Advertisement

Synthese

pp 1–12 | Cite as

Minimal approximations and Norton’s dome

  • Samuel C. Fletcher
S.I.: Infinite Idealizations in Science
  • 54 Downloads

Abstract

In this note, I apply Norton’s (Philos Sci 79(2):207–232, 2012) distinction between idealizations and approximations to argue that the epistemic and inferential advantages often taken to accrue to minimal models (Batterman in Br J Philos Sci 53:21–38, 2002) could apply equally to approximations, including “infinite” ones for which there is no consistent model. This shows that the strategy of capturing essential features through minimality extends beyond models, even though the techniques for justifying this extended strategy remain similar. As an application I consider the justification and advantages of the approximation of a inertial reference frame in Norton’s dome scenario (Philos Sci 75(5):786–798, 2008), thereby answering a question raised by Laraudogoitia (Synthese 190(14):2925–2941, 2013).

Keywords

Minimal models Idealization Approximation Determinism Classical physics Inertial reference frames 

References

  1. Batterman, R. W. (2002). Asymptotics and the role of minimal models. British Journal for the Philosophy of Science, 53, 21–38.CrossRefGoogle Scholar
  2. Fletcher, S. C. (2012). What counts as a Newtonian system? The view from Norton’s dome. European Journal for Philosophy of Science, 2(3), 275–297.CrossRefGoogle Scholar
  3. Fletcher, S. C. (2017). Indeterminism, gravitation, and spacetime theory. In G. Hofer-Szabó & L. Wroński (Eds.), Making it formally explicit: Probability, causality and indeterminism (pp. 179–191). Cham: Springer.CrossRefGoogle Scholar
  4. Goldenfeld, N. (1992). Lectures on phase transitions and the renormalization group. Reading, MA: Addison-Wesley.Google Scholar
  5. Knuuttila, T., & Boon, M. (2011). How do models give us knowledge? The case of Carnot’s ideal heat engine. European Journal for Philosophy of Science, 1, 309–334.CrossRefGoogle Scholar
  6. Korolev, A. (2007a). Indeterminism, asymptotic reasoning, and time irreversibility in classical physics. Philosophy of Science, 74(5), 943–956.CrossRefGoogle Scholar
  7. Korolev, A. (2007b). The Norton-type Lipschitz-indeterministic systems and elastic phenomena: Indeterminism as an artefact of infinite idealizations. In Philosophy of Science Association, 21st Biennial Meeting (Pittsburgh, PA). http://philsci-archive.pitt.edu/4314/.
  8. Laraudogoitia, J. P. (2013). On Norton’s dome. Synthese, 190(14), 2925–2941.CrossRefGoogle Scholar
  9. Malament, D. B. (2008). Norton’s slippery slope. Philosophy of Science, 75(5), 799–816.CrossRefGoogle Scholar
  10. Norton, J. D. (2008). The dome: An unexpectedly simple failure of determinism. Philosophy of Science, 75(5), 786–798.CrossRefGoogle Scholar
  11. Norton, J. D. (2012). Approximation and idealization: Why the difference matters. Philosophy of Science, 79(2), 207–232.CrossRefGoogle Scholar
  12. Norton, J. D. (2014). Infinite idealizations. In M. C. Galavotti, E. Nemeth, & F. Stadler (Eds.), European philosophy of science—Philosophy of science in Europe and the Viennese heritage (pp. 197–210). Cham: Springer.CrossRefGoogle Scholar
  13. Tamir, M. (2012). Proving the principle: Taking geodesic dynamics too seriously in Einstein’s theory. Studies in History and Philosophy of Modern Physics, 43(2), 137–154.CrossRefGoogle Scholar
  14. Thornton, S . T., & Marion, J . B. (2004). Classical dynamics of particles and systems (5th ed.). Belmont, CA: Brooks/Cole—Thomson Learning.Google Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of MinnesotaTwin Cities, MinneapolisUSA
  2. 2.MCMP, LMU MunichMunichGermany

Personalised recommendations