The paper discusses the recent literature on abstraction/idealization in connection with the “paradox of infinite idealization.” We use the case of taking thermodynamics limit in dealing with the phenomena of phase transition and critical phenomena to broach the subject. We then argue that the method of infinite idealization is widely used in the practice of science, and not all uses of the method are the same. We then confront the compatibility problem of infinite idealization with scientific realism. We propose and (...) defend a contextualist position for realism and argue that the cases for infinite idealization appear to be fully compatible with contextual realism. (shrink)

Charles Mills has argued against ideal theory in political philosophy on the basis that it contains idealizations. He calls for political philosophers to do more nonideal theory, namely political theory that pays more attention to the most visible oppressions in society, such as those based on race, gender, and class. Mills's argument relies on a distinction between idealization and abstraction. Idealizations involve adding false assumptions to one's model, which is unacceptable, whereas abstractions merely leave out details without undermining descriptive power. (...) By studying formal models of injustice, I argue that the idealization/abstraction distinction is unhelpful. Either the distinction exists only relative to one's modeling purposes, or all models in political theory contain idealizations. Either way, the distinction does not help Mills's cause. Furthermore, there are arguments from philosophy of science for the epistemic benefits of idealizations. However, Mills's call for greater emphasis on the most visible mechanisms of oppression can be supported without relying on an idealization/abstraction distinction. I provide three alternative reasons for why we should prefer political theories that place more emphasis on race-, class-, and gender-based oppression. (shrink)

Idealizing conditions are scapegoats for scientific hypotheses, too often blamed for falsehood better attributed to less obvious sources. But while the tendency to blame idealizations is common among both philosophers of science and scientists themselves, the blame is misplaced. Attention to the nature of idealizing conditions, the content of idealized hypotheses, and scientists’ attitudes toward those hypotheses shows that idealizing conditions are blameless when hypotheses misrepresent. These conditions help to determine the content of idealized hypotheses, and they do so in (...) a way that prevents those hypotheses from being false by virtue of their constituent idealizations. (shrink)

The goal of this paper is to encourage a reconfiguration of the discussion about typology in biology away from the metaphysics of essentialism and toward the epistemology of classifying natural phenomena for the purposes of empirical inquiry. First, I briefly review arguments concerning ‘typological thinking’, essentialism, species, and natural kinds, highlighting their predominantly metaphysical nature. Second, I use a distinction between the aims, strategies, and tactics of science to suggest how a shift from metaphysics to epistemology might be accomplished. Typological (...) thinking can be understood as a scientific tactic that involves representing natural phenomena using idealizations and approximations, which facilitates explanation, investigation, and theorizing via abstraction and generalization. Third, a variety of typologies from different areas of biology are introduced to emphasize the diversity of this representational reasoning. One particular example is used to examine how there can be epistemological conflict between typology and evolutionary analysis. This demonstrates that alternative strategies of typological thinking arise due to the divergent explanatory goals of researchers working in different disciplines with disparate methodologies. I conclude with several research questions that emerge from an epistemological reconfiguration of typology. (shrink)

Many phenomena in the natural world are complex, so scientists study them through simplified and idealised models. Philosophers of science have sought to explain how these models relate to the world. On most accounts, models do not represent the world directly, but through target systems. However, our knowledge of target systems is incomplete. First, what is the process by which target systems come about? Second, what types of entity are they? I argue that the basic conception of target systems, on (...) which other conceptions depend, is as parts of the world. I outline the process of target system specification and show that it is a crucial step in modelling. I also develop an account of target system evaluation, based on aptness. Paying close attention to target system specification and evaluation can help scientists minimise the frequency and extent of mistakes, when they are using models to investigate phenomena in complex real-world systems. (shrink)

Bogen and Woodward’s distinction between data and phenomena raises the need to understand the structure of the data-to-phenomena and theory-to-phenomena inferences. I suggest that one way to study the structure of these inferences is to analyze the role of the assumptions involved in the inferences: What kind of assumptions are they? How do these assumptions contribute to the practice of identifying phenomena? In this paper, using examples from atmospheric dynamics, I develop an account of the practice of identifying the target (...) in the data-to-phenomena and theory-to-phenomena inferences in which assumptions about spatiotemporal scales play a central role in the identification of parameters that describe the target system. I also argue that these assumptions are not only empirical but they are also idealizing and abstracting. I conclude the paper with a reflection on the role of idealizations in modeling. (shrink)

