Approximation and Idealization: Why the Difference Matters*

@article{Norton2012ApproximationAI,
  title={Approximation and Idealization: Why the Difference Matters*},
  author={J. Norton},
  journal={Philosophy of Science},
  year={2012},
  volume={79},
  pages={207 - 232}
}
  • J. Norton
  • Published 2012
  • Mathematics
  • Philosophy of Science
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 processes used in statistical physics can fail to provide idealizations but merely provide approximations. 
The infinite limit as an eliminable approximation for phase transitions
Abstract It is generally claimed that infinite idealizations are required for explaining phase transitions within statistical mechanics (e.g. Batterman 2011). Nevertheless, Menon and Callender (2013)Expand
The role of idealizations in the Aharonov–Bohm effect
TLDR
The goal of this paper is to bring to the attention of the philosophers of science these and other aspects of the AB effect which are neglected or inadequately treated in literature. Expand
Abstraction and its Limits: Finding Space for Novel Explanation.
TLDR
It is argued that changes of the quantities in terms of which the authors describe a system can lead to novel explanations that are not merely abstractions of some more detailed picture. Expand
Two Approaches to Fractional Statistics in the Quantum Hall Effect: Idealizations and the Curious Case of the Anyon
This paper looks at the nature of idealizations and representational structures appealed to in the context of the fractional quantum Hall effect, specifically, with respect to the emergence of anyonsExpand
Becoming Large, Becoming Infinite: The Anatomy of Thermal Physics and Phase Transitions in Finite Systems
This paper presents an in-depth analysis of the anatomy of both thermodynamics and statistical mechanics, together with the relationships between their constituent parts. Based on this analysis,Expand
The structure of asymptotic idealization
TLDR
This paper uses simple examples of asymptotic idealization in population genetics to argue for an affirmative answer and proposes a general schema for asymptic idealization, drawing on insights from Batterman's treatment and from John Norton’s subsequent critique. Expand
Studies in History and Philosophy of Modern Physics
Recent discussions of emergence in physics have focussed on the use of limiting relations, and often particularly on singular or asymptotic limits. We discuss a putative example of emergence thatExpand
Infinitesimal idealization, easy road nominalism, and fractional quantum statistics
TLDR
This essay argues that the phenomena of fractional quantum statistics bears negatively on Mary Leng’s proposed path to easy road nominalism, thereby partially defending Mark Colyvan's claim that there is no easy road to nominalism. Expand
Talk about toy models
TLDR
The status of toy models is elevated by distinguishing them from approximations and idealisations, by highlighting and elaborating on several ways the Kac ring, a simple statistical mechanical model, is used as a toy model, and by explaining why toy models can be used to successfully carry out important work without performing a representational function. Expand
Emergence Without Limits: the Case of Phonons
Abstract Recent discussions of emergence in physics have focussed on the use of limiting relations, and often particularly on singular or asymptotic limits. We discuss a putative example of emergenceExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 49 REFERENCES
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 theExpand
Critical phenomena and breaking drops: Infinite idealizations in physics
Thermodynamics and Statistical Mechanics are related to one another through the so-called "thermodynamic limit'' in which, roughly speaking the number of particles becomes infinite. At criticalExpand
The hard sphere gas in the Boltzmann-Grad limit
This talk will review what has been rigorously proved about the time-dependent behaviour of a gas of classical hard spheres in the limiting regime where the number n of particles per unit volumeExpand
Time evolution of large classical systems
We begin with some very general and elementary remarks about nonequilibrium statistical mechanics. We then establish our notation for discussing finite systems of classical point particles, constructExpand
Ineliminable idealizations, phase transitions, and irreversibility
The dissertation examines two putative explanations from statistical mechanics with the aim of understanding the nature and role of idealizations in those accounts, namely, the Yang-Lee account ofExpand
Taking Thermodynamics Too Seriously
This paper discusses the mistake of understanding the laws and concepts of thermodynamics too literally in the foundations of statistical mechanics. Arguing that this error is still pervasive (thoughExpand
The devil in the details : asymptotic reasoning in explanation, reduction, and emergence
Batterman examines a form of scientific reasoning called asymptotic reasoning, which he argues has important consequences for our understanding of the scientific process as a whole. He argues thatExpand
Reduction and Renormalization
This paper discusses the alleged reduction of Thermodynamics to Statistical Mechanics. It includes an historical discussion of J. Willard Gibbs' famous caution concerning the connections betweenExpand
Losing energy in classical, relativistic and quantum mechanics.
A Zenonian supertask involving an infinite number of colliding balls is considered, under the restriction that the total mass of all the balls is finite. Classical mechanics leads to the conclusionExpand
Whose Devil? Which Details?*
  • G. Belot
  • Philosophy
  • Philosophy of Science
  • 2005
Batterman has recently argued that fundamental theories are typically explanatorily inadequate, in that there exist physical phenomena whose explanation requires that the conceptual apparatus of aExpand
...
1
2
3
4
5
...