Philosophers of science increasingly recognize the importance of idealization: the intentional introduction of distortion into scientific theories. Yet this recognition has not yielded consensus about the nature of idealization. e literature of the past thirty years contains disparate characterizations and justifications, but little evidence of convergence towards a common position.

Recent work by Robert Batterman and Alexander Rueger has brought attention to cases in physics in which governing laws at the base level “break down” and singular limit relations obtain between base- and upper-level theories. As a result, they claim, these are cases with emergent upper-level properties. This paper contends that this inference—from singular limits to explanatory failure, novelty or irreducibility, and then to emergence—is mistaken. The van der Pol nonlinear oscillator is used to show that there can be a (...) full explanation of upper-level properties entirely in base-level terms even when singular limits are present. Whether upper-level properties are emergent depends not on the presence of a singular limit but rather on details of the ampliative approximation methods used. The paper suggests that focusing on explanatory deficiency at the base level is key to understanding emergence in physics. (shrink)

Robert Batterman and others have argued that certain idealizing explanations have an asymptotic form: they account for a state of affairs or behavior by showing that it emerges “in the limit”. Asymptotic idealizations are interesting in many ways, but is there anything special about them as idealizations? To understand their role in science, must we augment our philosophical theories of idealization? This paper uses simple examples of asymptotic idealization in population genetics to argue for an affirmative answer and proposes a (...) general schema for asymptotic idealization, drawing on insights from Batterman’s treatment and from John Norton’s subsequent critique. (shrink)

In this essay, I provide an overview of the debate on infinite and essential idealizations in physics. I will first present two ostensible examples: phase transitions and the Aharonov– Bohm effect. Then, I will describe the literature on the topic as a debate between two positions: Essentialists claim that idealizations are essential or indispensable for scientific accounts of certain physical phenomena, while dispensabilists maintain that idealizations are dispensable from mature scientific theory. I will also identify some attempts at finding a (...) middle ground between the essentialists and dispensabilists camps. Finally, I will raise questions for future research on essential and infinite idealizations via the notion of exploration. (shrink)

It is proposed that we use the term “approximation” for inexact description of a target system and “idealization” for another system whose properties also provide an inexact description of the target system. Since systems generated by a limiting process can often have quite unexpected, even inconsistent properties, familiar limit systems used in statistical physics can fail to provide idealizations, but are merely approximations. A dominance argument suggests that the limiting idealizations of statistical physics should be demoted to approximations.

Despite all the criticism showered on Nagel’s classic account of reduction, it meets a fundamental desideratum in an analysis of reduction that is difficult to question, namely of providing for a proper identification of the reducing theory. This is not clearly accommodated in radically different accounts. However, the same feature leads me to question Nagel’s claim that the reducing theory can be separated from the putative bridge laws, and thus to question his notion of heterogeneous reduction. A further corollary to (...) the requirement that all the necessary conditions be incorporated in an adequate formulation of the putative reducing theory is that the standard example of gas temperature is not reducible to average molecular kinetic energy. As originally conceived, Nagel’s conception of reduction takes no account of approximate reasoning and this failure has certainly restricted its applicability, perhaps to the point of making it unrealistic as a model of reduction in science. I suggest approximation can be accommodated by weakening the original requirement of deduction without jeopardizing the fundamental desideratum. Finally, I turn to briefly consider the idea sometimes raised of the ontological reducibility of chemistry. (shrink)

The history of the hydrogen bond provides a good example of the of an important chemical concept. It illustrates the interplay between empirical and theoretical approaches to the problem of delimiting what has proved to be quite an elusive notion, with chemists whittling away at the particular sorts of case with a view to obtaining a precise, unitary concept. Even though there is a return to a more theoretically inspired notion in more recent research, empirical characterisations remain a feature of (...) the report of a Task Group recently set up by the IUPAC to reconsider the definition of the hydrogen bond, and this situation—by no means unusual for chemical concepts and principles—is unlikely to change in the foreseeable future. These developments are reviewed in this paper, which includes an extended discussion of the enormous significance hydrogen bonding has for the philosopher’s standard example of a “natural kind”, water. There is little to suggest a reduction to what philosophers of physics are pleased to call fundamental principles, and the details raise further questions about what essentialists could possibly have in mind when talking about the microscopic essence of water. (shrink)

This book on the philosophy of science argues for an empiricism, opposed to the tradition of David Hume, in which singular rather than general causal claims are primary; causal laws express facts about singular causes whereas the general causal claims of science are ascriptions of capacities or causal powers, capacities to make things happen. Taking science as measurement, Cartwright argues that capacities are necessary for science and that these can be measured, provided suitable conditions are met. There are case studies (...) from both econometrics and quantum mechanics. (shrink)

This paper first queries what type of concept of emergence, if any, could be connected with the different chemical activities subsumed under the label ‘quantum chemistry’. In line with Roald Hoffmann, we propose a ‘rotation to research laboratory’ in order to point out how practitioners hold a molecular whole, its parts, and the surroundings together within their various methods when exploring chemical transformation. We then identify some requisite contents that a concept of emergence must incorporate in order to be coherent (...) from the standpoint of the scientific practices involved. In this respect, we finally propose a relational form of emergence which pays attention to the constitutive role of the modes of intervention and to the co-definition of the levels of organization. No metaphysical distinction between the higher and basic levels of organization is supposed, but only a plurality of modes of access. Moreover, these modes of access are not construed as mere ways of revealing intrinsic patterns of organization but, on the contrary, are considered to be active elements on which the constitution of those patterns depends. What is at stake in this paper is therefore not an ontological form of emergence but an agnostic one which fits what chemists do in their daily work. (shrink)

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

This paper looks at emergence in physical theories and argues that an appropriate way to understand socalled “emergent protectorates” is via the explanatory apparatus of the renormalization group. It is argued that mathematical singularities play a crucial role in our understanding of at least some well-defined emergent features of the world.

By their own account, physicalists are committed to the claim that physics is causally complete, or closed. The claim is presented as an empirical one. However, detailed and explicit empirical arguments for the claim are rare. I argue that molecular models are a key source of evidence but that, on closer inspection, they do not support the completeness claim.

Differing views on reduction are briefly reviewed and a suggestion is made for a working definition of 'approximate reduction'. Ab initio studies in quantum chemistry are then considered, including the issues of convergence and error bounds. This includes an examination of the classic studies on CH2 and the recent work on the Si2C molecule. I conclude that chemistry has not even been approximately reduced.