In this paper I argue, first, that ecologists have routinely treated humans—or more specifically, anthropogenic causal factors—as disturbing conditions. I define disturbing conditions as exogenous variables, variables “outside” a model, that when present in a target system, inhibit the applicability or accuracy of the model. This treatment is surprising given that humans play a dominant role in many ecosystems and definitions of ecology contain no fundamental distinction between human and natural. Second, I argue that the treatment of humans as disturbing (...) conditions is an idealization: since it is, and has long been, known that humans are pervasive, this treatment amounts to an intentionally introduced theoretical distortion. Finally, characterizing this treatment as idealization forces us to confront the question of its justification, and so, drawing on three different kinds of idealization, I evaluate how this treatment may be justified. (shrink)

This paper contributes to the philosophical accounts of generalisation in formal modelling by introducing a conceptual framework that allows for recognising generalisations that are epistemically beneficial in the sense of contributing to the truth of a model result or component. The framework is useful for modellers themselves because it is shown how to recognise different kinds of generalisation on the basis of changes in model descriptions. Since epistemically beneficial generalisations usually de-idealise the model, the paper proposes a reformulation of the (...) well-known distinction between abstraction and idealisation. A reformulated notion of abstraction is needed because the extant accounts yield wrong judgments when model-modifications introduce implicit assumptions. (shrink)

Abstraction and idealization are the two notions that are most often discussed in the context of assumptions employed in the process of model building. These notions are also routinely used in philosophical debates such as that on the mechanistic account of explanation. Indeed, an objection to the mechanistic account has recently been formulated precisely on these grounds: mechanists cannot account for the common practice of idealizing difference-making factors in models in molecular biology. In this paper I revisit the debate and (...) I argue that the objection does not stand up to scrutiny. This is because it is riddled with a number of conceptual inconsistencies. By attempting to resolve the tensions, I also draw several general lessons regarding the difficulties of applying abstraction and idealization in scientific practice. Finally, I argue that more care is needed only when speaking of abstraction and idealization in a context in which these concepts play an important role in an argument, such as that on mechanistic explanation. (shrink)

Scientific explanation is an important goal of scientific practise. Philosophers have proposed a striking diversity of seemingly incompatible accounts of explanation, from deductive-nomological to statistical relevance, unification, pragmatic, causal-mechanical, mechanistic, causal intervention, asymptotic, and model-based accounts. In this dissertation I apply two novel methods to reexamine our evidence about scientific explanation in practise and thereby address the fragmentation of philosophical accounts. I start by collecting a data set of 781 articles from one year of the journal Science. Using automated text (...) mining techniques I measure the frequency and distribution of several groups of philosophically interesting words, such as "explain", "cause", "evidence", "theory", "law", "mechanism", and "model". I show that "explain" words are much more common in scientific writing than in other genres, occurring in roughly half of all articles, and that their use is very often qualified or negated. These results about the use of words complement traditional conceptual analysis. Next I use random samples from the data set to develop a large number of small case studies across a wide range of scientific disciplines. I use a sample of "explain" sentences to develop and defend a new general philosophical account of scientific explanation, and then test my account against a larger set of randomly sampled sentences and abstracts. Five coarse categories can classify the explanans and explananda of my cases: data, entities, kinds, models, and theories. The pair of the categories of the explanans and explanandum indicates the "form" of an explanation. The explain-relation supports counterfactual reasoning about the dependence of qualities of the explanandum on qualities of the explanans. But for each form there is a different "core relation" between explanans and explanandum that supports the explain-relation. Causation, modelling, and argument are the core relations for different forms of scientific explanation between different categories of explanans and explananda. This flexibility allows me to resolve some of the fragmentation in the philosophical literature. I provide empirical evidence to show that my general philosophical account successfully describes a wide range of scientific practise across a large number of scientific disciplines. (shrink)

