The chapter argues that a model‐building methodology like that widespread in contemporary natural and social science already plays a significant role in philosophy. One neglected form of progress in philosophy over the past fifty years has been the development of better and better formal models of significant phenomena. Examples are given from both philosophy of language and epistemology. Philosophy can do still better in the future by applying model‐building methods more systematically and self‐consciously, with consequent readjustments (...) to its methodology. Although it is neither likely nor desirable for model‐building to become the sole or even main philosophical method, its use enhances the power and reliability of philosophical thinking. (shrink)

Open peer commentary on the article “Constructivist Model Building: Empirical Examples From Mathematics Education” by Catherine Ulrich, Erik S. Tillema, Amy J. Hackenberg & Anderson Norton. Upshot: The target article by Ulrich et al. is a good example of constructivist research in mathematics education, and illustrates how constructivism can ground a research endeavour toward modelling students’ mathematical understandings. I propose to delve into these issues of model building and reflect on Maturana’s notion of the observer. I (...) do this through discussing issues about the language used in the article and of data description, and of analysis of students’ mathematical activity. (shrink)

Concern about the role and the limits of modeling has heightened after repeated questions were raised regarding the dependability and suitability of the models that were used in the run-up to the 2008 financial crash. In this book, Lawrence Boland provides an overview of the practices of and the problems faced by model builders to explain the nature of models, the modeling process, and the possibility for and nature of their testing. In a reflective manner, the author raises serious (...) questions about the assumptions and judgments that model builders make in constructing models. In making his case, he examines the traditional microeconomics-macroeconomics separation with regard to how theoretical models are built and used and how they interact, paying particular attention to the use of equilibrium concepts in macroeconomic models and game theory and to the challenges involved in building empirical models, testing models, and using models to test theoretical explanations. (shrink)

This paper describes model building and manipulation in the solution of problems in mechanics. An automatic problem solver, MECHO, solving problems in several areas of mechanics, employs (1) a knowledge base representing the semantic content of the particular problem area, (2) a means-ends search strategy similar to GPS to produce sets of simultaneous equations and (3) a “focusing” technique, based on the data within the knowledge base, to guide the GSP-like search through possible equation instantiations. Sets of predicate (...) logic statements are employed to describe this model building activity. These clauses are used to give information content to the knowledge base and provide both basis and guidance for the goal driven search.It is hypothesized that humon subjects solving mechanics problems employ similar model building techniques. Protocols of several subjects are presented and comparisons are drawn with the traces of the automated problem solver. Adjustments are made to the program to provide a better fit of traces to protocols. Some implications are presented for using a rule based model for describing human problem solving performance in solving mechanics problems. (shrink)

In my paper I focus on the growth of knowledge in finance from an heuristic viewpoint and I propose the analysis of two different knowledge-advancing strategies usually adopted at the frontier of knowledge, i.e. problem-solving and model-building. I show how these two strategies, even though both effective in the short-run, nonetheless provide descriptions of the target object and which are different in their descriptive and knowledge-advancing depth. In order to do so, I propose a case study borrowed from (...) the modelling activities in the Libor market. (shrink)

In my paper I focus on the growth of knowledge in finance from an heuristic viewpoint and I propose the analysis of two different knowledge-advancing strategies usually adopted at the frontier of knowledge, i.e. problem-solving and model-building. I show how these two strategies, even though both effective in the short-run, nonetheless provide descriptions of the target object and which are different in their descriptive and knowledge-advancing depth. In order to do so, I propose a case study borrowed from (...) the modelling activities in the Libor market. (shrink)

Context: This paper outlines how radical constructivist theory has led to a particular methodological technique, developing second-order models of student thinking, that has helped mathematics educators to be more effective teachers of their students. Problem: The paper addresses the problem of how radical constructivist theory has been used to explain and engender more viable adaptations to the complexities of teaching and learning. Method: The paper presents empirical data from teaching experiments that illustrate the process of second-order model building. (...) Results: The result of the paper is an illustration of how second-order models are developed and how this process, as it progresses, supports teachers to be more effective. Implications: This paper has the implication that radical constructivism has the potential to impact practice. Key Words: Second-order model, radical constructivism, teaching, mathematics education. (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)

