Abstract
This paper is about the standard Reflection Principle (van Fraassen in J Philos 81(5):235–256, 1984) and the Group Reflection Principle (Elga in Nous 41(3):478–502, 2007; Bovens and Rabinowicz in Episteme 8(3):281–300, 2011; Titelbaum in Quitting certainties: a Bayesian framework modeling degrees of belief, OUP, Oxford, 2012; Hedden in Mind 124(494):449–491, 2015). I argue that these principles are incomplete as they stand. The key point is that deference is an intensional relation, and so whether you are rationally required to defer to a person at a time can depend on how that person and that time are designated. In this paper I suggest a way of completing the Reflection Principle and Group Reflection Principle, and I argue that so completed these principles are plausible. In particular, they do not fall foul of the Sleeping Beauty case (Elga in Analysis 60(2):143–147, 2000), the Cable Guy Paradox (Hajek in Analysis 65(286):112–119, 2005), Arntzenius’ prisoner cases (Arntzenius in J Philos, 100(7):356–370, 2003), or the Puzzle of the Hats (Bovens and Rabinowicz in Episteme 8(3):281–300, 2011).
Highlights
MahtaniTo see what ‘defers to’ means, take agents A and B and times ti and tj, where CrAi designates A’s credence function at time ti, and CrBj designates B’s credence function at time tj
This paper is about the standard Reflection Principle (van Fraassen in J Philos 81(5):235–256, 1984) and the Group Reflection Principle (Elga in Nous 41(3):478–502, 2007; Bovens and Rabinowicz in Episteme 8(3):281–300, 2011; Titelbaum in Quitting certainties: a Bayesian framework modeling degrees of belief, OUP, Oxford, 2012; Hedden in Mind 124(494):449–491, 2015)
—even if A at ti somehow came to learn that B at tj has a credence function that is A’s credence function at ti conditionalized on some additional evidence—there would be no particular reason to expect A at ti to defer to B at tj
Summary
To see what ‘defers to’ means, take agents A and B and times ti and tj, where CrAi designates A’s credence function at time ti, and CrBj designates B’s credence function at time tj. A at t0 is certain that her credence function at that future time (CrA1) will differ from her current credence function (CrA0) only if she acquires some new (true) evidence between t0 and t1, in which case she will conditionalize on that evidence It seems, that by the agent’s own lights at t0, CrA1 is an improvement on CrA0 (or at worst identical to CrA0), and so that A at t0 should defer to her future self at t1. Putting the Dutch Book Argument for the Reflection Principle aside, the motivation for accepting Reflection* is this intuitive thought: if you respect your future self, you see your future credence function as an improvement (or at worst identical) to your current credence function—and so if you are rational you defer to that future self. There is a counterexample aimed at the Group Reflection Principle (Bovens and Rabinowicz 2011), and I add my own counterexample (The Mug) to the heap
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