Lockean Belief, Dutch Books, and Scoring Systems
Abstract: On the Lockean thesis one ought to believe a proposition if and only if one assigns it a credence at or above a threshold (Foley 1992). The Lockean thesis, thus, provides a way of linking sets of all-or-nothing beliefs with credences. Recent work on the lexical semantics of attitude verbs such a ‘think’ and ‘believe’ suggest that Lockeanism is more plausible than the view that believing a proposition requires having full confidence in it (Hawthorne, Rothschild and Spectre, 2016). In this talk, I will give two independent characterizations of sets of full beliefs satisfying the Lockean thesis. One is in terms of betting dispositions associated with full beliefs and one is in terms of an accuracy scoring system for full beliefs. These characterizations are parallel to, but not merely derivative from, the more familiar Dutch book (de Finetti 1974) and accuracy arguments (Joyce 1998) for probabilism.
A draft of the paper is here: http://danielrothschild.com/materials/lockeandutchbook.pdf