In this paper we present a new framework of idealization in biology. We characterize idealizations as a network of counterfactual conditionals that can exhibit different degrees of contingency. We use the idea of possible worlds to say that, in departing more or less from the actual world, idealizations can serve numerous epistemic, methodological or heuristic purposes within scientific research. We defend that, in part, it is this structure what helps explain why idealizations, despite being deformations of reality, are so successful (...) in scientific practice. (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.

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)

In many applications of physics, boundary conditions have an essential role. The purpose of this paper is to examine from both a historical and philosophical perspective one such boundary condition, namely, the no-slip condition of fluid dynamics. The historical perspective is based on the works of George Stokes and serves as the foundation for the philosophical perspective. It is seen that historically the acceptance of the no-slip condition was problematic. Philosophically, the no-slip condition is interesting since the use of the (...) no-slip condition illustrates nicely the use of scientific models. But more importantly, both the use and justification of the no-slip condition illustrate clearly how theories can holistically approach the world through model construction. Further, since much of the debate over scientific realism occurs in the realm of models, a case is made that an understanding of the role of the no-slip condition has something to offer to this debate. (shrink)

After a brief comparison of Aliseda’s account with different approaches to abductive reasoning, I relate abduction, as studied by Aliseda, to idealization, a notion which also occupies a very important role in scientific change, as well as to different ways of dealing with the growth of scientific knowledge understood as a particular kind of non-monotonic process. A particularly interesting kind of abductive reasoning could be that of finding an appropriate concretization case for a theory, originally revealed as extraordinarily success-ful but (...) later discovered to be strictly false or only approximately or ideally true. I try to show this with the example of the Kepler-Newton relation. At the end of the paper, I give criteria in order to construe abduc-tive explanations in correspondence with a reasonable account of empirical progress. (shrink)

Measurement is a process aimed at acquiring and codifying information about properties of empirical entities. In this paper we provide an interpretation of such a process comparing it with what is nowadays considered the standard measurement theory, i.e., representational theory of measurement. It is maintained here that this theory has its own merits but it is incomplete and too abstract, its main weakness being the scant attention reserved to the empirical side of measurement, i.e., to measurement systems and to the (...) ways in which the interactions of such systems with the entities under measurement provide a structure to an empirical domain. In particular it is claimed that (1) it is on the ground of the interaction with a measurement system that a partition can be induced on the domain of entities under measurement and that relations among such entities can be established, and that (2) it is the usage of measurement systems that guarantees a degree of objectivity and intersubjectivity to measurement results. As modeled in this paper, measurement systems link the abstract theory of measuring, as developed in representational terms, and the practice of measuring, as coded in standard documents such as the International Vocabulary of Metrology. (shrink)

At first blush, the idea that fictions play a role in science seems to be off the mark. Realists and antirealists alike believe that science instructs us about how the world is (they part ways only over the question of what exactly science tells us about the world). Fiction not only seems to play no role in such an endeavour; it seems to detract from it. The aims of science and fiction seem to be (...) diametrically opposed and a view amalgamating the two rightly seems to be the cause of discomfort and concern. (shrink)

In the last few decades the role played by models and modeling activities has become a central topic in the scientific enterprise. In particular, it has been highlighted both that the development of models constitutes a crucial step for understanding the world and that the developed models operate as mediators between theories and the world. Such perspective is exploited here to cope with the issue as to whether error-based and uncertainty-based modeling of measurement are incompatible, and thus alternative with one (...) another, as sometimes claimed nowadays. The crucial problem is whether assuming this standpoint implies definitely renouncing to maintain a role for truth and the related concepts, particularly accuracy, in measurement. It is argued here that the well known objections against true values in measurement, which would lead to refuse the concept of accuracy as non-operational, or to maintain it as only qualitative, derive from a not clear distinction between three distinct processes: the metrological characterization of measuring systems, their calibration, and finally measurement. Under the hypotheses that (1) the concept of true value is related to the model of a measurement process, (2) the concept of uncertainty is related to the connection between such model and the world, and (3) accuracy is a property of measuring systems (and not of measurement results) and uncertainty is a property of measurement results (and not of measuring systems), not only the compatibility but actually the conjoint need of error-based and uncertainty-based modeling emerges. (shrink)

