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In Defense of Reflection

Published online by Cambridge University Press:  01 January 2022

Abstract

I discuss two ways of justifying reflection principles. First, I propose that an undogmatic reading of dynamic Dutch book arguments provides them with a sound foundation. Second, I show also that minimizing expected inaccuracy leads to a novel argument for reflection principles. The required inaccuracy measures comprise a natural class of functions that can be derived from a generalization of a condition known as propriety or immodesty. This shows that reflection principles are an essential feature not just of consistent degrees of belief but also of degrees of belief that approximate truth.

Type
Research Article
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

For helpful comments on earlier drafts of this article, I want to thank Kenny Easwaran, Brian Skyrms, Bas van Fraassen, Jonathan Weisberg, Kevin Zollman, and an anonymous referee for this journal.

References

Adams, Ernest W. 1962. “On Rational Betting Systems.” Archiv für mathematische Logik und Grundlagenforschung 6:729, 112–28.CrossRefGoogle Scholar
Armendt, Brad. 1980. “Is There a Dutch Book Argument for Probability Kinematics?Philosophy of Science 47:583–88.CrossRefGoogle Scholar
Armendt, Brad 1993. “Dutch Books, Additivity, and Utility Theory.” Philosophical Topics 21:120.CrossRefGoogle Scholar
Arntzenius, Frank. 2003. “Some Problems for Conditionalization and Reflection.” Journal of Philosophy 100:356–70.CrossRefGoogle Scholar
Bacchus, Fahiem, Kyburg, Henry E., and Thalos, Mariam. 1995. “Against Conditionalization.” Synthese 85:475506.CrossRefGoogle Scholar
Banerjee, Arindam, Guo, Xin, and Wang, Hui. 2005. “On the Optimality of Conditional Expectation as a Bregman Predictor.” IEEE Transactions on Information Theory 51:2664–69.CrossRefGoogle Scholar
Bovens, Luc. 1995. “‘P and I Will Believe That Not-P’: Diachronic Constraints on Rational Belief.” Mind 104:737–60.Google Scholar
Briggs, Rachael. 2009. “Distorted Reflection.” Philosophical Review 118:5985.CrossRefGoogle Scholar
Christensen, David. 1991. “Clever Bookies and Coherent Beliefs.” Philosophical Review 100:229–47.CrossRefGoogle Scholar
Christensen, David 1996. “Dutch Books Depragmatized: Epistemic Consistency for Partial Believers.” Journal of Philosophy 93:450–79.CrossRefGoogle Scholar
Easwaran, Kenny. 2013. “Expected Accuracy Supports Conditionalization—and Conglomerability and Reflection.” Philosophy of Science 80:119–42.CrossRefGoogle Scholar
Goldstein, Michael. 1983. “The Prevision of a Prevision.” Journal of the American Statistical Association 78:817–19.CrossRefGoogle Scholar
Good, Irving J. 1981. “The Weight of Evidence Provided by an Uncertain Testimony or an Uncertain Evidence.” Journal of Statistical Computation and Simulation 13:5660.CrossRefGoogle Scholar
Greaves, Hilary, and Wallace, David. 2006. “Justifying Conditionalization: Conditionalization Maximizes Expected Epistemic Utility.” Mind 115:607–32.CrossRefGoogle Scholar
Hacking, Ian. 1967. “Slightly More Realistic Personal Probability.” Philosophy of Science 34:311–25.CrossRefGoogle Scholar
Howson, Colin, and Urbach, Peter. 1993. Scientific Reasoning: The Bayesian Approach. 2nd ed. La Salle, IL: Open Court.Google Scholar
Jeffrey, Richard C. 1988. “Conditioning, Kinematics, and Exchangeability.” In Causation, Chance, and Credence, Vol. 1, ed. Brian Skyrms and William L. Harper, 221–55. Dordrecht: Kluwer.CrossRefGoogle Scholar
Joyce, James M. 1998. “A Nonpragmatic Vindication of Probabilism.” Philosophy of Science 65:575603.CrossRefGoogle Scholar
Joyce, James M. 2009. “Accuracy and Coherence: Prospects for an Alethic Epistemology of Partial Belief.” In Degrees of Belief, ed. Huber, Franz and Schmidt-Petri, Christoph, 263–97. New York: Springer.Google Scholar
Leitgeb, Hannes, and Pettigrew, Richard. 2010a. “An Objective Justification of Bayesianism.” Pt. 1, “Measuring Inaccuracy.” Philosophy of Science 77:201–35.Google Scholar
Leitgeb, Hannes, and Pettigrew, Richard 2010b. “An Objective Justification of Bayesianism.” Pt. 2, “The Consequences of Minimizing Inaccuracy.” Philosophy of Science 77:236–72.Google Scholar
Levi, Isaac. 1987. “The Demons of Decision.” Monist 70:193211.CrossRefGoogle Scholar
Maher, Patrick. 1992. “Diachronic Rationality.” Philosophy of Science 59:120–41.CrossRefGoogle Scholar
Ramsey, Frank P. 1931. “Truth and Probability.” In Foundations of Mathematics and Other Essays, ed. Braithwaite, Richard B.. New York: Harcourt Brace. Repr. in Studies in Subjective Probability, ed. Henry E. Kyburg and Howard E. Smokler (Huntington, NY: Krieger, 1964).Google Scholar
Schervish, Mark J., Seidenfeld, Teddy, and Kadane, Joseph B.. 2004. “Stopping to Reflect.” Journal of Philosophy 101:315–22.CrossRefGoogle Scholar
Selten, Reinhard. 1998. “Axiomatic Characterization of the Quadratic Scoring Rule.” Experimental Economics 1:4361.CrossRefGoogle Scholar
Skyrms, Brian. 1987a. “Coherence.” In Scientific Inquiry in Philosophical Perspective, ed. Rescher, Nicholas, 225342. Pittsburgh: University Press of America.Google Scholar
Rescher, Nicholas 1987b. “Dynamic Coherence and Probability Kinematics.” Philosophy of Science 54:120.Google Scholar
Rescher, Nicholas 1990. The Dynamics of Rational Deliberation. Cambridge, MA: Harvard University Press.Google Scholar
Rescher, Nicholas 2006. “Diachronic Coherence and Radical Probabilism.” Philosophy of Science 73:959–68.Google Scholar
Talbott, William. 1991. “Two Principles of Bayesian Epistemology.” Philosophical Studies 62:135–50.CrossRefGoogle Scholar
Teller, Paul. 1973. “Conditionalization and Observation.” Synthese 26:218–58.CrossRefGoogle Scholar
van Fraassen, Bas C. 1984. “Belief and the Will.” Journal of Philosophy 81:235–56.CrossRefGoogle Scholar
van Fraassen, Bas C. 1995. “Belief and the Problem of Ulysses and the Sirens.” Philosophical Studies 77:737.CrossRefGoogle Scholar
Weisberg, Jonathan. 2007. “Conditionalization, Reflection, and Self-Knowledge.” Philosophical Studies 135:179–97.CrossRefGoogle Scholar
Williams, David. 1991. Probability with Martingales. Cambridge: Cambridge University Press.CrossRefGoogle Scholar