In this sequence of philosophical essays about natural science, the author argues that fundamental explanatory laws, the deepest and most admired successes of modern physics, do not in fact describe regularities that exist in nature. Cartwright draws from many real-life examples to propound a novel distinction: that theoretical entities, and the complex and localized laws that describe them, can be interpreted realistically, but the simple unifying laws of basic theory cannot.

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.

Ecologist Richard Levins argues population biologists must trade‐off the generality, realism, and precision of their models since biological systems are complex and our limitations are severe. Steven Orzack and Elliott Sober argue that there are cases where these model properties cannot be varied independently of one another. If this is correct, then Levins's thesis that there is a necessary trade‐off between generality, precision, and realism in mathematical models in biology is false. I argue that Orzack and Sober's arguments fail since (...) Levins's thesis concerns the pragmatic features of model building not just the formal properties of models. (shrink)

In this essay, I argue for four related claims. First, Richard Levins’ classic “The Strategy of Model Building in Population Biology” was a statement and defense of theoretical population biology growing out of collaborations between Robert MacArthur, Richard Lewontin, E. O. Wilson, and others. Second, I argue that the essay served as a response to the rise of systems ecology especially as pioneered by Kenneth Watt. Third, the arguments offered by Levins against systems ecology and in favor of his own (...) methodological program are best construed as “pragmatic”. Fourth, I consider limitations of Levins’ arguments given contemporary population biology. (shrink)

This article serves as an introduction to the laws-of-biology debate. After introducing the main issues in an introductory section, arguments for and against laws of biology are canvassed in Section 2. In Section 3, the debate is placed in wider epistemological context by engaging a group of scholars who have shifted the focus away from the question of whether there are laws of biology and toward offering good accounts of explanation(s) in the biological sciences. Section 4 introduces two relatively new (...) pieces of science – metabolic scaling theory and ecological stoichiometry – that have not been topics of much discussion by philosophers but are relevant because they have at least some of the hallmarks of laws of nature. Section 5 concludes by pointing out that discovering laws of biology, if any there be, will not necessarily answer the questions raised by the debate in the first place: we will still want to know how biology compares to other sciences, how to characterize its systems and processes, and whether accounts in terms of laws always or usually constitute adequate explanations in various sciences. (shrink)

This is the second in a series of three papers that charts the history of the Lenz–Ising model (commonly called just the Ising model in the physics literature) in considerable detail, from its invention in the early 1920s to its recognition as an important tool in the study of phase transitions by the late 1960s. By focusing on the development in physicists’ perception of the model’s ability to yield physical insight—in contrast to the more technical perspective in previous historical accounts, (...) for example, Brush (Rev Modern Phys 39: 883–893, 1967) and Hoddeson et al. (Out of the Crystal Maze. Chapters from the History of Solid-State Physics. Oxford University Press, New York, pp. 489–616, 1992)—the series aims to cover and explain in depth why this model went from relative obscurity to a prominent position in modern physics, and to examine the consequences of this change. In the present paper, which is self-contained, I deal with the development from the early 1950s to the 1960s and document that this period witnessed a major change in the perception of the model: In the 1950s it was not in the cards that the model was to become a pivotal tool of theoretical physics in the following decade. In fact, I show, based upon recollections and research papers, that many of the physicists in the 1950s interested in understanding phase transitions saw the model as irrelevant for this endeavor because it oversimplifies the nature of the microscopic constituents of the physical systems exhibiting phase transitions. However, one group, Cyril Domb’s in London, held a more positive view during this decade. To bring out the basis for their view, I analyze in detail their motivation and work. In the last part of the paper I document that the model was seen as much more physically relevant in the early 1960s and examine the development that led to this change in perception. I argue that the main factor behind the change was the realization of the surprising and striking agreement between aspects of the model, notably its critical behavior, and empirical features of the physical phenomena. (shrink)

Loop analysis is a method of qualitative modeling anticipated by Sewall Wright and systematically developed by Richard Levins. In Levins’ (1966) distinctions between modeling strategies, loop analysis sacrifices precision for generality and realism. Besides criticizing the clarity of these distinctions, Orzack and Sober (1993) argued qualitative modeling is conceptually and methodologically problematic. Loop analysis of the stability of ecological communities shows this criticism is unjustified. It presupposes an overly narrow view of qualitative modeling and underestimates the broad role models play (...) in scientific research, especially in helping scientists represent and understand complex systems. (shrink)

In his 1966 paper “The Strategy of model-building in Population Biology”, Richard Levins argues that no single model in population biology can be maximally realistic, precise and general at the same time. This is because these desirable model properties trade-off against one another. Recently, philosophers have developed Levins’ claims, arguing that trade-offs between these desiderata are generated by practical limitations on scientists, or due to formal aspects of models and how they represent the world. However this project is not complete. (...) The trade-offs discussed by Levins had a noticeable effect on modelling in population biology, but not on other sciences. This raises questions regarding why such a difference holds. I claim that in order to explain this finding, we must pay due attention to the properties of the systems, or targets modelled by the different branches of science.Keywords: Trade-offs; Population biology; Scientific models; Generality; Precision. (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)