Nancy Cartwright is one of the most distinguished and influential contemporary philosophers of science. Despite the profound impact of her work, until now there has not been a systematic exposition of Cartwright's philosophy of science nor a collection of articles that contains in-depth discussions of the major themes of her philosophy. This book is devoted to a critical assessment of Cartwright's philosophy of science and contains contributions from Cartwright's champions and critics. Broken into three parts, the book begins by addressing (...) Cartwright's views on the practice of model building in science and the question of how models represent the world before moving on to a detailed discussion of methodologically and metaphysically challenging problems. Finally, the book addresses Cartwright's original attempts to clarify profound questions concerning the metaphysics of science. With contributions from leading scholars, such as Ronald N. Giere and Paul Teller, this unique volume will be extremely useful to philosophers of science the world over. (shrink)

Many models in economics are very unrealistic. At the same time, economists put a lot of effort into making their models more realistic. I argue that in many cases, including the Modigliani-Miller irrelevance theorem investigated in this paper, the purpose of this process of concretization is explanatory. When evaluated in combination with their assumptions, a highly unrealistic model may well be true. The purpose of relaxing an unrealistic assumption, then, need not be to move from a false model to a (...) true one. Instead, it may be providing an explanation of some phenomenon by invoking the factor that figures in the assumption. This idea is developed in terms of the contrastive account of explanation. It is argued that economists use highly unrealistic assumptions to determine a contrast that is worth explaining. The process of concretization also motivates new explanatory questions. A high degree of explanatory power, then, may well be due to a high number of unrealistic assumptions. Thus, highly unrealistic models can be powerful explanatory engines. Key Words: concretization • explanation • explanatory power • idealization • model • Modigliani-Miller theorem • unrealistic assumption. (shrink)

Both von Neumann and Wiener were outsiders to biology. Both were inspired by biology and both proposed models and generalizations that proved inspirational for biologists. Around the same time in the 1940s von Neumann developed the notion of self reproducing automata and Wiener suggested an explication of teleology using the notion of negative feedback. These efforts were similar in spirit. Both von Neumann and Wiener used mathematical ideas to attack foundational issues in biology, and the concepts they articulated had lasting (...) effect. But there were significant differences as well. Von Neumann presented a how-possibly model, which sparked interest by mathematicians and computer scientists, while Wiener collaborated more directly with biologists, and his proposal influenced the philosophy of biology. The two cases illustrate different strategies by which mathematicians, the “professional outsiders” of science, can choose to guide their engagement with biological questions and with the biological community, and illustrate different kinds of generalizations that mathematization can contribute to biology. The different strategies employed by von Neumann and Wiener and the types of models they constructed may have affected the fate of von Neumann’s and Wiener’s ideas – as well as the reputation, in biology, of von Neumann and Wiener themselves. (shrink)

Richard Goldschmidt famously rejected the notion of atomic and corpuscular genes, arranged on the chromosome like beads-on-a-string. I provide an exegesis of Goldschmidt’s intuition by analyzing his repeated and extensive use of metaphorical language and analogies in his attempts to convey his notion of the nature of the genetic material and specifically the significance of chromosomal pattern. The paper concentrates on Goldschmidt’s use of metaphors in publications spanning 1940-1955. -/- .

The problem for the scientist created by using idealizations is to determine whether failures to achieve experimental fit are attributable to experimental error, falsity of theory, or of idealization. Even in the rare case when experimental fit within experimental error is achieved, the scientist must determine whether this is so because of a true theory and fortuitously canceling idealizations, or due to a fortuitous combination of false theory and false idealizations. For the engineer, the problem seems rather different. Experiment for (...) the engineer reveals the closeness of predictive fit that can be achieved by theory and idealization for a particular case. If the closeness of fit is good enough for some practical purpose, the job is done. If not, or there are reasons to consider variation, then the engineer needs to know how well the experimentally determined closeness of fit will extrapolate to new cases. This paper focuses on engineering measures of closeness of fit and the projectibility of those measures to new cases. (shrink)

Two types of idealization in theory construction are distinguished, and the distinction is used to give a critique of Ron Laymon's account of confirming idealized theories and his argument for scientific realism.

