Centering the Principal Principle
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Centering the Principal Principle Isaac Wilhelm1
Ó Springer Nature B.V. 2020
Abstract I show that centered propositions—also called de se propositions, and usually modeled as sets of centered worlds—pose a serious problem for various versions of Lewis’s Principal Principle. The problem, put roughly, is that in scenarios like Elga’s ‘Sleeping Beauty’ case, those principles imply that rational agents ought to have obviously irrational credences. To solve the problem, I propose a centered version of the Principal Principle. My version allows centered propositions to be objectively chancy.
1 Introduction According to various versions of the Principal Principle—for example, one formulated by Lewis (1980), one suggested by Hall (1994), and one advocated by Ismael (2008)—agents ought to set their credences in propositions equal to the known chances of those propositions. In slogan form: rational credence is constrained by chance. For example, suppose Susie knows that the chance of a coin landing heads is 12, and suppose Susie has no other information about the upcoming coin flip. Then in order to be rational, Susie must have credence 12 in the coin landing heads. Typically, all three versions of the Principal Principle are taken to constrain rational uncentered credences, where an uncentered credence is a credence in an uncentered proposition. But throughout the literature, these principles are often assumed to constrain rational centered credences as well (Elga 2000; Lewis 2001; Meacham 2008; Ross 2010; Weatherson 2013), where a centered credence is a & Isaac Wilhelm [email protected] 1
Rutgers University, 106 Somerset St., 5th Floor, New Brunswick, NJ 08901, USA
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I. Wilhelm
credence in a centered proposition like ‘‘It is Monday.’’ So some natural questions arise. Do these principles need to be adjusted, when applied to centered credences? Or do these principles constrain centered credence in basically the same way that they constrain uncentered credence? As I will show, all three versions of the Principal Principle face a serious problem when applied to centered propositions: each implies that rational agents ought to have obviously irrational credences. The problem arises in a scenario modeled after Elga’s ‘Sleeping Beauty’ case (2000). According to these principles, rationality requires the agent in Elga’s case to have particular credences in particular propositions. But those particular credences, in those particular propositions, force the agent to have irrational credences in other propositions. So the rational constraints imposed by these principles lead, ultimately, to irrationality. After presenting the problem, I propose a way out. My solution postulates centered chances: chances, that is, of centered propositions. Centered chances are liable to strike many readers as odd: how can centered propositions—like ‘‘It is Monday’’—be objectively chancy? But as I will show, centered chances are not as obscure as they initially seem to be: many strategies for explicating uncentered chances—chances, th
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