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Bayesian Confirmation of Theories That Incorporate Idealizations

Published online by Cambridge University Press:  01 April 2022

Michael J. Shaffer
Michael J. Shaffer*
Affiliation:
The University of North Carolina at Wilmington
*
†Send requests for reprints to the author, Department of Philosophy and Religion, University of North Carolina at Wilmington, Wilmington, NC 28403–3297. shafferm@uncwil.edu.
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Abstract

Following Nancy Cartwright and others, I suggest that most (if not all) theories incorporate, or depend on, one or more idealizing assumptions. I then argue that such theories ought to be regimented as counterfactuals, the antecedents of which are simplifying assumptions. If this account of the logical form of theories is granted, then a serious problem arises for Bayesians concerning the prior probabilities of theories that have counterfactual form. If no such probabilities can be assigned, then posterior probabilities will be undefined, as the latter are defined in terms of the former. I argue here that the most plausible attempts to address the problem of probabilities of conditionals fail to help Bayesians, and, hence, that Bayesians are faced with a new problem. In so far as these proposed solutions fail, I argue that Bayesians must give up Bayesianism or accept the counterintuitive view that no theories that incorporate any idealizations have ever really been confirmed to any extent whatsoever. Moreover, as it appears that the latter horn of this dilemma is highly implausible, we are left with the conclusion that Bayesianism should be rejected, at least as it stands.

Type
Research Article
Information
Philosophy of Science , Volume 68 , Issue 1 , March 2001 , pp. 36 - 52
Copyright
Copyright © 2001 by the Philosophy of Science Association

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Footnotes

‡

I would like to thank Harold Brown, Risto Hilpinen, A.J. Kreider, Pawel Kawalec, two anonymous referees, and the editors for comments on earlier drafts of this paper. I would also like to thank the University of Miami Philosophy Department for providing me with support while this work was done. Earlier versions of this paper were presented at the Second Summer School for the Theory of Knowledge held in Warsaw in 1999 and at the 1999 meeting of the Florida Philosophical Association in Miami. I thank the participants of both conferences for their comments.

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