I first give a brief summary of a critique of the traditional theories of approximation and idealization; and after identifying one of the major roles of idealization as detaching component processes or systems from their joints, a detailed analysis is given of idealized laws – which are discoverable and/or applicable – in such processes and systems (i.e., idealized model systems). Then, I argue that dispositional properties should be regarded as admissible properties for laws and that such an inclusion supplies the (...) much needed connection between idealized models and the laws they `produce'' or `accommodate''. And I then argue that idealized law-statements so produced or accommodated in the models may be either true simpliciter or true approximately, but the latter is not because of the idealizations involved. I argue that the kind of limiting-case idealizations that produce approximate truth is best regarded as approximation; and finally I compare my theory with some existing theories of laws of nature.We seem to trace [in KingLear] ... the tendency of imagination toanalyse and abstract, to decomposehuman nature into its constituentfactors, and then to construct beings in whomone or more of these factors isabsent or atrophied or only incipient. (shrink)

I first give a brief summary of a critique of the traditional theories of approximation and idealization; and after identifying one of the major roles of idealization as detaching component processes or systems from their joints, a detailed analysis is given of idealized laws -- which are discoverable and/or applicable -- in such processes and systems (i.e., idealized model systems). Then, I argue that dispositional properties should be regarded as admissible properties for laws and that such an inclusion supplies the (...) much needed connection between idealized models and the laws they 'produce' or 'accommodate'. And I then argue that idealized law-statements so produced or accommodated in the models may be either true simpliciter or true approximately, but the latter is not because of the idealizations involved. I argue that the kind of limiting-case idealizations that produce approximate truth is best regarded as approximation; and finally I compare my theory with some existing theories of laws of nature. (shrink)

In this paper, a criticism of the traditional theories of approximation and idealization is given as a summary of previous works. After identifying the real purpose and measure of idealization in the practice of science, it is argued that the best way to characterize idealization is not to formulate a logical model – something analogous to Hempel's D-N model for explanation – but to study its different guises in the praxis of science. A case study of it is then made (...) in thermostatistical physics. After a brief sketch of the theories for phase transitions and critical phenomena, I examine the various idealizations that go into the making of models at three difference levels. The intended result is to induce a deeper appreciation of the complexity and fruitfulness of idealization in the praxis of model-building, not to give an abstract theory of it. (shrink)

In this paper, a criticism of the traditional theories of approximation and idealization is given. After identifying the real purpose and measure of idealization in the practice of science, it is argued that the best way to characterize idealization is not to formulate a logical model -- something analogous to Hempel's D-N model for explanation -- but to study its different guises in the praxis of science. A case study of it is then made in thermostatistical physics. After a brief (...) sketch of the theories for phase transitions and critical phenomena, I examine the various idealizations that go into the making of models at three difference levels. (shrink)

This article shows how the MISS account of models—as isolations and surrogate systems—accommodates and elaborates Sugden’s account of models as credible worlds and Hausman’s account of models as explorations. Theoretical models typically isolate by means of idealization, and they are representatives of some target system, which prompts issues of resemblance between the two to arise. Models as representations are constrained both ontologically (by their targets) and pragmatically (by the purposes and audiences of the modeller), and these relations are coordinated by (...) a model commentary. Surrogate models are often about single mechanisms. They are distinguishable from substitute models, which are examined without any concern about their connections with the target. Models as credible worlds are surrogate models that are believed to provide access to their targets on account of their credibility (of which a few senses are distinguished). (shrink)

Despite their best efforts, scientists may be unable to construct models that simultaneously exemplify every theoretical virtue. One explanation for this is the existence of tradeoffs: relationships of attenuation that constrain the extent to which models can have such desirable qualities. In this paper, we characterize three types of tradeoffs theorists may confront. These characterizations are then used to examine the relationships between parameter precision and two types of generality. We show that several of these relationships exhibit tradeoffs and discuss (...) what consequences those tradeoffs have for theoretical practice. (shrink)

According to Popper's rationality principle, agents act in the most adequate way according to the objective situation. I propose a new interpretation of the rationality principle as consisting of an idealization and two abstractions. Based on this new interpretation, I critically discuss the privileged status that Popper ascribes to it as an integral part of all social scientific models. I argue that as an idealization, the rationality principle may play an important role in the social sciences, but it also has (...) inherent limitations that inhibit it from having the privileged status that Popper ascribes to it in all cases. (shrink)

In this paper, I propose that the debate in epistemology concerning the nature and value of understanding can shed light on the role of scientific idealizations in producing scientific understanding. In philosophy of science, the received view seems to be that understanding is a species of knowledge. On this view, understanding is factive just as knowledge is, i.e., if S knows that p, then p is true. Epistemologists, however, distinguish between different kinds of understanding. Among epistemologists, there are those who (...) think that a certain kind of understanding—objectual understanding—is not factive, and those who think that objectual understanding is quasi-factive. Those who think that understanding is not factive argue that scientific idealizations constitute cognitive success, which we then consider as instances of understanding, and yet they are not true. This paper is an attempt to draw lessons from this debate as they pertain to the role of idealizations in producing scientific understanding. I argue that scientific understanding is quasi-factive. (shrink)

