Indexical beliefs pose a special problem for standard theories of Bayesian updating. Sometimes we are uncertain about our location in time and space. How are we to update our beliefs in situations like these? In a stepwise fashion, I develop a constraint on the dynamics of indexical belief. As an application, the suggested constraint is brought to bear on the Sleeping Beauty problem.
KeywordsContextual Change Credence Function Epistemic Possibility Initial Credence Uncertain Evidence
This paper has greatly profited from discussion with Heather Demarest, Nick Haverkamp, Miguel Hoeltje, Thomas Kroedel, Alexander Steinberg, Alastair Wilson, and the participants of the MLE seminar 2006 in Oxford at which I first learned about the Sleeping Beauty problem. I would also like to thank two anonymous referees of this journal for their extensive and very helpful comments. Special thanks are due to Benjamin Schnieder for numerous help with various earlier drafts of the paper. Research for the present paper has been made possible through the generous support of the Deutsche Forschungsgemeinschaft.
- Arntzenius, F. (2003). Some problems for conditionalization and reflection. The Journal of Philosophy, 7, 356–370.Google Scholar
- Lewis, D. (1980). A subjectivists guide to objective chance. In: R. C. Jeffrey (Ed.) Studies in Inductive Logic and Probability, 2, (pp. 263–93). Berkeley: University of California Press.Google Scholar
- Williamson, T. (2000). Knowledge and Its Limits. Oxford: Oxford University Press.Google Scholar
- Williamson, T. (2006). Indicative versus subjunctive conditionals, congruential versus non-hyperintensional contexts. In: E. Sosa, & E. Villanueva (Eds.). Philosophical Issues, 16, 310–333.Google Scholar