Synthese

, Volume 179, Issue 2, pp 321–338

Confirmation and reduction: a Bayesian account

Open Access
Article

Abstract

Various scientific theories stand in a reductive relation to each other. In a recent article, we have argued that a generalized version of the Nagel-Schaffner model (GNS) is the right account of this relation. In this article, we present a Bayesian analysis of how GNS impacts on confirmation. We formalize the relation between the reducing and the reduced theory before and after the reduction using Bayesian networks, and thereby show that, post-reduction, the two theories are confirmatory of each other. We then ask when a purported reduction should be accepted on epistemic grounds. To do so, we compare the prior and posterior probabilities of the conjunction of both theories before and after the reduction and ask how well each is confirmed by the available evidence.

Keywords

Nagelian reduction Bayesian epistemology Thermodynamics and statistical mechanics Bayesian network models 

References

  1. Batterman R. W. (2002) The devil in the details: Asymptotic reasoning in explanation, reduction, and emergence. Oxford University Press, OxfordGoogle Scholar
  2. Bovens L., Hartmann S. (2003) Bayesian epistemology. Oxford University Press, OxfordGoogle Scholar
  3. Callender C. (2001) Taking thermodynamics too seriously. Studies in the History and Philosophy of Modern Physics 32: 539–553CrossRefGoogle Scholar
  4. Dizadji-Bahmani, F., Frigg, R., & Hartmann, S. (2010). Who is afraid of Nagelian reduction? Erkenntnis (forthcoming).Google Scholar
  5. Earman J. (1992) Bayes or bust?. The MIT Press, Cambridge, MAGoogle Scholar
  6. Fitelson B. (1999) The plurality of Bayesian measures of confirmation and the problem of measure sensitivity. Philosophy of Science 66: S362–S378CrossRefGoogle Scholar
  7. Frigg R. (2008) A field guide to recent work on the foundations of statistical mechanics. In: Rickles D. (eds) The Ashgate companion to contemporary philosophy of physics. Ashgate, London, pp 99–196Google Scholar
  8. Hájek A., Hartmann S. (2010) Bayesian epistemology. In: Dancy J. (eds) A companion to epistemology (pp. 93–106). Blackwell, OxfordGoogle Scholar
  9. Hartmann S. (1999) Models and stories in Hadron physics. In: Morgan M., Morrison M. (eds) Models as mediators. Cambridge University Press, Cambridge, pp 326–346CrossRefGoogle Scholar
  10. Hartmann S., Sprenger J. (2010) Bayesian epistemology, to appear. In: Bernecker S., Pritchard D. (eds) Routledge companion to epistemology. Routledge, LondonGoogle Scholar
  11. Howson C., Urbach P. (2005) Scientific reasoning: The Bayesian approach. Open Court, La SalleGoogle Scholar
  12. Klein C. (2009) Reduction without reductionism: A defence of Nagel on connectability. Philosophical Quarterly 59: 39–53CrossRefGoogle Scholar
  13. Nagel E. (1961) The structure of science. Routledge and Keagan Paul, LondonGoogle Scholar
  14. Neapolitan R. (2003) Learning Bayesian networks. Prentice Hall, Upper Saddle River, NJGoogle Scholar
  15. Needham P. (2009) Reduction and emergence: A critique of Kim. Philosophical Studies 146: 93–116CrossRefGoogle Scholar
  16. Pearl J. (1988) Probabilistic reasoning in intelligent systems: Networks of plausible inference. Morgan Kauffman, San FranciscoGoogle Scholar
  17. Schaffner K. (1967) Approaches to reduction. Philosophy of Science 34: 137–147CrossRefGoogle Scholar
  18. Spirtes P., Glymour C., Scheines R. (2001) Causation, prediction and search. MIT Press, Cambridge, MAGoogle Scholar
  19. Winther R. (2009) Schaffner’s model of theory reduction: Critique and reconstruction. Philosophy of Science 76: 119–142CrossRefGoogle Scholar

Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Department of PhilosophyLogic and Scientific Method, London School of Economics and Political ScienceLondonUK
  2. 2.Tilburg Center for Logic and Philosophy of ScienceTilburg UniversityTilburgThe Netherlands

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