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AGREEMENT THEOREMS FOR SELF-LOCATING BELIEF

Published online by Cambridge University Press:  05 April 2016

MICHAEL CAIE
MICHAEL CAIE*
Affiliation:
University of Pittsburgh
*
*UNIVERSITY OF PITTSBURGH DEPARTMENT OF PHILOSOPHY 1001 CATHEDRAL OF LEARNING PITTSBURGH, PA, 15260 E-mail: [email protected]
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Abstract

In this paper, I first outline Aumann’s famous “no agreeing to disagree” theorem, and a second related theorem. These results show that if two or more agents, who have epistemic and credal states that are defined over algebras that do not include any self-locating propositions, have certain information about one another’s epistemic and credal states, then such agents must assign the same credence to certain propositions. I show, however, that both of these theorems fail when we consider agents who have epistemic and credal states that are defined over algebras that do include self-locating propositions. Importantly, these theorems fail for such agents even when we restrict our attention to the credences that such agents have in non-self-locating propositions. Having established this negative result, I then outline and prove three agreement theorems that hold for such agents.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 9 , Issue 2 , June 2016 , pp. 380 - 407
Copyright
Copyright © Association for Symbolic Logic 2016 

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