Hostname: page-component-848d4c4894-nmvwc Total loading time: 0 Render date: 2024-06-15T19:08:47.541Z Has data issue: false hasContentIssue false
  • English
  • Français

Approximation and Idealization: Why the Difference Matters

Published online by Cambridge University Press:  01 January 2022

John D. Norton
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Type
Research Article
Information
Philosophy of Science , Volume 79 , Issue 2 , April 2012 , pp. 207 - 232
Copyright
Copyright © The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

‡

I thank Elay Sheck, Mike Tamir, and Giovanni Valente for helpful discussion and Bob Batterman, Nazim Bouatta, Jeremy Butterfield, Erik Curiel, and Wayne Myrvold (and students of the last two at the University of Western Ontario) for helpful remarks on an earlier draft.

References

Atkinson, D. 2007. “Losing Energy in Classical, Relativistic and Quantum Mechanics.” Studies in History and Philosophy of Modern Physics 38:170–80.CrossRefGoogle Scholar
Batterman, Robert. 2002. The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, and Emergence. New York: Oxford University Press.Google Scholar
Batterman, Robert. 2005. “Critical Phenomena and Breaking Drops: Infinite Idealizations in Physics.” Studies in History and Philosophy of Modern Physics 36:225–44.CrossRefGoogle Scholar
Batterman, Robert. 2010. “Reduction and Renormalization.” In Time, Chance, and Reduction: Philosophical Aspects of Statistical Mechanics, ed. Hüttemann, A. and Ernst, G., 159–79. Cambridge: Cambridge University Press.Google Scholar
Batterman, Robert. 2011. “Emergence, Singularities, and Symmetry Breaking.” Foundations of Physics 41:1031–50.CrossRefGoogle Scholar
Belot, Gordon. 2005. “Whose Devil? Which Details?” Philosophy of Science 72:128–53.CrossRefGoogle Scholar
Butterfield, Jeremy. 2011a. “Emergence, Reduction and Supervenience: A Varied Landscape.” Foundations of Physics 41:920–59.CrossRefGoogle Scholar
Butterfield, Jeremy. 2011b. “Less Is Different: Emergence and Reduction Reconciled.” Foundations of Physics 41:1065–1135.CrossRefGoogle Scholar
Butterfield, Jeremy, and Bouatta, Nazim. 2011. “Emergence and Reduction Combined in Phase Transitions.” PhilSci Archive. http://philsci-archive.pitt.edu/id/eprint/8554.CrossRefGoogle Scholar
Callender, Craig. 2001. “Taking Thermodynamics Too Seriously.” Studies in History and Philosophy of Modern Physics 32:539–53.CrossRefGoogle Scholar
Compagner, A. 1989. “Thermodynamics as the Continuum Limit of Statistical Mechanics.” American Journal of Physics 57:106–17.CrossRefGoogle Scholar
Fisher, Michael. 1982. “Scaling, University and Renormalization Group Theory.” In Critical Phenomena: Lecture Notes in Physics, Vol. 186, ed. Hahne, F., 1–139. Berlin: Springer.Google Scholar
Frigg, Roman, and Hartmann, Stephan. 2009. “Models in Science.” In Stanford Encyclopedia of Philosophy, ed. Zalta, Edward N.. Stanford, CA: Stanford University. http://plato.stanford.edu/archives/sum2009/entries/models-science/.Google Scholar
Hempel, Carl, and Oppenheim, Paul. 1948. “Studies in the Logic of Explanation.” Philosophy of Science 15:135–75. Repr. in Aspects of Scientific Explanation and Other Essays in the Philosophy of Science, ed. C. Hempel (New York: Free Press, 1965), 245–90.Google Scholar
Hille, Einar. 1961. “Pathology of Infinite Systems of Linear First Order Differential Equations with Constant Coefficients.” Annali di Matematica Pura ed Applicata 55:133–48.CrossRefGoogle Scholar