As scientists begin to study increasingly complex questions, many have turned to computer simulation to assist in their inquiry. This methodology has been challenged by both analytic modelers and experimentalists. A primary objection of analytic modelers is that simulations are simply too complicated to perform model verification. From the experimentalist perspective it is that there is no means to demonstrate the reality of simulation. The aim of this paper is to consider objections from both of these perspectives, and to argue (...) that a proper understanding and application of robustness analysis is able to resolve them. ‡The author would like to thank Cristina Bicchieri, Michelle Foa, Paul Humphreys and Michael Weisberg for their helpful comments and suggestions. †To contact the author, please write to: Department of Philosophy, University of Pennsylvania, 433 Logan Hall, 249 S. 36th Street, Philadelphia, PA, 19104-6304; e-mail: rmuldoon@sas.upenn.edu. (shrink)

A distinction is made between theory-driven and phenomenological models. It is argued that phenomenological models are significant means by which theory is applied to phenomena. They act both as sources of knowledge of their target systems and are explanatory of the behaviors of the latter. A version of the shell-model of nuclear structure is analyzed and it is explained why such a model cannot be understood as being subsumed under the theory structure of Quantum Mechanics. Thus its representational capacity does (...) not stem from its close link to theory. It is shown that the shell model yields knowledge about the target and is explanatory of certain behaviors of nuclei. Aspects of the process by which the shell model acquires its representational capacity are analyzed. It is argued that these point to the conclusion that the representational status of the model is a function of its capacity to function as a source of knowledge and its capacity to postulate and explain underlying mechanisms that give rise to the observed behavior of its target. (shrink)

After a brief comparison of Aliseda’s account with different approaches to abductive reasoning, I relate abduction, as studied by Aliseda, to idealization, a notion which also occupies a very important role in scientific change, as well as to different ways of dealing with the growth of scientific knowledge understood as a particular kind of non-monotonic process. A particularly interesting kind of abductive reasoning could be that of finding an appropriate concretization case for a theory, originally revealed as extraordinarily success-ful but (...) later discovered to be strictly false or only approximately or ideally true. I try to show this with the example of the Kepler-Newton relation. At the end of the paper, I give criteria in order to construe abduc-tive explanations in correspondence with a reasonable account of empirical progress. (shrink)

This paper, which is based on recent empirical research at the University of Leeds, the University of Edinburgh, and the University of Bristol, presents two difficulties which arise when condensed matter physicists interact with molecular biologists: (1) the former use models which appear to be too coarse-grained, approximate and/or idealized to serve a useful scientific purpose to the latter; and (2) the latter have a rather narrower view of what counts as an experiment, particularly when it comes to computer simulations, (...) than the former. It argues that these findings are related; that computer simulations are considered to be undeserving of experimental status, by molecular biologists, precisely because of the idealizations and approximations that they involve. The complexity of biological systems is a key factor. The paper concludes by critically examining whether the new research programme of ‘systems biology’ offers a genuine alternative to the modelling strategies used by physicists. It argues that it does not. (shrink)

Following Nancy Cartwright and others, I suggest that most (if not all) theories incorporate, or depend on, one or more idealizing assumptions. I then argue that such theories ought to be regimented as counterfactuals, the antecedents of which are simplifying assumptions. If this account of the logic form of theories is granted, then a serious problem arises for Bayesians concerning the prior probabilities of theories that have counterfactual form. If no such probabilities can be assigned, the the posterior probabilities will (...) be undefined, as the latter are defined in terms of the former. I argue here that the most plausible attempts to address the problem of probabilities of conditionals fail to help Bayesians, and, hence, that Bayesians are faced with a new problem. In so far as these proposed solutions fail, I argue that Bayesians must give up Bayesianism or accept the counterintuitive view that no theories that incorporate any idealizations have ever really been confirmed to any extent whatsoever. Moreover, as it appears that the latter horn of this dilemma is highly implausible, we are left with the conclusion that Bayesianism should be rejected, at least as it stands. (shrink)

This paper introduces Weylean skepticism, the view that objectivity and intelligibility are opposite ideals of science, explains the motivation for it and the argument that justifies it. The paper indicates also a couple of ways in which this skepticism could be resisted.

