Approximation,Idealization, and Laws of Nature

Traditional theories construe approximate truth or truthlikeness as a measure of closeness to facts, singular facts, and idealization as an act of either assuming zero of otherwise very small differences from facts or imagining ideal conditions under which scientific laws are either approximately true or will be so when the conditions are relaxed. I first explain the serious but not insurmountable difficulties for the theories of approximation, and then argue that more serious and perhaps insurmountable difficulties for the theory of idealization force us to sever its close tie to approximation. This leads to an appreciation of lawlikeness as a measure of closeness to laws, which I argue is the real measure of idealization whose main purpose is to carve nature at its joints. This revised version was published online in June 2006 with corrections to the Cover Date.     

Approximations, Idealizations, and Models in Statistical Mechanics

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.     

Analytic Idealizations and the Disavowed: Winnicott,His Patients,and Us

This paper explores the dynamics of mutual idealization within the analytic dyad. While the subject of idealization is not a new one, very little has been written about the analyst's own participation in patients' idealizations or her vulnerability to idealizing the patient. I use both published and unpublished materials to muse about coconstructed idealizations as they appear to have coalesced in Winnicott's treatment of Masud Khan and Harry Guntrip. Because the notion that we might be involved in being idealized by our patients—or in idealizing them—collides with our professional vision, we tend to be highly resistant to acknowledging these dynamics and often turn to denigration when they are unmasked. I argue for the ubiquity of idealization's dynamics and against the demonization of Winnicott.     

How to avoid inconsistent idealizations

Idealized scientific representations result from employing claims that we take to be false. It is not surprising, then, that idealizations are a prime example of allegedly inconsistent scientific representations. I argue that the claim that an idealization requires inconsistent beliefs is often incorrect and that it turns out that a more mathematical perspective allows us to understand how the idealization can be interpreted consistently. The main example discussed is the claim that models of ocean waves typically involve the false assumption that the ocean is infinitely deep. While it is true that the variable associated with depth is often taken to infinity in the representation of ocean waves, I explain how this mathematical transformation of the original equations does not require the belief that the ocean being modeled is infinitely deep. More generally, as a mathematical representation is manipulated, some of its components are decoupled from their original physical interpretation.     

Idealizations and scientific understanding

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

Essentialism and the Necessity of the Laws of Nature

In this paper I discuss and evaluate different arguments for the view that the laws of nature are metaphysically necessary. I conclude that essentialist arguments from the nature of natural kinds fail to establish that essences are ontologically more basic than laws, and fail to offer an a priori argument for the necessity of all causal laws. Similar considerations carry across to the argument from the dispositionalist view of properties, which may end up placing unreasonable constraints on property identity across possible worlds. None of my arguments preclude the possibility that the laws may turn out to be metaphysically necessary after all, but I argue that this can only be established by a posteriori scientific investigation. I therefore argue for what may seem to be a surprising conclusion: that a fundamental metaphysical question – the modal status of laws of nature – depends on empirical facts rather than purely on a priori reasoning.     

Metaphysics within Chemical Physics: The Case of Ab Initio Molecular Dynamics

This paper combines naturalized metaphysics and a philosophical reflection on a recently evolving interdisciplinary branch of quantum chemistry, ab initio molecular dynamics. Bridging the gaps among chemistry, physics, and computer science, this cutting-edge research field explores the structure and dynamics of complex molecular many-body systems through computer simulations. These simulations are allegedly crafted solely by the laws of fundamental physics, and are explicitly designed to capture nature as closely as possible. The models and algorithms employed, however, involve many approximations and significant degrees of idealization of their target systems. Therefore, for philosophers of science the pivotal question of whether relying only on the fundamental laws of physics supports a reductionist or realist stance arises. One conceivable answer to this question is that the irreducible approximations and idealizations support rather anti-realist positions. After reviewing an influential attitude in the philosophy of computer simulations and the debate concerning scientific realism, I offer a fair interpretation of such ab initio modelling in quantum chemistry within a naturalistic metaphysical framework that gives rise to a specific type of ontic structural realism.     

Explaining with Models: The Role of Idealizations

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 serves to highlight the relevant features of the target system.     

Idealized laws,antirealism, and applied science: A case in hydrogeology

When is a law too idealized to be usefully applied to a specific situation? To answer this question, this essay considers a law in hydrogeology called Darcy's Law, both as it is used in what is called the symmetric-cone model, and as it is used in equations to determine a well's groundwater velocity and hydraulic conductivity. After discussing Darcy's law and its applications, the essay concludes that this idealized law, as well as associated models and equations in hydrogeology, are not realistic in the sense required by the D-N account. They exhibit what McMullin calls mathematical idealization, construct idealization, empirical-causal idealization, and subjunctive-causal idealization. Yet this lack of realism in hydrogeology is problematic for reasons unrelated to the status of the D-N account. These idealizations are also problematic in applied situations. Their problems require developing two supplemental criteria, necessary for their productive application.     

