Two Approaches to Belief Revision
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In this paper, we compare and contrast two methods for the revision of qualitative (viz., “full”) beliefs. The first (“Bayesian”) method is generated by a simplistic diachronic Lockean thesis requiring coherence with the agent’s posterior credences after conditionalization. The second (“Logical”) method is the orthodox AGM approach to belief revision. Our primary aim is to determine when the two methods may disagree in their recommendations and when they must agree. We establish a number of novel results about their relative behavior. Our most notable (and mysterious) finding is that the inverse of the golden ratio emerges as a non-arbitrary bound on the Bayesian method’s free-parameter—the Lockean threshold. This “golden threshold” surfaces in two of our results and turns out to be crucial for understanding the relation between the two methods.
- Dorst, K. (2014). An epistemic utility argument for the threshold view of outright belief (Forthcoming).Google Scholar
- Foley, R. (1992). Working without a net. Oxford: Oxford University Press.Google Scholar
- Genin, K. (2017). How inductive is Bayesian conditioning. (Unpublished Manuscript).Google Scholar
- Gärdenfors, P. (1988). Knowledge in flux. Cambridge: MIT Press.Google Scholar
- Gärdenfors, P., & Rott, H. (1995). Belief revision. Handbook of logic in artificial intelligence and logic programming (Vol. 4, pp. 35–132). Oxford: Oxford University Press.Google Scholar
- Gärdenfors, P., & Makinson, D. (1988). Revision of knowledge systems using epistemic entrenchment. In TARK ’88 Proceedings of the second conference of theoretical aspects of reasoning about knowledge (Vol. 3, pp. 83–95).Google Scholar
- Hawthorne, J. (2005). The case for closure. In M. Steup & E. Sosa (Eds.), Contemporary debates in epistemology (pp. 26–42). Oxford: Blackwell.Google Scholar
- Hempel, C. (1962). Deductive-nomological vs. statistical explanation. Minnesota Studies in the Philosophy of Science, 3, 98–169.Google Scholar
- James, W. (1896). The will to believe. The New World, 5, 327–347.Google Scholar
- Katsuno, H., & Mendelzon, A. O. (1991). On the difference between updating a knowledge base and revising it. In J. Allen, R. Fikes, & E. Sandewall (Eds.), Principles of knowledge representation and reasoning: Proceedings of the second international conference (KR ’91) (pp. 387–394). Burlington: Morgan Kaufmann.Google Scholar
- Kyburg, H. (1961). Probability and the logic of rational belief. Middletown: Wesleyan University Press.Google Scholar
- Lehmann, D., & Magidor, M. (2002). What does a conditional knowledge base entail? Journal of Artificial Intelligence, 44(1), 167–207.Google Scholar
- Leitgeb, H. (2013). The review paradox: On the diachronic costs of not closing rational belief under conjunction. Noûs, 78(4), 781–793.Google Scholar
- Leitgeb, H. (2016). Stability theory of belief. Oxford: Oxford University Press.Google Scholar
- Levi, I. (1973). Gambling with truth: An essay on induction and the aims of science. Cambridge: MIT Press.Google Scholar
- Makinson, D., & Hawthorne, J. (2015). Lossy inference rules and their bounds: A brief review. In A. Koslow, & A. Buchsbaum (Eds.), The road to universal logic. Studies in universal logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-10193-4_18.
- Pettigrew R. (2016). Epistemic utility arguments for probabilism. In: E. Zalta (Ed.) The Stanford encyclopedia of philosophy (Spring 2016 Edition). http://plato.stanford.edu/archives/spr2016/entries/epistemic-utility/.
- Rabinowicz, W. (1995). Stable revision, or is preservation worth preserving? In A. Fuhrmann, & H. Rott (Eds.) Logic, action and information: Essays on logic in philosophy and artificial intelligence (pp. 101–128). Berlin.Google Scholar
- Rodrigues, O., Gabbay, D. M., & Russo, A. (2011). Belief revision. In D. Gabbay & F. Guenthner (Eds.), Handbook of philosophical logic v. 16 (pp. 1–114). New York, NY: Springer.Google Scholar
- Rott, H. (2001). Change, choice, and inference. Oxford: Oxford University Press.Google Scholar
- van Eijck, J., & Renne, B. (2014). Belief as willingness to bet. http://arxiv.org/abs/1412.5090.