Michael Strevens’s book Depth is a great achievement.1 To say anything interesting, useful and true about explanation requires taking on fundamental issues in the metaphysics and epistemology of science. So this book not only tells us a lot about scientific explanation, it has a lot to say about causation, lawhood, probability and the relation between the physical and the special sciences. It should be read by anyone interested in any of those questions, which includes presumably the vast majority of readers (...) of this journal. One of its many virtues is that it lets us see more clearly what questions about explanation, causation, lawhood and so on need answering, and frames those questions in perspicuous ways. I’m going to focus on one of these questions, what I’ll call the Goldilocks problem. As it turns out, I’m not going to agree with all the details of Strevens’s answer to this problem, though I suspect that something like his answer is right. At least, I hope something like his answer is right; if it isn’t, I’m not sure where else we can look. (shrink)

Theorizing in ecology and evolution often proceeds via the construction of multiple idealized models. To determine whether a theoretical result actually depends on core features of the models and is not an artifact of simplifying assumptions, theorists have developed the technique of robustness analysis, the examination of multiple models looking for common predictions. A striking example of robustness analysis in ecology is the discovery of the Volterra Principle, which describes the effect of general biocides in predator-prey systems. This paper details (...) the discovery of the Volterra Principle and the demonstration of its robustness. It considers the classical ecology literature on robustness and introduces two individual-based models of predation, which are used to further analyze the Volterra Principle. The paper also introduces a distinction between parameter robustness, structural robustness, and representational robustness, and demonstrates that the Volterra Principle exhibits all three kinds of robustness. *Received September 2006; revised May 2007. ‡Earlier versions of this paper were presented at the Australasian Association of Philosophy, the London School of Economics, and the University of Bristol. The authors wish to thank those audiences as well as Patrick Forber, Ken Waters, Deena Skolnick Weisberg, Uri Wilensky, and Bill Wimsatt for many helpful comments. Special thanks to Giacomo Sillari for his assistance in translating Volterra's original paper and his insightful thoughts about Volterra's aims and methods. Some of the research in this paper was supported by NSF grant SES-0620887 to MW. †To contact the authors, please write to: Michael Weisberg, Department of Philosophy, University of Pennsylvania, 433 Logan Hall, Philadelphia, PA 19104; e-mail: weisberg@phil.upenn.edu; Kenneth Reisman, Pluribo, Inc., 100 Park Avenue, Suite 1600, New York, NY 10017; e-mail: ken@pluribo.com. (shrink)

Schaffner’s model of theory reduction has played an important role in philosophy of science and philosophy of biology. Here, the model is found to be problematic because of an internal tension. Indeed, standard antireductionist external criticisms concerning reduction functions and laws in biology do not provide a full picture of the limits of Schaffner’s model. However, despite the internal tension, his model usefully highlights the importance of regulative ideals associated with the search for derivational, and embedding, deductive relations among mathematical (...) structures in theoretical biology. A reconstructed Schaffnerian model could therefore shed light on mathematical theory development in the biological sciences and on the epistemology of mathematical practices more generally. *Received November 2006; revised March 2009. †To contact the author, please write to: Philosophy Department, University of California, Santa Cruz, 1156 High St., Santa Cruz, CA 95064; e‐mail: rgw@ucsc.edu. (shrink)

Two controversies exist regarding the appropriate characterization of hierarchical and adaptive evolution in natural populations. In biology, there is the Wright-Fisher controversy over the relative roles of random genetic drift, natural selection, population structure, and interdemic selection in adaptive evolution begun by Sewall Wright and Ronald Aylmer Fisher. There is also the Units of Selection debate, spanning both the biological and the philosophical literature and including the impassioned groupselection debate. Why do these two discourses exist separately, and interact relatively little? (...) We postulate that the reason for this schism can be found in the differing focus of each controversy, a deep difference itself determined by distinct general styles of inquiry (e.g., Hacking 2002; Elwick 2007; Winther 2012, 2013) guiding each discourse. That is, the Wright-Fisher debate focuses on /adaptive process/, and tends to be instructed by the /mathematical modeling style/, while the focus of the Units of Selection controversy is /adaptive product/, and is typically guided by the /function style/. The differences between the two discourses can be usefully tracked by examining their interpretations of two contested strategies for theorizing hierarchical selection: /horizontal/ and /vertical/ averaging. (shrink)

In this paper we present a new framework of idealization in biology. We characterize idealizations as a network of counterfactual and hypothetical conditionals that can exhibit different “degrees of contingency”. We use this idea to say that, in departing more or less from the actual world, idealizations can serve numerous epistemic, methodological or heuristic purposes within scientific research. We defend that, in part, this structure explains why idealizations, despite being deformations of reality, are so successful in scientific practice. For illustrative (...) purposes, we provide an example from population genetics, the Wright-Fisher Model. (shrink)