Skip to main content
Log in

Invariance, Symmetry And Rationality

  • Published:
Synthese Aims and scope Submit manuscript

Abstract

Using recent work by Forster and Sober, I identify circumstances in which appeals to symmetries in physical laws are rational with respect to the aim of predictive accuracy. I then consider a Bayesian account of symmetry, and argue that such an account faces serious problems explaining when and why appeals to symmetry would be rational.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Akaike, H.: 1973, 'Information Theory and an Extension of the Maximum Likelihood Principle', in B. N. Petrov and F. Csaki (eds), Second International Symposium on Information Theory, Akademiai Kiado, Budapest, pp. 267–281.

    Google Scholar 

  • Akaike, H.: 1979, 'Likelihood and the Bayes Procedures', in J. M. Bernardo, M. G. De-Groot, D. V. Lindley, and A. F. M. Smith (eds), Bayesian Statistics: Proceedings of the First International Meeting, University Press, Valencia, Spain (1980), pp. 143–166

  • Bandyopadhyay, P., R. Boik and P. Basu: 1996, 'The Curve Fitting Problem: A Bayesian Approach', Philosophy of Science 63(Suppl.), S264–S272.

    Google Scholar 

  • Berger, J. O. and L. Pericchi: 1996, 'The Intrinsic Bayes Factor for Model Selection and Prediction', The Journal of the American Statistical Association 91, 109–122.

    Google Scholar 

  • Bhansali, R. J. and D. Y. Downham: 1977, 'Some Properties of the Order of an Autoregressive Model Selected by a Generalization of Akaike's EPF Criterion', Biometrika 64(3), 547–551.

    Google Scholar 

  • Box, G.: 1979, 'Sampling Inference, Bayes's Inference, and Robustness in the Advancement of Learning', in Bernardo et al. (eds), 1980, pp. 366–381.

  • Box, G.: 1980, 'Sampling and Bayes' Inference in Scientific Modelling and Robustness', Journal of the Royal Statistical Society Series A 143(4), 383–430.

    Google Scholar 

  • Craméer, H.: 1946, Mathematical Methods of Statistics, Princeton University Press, Princeton.

  • Earman, J.: 1992, Bayes or Bust?: A Critical Examination of Bayesian Confirmation Theory, Cambridge University Press, Cambridge.

  • Feynman, R. P., R. Leighton, and M. Sands: 1965, The Feynman Lectures on Physics, Addison-Wesley, Reading, MA.

  • Forster, M.: 1994, 'Non-Bayesian Foundations for Statistical Estimation, Prediction, and the Ravens Example', Erkenntnis 40, 357–376.

    Google Scholar 

  • Foster, M.: 1995, 'Bayes and Bust: Simplicity as a Problem for a Probabilist's Approach to Confirmation', The British Journal for the Philosophy of Science 46, 399–424.

    Google Scholar 

  • Foster, M.: 1995, 'The Golfer's Dilemma: A Reply to Kukla on Curve-Fitting', The British Journal for the Philosophy of Science 46, pp. 348–360.

    Google Scholar 

  • Forster, M. and E. Sober: 1994, 'How to Tell when Simpler, More Unified, or Less Ad Hoc Theories will Provide More Accurate Predictions', The British Journal for the Philosophy of Science 45, 1–35.

    Google Scholar 

  • French, S. and H. Kamminga (eds): 1993, Correspondence, Invariance and Heuristics: Essay in Honour of Heintz Post, Kluwer, Dordrecht.

  • Hegstron, R. A. and Kondepudi, D. K.: 1990, 'The Handedness of the Universe', Scientific American 98–105.

  • Hon, G.: 1993, 'The Unnatural Nature of the Laws of Nature', in French and Kamminga (eds) 1993, pp. 171–187.

  • Houtappel, R. M. F., H. van Dam, and E. P. Wigner: 1965, 'The Conceptual Basis and Use of the Geometric Invariance Principles', Review of Modern Physics 37, 595–631.

    Google Scholar 

  • Hughes, I. S.: 1993, Elementary Particles, 3rd edn, Cambridge University Press, Cambridge.

  • Icke, V.: 1995, The Force of Symmetry, Cambridge University Press, Cambridge.

  • Lehmann, E. L.: 1983, Theory of Point Estimation, John Wiley, New York.

  • Linhart, H. and W. Zucchini: 1996, Model Selection, John Wiley, New York.

  • Kass, R. E. and A. E. Raftery: 1995, 'Bayes Factors, Journal of the American Statistical Association 90(430), 773–795.

    Google Scholar 

  • Kruse, M.: 1997, 'Variation and the Accuracy of Prediction', The British Journal for the Philosophy of Science 48, 181–193.

    Google Scholar 

  • Mach, E.: [1893] 1974, The Science of Mechanics, Open Court: LaSalle, IL.

    Google Scholar 

  • O'Hagan, A.: 1995, 'Fractoral Bayes Factors for Model Comparison (with discussion)', Journal of the Royal Statistical Society Series B, 57, 99–138.

    Google Scholar 

  • Popper, K.: 1959, The Logic of Scientific Discovery, Basic Books, New York.

  • Post, H. R.: [1971] 1993, 'Correspondence, Invariance and Heuristics', reprinted in S. French and H. Kamminga (eds), 1993, pp. 1–43.

  • Redhead, M.: 1975, 'Symmetry in Intertheory Relations', Synthese 32, 77–112.

    Google Scholar 

  • Robert, C. P.: 1994, The Bayesian Choice: A Decision-Theoretic Motivation, Springer-Verlag, New York.

  • Sakamoto, Y., M. Ishiguro, and G. Kitagawa: 1986, Akaike Information Criterion Statistics, Kluwer, Dordrecht.

  • Schwarz, G.: 1978, 'Estimating the Dimension of a Model', The Annals of Statistics 6(2), 461–464.

    Google Scholar 

  • Smith, A. F. M. and D. J. Spiegelhalter: 1980, 'Bayes Factors and Choice Criteria for Linear Models', Journal of the Royal Statistical Society Series B, 213–220.

  • Van Fraassen, B. C.: 1989, Laws and Symmetry, Clarendon Press, Oxford.

  • Weyl, H.: 1973, Symmetry, Princeton University Press, Princeton, NJ.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kruse, M. Invariance, Symmetry And Rationality. Synthese 122, 337–357 (2000). https://doi.org/10.1023/A:1005048811720

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1005048811720

Keywords

Navigation