A problem for the alternative difference measure of confirmation
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Among Bayesian confirmation theorists, several quantitative measures of the degree to which an evidential proposition E confirms a hypothesis H have been proposed. According to one popular recent measure, s, the degree to which E confirms H is a function of the equation P(H|E) − P(H|~E). A consequence of s is that when we have two evidential propositions, E1 and E2, such that P(H|E1) = P(H|E2), and P(H|~E1) ≠ P(H|~E2), the confirmation afforded to H by E1 does not equal the confirmation afforded to H by E2. I present several examples that demonstrate the unacceptability of this result, and conclude that we should reject s (and other measures that share this feature) as a measure of confirmation.
KeywordsConfirmation Evidence Bayesian epistemology Probability
This paper had its genesis in a graduate seminar on probability at Western Michigan University in Fall 2009. I am grateful to Timothy McGrew for teaching that class and helping me think through these issues. I would also like to thank David Christensen for insightful correspondence on this project, as well as Matthew Lee and an anonymous reviewer for helpful comments on earlier drafts.
- Carnap, R. (1962). Logical foundations of probability (2nd ed.). Chicago: University of Chicago Press.Google Scholar
- Crupi, V., Festa, R., & Buttasi, C. (2010). Towards a grammar of Bayesian confirmation. In M. Suárez, M. Dorato, & M. Rèdei (Eds.), Epistemology and methodology of science (pp. 73–93). Berlin: Springer.Google Scholar
- Earman, J. (1992). Bayes or bust?: A critical examination of Bayesian confirmation theory. Cambridge: MIT Press.Google Scholar
- Horwich, P. (1982). Probability and evidence. Cambridge: Cambridge University Press.Google Scholar
- Mortimer, H. (1988). The logic of induction. Paramus: Prentice Hall.Google Scholar
- Nozick, R. (1981). Philosophical explanations. Cambridge: Harvard University Press.Google Scholar