In this paper, I first argue against various attempts to justify idealizations in scientific models that explain by showing that they are harmless and isolable distortions of irrelevant features. In response, I propose a view in which idealized models are characterized as providing holistically distorted representations of their target system. I then suggest an alternative way that idealized modeling can be justified by appealing to universality.

This paper calls into question one fundamental claim at the basis of an alleged puzzle for veritistic accounts of the value of idealized models: the claim that idealized models cannot be veridical representations of the world. Catherine Elgin has argued that the value of idealized models can only be explained if we construe them as exemplars, which do not represent the world. I argue that Elgin’s proposal is problematic and cannot accommodate central cases of (...) idealization. Nevertheless, there is value in Elgin’s proposal. I rescue her notion of selectiveness in exemplification and incorporate it within a revised account of representation. I provide independent motivation in favour of a form of veritism, which motivates a revision of Elgin’s case against it. I argue that an account based on selective representation has the resources to rescue veritism from the problems raised by Elgin. In the proposal I advance, idealized models are literally veridical representations of the world. (shrink)

This paper erects a framework for analyzing some idealized models as (what I call) inferentially veridical representations. It adopts a version of the semantic view of theories that focuses on properties, and mobilizes conceptual resources associated with properties and the way that properties are related in various ways. The outcome is an elaboration of some aspects of the analysis of Jones (2005).

In this paper a model is presented for the growth of knowledge in a dynamic scientific system. A system which is in some respects an idealization of a Lakatosian research program. The kinematics of the system is described in terms of two probabilistic variables, one of which is related to the evolution of its theoretical component and the other--to the growth of the empirical component. It is shown that when the empirical growth is faster than the theoretical growth the posterior (...) probability of the theoretical component increases. Thus, empirical progressiveness of a research program, as explicated in this model, is accompanied by an increase in the degree of confirmation. In such a case the system grows in a Popperian-like spirit, while learning from experience in a Bayesian manner. (shrink)

Many accounts of scientific modelling assume that models can be decomposed into the contributions made by their accurate and inaccurate parts. These accounts then argue that the inaccurate parts of the model can be justified by distorting only what is irrelevant. In this paper, I argue that this decompositional strategy requires three assumptions that are not typically met by our best scientific models. In response, I propose an alternative view in which idealized models are characterized as (...) holistically distorted representations that are justified by allowing for the application of various modelling techniques. (shrink)

In the methodology of theory construction, the concept of "intuitions" is commonly assigned a central role. This is especially true of philosophical and social scientific theories or rational human agency. An equally important trait of such accounts is the theorist's employment of "ideal models" or rational agency. It is frequently supposed that the concept of intuitions and the concept of ideal models link in such a way as to give rise to a coherent and load-bearing notion of "objective (...) normativity." This paper shows, with reference to a wide range of contemporary theories, that the employment of ideal models is otiose, and that the supposedly related concept of objective normativity is groundless. (shrink)

Both questions as abstract objects and the speech acts, here called requests, by which we ask them play an enormous role in all argumentative practices. Nonetheless, there is hardly a proper systematic treatment of questions and requests in current argumentation theories. This paper is a first attempt at providing such a systematic treatment. This is achieved by following the ideal model of a critical discussion as elaborated over the years by the Amsterdam school of pragma-dialectics. After introducing the distinction between (...) questions and requests, the paper sets forth and illustrates the norms of questioning which implicitly underlie the four stages of a critical discussion in the standard order: confrontation, opening, argumentation, and conclusion. Among other things, it is shown that crucial insights of pragma-dialectics are illuminated by the questioning perspective, in particular the distinction between single and multiple differences of opinion, the duties of the antagonist and protagonist roles, the precise character of the argumentation stage, and the different ways in which a disagreement can be resolved. (shrink)

Scientific models typically contain idealizations, or assumptions that are known not to be true. Philosophers have long questioned the nature of idealizations: Are they heuristic tools that will be abandoned? Or rather fictional representations of reality? And how can we reconcile them with realism about knowledge of nature? Immanuel Kant developed an account of scientific investigation that can inspire a new approach to the contemporary debate. Kant argued that scientific investigation is possible only if guided by ideal assumptions—what he (...) calls “regulative ideas”. These ideas are not true of objects of nature, and yet they are not heuristic tools or fictional represen- tations. They are necessary rules governing the construction and assessment of scientific explanations. In this paper, I suggest that some idealizations can be interpreted as having necessary regulative value and as being compatible with scientific realism. I first analyze the puzzle of the nature of idealization and present the main approaches to this topic in the literature. Second, I reconsider the puzzle vis-a-vis a restricted, Kantian definition of idealization and a novel characterization of the relation between idealization and truth. Finally, I discuss in detail an example of idealization (the Hardy-Weinberg equilibrium) along the suggested Kantian lines. (shrink)

