Abstract
Horgan and Mahtani (Erkenntnis 78: 333–351, 2013) present a new argument for the 1/3 answer to the Sleeping Beauty problem resting on a principle for updating probabilities which they call “generalized conditionalization.” They allege that this new argument is immune to two attacks which have been recently leveled at other arguments for thirdism. I argue that their new argument rests on a probability distribution which is (a) no more justified than an alternative distribution favoring a different answer to the problem, and (b) ultimately unjustified. I go on to show that generalized conditionalization cannot be applied in the manner suggested, given the cogency of the aforementioned attacks on thirder arguments. Hence, the new argument fails to advance the case for the 1/3 answer.
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Notes
My (2012) argues that the objects of credence expressed by temporally indexical statements are indeed essentially synchronic.
The Elga-Lewis indifference principle holds that indistinguishable centered worlds associated with a given uncentered world should receive the same credence. Actually, the appeal to the Elga-Lewis indifference principle is unnecessary for the envisioned halfer argument here because any distribution of preliminary probabilities over the various finest-grain indexical possibilities which is consistent with (*) and assigns zero only to epistemic impossibilities will, if synchronic conditionalization is acceptable, yield P(HEADS) = 1/2 after such conditionalization on one of Ri.
I make no substantive assumption about the nature of chance beyond its being non-epistemic.
See my (2007) for further discussion of this point and its implications for a variety of philosophical arguments.
My (2013) argues that even given Horgan’s preferred conception of epistemic probability as a quasi-logical support relation, his case for the thirder verdict fails.
Lewis’ (2001) argument for the halfer position is also vitiated by TIC.
A referee points out that my (2012) argument appears to assume that temporally indexical thoughts featuring “thicker” temporal terms, such as “today,” are not diachronically available. Though they express some reservations about such an assumption (349–350), Horgan and Mahtani's new argument is explicitly meant to be consistent with it.
Some of what they write suggests that Horgan and Mahtani think it is merely the fact that they propose updating on the non-temporally-indexical R1 which enables them to evade my argument. This would be incorrect, as my point, if correct, holds also for the essentially temporally indexical hypotheses the probability of which is supposed to be altered by conditionalization on R1. So, given TIC, their new argument requires that they appeal to an essentially synchronic instance of generalized conditionalization.
The same is true for the corresponding argument for 1/2 based on the credence distribution of Table 3, so the present point would equally undermine an attempt to justify the halfer position by such reasoning.
See Sobel (1987) on introspective omniscience as a rational ideal justified by a synchronic Dutch Book argument.
Those convinced by Williamson’s (2000) arguments against “luminosity” might reject the assumption.
As I discuss elsewhere, it also follows that the standard account of incremental confirmation, according to which E confirms H on background knowledge K IFF P(H/E&K) > P(H/K), cannot include temporally indexical knowledge in K and E or they will be inconsistent.
For helpful comments on previous drafts of this paper, I thank Kai Draper, three anonymous referees for this journal, an audience at a conference in Bled, and, especially, Terry Horgan.
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Pust, J. Beauty and Generalized Conditionalization: Reply to Horgan and Mahtani. Erkenn 79, 687–700 (2014). https://doi.org/10.1007/s10670-013-9532-6
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DOI: https://doi.org/10.1007/s10670-013-9532-6