Beliefs, buses and lotteries: Why rational belief can’t be stably high credence
Until recently, it seemed like no theory about the relationship between rational credence and rational outright belief could reconcile three independently plausible assumptions: that our beliefs should be logically consistent, that our degrees of belief should be probabilistic, and that a rational agent believes something just in case she is sufficiently confident in it. Recently a new formal framework has been proposed that can accommodate these three assumptions, which is known as “the stability theory of belief” or “high probability cores.” In this paper, I examine whether the stability theory of belief can meet two further constraints that have been proposed in the literature: that it is irrational to outright believe lottery propositions, and that it is irrational to hold outright beliefs based on purely statistical evidence. I argue that these two further constraints create a dilemma for a proponent of the stability theory: she must either deny that her theory is meant to give an account of the common epistemic notion of outright belief, or supplement the theory with further constraints on rational belief that render the stability theory explanatorily idle. This result sheds light on the general prospects for a purely formal theory of the relationship between rational credence and belief, i.e. a theory that does not take into account belief content. I argue that it is doubtful that any such theory could properly account for these two constraints, and hence play an important role in characterizing our common epistemic notion of outright belief.
KeywordsCredence Belief Rationality Stability theory Formal epistemology
I would like to thank Fay Edwards, Branden Fitelson, Alan Hájek, Hannes Leitgeb, Hanti Lin, Richard Pettigrew, Ryan Platte, Brian Talbot, and an anonymous referee for helpful comments and discussion.
- Fitelson, B. (2015). Belief and credence: The view from Naïve epistemic utility theory. Manuscript.Google Scholar
- Foley, R. (2009). Beliefs, degrees of belief, and the Lockean thesis. In: F. Huber, & C. Schmidt-Petri (Eds.), Degrees of belief, Synthese Library 342. Springer.Google Scholar
- Hawthorne, J. (2004). Knowledge and lotteries. Oxford: Oxford University Press.Google Scholar
- Kyburg, H. E. (1961). Probability and the logic of rational belief. Middletown: Wesleyan University Press.Google Scholar
- Schurz, G. (2015). Impossibility results for rational belief. Manuscript.Google Scholar
- Vogel, J. (1990). Are there counterexamples to the closure principle? In M. Roth & G. Ross (Eds.), Doubting: Contemporary perspectives in Skepticism. Boston: Kluwer.Google Scholar
- Williamson, T. (2000). Knowledge and its limits. Oxford: Oxford University Press.Google Scholar