This essay examines the issue of false assumptions in models via a case study of a prominent economic model of sustainable development, wherein the assumption of an infinite future plays a central role. Two proposals are found to be helpful for this case, one based on the concept of derivational robustness and the other on understanding. Both suggest that the assumption of an infinite future, while arguably legitimate in some applications of the model, is problematic with respect to what I (...) call “Parfitian” welfare functions. This result is relevant to debates about discounting the future in economics and environmental ethics. (shrink)

There are two notions of abstraction that are often confused. The material view implies that the products of abstraction are not concrete. It is vulnerable to the criticism that abstracting introduces misrepresentations to the system, hence abstraction is indistinguishable from idealization. The omission view fares better against this criticism because it does not entail that abstract objects are non-physical and because it asserts that the way scientists abstract is different to the way they idealize. Moreover, the omission view better captures (...) the way that abstraction is used in many parts of science. Disentangling the two notions is an important prerequisite for determining how to evaluate the use abstraction in science. (shrink)

The paper discusses the recent literature on abstraction/idealization in connection with the “paradox of infinite idealization.” We use the case of taking thermodynamics limit in dealing with the phenomena of phase transition and critical phenomena to broach the subject. We then argue that the method of infinite idealization is widely used in the practice of science, and not all uses of the method are the same. We then confront the compatibility problem of infinite idealization with scientific realism. We propose and (...) defend a contextualist position for realism and argue that the cases for infinite idealization appear to be fully compatible with contextual realism. (shrink)

Call a bit of scientific discourse a description of a missing system when (i) it has the surface appearance of an accurate description of an actual, concrete system (or kind of system) from the domain of inquiry, but (ii) there are no actual, concrete systems in the world around us fitting the description it contains, and (iii) that fact is recognised from the outset by competent practitioners of the scientific discipline in question. Scientific textbooks, classroom lectures, and journal articles abound (...) with such passages; and there is a widespread practice of talking and thinking as though there are systems which fit the descriptions they contain perfectly, despite the recognition that no actual, concrete systems do so—call this the face value practice. There are, furthermore, many instances in which philosophers engage in the face value practice whilst offering answers to epistemological and methodological questions about the sciences. Three questions, then: (1) How should we interpret descriptions of missing systems? (2) How should we make sense of the face value practice? (3) Is there a set of plausible answers to (1) and (2) which legitimates reliance on the face value practice in our philosophical work, and can support the weight of the accounts which are entangled with that practice? In this paper I address these questions by considering three answers to the first: that descriptions of missing systems are straightforward descriptions of abstract objects, that they are indirect descriptions of “property-containing” abstracta, and that they are (in a different way) indirect descriptions of mathematical structures. All three proposals are present in the literature, but I find them wanting. The result is to highlight the importance of developing a satisfactory understanding of descriptions of missing systems and the face value practice, to put pressure on philosophical accounts which rely on the practice, and to help us assess the viability of certain approaches to thinking about models, theory structure, and scientific representation. (shrink)

Network theory is applied across the sciences to study phenomena as diverse as the spread of SARS, the topology of the cell, the structure of the Internet and job search behaviour. Underlying the study of networks is graph theory. Whether the graph represents a network of neurons, cells, friends or firms, it displays features that exclusively depend on the mathematical properties of the graph itself. However, the way in which graph theory is implemented to the modelling of networks differs significantly (...) across scientific fields. This article compares the economics variant of network theory with those of other fields. It shows how the methodology employed by economists to model networks is shaped by two explanatory desiderata: that the explanandum phenomenon is based on micro-economic foundations and that the explanation is general. (shrink)

One of the most unsettling problems in the history of philosophy examines how mathematics can be used to adequately represent the world. An influential thesis, stated by Eugene Wigner in his paper entitled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," claims that "the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve." Contrary to this view, this thesis delineates and implements (...) a strategy to show that the applicability of mathematics is very reasonable indeed. I distinguish three forms of the problem of the applicability of mathematics, and focus on one I call the problem of uncanny accuracy: Given that the construction and manipulation of mathematical representations is pervaded by uncertainty, error, approximation, and idealization, how can their apparently uncanny accuracy be explained? I argue that this question has found no satisfactory answer because our rational reconstruction of scientific practice has not involved tools rich enough to capture the logic of mathematical modelling. Thus, I characterize a general schema of mathematical analysis of real systems, focusing on the selection of modelling assumptions, on the construction of model equations, and on the extraction of information, in order to address contextually determinate questions on some behaviour of interest. A concept of selective accuracy is developed to explain the way in which qualitative and quantitative solutions should be utilized to understand systems. The qualitative methods rely on asymptotic methods and on sensitivity analysis, whereas the quantitative methods are best understood using backward error analysis. The basic underpinning of this perspective is readily understandable across scientific fields, and it thereby provides a view of mathematical tractability readily interpretable in the broader context of mathematical modelling. In addition, this perspective is used to discuss the nature of theories, the role of scaling, and the epistemological and semantic aspects of experimentation. In conclusion, we argue for a method of local and global conceptual analysis that goes beyond the reach of the tools standardly used to capture the logic of science; on their basis, the applicability of mathematics finds itself demystified. (shrink)

