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Direct Inference, Reichenbach's Principle, and the Sleeping Beauty Problem

Published online by Cambridge University Press:  11 November 2019

Terry Horgan Open the ORCID record for Terry Horgan [Opens in a new window]
Terry Horgan*
Affiliation:
University of Arizona, Tucson, USA
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*Email: [email protected]
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Abstract

A group of philosophers led by the late John Pollock has applied a method of reasoning about probability, known as direct inference and governed by a constraint known as Reichenbach's principle, to argue in support of ‘thirdism’ concerning the Sleeping Beauty Problem. A subsequent debate has ensued about whether their argument constitutes a legitimate application of direct inference. Here I defend the argument against two extant objections charging illegitimacy. One objection can be overcome via a natural and plausible definition, given here, of the binary relation ‘logically stronger than’ between two properties that can obtain even when the respective properties differ from one another in ‘arity’; given this definition, the Pollock group's argument conforms to Reichenbach's principle. Another objection prompts a certain refinement of Reichenbach's principle that is independently well-motivated. My defense of the Pollock group's argument has epistemological import beyond the Sleeping Beauty problem, because it both widens and sharpens the applicability of direct inference as a method for inferring single-case epistemic probabilities on the basis of general information of a probabilistic or statistical nature.

Keywords

Sleeping Beautyprobabilitydirect inferenceReichenbach's principle
Type
Article
Information
Episteme , Volume 18 , Issue 4 , December 2021 , pp. 640 - 653
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Copyright
Copyright © Cambridge University Press 2019

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References

Bacchus, F. (1990). Representing and Reasoning with Probabilistic Knowledge. Cambridge, MA: MIT Press.Google Scholar
Draper, K. (2017). ‘Even for Objectivists, Sleeping Beauty isn't so Simple.’ Analysis 77(1), 29–37.CrossRefGoogle Scholar
Draper, K. (in press). ‘Direct Inference and the Sleeping Beauty Problem.’ Synthese.Google Scholar
Fisher, R.A. (1922). ‘On the Mathematical Foundations of Theoretical Statistics.’ Philosophical Transactions of the Royal Society A 222, 309–68.Google Scholar
Follesdal, D. (1967). ‘Knowledge, Identity, and Existence.’ Theoria 33(1), 1–27.CrossRefGoogle Scholar
Halpern, J. (1990). ‘An Analysis of First-Order Logics of Probability.’ Artificial Intelligence 46, 311–50.CrossRefGoogle Scholar
Horgan, T. (2004). ‘Sleeping Beauty Awakened: New Odds at the Dawn of the New Day.’ Analysis 64(1), 10–21. Reprinted in Essays on Paradoxes, pp. 209–19. New York, NY: Oxford University Press.CrossRefGoogle Scholar
Horgan, T. (2008). ‘Synchronic Bayesian Updating the Sleeping Beauty Problem: Reply to Pust.’ Synthese 160(2), 155–9. Reprinted in Essays on Paradoxes, pp. 220–5. New York, NY: Oxford University Press.CrossRefGoogle Scholar
Horgan, T. (2017 a). ‘Epistemic Probability.’ In Essays on Paradoxes, pp. 281–318. New York, NY: Oxford University Press.Google Scholar
Horgan, T. (2017 b). ‘Troubles for Bayesian Formal Epistemology.’ Res Philosophica 94(2), 233–55.CrossRefGoogle Scholar
Kyburg, H.E. (1974). The Logical Foundations of Statistical Inference. Dordrecht: Reidel.CrossRefGoogle Scholar
Kyburg, H.E. and Teng, C. (2001). Uncertain Inference. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Pollock, J. (1990). Nomic Probability and the Foundations of Induction. New York, NY: Oxford University Press.CrossRefGoogle Scholar
Popper, I. (1956). ‘The Propensity Interpretation of Probability.’ British Journal for the Philosophy of Science 10(37), 25–42.CrossRefGoogle Scholar
Pust, J. (2011). ‘Sleeping Beauty and Direct Inference.’ Analysis 71(2), 290–3.CrossRefGoogle Scholar
Reichenbach, H. (1949). A Theory of Probability. Berkeley, CA: University of California Press.Google Scholar
Seminar, O. (2008). ‘An Objectivist Argument for Thirdism.’ Analysis 68(2), 149–55.CrossRefGoogle Scholar
Thorn, P. (2011). ‘Undercutting Defeat via Reference Properties of Different Arity: A Reply to Pust.’ Analysis 71(4), 662–7.CrossRefGoogle Scholar
Thorn, P. (2012). ‘Two Problems of Direct Inference.’ Erkenntnis 76(3), 299–318.CrossRefGoogle Scholar
Thorn, P. (in press). ‘A Formal Solution to Reichenbach's Reference Class Problem.’ Dialectica.Google Scholar