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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.

References

Adams, Ernest (1975), The Logic of Conditionals. Dordrecht: D. Reidel.CrossRefGoogle Scholar
Adams, Ernest (1976), “Prior Probabilities and Counterfactual Conditionals”, in Harper, William L. and Hooker, Clifford A. (eds.), Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, Vol. 1. Dordrecht: D. Reidel, 1–21.Google Scholar
Adams, Ernest (1993), “On the Rightness of Certain Counterfactuals”, Pacific Philosophical Quarterly 74: 1–10.CrossRefGoogle Scholar
Alchourrón, Carlos, Gärdenfors, Peter, and Makinson, David (1985), “On the Logic of Theory Change: Partial Meet Contraction and Revision Functions”, The Journal of Symbolic Logic 50: 510–530.CrossRefGoogle Scholar
Arló Costa, Horacio and Levi, Isaac (1996), “Two Notions of Epistemic Validity”, Synthese 109: 217–262.CrossRefGoogle Scholar
Arthur, Wallace and Fenster, Saul (1969), Mechanics. New York: Holt, Rinehart, and Winston.Google Scholar
Brewka, Gerhard, Jurgen, Dix, and Konolige, Kurt (1997), Nonmonotonic Reasoning: An Overview. Stanford: CSLI.Google Scholar
Brown, Harold (1988), Rationality. New York: Routledge.Google Scholar
Brown, Harold (1994), “Reason, Judgment and Bayes's Law”, Philosophy of Science 61: 351–369.10.1086/289808CrossRefGoogle Scholar
Butts, Richard and Pitt, Joseph (eds.) (1978), New Perspectives on Galileo. Dordrecht: D. Reidel.CrossRefGoogle Scholar
Cartwright, Nancy (1983), How the Laws of Physics Lie. New York: Oxford University Press.CrossRefGoogle Scholar
Casti, John L. and Karlqvist, Anders (eds.) (1996), Boundaries and Barriers: On the Limits to Scientific Knowledge. New York: Addison-Wesley.Google Scholar
Cherniak, Christopher (1986), Minimal Rationality. Cambridge: MIT Press.Google Scholar
Chiara, Dalla, Luisa, Maria (1992) “Possible Worlds, Counterfactuals, and Epistemic Operators”, in Christina Bicchieri and Maria Luisa Dalla Chiara (eds.) Knowledge, Belief, and Strategic Interaction. New York: Cambridge University Press, 155–166.CrossRefGoogle Scholar
Doherty, Patrick (ed.) (1996), Partiality, Modality and Nonmonotonicity. Stanford: CSLI Publications.Google Scholar
Earman, John (1992), Bayes or Bust? Cambridge: MIT Press.Google Scholar
Edgington, Dorothy (1986), “Do Conditionals Have Truth-Conditions?”, Critica: 18, 3–30.Google Scholar
Fetzer, James (1981), Scientific Knowledge. Dordrecht: D. Reidel.CrossRefGoogle Scholar
Fetzer, James and Nute, Donald (1979), “Syntax, Semantics, and Ontology: A Probabilistic Causal Calculus”, Synthese 40: 453–495.CrossRefGoogle Scholar
Gärdenfors, Peter (1986), “Belief Revision and the Ramsey Test for Conditionals”, The Philosophical Review 95: 81–93.CrossRefGoogle Scholar
Gärdenfors, Peter (1988), Knowledge in Flux. Cambridge: MIT Press.Google Scholar
Gärdenfors, Peter (1992), “The Dynamics of Belief Systems: Foundations versus Coherence Theories”, in Christina Bicchieri and Maria Luisa Dalla Chiara (eds.) Knowledge. Belief, and Strategic Interaction. New York: Cambridge University Press, 377–396.CrossRefGoogle Scholar
Garey, Michael and Johnson, David (1979), Computers and Intractability: A Guide to the Theory of NP-completeness. New York: W.H. Freeman.Google Scholar