Embryonic stem cells are derived from the preimplantation embryo and can differentiate into virtually any other cell type, which is governed by lineage specific transcriptions factors binding to cis regulatory elements to mediate changes in gene expression. The reliance on transcriptional regulation to maintain pluripotency makes ESCs a valuable model to study the role of distal CREs such as enhancers in modulating gene expression to affect cell fate decisions. This review will highlight recent advance on transcriptional enhancers, focusing on studies (...) performed in ESCs. In addition, we argue that the Nanog locus, which encodes for an ESC-critical TF, is particularly informative because it contains multiple co-regulated genes and enhancers in close proximity to one another. The unique landscape at Nanog permits the study of ongoing questions including whether multiple enhancers function additively versus synergistically, determinants of gene specificity, and cell-to-cell variability in gene expression. Nanog encodes a transcription factor required to maintain ESC pluripotency. The Nanog locus is an ideal model to study enhancers because it contains multiple highly potent super-enhancers within a small region. Nanog and three super-enhancers are in close physical proximity but only two SEs are required for Nanog expression. (shrink)

The precocious induction in vivo and in culture of insect and amphibian metamorphosis by exogenous ecdysteroids and thyroid hormones, and its retardation or inhibition by juvenile hormone and prolactin, respectively, has allowed the analysis of such diverse processes of post‐embryonic development as morphogenesis, tissue remodelling, functional reorganization, and programmed cell death. Metamorphosis in vertebrates also shares many similarities with mammalian development in the late foetal and perinatal period. This review describes the regulation of expression of some of the ‘adult’ gene (...) products during metamorphosis in invertebrates and vertebrates. Recent studies on metamorphosis have revealed the important role played by auto‐induction of hormone receptor genes, based on which a model will be presented to explain the activation of ‘downstream’ genes which give rise to the adult phenotype. It will also be argued that metamorphosis is an ideal model for analyzing some of the major mechanisms governing post‐embryonic development. (shrink)

The aim of this article is to return to the concept of bricolage as theorized in 1962 by the French anthropologist Claude Lévi-Strauss and examine its presence and utility in the art and architectural history of the twentieth century. While Lévi-Strauss was the first theorist to present bricolage as an analogy for the creation of mythical thought among indigenous cultures, the concept has seen a wide range of conceptual, methodological and practical applications across different fields, including design, visual arts, urban (...) planning and the built environment. This article will examine the applicability of bricolage as a technical metaphor for the creative process and its relevance to artistic creation by tracing its trajectory over the course of the twentieth century. It will evaluate the significance of objects and events of ‘everyday life’ in the creative practices of contemporary artists, and draw attention to the emerging role of the architect as bricoleur or improviser, to conclude that it was the art of the ‘ordinary’ that gave creative inspiration to twentieth-century artists and architects to engage with the materiality and past experiences of the world. (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)

The book "Idealization XIV: Models in Science" offers a detailed ontological, epistemological and historical account of the role of models in scientific practice. The volume contains contributions of different international scholars who developed many aspects of the use of idealizations and models both in the natural and the social sciences. This volume is particularly relevant because it offers original contributions concerning one of the main topic in philosophy of science: the role of models in such branches (...) of the sciences and the humanities like comparative historical sociology, economics, history, linguistics and political philosophy. -/- Contributors are: Giacomo Borbone, Krzysztof Brzechczyn, Mieszko Ciesielski, Adam Czerniak, Xavier de Donato Rodríguez, José L. Falguera, Adolfo García de la Sienra, Lidia Godek, Igor Hanzel, Łukasz Hardt, Krzysztof Kiedrowski, Barbara Konat, Zenonas Norkus, Piotr Przybysz, Piotr Szwochert. (shrink)

