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This is the end, Beautiful friend

McCutcheon, Randall G. (2014) This is the end, Beautiful friend. [Preprint]

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The main theses of this paper are roughly as follows:

1. The solution to Sleeping Beauty is a matter of convention in the explication of "credence". The halfer view is basically that credences are analogous to population proportions, while the thirder view is that credences are analogous to sample proportions.

2. The rival explications of "credence" have underpinnings in two competing conventions about the accrual of certain decision-theoretic quantities. Following Jacob Ross, I term these conventions "Single Awakening Legitimacy" and "Every Awakening Legitimacy".

3. Acceptance of Every Awakening Legitimacy implies that "I am awakened now" is informative despite being grounded in no certain proposition. (For reasons more or less familiar from instances of application of so-called Jeffrey conditionalization.) This supports thirding.

4. Acceptance of Single Awakening Legitimacy leads to halfing, grounded in Lewisian "sample weight dilution" of tails awakenings. This perspective keeps halfers in line with the so-called "self indicating assumption".

5. Halfing schemes at odds with self-indication (so-called "double halfing" schemes) violate diachronic norms, and indeed launch from the very misunderstanding responsible for the Monty Hall fallacy. So self indication is mandatory for everyone.

6. In Ross's argument that self indication is at odds with countable additivity of credences, self indication is a red herring. Indeed, the argument requires premises that wreck rational decision irrespective of one's views on self indication. Countable additivity meanwhile is non-negotiable, as evidenced by a new finitary diachronic Dutch book argument in its favor.

7. As can be seen by analogy with Arntzenius's Prisoner, it's the univocality of the ostensive indexical "now" in "I am awakened now" that precludes internalist parsing of the latter, which in turn makes it potentially informative (and hence not neglectable); the only way to deny equivocality
of internalist parsing is to engage in Lewisian dilution, and Lewisian dilution is strange.

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Item Type: Preprint
McCutcheon, Randall G.
Additional Information: Tagline: Beauty died today. Or maybe yesterday; I can't be sure.
Keywords: Sleeping Beauty Problem; countable additivity, self-indication, personal credence, Jeffrey conditionalization; Monty Hall Problem
Subjects: Specific Sciences > Probability/Statistics
Depositing User: Dr. Randall G. McCutcheon
Date Deposited: 03 Apr 2014 19:46
Last Modified: 03 Apr 2014 19:46
Item ID: 10578
Subjects: Specific Sciences > Probability/Statistics
Date: 3 April 2014

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