Confirmation and reduction: a Bayesian account

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.

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Acknowledgments

We would like to thank Kristina Liefke, Jan Sprenger and the editors for comments on an earlier draft. We have learned a lot about reduction in discussions with David Chalmers, Anjan Chakravartty, José Diez, Conrad Heilmann, Catherine Howard, Colin Howson, Margie Morrison, Miklós Rédei, Jos Uffink and Marcel Weber, and from comments made by the audiences in Bremen, Columbia (SC), Groningen, Konstanz, LSE, Pine Point (MI), Sydney, St. Andrews, Tilburg and Toronto.

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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Dizadji-Bahmani, F., Frigg, R. & Hartmann, S. Confirmation and reduction: a Bayesian account. Synthese 179, 321–338 (2011). https://doi.org/10.1007/s11229-010-9775-6

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Keywords

  • Nagelian reduction
  • Bayesian epistemology
  • Thermodynamics and statistical mechanics
  • Bayesian network models