This book provides both an introduction to the philosophy of scientific modeling and a contribution to the discussion and clarification of two recent philosophical conceptions of models: artifactualism and fictionalism. These can be viewed as different stances concerning the standard representationalist account of scientific models. By better understanding these two alternative views, readers will gain a deeper insight into what a model is as well as how models function in different sciences. Fictionalism has been a traditional epistemological (...) stance related to antirealist construals of laws and theories, such as instrumentalism and inferentialism. By contrast, the more recent fictional view of models holds that scientific models must be conceived of as the same kind of entities as literary characters and places. This approach is essentially an answer to the ontological question concerning the nature of models, which in principle is not incompatible with a representationalist account of the function of models. The artifactual view of models is an approach according to which scientific models are epistemic artifacts, whose main function is not to represent the phenomena but rather to provide epistemic access to them. It can be conceived of as a non-representationalist and pragmatic account of modeling, which does not intend to focus on the ontology of models but rather on the ways they are built and used for different purposes. The different essays address questions such as the artifactual view of idealization, the use of information theory to elucidate the concepts of abstraction and idealization, the deidealization of models, the nature of scientific fictions, the structural account of representation and the ontological status of structures, the role of surrogative reasoning with models, and the use of models for explaining and predicting physical phenomena. (shrink)

We introduce a new sheaf-theoretic construction called the ideal completion of a category and investigate its logical properties. We show that it satisfies the axioms for a category of classes in the sense of Joyal and Moerdijk [17], so that the tools of algebraic set theory can be applied to produce models of various elementary set theories. These results are then used to prove the conservativity of different set theories over various classical and constructive type theories.

We show that many large cardinal notions up to measurability can be characterized through the existence of certain filters for small models of set theory. This correspondence will allow us to obtain a canonical way in which to assign ideals to many large cardinal notions. This assignment coincides with classical large cardinal ideals whenever such ideals had been defined before. Moreover, in many important cases, relations between these ideals reflect the ordering of the corresponding large cardinal properties both under (...) direct implication and consistency strength. (shrink)

Scientific research is almost always conducted by communities of scientists of varying size and complexity. Such communities are effective, in part, because they divide their cognitive labor: not every scientist works on the same project. Philip Kitcher and Michael Strevens have pioneered efforts to understand this division of cognitive labor by proposing models of how scientists make decisions about which project to work on. For such models to be useful, they must be simple enough for us to understand (...) their dynamics, but faithful enough to reality that we can use them to analyze real scientific communities. To satisfy the first requirement, we must employ idealizations to simplify the model. The second requirement demands that these idealizations not be so extreme that we lose the ability to describe real-world phenomena. This paper investigates the status of the assumptions that Kitcher and Strevens make in their models, by first inquiring whether they are reasonable representations of reality, and then by checking the models' robustness against weakenings of these assumptions. To do this, we first argue against the reality of the assumptions, and then develop a series of agent-based simulations to systematically test their effects on model outcomes. We find that the models are not robust against weakenings of these idealizations. In fact we find that under certain conditions, this can lead to the model predicting outcomes that are qualitatively opposite of the original model outcomes. (shrink)

Two approaches to understanding the idealizations that arise in the Aharonov–Bohm effect are presented. It is argued that a common topological approach, which takes the non-simply connected electron configuration space to be an essential element in the explanation and understanding of the effect, is flawed. An alternative approach is outlined. Consequently, it is shown that the existence and uniqueness of self-adjoint extensions of symmetric operators in quantum mechanics have important implications for philosophical issues. Also, the alleged indispensable explanatory role of (...) said idealizations is examined via a minimal model explanatory scheme. Last, the idealizations involved in the AB effect are placed in a wider philosophical context via a short survey of part of the literature on infinite and essential idealizations. (shrink)

The ArgumentIdealizations and approximations are an indispensable tool for the scientist. This paper argues that idealizations and approximations are equally indispensable for the philosopher of science. In particular, it is shown that the deductive model of scientific theories is an idealization in precisely the same sense that frictionless motion is an idealization in mechanics. By its very nature, an idealization cannot be criticized as not being absolutely true to the facts, for it need not be. Thus, the usual type of (...) criticism levelled against the deductive model is shown to be irrelevant. The main step in the argument consists in using a logic of approximation to clarify the notions of approximate implication and approximate entailment, which are usually rejected as hopelessly vague. More generally, the conception underlying the paper is that the desiderata of science should be formulated in such a way that complying with them could be a matter of degree, and that pragmatic considerations could be taken into account. This conception is motivated by the wish to introduce some quantitative concepts in the philosophy of science, thereby bringing the philosopher's perspective closer to that of the scientist. (shrink)

Highly idealized models, such as the Hawk-Dove game, are pervasive in biological theorizing. We argue that the process and motivation that leads to the introduction of various idealizations into these models is not adequately captured by Michael Weisberg’s taxonomy of three kinds of idealization. Consequently, a fourth kind of idealization is required, which we call hypothetical pattern idealization. This kind of idealization is used to construct models that aim to be explanatory but do not aim to (...) be explanations. (shrink)

ISBN 9042003030 (paperback) NLG 45.00 Main headings: I. Philosophical and methodological problems of the process of cognition.- II. The structure of ideal learning process.- III. Control processes in memory. disillusion.