Idealized and perspectival representations: some reasons for making a distinction

I argue that an adequate understanding of the practice of constructing models in physics requires a distinction between two strategies that are commonly both labeled ‘idealization’. The formal characteristic of both methods is to let a parameter in the equations for a target system go to zero. But the discussion of examples from various applications of perturbation theory shows that there is in general a difference with respect to the aims such limiting procedures are supposed to serve; and with different aims comes the need to characterize the means (the interpretation of the limits) differently. I therefore suggest that we distinguish ‘idealizations’ from ‘perspectives’ or perspectival representations.     

Genuine Violations of Laws

Could laws of nature be violated, in the sense that some proposition is both a law and false? I argue that opponents of regularity theories of laws should accept the metaphysical possibility of such genuine violations. I begin with a clarification of this claim. The main argument is then developed in three steps. I first argue that opponents of regularity theory should endorse the modal-essence view: certain modal principles are essential to the laws of nature. Second, I argue that the modal-essence view entails sophisticated modal primitivism. Third, I argue from sophisticated primitivism to the metaphysical possibility of genuine violations of laws.     

Idealization and abstraction in scientific modeling

I argue that we cannot adequately characterize idealization and abstraction and the distinction between the two on the grounds that they have distinct semantic properties. By doing so, on the one hand, we focus on the conceptual products of the two processes in making the distinction and we overlook the importance of the nature of the thought processes that underlie model-simplifying assumptions. On the other hand, we implicitly rely on a sense of abstraction as subtraction, which is unsuitable for explicating scientific model construction. Instead, I argue that a sense of abstraction as extraction is more suitable. Finally, I suggest a different way to distinguish the two processes that avoids these problems. Namely, that both idealization and abstraction could be understood as particular modes of application of the same cognitive process: selective attention.

     

Applying idealized scientific theories to engineering

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

The true and the false

A dispositional property is a tendency, or potency, to manifest some characteristic behaviour in some appropriate context. The mainstream view in the twentieth century was that such properties are to be explained in terms of more fundamental non-dispositional properties, together with the laws of nature. In the last few decades, however, a rival view has become popular, according to which some properties are essentially dispositional in nature, and the laws of nature are to be explained in terms of these fundamental dispositions. The supposed ability of fundamental dispositions to ground natural laws is one of the most attractive features of the dispositional essentialist position. In this paper, however, I cast doubt on the ability of dispositional essences to ground the laws of nature. In particular I argue that the dispositional essentialist position is not able to coherently respond—sympathetically or otherwise—to Cartwright's challenge that there are no true general laws of nature.     

Hume’s definitions of ‘Cause’: Without idealizations,within the bounds of science

Interpreters have found it exceedingly difficult to understand how Hume could be right in claiming that his two definitions of ‘cause’ are essentially the same. As J. A. Robinson points out, the definitions do not even seem to be extensionally equivalent. Don Garrett offers an influential solution to this interpretative problem, one that attributes to Hume the reliance on an ideal observer. I argue that the theoretical need for an ideal observer stems from an idealized concept of definition, which many interpreters, including Garrett, attribute to Hume. I argue that this idealized concept of definition indeed demands an unlimited or infinite ideal observer. But there is substantial textual evidence indicating that Hume disallows the employment of idealizations in general in the sciences. Thus Hume would reject the idealized concept of definition and its corresponding ideal observer. I then put forward an expert-relative reading of Hume’s definitions of ‘cause’, which also renders both definitions extensionally equivalent. On the expert-relative reading, the meaning of ‘cause’ changes with better observations and experiments, but it also allows Humean definitions to play important roles within our normative practices. Finally, I consider and reject Henry Allison’s argument that idealized definitions and their corresponding infinite minds are necessary for expert reflection on the limitations of current science.     

Are Mathematical Theories Reducible to Non-analytic Foundations?

In this article I intend to show that certain aspects of the axiomatical structure of mathematical theories can be, by a phenomenologically motivated approach, reduced to two distinct types of idealization, the first-level idealization associated with the concrete intuition of the objects of mathematical theories as discrete, finite sign-configurations and the second-level idealization associated with the intuition of infinite mathematical objects as extensions over constituted temporality. This is the main standpoint from which I review Cantor’s conception of infinite cardinalities and also the metatheoretical content of some later well-known theorems of mathematical foundations. These are, the Skolem-Löwenheim Theorem which, except for its importance as such, it is also chosen for an interpretation of the associated metatheoretical paradox (Skolem Paradox), and Gödel’s (first) incompleteness result which, notwithstanding its obvious influence in the mathematical foundations, is still open to philosophical inquiry. On the phenomenological level, first-level and second-level idealizations, as above, are associated respectively with intentional acts carried out in actual present and with certain modes of a temporal constitution process.     

Response to Phillips,Hopkins, and Berman

Adam Phillips asks why we need to engage in professional policing. He exceeds my own professional comfort zone when he suggests that a great thing about psychoanalysis is that “it does not necessarily make people better.” I make a plea for a measure of professional idealism that takes account of the analyst's power. In her discussion, Linda Hopkins provides fascinating anecdotes that support my ideas about Masud Khan's analysis. Hopkins also argues for the value of idealization in therapeutic process, noting that I excessively emphasize its problematics. I agree with Hopkins's perspective and muse about why my paper reads otherwise. Emanuel Berman distinguishes institutional from individual idealizations and argues for the value of the latter while underscoring the difference between de-idealization and devaluation. I query the inevitably problematic nature of institutional idealizations.