The terms “model” and “model-building” have been used to characterize the field of formal philosophy, to evaluate philosophy’s and philosophical logic’s progress and to define philosophical logic itself. A model is an idealization, in the sense of being a deliberate simplification of something relatively complex in which several important aspects are left aside, but also in the sense of being a view too perfect or excellent, not found in reality, of this thing. Paraconsistent logic is a (...) branch of philosophical logic. It is however not clear how paraconsistent logic can be seen as model-building. What exactly is modeled? In this paper I adopt the perspective of looking at a particular instance of paraconsistent logic—paranormal modal logic—which might be seen as a model of a specific kind of agent: inductive agents. After ntroducing what I call the highlevel and low-level models of inductive agents, I analyze the extent to which the above-mentioned idealizing features of model-building appear in paranormal modal logic and how they affect its philosophical significance. (shrink)

This paper contrasts and compares strategies of model-building in condensed matter physics and biology, with respect to their alleged unequal susceptibility to trade-offs between different theoretical desiderata. It challenges the view, often expressed in the philosophical literature on trade-offs in population biology, that the existence of systematic trade-offs is a feature that is specific to biological models, since unlike physics, biology studies evolved systems that exhibit considerable natural variability. By contrast, I argue that the development of ever more (...) sophisticated experimental, theoretical, and computational methods in physics is beginning to erode this contrast, since condensed matter physics is now in a position to measure, describe, model, and manipulate sample-specific features of individual systems – for example at the mesoscopic level – in a way that accounts for their contingency and heterogeneity. Model-building in certain areas of physics thus turns out to be more akin to modeling in biology than has been supposed and, indeed, has traditionally been the case. (shrink)

In 1966, Richard Levins argued that there are different strategies in model building in population biology. In this paper, I reply to Orzack and Sober’s (1993) critiques of Levins, and argue that his views on modeling strategies apply also in the context of evolutionary genetics. In particular, I argue that there are different ways in which models are used to ask and answer questions about the dynamics of evolutionary change, prospectively and retrospectively, in classical versus molecular evolutionary genetics. (...) Further, I argue that robustness analysis is a tool for, if not confirmation, then something near enough, in this discipline. (shrink)

In this article we defend the inferential view of scientific models and idealisation. Models are seen as “inferential prostheses” (instruments for surrogative reasoning) construed by means of an idealisation-concretisation process, which we essentially understand as a kind of counterfactual deformation procedure (also analysed in inferential terms). The value of scientific representation is understood in terms not only of the success of the inferential outcomes arrived at with its help, but also of the heuristic power of representation and their capacity to (...) correct and improve our models. This provides us with an argument against Sugden’s account of credible models: the likelihood or realisticness (their “credibility”) is not always a good measure of their acceptability. As opposed to “credibility” we propose the notion of “enlightening”, which is the capacity of giving us understanding in the sense of an inferential ability. (shrink)

Modelling became one of the primary tools of mathematical economic research in the twentieth century, but when we look at examples of how nonanalogical models were first built in economics, both the process of making representations and aspects of the representing relation remain opaque. Like early astronomers, economists have to imagine how the hidden parts of their world are arranged and to make images, that is, create models, to represent how they work. The case of the Edgeworth Box, a (...) class='Hi'>model widely used for theoretical work in twentieth-century economics, provides a good example to explore the process of making mathematical representations of the economy. It shows how, in making these new representations, conceptual elements were developed which could not have been represented in the older verbal forms of economics. (shrink)

In the 1960s, theoretical biologist Richard Levins criticised modellers in his own discipline of population biology for pursuing the “brute force” strategy of building hyper-realistic models. Instead of exclusively chasing complexity, Levins advocated for the use of multiple different kinds of complementary models, including much simpler ones. In this paper, I argue that the epistemic challenges Levins attributed to the brute force strategy still apply to state-of-the-art climate models today: they have big appetites for unattainable data, they are limited (...) by computational tractability, and they are incomprehensible to the human modeller. Along the lines Levins described, this uncertainty generates a trade-off between realistic, precise models with predictive power and simple, highly idealised models that facilitate understanding. In addition to building ensembles of highly complex dynamical models, climate modellers can address model uncertainty by comparing models of different types, such as dynamical and data-driven models, and by systematically comparing models at different levels of what climate modellers call the model hierarchy. Despite its age, Levins’ paper remains incredibly insightful and should be considered an important entry into the philosophy of computational modelling. (shrink)