The present paper argues that ‘mature mathematical formalisms’ play a central role in achieving representation via scientific models. A close discussion of two contemporary accounts of how mathematical models apply—the DDI account (according to which representation depends on the successful interplay of denotation, demonstration and interpretation) and the ‘matching model’ account—reveals shortcomings of each, which, it is argued, suggests that scientific representation may be ineliminably heterogeneous in character. In order to achieve a degree of unification that is compatible with successful (...) representation, scientists often rely on the existence of a ‘mature mathematical formalism’, where the latter refers to a—mathematically formulated and physically interpreted—notational system of locally applicable rules that derive from (but need not be reducible to) fundamental theory. As mathematical formalisms undergo a process of elaboration, enrichment, and entrenchment, they come to embody theoretical, ontological, and methodological commitments and assumptions. Since these are enshrined in the formalism itself, they are no longer readily obvious to either the novice or the proficient user. At the same time as formalisms constrain what may be represented, they also function as inferential and interpretative resources. (shrink)

Cartwright and her collaborators have elaborated a provocative view of science which emphasises the independence from theory &unknown;in methods and aims&unknown; of phenomenological model building. This thesis has been supported in a recent paper by an analysis of the London and London model of superconductivity. In the present work we begin with a critique of Cartwright's account of the relationship between theoretical and phenomenological models before elaborating an alternative picture within the framework of the partial structures version of the semantic (...) approach to theories. Drawing on the recent histories of superconductivity by Dahl and Gavroglu, together with the original works by London and London and by F. London separately, and taking due consideration of the heuristic aspects, we argue that the historical details fail to support Cartwright et al.'s claims but that they fit comfortably within the partial structures framework. (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.

What do biologists want? If, unlike their counterparts in physics, biologists are generally wary of a grand, overarching theory, at what kinds of explanation do biologists aim? A history of the diverse and changing nature of biological explanation in a particularly charged field, "Making Sense of Life" draws our attention to the temporal, disciplinary, and cultural components of what biologists mean, and what they understand, when they propose to explain life.

In Making Sense of Life , Keller emphasizes several differences between biology and physics. Her analysis focuses on significant ways in which modelling practices in some areas of biology, especially developmental biology, differ from those of the physical sciences. She suggests that natural models and modelling by homology play a central role in the former but not the latter. In this paper, I focus instead on those practices that are importantly similar, from the point of view of epistemology and cognitive (...) science. I argue that concrete and abstract models are significant in both disciplines, that there are shared selection criteria for models in physics and biology, e.g. familiarity, and that modelling often occurs in a similar fashion. (shrink)

Roald Hoffmann and other theorists claim that we ought to use highly idealized chemical models (“qualitative models”) in order to increase our understanding of chemical phenomena, even though other models are available which make more highly accurate predictions. I assess this norm by examining one of the tradeoffs faced by model builders and model users—the tradeoff between precision and generality. After arguing that this tradeoff obtains in many cases, I discuss how the existence of this tradeoff can help us defend (...) Hoffmann's norm for modelling. (shrink)

Philosophers like Duhem and Cartwright have argued that there is a tension between laws' abilities to explain and to represent. Abstract laws exemplify the first quality, phenomenological laws the second. This view has both metaphysical and methodological aspects: the world is too complex to be represented by simple theories; supplementing simple theories to make them represent reality blocks their confirmation. We argue that both aspects are incompatible with recent developments in nonlinear dynamics. Confirmation procedures and modelling strategies in nonlinear dynamics (...) show that there are simple, abstract theories that can be confirmed without encountering the problems pointed to by Cartwright. (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)

The paper studies the nature of understanding in condensed matter physics (CMP), mediated by the successful employment of its models. I first consider two obvious candidates for the criteria of model-based understanding, Van Fraassen's sense of empirical adequacy and Hacking's instrumental utility , and conclude that both are unsatisfactory. Inspired by Hasok Chang's recent proposal to reformulate realism as the pursuit of ontological plausibility in our system of knowledge, we may require the model under consideration to be understood (or intelligible) (...) before claiming model-based understanding. Here the understanding of a model typically consists of the following: figuring out at least one plausible (preferably realistic) physical mechanism for the model, determining the theoretical consequences of the model by mathematically probing it and developing our physical intuitions about the model. I consider the q-state Potts model to illustrate. After having understood a model, we may employ the model to understand its target phenomena in the world. This is done by matching one of the interpretative models of the model with the central features of the phenomena. The matching should be motivated (ideally both theoretically and empirically) in the sense that we have good reason to believe that the central features of the phenomena can be thought of as having more or less the same structure as postulated by the interpretative model. In conclusion, I propose a two-stage account of model-based understanding in CMP: (1) understanding of a model and (2) matching a target phenomenon with a well-motivated interpretative model of the model. Empirical success and instrumental utility both play their roles in the evaluation of how successful the model is, but are not the essential part of model-based understanding. (shrink)