (literally untrue) Bohr atomic model to give an argument for scientific realism.

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  • Levy, Arnon. Models, Fictions & Realism: Two Packages. Philosophy of Science 79.5 (2012): 738–748.

    DOI: 10.1086/667992Save Citation »Export Citation » Share Citation »

    NNNArgues for two ways in which the use of fictions in scientific modeling is compatible with scientific realism.

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  • Mäki, Uskali. “The Truth of False Idealizations in Modeling.” In Models, Simulations, and Representations. Edited by Paul Humphreys and Cyrille Imbert, 216–233. London: Routledge, 2011.

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    NNNThis article gives a novel take on the interpretation of false idealizations in modeling. Maki argues that while certain idealizations are false in the target, they are yet true in the model.

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  • McMullin, Ernan. “A Case for Scientific Realism.” In Scientific Realism. Edited by J. Leplin, 8–40. Berkeley: University of California Press, 1984.

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    NNNArgues that idealized models can provide realistic explanations just in case their idealizations can be, in principle, removed via processes of de-idealization.

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  • Saatsi, Juha. “Idealized Models as Inferentially Veridical Representations: A Conceptual Framework.” In Models, Simulations, and Representations. Edited by Paul Humphreys and Cyrille Imbert, 234–249. London: Routledge, 2011.

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    NNNAn interesting defense of the view that, in certain cases, idealized models can “latch on” to reality and thereby give accurate predictions.

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  • Suarez, Mauricio. “Fictions, Inference and Realism.” In Fictions and Models: New Essays. Edited by John Woods. Munich: Philosophia Verlag, 2010.

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    NNNA well-written article that advances the argument that the use of fictions in science is compatible with scientific realism.

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  • Wimsatt, William. “False Models as Means to Truer Theories.” In Neutral Models in Biology. Edited by M. Nitecki and A. Hoffman, 23–55. New York: Oxford University Press, 1987.

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    NNNArgues that one of the main values of false, or idealized, models is that they can be used as stepping stones to more realistic models which in turn can reveal truths about the empirical world.

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