This paper is an interpretation and defense of Richard Levins’ “The Strategy of Model Building in Population Biology,” which has been extremely influential among biologists since its publication 40 years ago. In this article, Levins confronted some of the deepest philosophical issues surrounding modeling and theory construction. By way of interpretation, I discuss each of Levins’ major philosophical themes: the problem of complexity, the brute-force approach, the existence and consequence of tradeoffs, and robustness analysis. I argue that Levins’ (...) article is concerned, at its core, with justifying the use of multiple, idealized models in population biology. (shrink)

Brian Epstein has recently argued that a thoroughly microfoundationalist approach towards economics is unconvincing for metaphysical reasons. Generally, Epstein argues that for an improvement in the methodology of social science we must adopt social ontology as the foundation of social sciences; that is, the standing microfoundationalist debate could be solved by fixing economics’ ontology. However, as I show in this paper, fixing the social ontology prior to the process of model construction is optional instead of necessary and that metaphysical-ontological (...) commitments are often the outcome of model construction, not its starting point. By focusing on the practice of modeling in economics the paper provides a useful inroad into the debate about the role of metaphysics in the natural and social sciences more generally. (shrink)

In this article we defend the inferential view of scientific models and idealisation. Models are seen as “inferential prostheses” (instruments for surrogative reasoning) construed by means of an idealisation-concretisation process, which we essentially understand as a kind of counterfactual deformation procedure (also analysed in inferential terms). The value of scientific representation is understood in terms not only of the success of the inferential outcomes arrived at with its help, but also of the heuristic power of representation and their capacity to (...) correct and improve our models. This provides us with an argument against Sugden’s account of credible models: the likelihood or realisticness (their “credibility”) is not always a good measure of their acceptability. As opposed to “credibility” we propose the notion of “enlightening”, which is the capacity of giving us understanding in the sense of an inferential ability. (shrink)

Recently, there has been a rise in pessimism concerning what theoretical ecology can offer conservation biologists in the formation of reasonable environmental policies. In this paper, I look at one of the pessimistic arguments offered by Kristin Shrader-Frechette and E. D. McCoy (1993, 1994)--the argument from conceptual imprecision. I suggest that their argument rests on an inadequate account of the concepts of ecological stability and that there has been conceptual progress with respect to complexity-stability hypotheses. Such progress, I maintain, can (...) supply important resources for conservation biologists in determining environmental policies. (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)

Recently, there has been a rise in pessimism concerning what theoretical ecology can offer conservation biologists in the formation of reasonable environmental policies. In this paper, I look at one of the pessimistic arguments offered by Kristin Shrader-Frechette and E. D. McCoy -the argument from conceptual imprecision. I suggest that their argument rests on an inadequate account of the concepts of ecological stability and that there has been conceptual progress with respect to complexity-stability hypotheses. Such progress, I maintain, can supply (...) important resources for conservation biologists in determining environmental policies. (shrink)

This article addresses the contributions of the literature on the new mechanistic philosophy of science for the scientific practice of model building in ecology. This is reflected in a one-to-one interdisciplinary collaboration between an ecologist and a philosopher of science during science-in-the-making. We argue that the identification, reconstruction and understanding of mechanisms is context-sensitive, and for this case study mechanistic modeling did not present a normative role but a heuristic one. We expect our study to provides useful epistemic (...) tools for the improvement of empirically-riven work in the debates about mechanistic explanation of ecological phenomena. (shrink)