Geroch, Robert and Hartle, J. B. (1986), “Computability and Physical Theories”, Foundations of Physics 16: 533–550.CrossRefGoogle Scholar
Glymour, Clark (1981), Theory and Evidence. Chicago: University of Chicago Press.Google Scholar
Good, Irving J. (1983), “46656 Varieties of Bayesians”, in his Good Thinking. Minneapolis: University of Minnesota Press, 20–21.Google Scholar
Hacking, Ian (1983), Representing and Intervening. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Hájek, Alan (1989), “Probabilities of Conditionals Revisited”, Journal of Philosophical Logic 18: 423–428.CrossRefGoogle Scholar
Hanson, Norwood R. (1965), “Newton's First Law: A Philosopher's Door into Natural Philosophy”, in Colodny, Robert (ed.), Beyond the Edge of Certainty. New Jersey: Prentice-Hall, 6–28.Google Scholar
Hansson, Sven O. (1995), “The Emperor's New Clothes: Some Recurring Problems in the Formal Analysis of Counterfactuals”, in Crocco, G., Farinas, L. Cerro, Del, and Herzig, A. (eds.), Conditionals: From Philosophy to Computer Science. Oxford: Clarendon Press, 13–31.Google Scholar
Howson, Colin (1995), “Theories of Probability”, British Journal for the Philosophy of Science 46: 1–32.CrossRefGoogle Scholar
Howson, Colin and Urbach, Peter (1993), Scientific Reasoning: The Bayesian Approach, 2nd ed. Chicago: Open Court.Google Scholar
Hughes, R. I. G. (1990), “The Bohr Atom, Models and Realism”, Philosophical Topics 18: 71–84.CrossRefGoogle Scholar
Koyré, Alexander (1968), Metaphysics and Measurement. Cambridge: Harvard University Press.Google Scholar
Kyburg, Henry (1978), “Subjective Probability: Criticisms, Reflections, and Problems”, Journal of Philosophical Logic 7: 157–180.CrossRefGoogle Scholar
Langholm, Tore (1996), “How Different is Partial Logic?”, in Doherty, Patrick (ed.), Partiality, Modality, and Nonmonotonicity. Stanford: CSLI Publications, 3–34.Google Scholar
Laymon, Ronald (1989), “Cartwright and the Lying Laws of Physics”, Journal of Philosophy 86: 353–372.CrossRefGoogle Scholar
Leff, Harvey S. and Rex, Andrew (eds.) (1990), Maxwell's Demon: Entropy, Information, and Computing. Princeton: Princeton University Press.CrossRefGoogle Scholar
Levi, Isaac (1996), For the Sake of the Argument: Ramsey Test Conditionals, Inductive Inference, and Nonmonotonic Reasoning. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Lewis, David (1976), “Probabilities of Conditionals and Conditional Probabilities”, Philosophical Review 85: 297–315.CrossRefGoogle Scholar
Lewis, David (1986), “Probabilities of Conditionals and Conditional Probabilities II”, Philosophical Review 95: 581–589.CrossRefGoogle Scholar
Lifschitz, Vladimir (1994), “Circumscription”, in Dov Gabbay, C. Hogger, and Robinson, J. (eds.), Nonmonotonic and Uncertain Reasoning. Vol. 3 of Handbook of Logic in Artificial Intelligence and Logic Programming. Oxford: Oxford University Press, 297–352.Google Scholar
Lindström, Sten and Rabinowicz, Wlodzimierz (1989), “On Probabilistic Representation of Non-probabilistic Belief Revision”, Journal of Philosophical Logic 18: 69–101.CrossRefGoogle Scholar
Lindström, Sten and Rabinowicz, Wlodzimierz (1990), “Epistemic Entrenchment with Incomparabilities and Rational Belief Revision”, in Furhmann, A. and Morreau, M. (eds.), The Logic of Theory Change. Berlin: Springer-Verlag, 93–126.Google Scholar
