Diachronic Norms for Self-Locating Beliefs

Abstract

How should rational beliefs change over time? The standard Bayesian answer is: by conditionalization (a.k.a. Bayes' Rule). But conditionalization is not an adequate rule for updating beliefs in "centred" propositions whose truth-value may itself change over time. In response, some have suggested that the objects of belief must be uncentred; others have suggested that beliefs in centred propositions are not subject to diachronic norms. I argue that these views do not offer a satisfactory account of self-locating beliefs and their dynamics. A third response is to replace conditionalization by a new norm that can deal with centred propositions. I critically survey a number of new norms that have been proposed, and defend one particular approach.

Multiple Universes and Self-Locating Evidence

“…Of course, one can easily find many more than three theories of selflocating belief in the philosophy literature. (For helpful overview see Titelbaum 2013Titelbaum , 2016; for a few more recent approaches see also Meacham 2016;Arntzenius and Dorr 2017;Schwarz 2017;Builes 2020). But many of the differences between these theories are in their answers to questions that don't immediately arise here: questions about the passage of time, forgetting information, or people or universes that undergo fission and branching.…”

Imaginary Foundations

“…These updated probabilities are then conditionalized on the new evidence R × {ρ(S )} × {0}. See Schwarz (2017) for further details and motivation.…”

Higher-Order Evidence and the Dynamics of Self-Location: An Accuracy-Based Argument for Calibrationism

“…15 into the centered-proposition framework, what we get is the thesis that should be equal to , that the agent’s attitudes toward centered propositions on supposing n has passed should match her present attitudes toward the minus- n -shifted counterparts of those propositions. If this thesis were correct, we could conclude that should be equal to —i.e., that self-certain agents should conform to a version of the update procedure Schulz ( 2010 ) calls continuous conditionalization and Schwarz ( 2012 , 2015 , 2017 ) calls (SC) , or shifted conditioning . (Both Schulz and Schwarz endorse this procedure as a rational requirement in cases of agents that don’t lose track of time.…”