Jones, Nicholaos. 2006. “Ineliminable Idealizations, Phase Transitions, and Irreversibility.” PhD diss., Ohio State University.Google Scholar
Kadanoff, Leo. 2000. Statistical Physics: Statics, Dynamics and Renormalization. Singapore: World Scientific.CrossRefGoogle Scholar
Lanford, Oscar. 1968. “The Classical Mechanics of One-Dimensional Systems of Infinitely Many Particles.” Pt. 1, “An Existence Theorem.” Communications in Mathematical Physics 9:176–91.CrossRefGoogle Scholar
Lanford, Oscar. 1975. “Time Evolution of Large Classical Systems.” In Dynamical Systems, Theory and Applications: Lecture Notes in Theoretical Physics, Vol. 38, ed. Moser, J., 1–111. Heidelberg: Springer.CrossRefGoogle Scholar
Lanford, Oscar. 1981. “The Hard Sphere Gas in the Boltzmann-Grad Limit.” Physica A 106:70–76.CrossRefGoogle Scholar
Lanford, Oscar, and Lebowitz, Joel. 1975. “Time Evolution and Ergodic Properties of Harmonic Systems.” In Dynamical Systems, Theory and Applications: Lecture Notes in Theoretical Physics, Vol. 38, ed. Moser, J., 144–77. Heidelberg: Springer.Google Scholar
Laraudogoitia, Jon Pérez,. 2011. “Supertasks.” In Stanford Encyclopedia of Philosophy, ed. Zalta, Edward N.. Stanford, CA: Stanford University. http://plato.stanford.edu/archives/spr2011/entries/spacetime-supertasks/.Google Scholar
Laudan, Larry. 1981. “A Confutation of Convergent Realism.” Philosophy of Science 48:19–49.CrossRefGoogle Scholar
Le Bellac, Michel, Mortessagne, Fabrice, and Batrouni, G. George. 2004. Equilibrium and Non-equilibrium Statistical Thermodynamics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Lee, Chunghyoung. 2011. “Nonconservation of Momentum in Classical Mechanics.” Studies in History and Philosophy of Modern Physics 42:68–73.CrossRefGoogle Scholar
Liu, Chuang. 1999. “Explaining the Emergence of Cooperative Phenomena.” Philosophy of Science 66 (Proceedings): S92–S106.CrossRefGoogle Scholar
Liu, Chuang. 2004. “Approximations, Idealizations, and Models in Statistical Mechanics.” Erkenntnis 60:235–63.CrossRefGoogle Scholar
McMullin, Ernan. 1985. “Galilean Idealization.” Studies in History and Philosophy of Science 16:247–73.CrossRefGoogle Scholar
Menon, Tarun, and Callender, Craig. 2011. “Turn and Face the Strange … Ch-ch-changes: Philosophical Questions Raised by Phase Transitions.” PhilSci Archive. http://philsci-archive.pitt.edu/id/eprint/8757.Google Scholar
Nagel, Ernest. 1961. The Structure of Scientific Theories: Problems in the Logic of Scientific Explanation. New York: Harcourt Brace & Co.Google Scholar
Norton, John D. 1999. “A Quantum Mechanical Supertask.” Foundations of Physics 29:1265–1302.CrossRefGoogle Scholar
Norton, John D.. 2011. “Dense and Sparse Meaning Spaces.” Unpublished manuscript, Department of History and Philosophy of Science, University of Pittsburgh.Google Scholar
Ruelle, David. 1999/2007. Statistical Mechanics: Rigorous Results. Repr. Singapore: World Scientific.CrossRefGoogle Scholar
Ruelle, David. 2004. Thermodynamic Formalism. 2nd ed. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Schaffner, Kenneth F. 1967. “Approaches to Reduction.” Philosophy of Science 34:137–47.CrossRefGoogle Scholar
Weisberg, Michael. 2007. “Three Kinds of Idealization.” Journal of Philosophy 104:639–59.CrossRefGoogle Scholar
Yeomans, J. M. 1992/2002. Statistical Mechanics of Phase Transitions. Repr. Oxford: Clarendon.Google Scholar