I argue that fictional models, construed as models that misrepresent certain ontological aspects of their target systems, can nevertheless explain why the latter exhibit certain behaviour. They can do this by accurately representing whatever it is that that behaviour counterfactually depends on. However, we should be sufficiently sensitive to different explanatory questions, i.e., ‘why does certain behaviour occur?’ versus ‘why does the counterfactual dependency invoked to answer that question actually hold?’. With this distinction in mind, I argue that whilst fictional (...) models can answer the first sort of question, they do so in an unmysterious way. Moreover, I claim that the second question poses a dilemma for the defender of the idea that fictions can explain: either these models cannot answer these sorts of explanatory questions, precisely because they are fictional; or they can, but in a way that requires reinterpreting them such that they end up accurately representing the ontological basis of the counterfactual dependency, i.e., reinterpreting them so as to rob them of their fictional status. Thus, the existence of explanatory fictions does not put pressure on the idea that accurate representation of some aspect of a target system is a necessary condition on explaining that aspect. (shrink)

Generative models have been proposed as a new type of non-representational scientific models recently. A generative model is characterized with the capacity of producing new models on the basis of the existing one. The current accounts do not explain sufficiently the mechanism of the generative capacity of a generative model. I attempt to accomplish this task in this paper. I outline two antecedent accounts of generative models. I point out that both types of generative models function to generate new homogenous (...) models in the sense that the latter is a straightforward derivative of the former, both of which share many similar features. Unfortunately, both accounts are implicit about the generative capacity of generative models. Using a case study, I articulate that a two-staged process of abstraction and idealization in modeling may contribute to the generative capacity of a scientific model. I also demonstrate that this two-staged process may go beyond the capacity of generating new homogenous models to generating new heterogeneous models. (shrink)

We argue that two powerful error-theoretic concepts provide a general framework that satisfactorily accounts for key aspects of the explanation of physical patterns. This method gives an objective criterion to determine which mathematical models in a class of neighboring models are just as good as the exact one. The method also emphasizes that abstraction is essential for explanation and provides a precise conceptual framework that determines whether a given abstraction is explanatorily relevant and justified. Hence, it increases our epistemological understanding (...) of how one should go about reconstructing scientific practices by making clear that, at a fundamental level, a key aspect of mathematical modeling consists in exactly solving nearby problems. (shrink)

Is there a unique way to de-idealize models? If not, how might the possible ways of reducing the distortion between models and reality differ from each other? Based on an empirical case study conducted in financial markets, this paper discusses how a popular valuation model (the Discounted Cash Flow model) idealizes reality and how the market participants de-idealize it in concrete market situations. In contrast to Cartwright's view that economic models are generally over-constrained, this paper suggests that valuation models are (...) under-constrained. This serves as the reason why the relaxation of simplifying assumptions and concretization do not work as methods of de-idealization. The paper finds that financial market participants de-idealize models using commentary that takes the form of judgment. As a conclusion, a hypothesis is formulated that proposes that the more underdetermined the model is the bigger role narrative and other pragmatic elements play in the process of model application. (shrink)

Idealization is ubiquitous in human cognition, and so is the inclination to be puzzled by it: what to make of ideal gas, infinitely large populations, homo economicus, perfectly just society, known to violate matters of fact? This is apparent in social science theorizing, recent philosophy of science analyzing scientific modeling, and the debate over ideal and non-ideal theory in political philosophy. I will offer a set of concepts and principles to improve transparency about the precise contents of idealizations and their (...) distinct functions. (shrink)