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)

Natalia Carrillo and Tarja Knuuttila claim that there are two traditions of thinking about idealization offering almost opposite views on their functioning and epistemic status. While one tradition views idealizations as epistemic deficiencies, the other one highlights the epistemic benefits of idealization. Both of them treat idealizations as deliberate misrepresentations, however. They then argue for an artifactual account of idealization, comparing it to the traditional accounts of idealization, and exemplifying it through the Hodgkin and Huxley model of the nerve impulse. (...) From the artifactual perspective, the epistemic benefits and deficiencies introduced by idealization frequently come in a package due to the way idealization draws together different resources in model construction. Accordingly, idealization tends to be holistic in that it is not often easily attributable to some specific parts of the model. They conclude that the artifactual approach offers a unifying view into idealization in that it is able to recover several basic philosophical insights motivating both the deficiency and epistemic benefit accounts, while being simultaneously detached from the idea of distortion by misrepresentation. (shrink)

Ecologists attempt to understand the diversity of life with mathematical models. Often, mathematical models contain simplifying idealizations designed to cope with the blooming, buzzing confusion of the natural world. This strategy frequently issues in models whose predictions are inaccurate. Critics of theoretical ecology argue that only predictively accurate models are successful and contribute to the applied work of conservation biologists. Hence, they think that much of the mathematical work of ecologists is poor science. Against this view, (...) I argue that model building is successful even when models are predictively inaccurate for at least three reasons: models allow scientists to explore the possible behaviors of ecological systems; models give scientists simplified means by which they can investigate more complex systems by determining how the more complex system deviates from the simpler model; and models give scientists conceptual frameworks through which they can conduct experiments and fieldwork. Critics often mistake the purposes of model building, and once we recognize this, we can see their complaints are unjustified. Even though models in ecology are not always accurate in their assumptions and predictions, they still contribute to successful science. (shrink)

Mauricio Suárez and Agnes Bolinska apply the tools of communication theory to scientific modeling in order to characterize the informational content of a scientific model. They argue that when represented as a communication channel, a model source conveys information about its target, and that such representations are therefore appropriate whenever modeling is employed for informational gain. They then extract two consequences. First, the introduction of idealizations is akin in informational terms to the introduction of noise in a signal; for in (...) an idealization we introduce ‘extraneous’ elements into the model that have no correlate in the target. Second, abstraction in a model is informationally equivalent to equivocation in the signal; for in an abstraction we “neglect” in the model certain features that obtain in the target. They conclude that it becomes possible in principle to quantify idealization and abstraction in informative models, although precise absolute quantification will be difficult to achieve in practice. (shrink)

There are two traditions of thinking about idealization offering almost opposite views on their functioning and epistemic status. While one tradition views idealizations as epistemic deficiencies, the other one highlights the epistemic benefits of idealization. Both of these, however, identify idealization with misrepresentation. In this article, we instead approach idealization from the artifactual perspective, comparing it to the distortion-to-reality accounts of idealization, and exemplifying it through the case of the Hodgkin and Huxley model of nerve impulse. From the artifactual perspective, (...) the epistemic benefits and deficiencies introduced by idealization frequently come in a package due to the way idealization draws together different resources in model construction. Accordingly, idealization tends to be holistic in that it is not often easily attributable to just some specific parts of the model. Instead, the idealizing process tightly embeds theoretical concepts and formal tools into the construction of a model. (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)

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)

Political philosophy has traditionally been defined as a normative discipline with a distinctively ideal component, largely informed by moral philosophy. In this paper, I investigate a prominent critique of ideal theory specifically with the goal of resituating the debate within a larger framework in the philosophy of science. I then mount a novel case for how ideal theory should be viewed in terms of scientific modelling. I close with a discussion of how this view can dissolve apparent paradoxes and provide (...) distinct advantages to the political theorist. (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)

Phylogenetic models traditionally represent the history of life as having a strictly-branching tree structure. However, it is becoming increasingly clear that the history of life is often not strictly-branching; lateral gene transfer, endosymbiosis, and hybridization, for example, can all produce lateral branching events. There is thus motivation to allow phylogenetic models to have a reticulate structure. One proposal involves the reconciliation of genealogical discordance. Briefly, this method uses patterns of disagreement – discordance – between trees of different genes (...) to add lateral branching events to phylogenetic trees of taxa, and to estimate the most likely cause of these events. I use this practice to argue for: (1) a need for expanded accounts of multiple-models idealization, (2) a distinction between automatic and manual de-idealization, and (3) recognition that idealization may serve the meso-level aims of science in a different way than hitherto acknowledged. (shrink)