In this article we defend the inferential view of scientific models and idealisation. Models are seen as “inferential prostheses” (instruments for surrogative reasoning) construed by means of an idealisation-concretisation process, which we essentially understand as a kind of counterfactual deformation procedure (also analysed in inferential terms). The value of scientific representation is understood in terms not only of the success of the inferential outcomes arrived at with its help, but also of the heuristic power of representation and their capacity to (...) correct and improve our models. This provides us with an argument against Sugden’s account of credible models: the likelihood or realisticness (their “credibility”) is not always a good measure of their acceptability. As opposed to “credibility” we propose the notion of “enlightening”, which is the capacity of giving us understanding in the sense of an inferential ability. (shrink)

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)

Disagreement about how best to think of the relation between theories and the realities they represent has a longstanding and venerable history. We take up this debate in relation to the free energy principle (FEP) - a contemporary framework in computational neuroscience, theoretical biology and the philosophy of cognitive science. The FEP is very ambitious, extending from the brain sciences to the biology of self-organisation. In this context, some find apparent discrepancies between the map (the FEP) and the territory (target (...) systems) a compelling reason to defend instrumentalism about the FEP. We take this to be misguided. We identify an important fallacy made by those defending instrumentalism about the FEP. We call it the literalist fallacy: this is the fallacy of inferring the truth of instrumentalism based on the claim that the properties of FEP models do not literally map onto real-world, target systems. We conclude that scientific realism about the FEP is a live and tenable option. (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)

Modern integrative systems biology defines itself by the complexity of the problems it takes on through computational modeling and simulation. However in integrative systems biology computers do not solve problems alone. Problem solving depends as ever on human cognitive resources. Current philosophical accounts hint at their importance, but it remains to be understood what roles human cognition plays in computational modeling. In this paper we focus on practices through which modelers in systems biology use computational simulation and other tools to (...) handle the cognitive complexity of their modeling problems so as to be able to make significant contributions to understanding, intervening in, and controlling complex biological systems. We thus show how cognition, especially processes of simulative mental modeling, is implicated centrally in processes of model-building. At the same time we suggest how the representational choices of what to model in systems biology are limited or constrained as a result. Such constraints help us both understand and rationalize the restricted form that problem solving takes in the field and why its results do not always measure up to expectations. (shrink)

Some ecologists have argued that theoretical model building in population and community ecology has gone evidentially unconstrained. In the essay, I argue that "bottle experiments" offer ecological model building evidential constraints and illustrate this by considering work on chaotic models tested by the dynamics of flour beetles. Critics reply that these experiments are importantly unlike nonmanipulated natural systems and thus do not constitute genuine tests of the models. I conclude by considering two responses to this worry (...) and a suggestion on how to move forward on this debate. (shrink)

The prevalence of optimality models in the literature of evolutionary biology is testimony to their popularity and importance. Evolutionary biologist R. C. Lewontin, whose criticisms of optimality models are considered here, reflects that "optimality arguments have become extremely popular in the last fifteen years, and at present represent the dominant mode of thought." Although optimality models have received little attention in the philosophical literature, these models are very interesting from a philosophical point of view. As will be argued, optimality models (...) are central to evolutionary thought, yet they are not readily accomodated by the traditional view of scientific theories. According to the traditional view, we would expect optimality models to employ general, empirical laws of nature, but they do not. Fortunately, the semantic view of scientific theories, a recent alternative to the traditional view, more readily accomodates optimality models. As we would expect on the semantic view, optimality models can be construed as specifications of ideal systems. These specifications may be used to describe empirical systems--that is, the specifications may have empirical instances. But the specifications are not empirical claims, much less general, empirical laws. Although philosophers have yet to discuss the general features and uses of optimality models, these topics have stimulated much recent discussion among evolutionary biologists. Their discussions raise a number of precautions concerning the proper use of optimality models. Moreover, many of their caveats can be interpreted as general reminders that 1) optimality models specify ideal systems whose empirical instantiations may be quite restricted, and that 2) optimality models should not be construed as general, empirical laws. As G. F. Oster and E. O. Wilson caution, "the prudent course is to regard optimality models as provisional guides to further empirical research and not necessarily as the key to deeper laws of nature." It seems, then, that the semantic view of theories is more sensitive to the nature and limitations of optimality models than is the more traditional view of theories. (shrink)

