The Dynamics of Indexical Belief Moritz Schulz Penultimate draft. Please quote from the published version (Erkenntnis 2010). Abstract Indexical beliefs pose a special problem for standard theories of bayesian updating. Sometimes we are uncertain about our location in time and space. How are we to update our beliefs in situations like these? In a stepwise fashion, I develop a constraint on the dynamics of indexical be- lief. As an application, the suggested constraint is brought to bear on the Sleeping Beauty problem. 1 Introduction Indexical belief constitutes a problem for epistemic dynamics right at the out- set. Suppose I believe on Sunday what I would express by ‘Today is Sunday’. What should I believe on Monday? In the most natural circumstances, I should not continue to believe what would be expressed by ‘Today is Sunday’. Rather, I should come to accept ‘Yesterday was Sunday’. Thus, continuity of indexical belief does not manifest itself in assent to the same sentence. Moreover, some- times the evidence we acquire is indexical. On Monday, I may learn ‘Today is Jacky’s birthday’. How should my new credences relate to my past credences on Sunday? Clearly, I should not conditionalize my Sunday credences on ‘Today is Jacky’s birthday’. The problem becomes worse. In some cases, we cannot keep track of the relevant contextual features. Around midnight on Sunday, I may be unsure whether it is still Sunday or already Monday. As a result, I become uncertain whether I should belief ‘Today is Sunday’ or ‘Today is Monday’. How should our credence evolve when we lose track of our location in time and space? The problem of updating in situations of uncertainty concerning our spatio- temporal location has emerged from the Sleeping Beauty problem (which will be reviewed in section 5). But, as the foregoing considerations indicate, the problem of indexical belief is much more general. In this paper, I develop in a stepwise fashion a general constraint on the dynamics of indexical belief which 1