Because they contain idealizations, scientific models are often considered to be misrepresentations of their target systems. An important question is therefore how models can explain the behaviours of these systems. Most of the answers to this question are representationalist in nature. Proponents of this view are generally committed to the claim that models are explanatory if they represent their target systems to some degree of accuracy; in other words, they try to determine the conditions under which idealizations (...) can be made without jeopardizing the representational function of models. In this article, we first outline several forms of this representationalist view. We then argue that this view, in each of these forms, omits an important role of idealizations: that of facilitating the identification of the explanatory components within a model. Via examination of a case study from contemporary astrophysics, we show that one way in which idealizations can do this is by creating a comparison case that s... (shrink)

That many of our most successful scientific theories involve one or more idealizations poses a challenge to traditional models of theory confirmation. One popular response amongst scientific realists is the “improvement model of confirmation”: if tightening up one or more of the idealizations leads to greater predictive accuracy, then this supports the belief that the theory’s inaccuracy is a result of its idealizations and not because it is wrong. In this article I argue that the improvement model is deeply (...) flawed and that therefore idealizations continue to undermine “success-to-truth” arguments for scientific realism. (shrink)

The principal task of the book series Poznan Studies in the Philosophy of the Sciences and the Humanities is to promote those developments in philosophy that respect the tradition of great philosophical ideas, on the one hand, and the manner of philosophical thinking introduced by analytical philosophy, on the other. The aim is to contribute to practicing philosophy as deep as Marxism and as caring about justification as positivism.

Starting with a measurable cardinal κ of the Mitchell order κ++ we construct a model with a precipitous ideal on ℵ1 but without normal precipitous ideals. This answers a question by T. Jech and K. Prikry. In the constructed model there are no Q-point precipitous filters on ℵ1, i. e. those isomorphic to extensions of Cubℵ1.

Our concern is in explaining how and why models give us useful knowledge. We argue that if we are to understand how models function in the actual scientific practice the representational approach to models proves either misleading or too minimal. We propose turning from the representational approach to the artefactual, which implies also a new unit of analysis: the activity of modelling. Modelling, we suggest, could be approached as a specific practice in which concrete artefacts, i.e., (...) class='Hi'>models, are constructed with the help of specific representational means and used in various ways, for example, for the purposes of scientific reasoning, theory construction and design of experiments and other artefacts. Furthermore, in this activity of modelling the model construction is intertwined with the construction of new phenomena, theoretical principles and new scientific concepts. We will illustrate these claims by studying the construction of the ideal heat engine by Sadi Carnot. (shrink)

The article presents an agent-based model of scientific interaction aimed at examining how different degrees of connectedness of scientists impact their efficiency in knowledge acquisition. The model is built on the basis of Zollman’s ABM by changing some of its idealizing assumptions that concern the representation of the central notions underlying the model: epistemic success of the rivalling scientific theories, scientific interaction and the assessment in view of which scientists choose theories to work on. Our results suggest that whether and (...) to what extent the degree of connectedness of a scientific community impacts its efficiency is a highly context-dependent matter since different conditions deem strikingly different results. More generally, we argue that simplicity of ABMs may come at a price: the requirement to run extensive robustness analysis before we can specify the adequate target phenomenon of the model.1 1Introduction2Zollman's 2010 Model3Static versus Dynamic Epistemic Success 3.1Introducing the notion of dynamic epistemic success3.2Implementation and results for the basic setup4Critical Interaction 4.1Introducing critique4.2Implementation and results5Inertia of Inquiry 5.1Introducing rational inertia5.2Implementation and results6Threshold Below Which Theories Are Equally Promising 6.1An inquiry that is even more difficult6.2Implementation and results7Discussion8Conclusion. (shrink)

The equations of state for the ideal classical gas are generalized with two characteristic constants known as the state indices. A simple and complete representation is developed for the super-ideal gas, with explicit results which are general enough to cover a wide range of equilibrium systems and states. Evidence and justification are provided in terms of examples and results of statistical physics. The new model should prove useful for treating problems involving physical behavior and properties which might otherwise call for (...) specialized or advanced methods of statistical mechanics. (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.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)

Abstract Three main concepts of model in science are distinguished: (1) semantical model of a theory; (2) real model of another real thing; (3) mathematical model of a real thing. The last concept is the most important for the empirical sciences. The mathematical model is not identical with a theory: it is an ideal object which is directly described by the theory. We have here an intermediate level between reality and theory.