Lindström, Sten and Rabinowicz, Wlodzimierz (1992), “Belief Revision, Epistemic Conditionals, and the Ramsey Test”, Synthese 91: 195–237.CrossRefGoogle Scholar
Lindström, Sten and Rabinowicz, Wlodzimierz (1995), “The Ramsey Test Revisited”, in Crocco, G., Farinas Del Cerro, L., and Herzig, A. (eds.), Conditionals: From Philosophy to Computer Science. Oxford: Clarendon Press, 147–191.Google Scholar
Makinson, David (1994), “General Patterns in Nonmonotonic Reasoning”, in Dov Gabbay, C. Hogger, and Robinson, J. (eds.), Nonmonotonic and Uncertain Reasoning. Vol. 3 of Handbook of Logic in Artificial Intelligence and Logic Programming. Oxford: Oxford University Press, 35–110.Google Scholar
McGee, Vann (1989), “Conditional Probabilities and Compounds of Conditionals”, The Philosophical Review 97: 485–541.CrossRefGoogle Scholar
McMullin, Ernan (1985), “Galilean Idealization”, Studies in the History and Philosophy of Science 16: 247–273.CrossRefGoogle Scholar
Milne, Peter (1997), “Bruno de Finetti and the Logic of Conditional Events”, British Journal For the Philosophy of Science 48: 195–232.CrossRefGoogle Scholar
Nowak, Leszak (1980), The Structure of Idealization. Dordrecht: D. Reidel.CrossRefGoogle Scholar
Pitowsky, Itamar (1990), “The Physical Church Thesis and Physical Computational Complexity”, Iyyun 39: 81–99.Google Scholar
Pitt, Joseph (1992), Galileo, Human Knowledge, and the Book of Nature. Dordrecht: D. Reidel.CrossRefGoogle Scholar
Poole, David (1994), “Default Logic”, in Dov Gabbay, C. Hogger, and Robinson, J. (eds.), Nonmonotonic and Uncertain Reasoning. Vol. 3 of Handbook of Logic in Artificial Intelligence and Logic Programming. Oxford: Oxford University Press, 189–215.Google Scholar
Pylyshyn, Zenon (ed.) (1986), The Robot's Dilemma. New Jersey: Norwood.Google Scholar
Railton, Peter (1981), “Probability, Explanation, and Information”, Synthese 48: 233–256.CrossRefGoogle Scholar
Ramsey, F. P. (1990), Philosophical Papers. Edited by David H. Mellor. Cambridge: Cambridge University Press.Google Scholar
Redhead, Michael (1980), “Models in Physics”, British Journal for the Philosophy of Science 31: 154–163.CrossRefGoogle Scholar
Rosenkrantz, Richard (1981), Foundations and Applications of Inductive Probability. Atascadero, CA: Ridgeview Press.Google Scholar
Salmon, Wesley (1990), “Rationality and Objectivity in Science or Tom Kuhn Meets Tom Bayes”, in Savage, C. Wade (ed.), Minnesota Studies in the Philosophy of Science, vol. 14. Minneapolis: University of Minnesota Press, 175–204.Google Scholar
Shaffer, Michael (2000), Idealization and Empirical Testing. Ph.D. dissertation. Miami, FL: University of Miami.Google Scholar
Shapere, Dudley (1974), Galileo: A Philosophical Study. Chicago: University of Chicago Press.Google Scholar
Shoham, Yoav (1988), Reasoning about Change. Cambridge: MIT Press.Google Scholar
Stalnaker, Robert (1970), “A Theory of Conditionals”, in Harper, William L., Stalnaker, Robert, and Pearce, G. (eds.), Ifs. London: Blackwell, 41–55.Google Scholar
Stich, Stephen (1990), The Fragmentation of Reason. Cambridge: MIT Press.Google Scholar
Walker, Elbert A. (1994), “Stone Algebras, Conditional Events, and Three Valued Logic”, IEEE Transactions on Systems, Man, and Cybernetics 24: 1699–1707.CrossRefGoogle Scholar