Against Belief Closure

Abstract

I argue that we should solve the Lottery Paradox by denying that rational belief is closed under classical logic. To reach this conclusion, I build on my previous result that (a slight variant of) McGee’s election scenario is a lottery scenario (see Lissia 2019). Indeed, this result implies that the sensible ways to deal with McGee’s scenario are the same as the sensible ways to deal with the lottery scenario: we should either reject the Lockean Thesis or Belief Closure. After recalling my argument to this conclusion, I demonstrate that a McGee-like example (which is just, in fact, Carroll’s barbershop paradox) can be provided in which the Lockean Thesis plays no role: this proves that denying Belief Closure is the right way to deal with both McGee’s scenario and the Lottery Paradox. A straightforward consequence of my approach is that Carroll’s puzzle is solved, too.

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Lina Maria Lissia
University of Turin

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References found in this work

Elusive knowledge.David K. Lewis - 1996 - Australasian Journal of Philosophy 74 (4):549 – 567.
Probability and the Logic of Rational Belief.Henry E. Kyburg Jr - 1961 - Middletown, CT, USA: Wesleyan University Press.

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