Stability and Scepticism in the Modelling of Doxastic States: Probabilities and Plain Beliefs
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There are two prominent ways of formally modelling human belief. One is in terms of plain beliefs (yes-or-no beliefs, beliefs simpliciter), i.e., sets of propositions. The second one is in terms of degrees of beliefs, which are commonly taken to be representable by subjective probability functions. In relating these two ways of modelling human belief, the most natural idea is a thesis frequently attributed to John Locke: a proposition is or ought to be believed (accepted) just in case its subjective probability exceeds a contextually fixed probability threshold \(t<1\). This idea is known to have two serious drawbacks: first, it denies that beliefs are closed under conjunction, and second, it may easily lead to sets of beliefs that are logically inconsistent. In this paper I present two recent accounts of aligning plain belief with subjective probability: the Stability Theory of Leitgeb (Ann Pure Appl Log 164(12):1338–1389, 2013; Philos Rev 123(2):131–171, 2014; Proc Aristot Soc Suppl Vol 89(1):143–185, 2015a; The stability of belief: an essay on rationality and coherence. Oxford University Press, Oxford, 2015b) and the Probalogical Theory (or Tracking Theory) of Lin and Kelly (Synthese 186(2):531–575, 2012a; J Philos Log 41(6):957–981, 2012b). I argue that Leitgeb’s theory may be too sceptical for the purposes of real life.
KeywordsPlain belief Subjective probability Formal epistemology Lockean thesis Stability Theory of belief Leitgeb Lin Kelly
I am grateful to audiences in Etelsen, Regensburg, Patras, Uppsala and Maastricht, to John Cantwell, Paul Égré, Tim Kraft, an anonymous referee of this journal, and most of all to Hannes Leitgeb for valuable discussions of various versions of this paper. I have checked the correctness of my calculations for the space of four possibilities (Sect. 5) by determining the values for particular thresholds in numerous special cases. In doing this, I have made extensive use of the websites www.rechneronline.de/function-graphs and www.polymake.org. I am grateful to the people running these sites.
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