An important epistemic issue in climate modelling concerns structural uncertainty: uncertainty about whether the mathematical structure of a model accurately represents its target. How does structural uncertainty affect our knowledge and predictions about the climate? How can we identify sources of structural uncertainty? Can we manage the effect of structural uncertainty on our knowledge claims? These are some of the questions that an epistemology of structural uncertainty faces, and these questions are also important for climate scientists and policymakers. I (...) develop three desiderata for an epistemological account of structural uncertainty. In my view, an account of structural uncertainty should identify sources of structural uncertainty, explain how these sources limit the applicability of a model, and show how the severity of structural uncertainty depends on the questions that can be asked of a model. I argue that analyzing structural uncertainty by paying attention to the details of model building can satisfy these desiderata. I focus on parametrizations, which are representations of important processes occurring at scales that are not resolved by climate models. Parametrizations are often thought to be ad-hoc, but I show that some important parametrizations are theoretically justified by explicit or implicit scale separation assumptions. These assumptions can also be supported empirically. Analyzing these theoretical and empirical justificatory roles of the scale separation assumptions can provide insights into how parametrizations contribute to structural uncertainty. I conclude by sketching how my approach can satisfy the desiderata I set out at the beginning, highlighting its importance for policy-relevant scientific statements about the climate. (shrink)

In this paper, we argue that rather than exclusively focusing on trying to determine if an idealized model fits a particular account of scientific explanation, philosophers of science should also work on directly analyzing various explanatory schemas that reveal the steps and justification involved in scientists’ use of highly idealized models to formulate explanations. We develop our alternative methodology by analyzing historically important cases of idealized statistical modeling that use a three-step explanatory schema involving idealization, mathematical operation, and explanatory (...) interpretation. (shrink)

Open peer commentary on the article “Constructivist Model Building: Empirical Examples From Mathematics Education” by Catherine Ulrich, Erik S. Tillema, Amy J. Hackenberg & Anderson Norton. Upshot: I argue that radical constructivism poses a series of deep methodological constraints on educational research. We focus on the work of Ulrich et al. to illustrate the practical implications of these constraints.

Open peer commentary on the article “Constructivist Model Building: Empirical Examples From Mathematics Education” by Catherine Ulrich, Erik S. Tillema, Amy J. Hackenberg & Anderson Norton. Upshot: I concur with Ulrich et al. that second-order models can be powerful tools for investigating students’ mathematical learning. I argue for a role that a dynamic, learner-centered perspective on context could play in constructivist model building.

Open peer commentary on the article “Constructivist Model Building: Empirical Examples From Mathematics Education” by Catherine Ulrich, Erik S. Tillema, Amy J. Hackenberg & Anderson Norton. Upshot: The suggestion that model building can be used by teachers to enable productive interactions with students is taken up. Challenges and possibilities in exploring constructivist model building by examining mathematics teacher educators’ interactions with teachers are investigated.

In our 1993 paper, “A Critical Look,‘ Elliott Sober and I concluded that the famous claim about model formulation and constraints made by Richard Levins in his influential 1966 article on model building in population biology is neither true nor normative. Here, I comment upon the claim of Odenbaugh that the conclusions of “A Critical Look‘ are incorrect. My conclusions remain that Levins’ claim about the tradeoff between model properties lacks logical coherence, generates an arbitrary (...) class='Hi'>model classification, and lacks normative utility. Accordingly, I view his claim as providing no useful insight into the nature of models and model building in population biology. (shrink)

Modelling became one of the primary tools of economic research in the 20th century and economists understand their mathematical models as giving some kind of representation of the economic world, one adequate enough for the purpose of reasoning about that world. But when we look at examples of how non-analogical models were first built in economics, both the process of making representations and aspects of the representing relation remain opaque. Like early astronomers, economists have to imagine how the hidden parts (...) of their world are arranged and to make images, that is, create models, to represent how they work. The case of the Edgeworth Box, a widely used model in 20th century economics, provides a good example to explore the role of imagination and images in the process of making representations of the economy. (shrink)