Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-05T13:09:53.236Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

Arntzenius, Frank. (2003). Some problems for conditionalization and reflection. Journal of Philosophy, 100(7), 356–370.CrossRefGoogle Scholar
Aumann, Robert. (1976). Agreeing to disagree. The Annals of Statistics, 4(6), 1236–1239.Google Scholar
Bacharach, Michael. (1985). Some extensions of a claim of aumann in an axiomatic model of knowledge. Journal of Economic Theory, 37(1), 167–190.CrossRefGoogle Scholar
Barwise, Jon. (1988). Three views of common knowledge. In Proceedings of the 2nd Conference on Theoretical Aspects of Reasoning about Knowledge. Morgan Kaufmann San Francisco, California, pp. 365–379.Google Scholar
Bostrom, Nick. (2000) Observer-relative chances in anthropic reasoning? Erkenntnis, 52, 93–108.Google Scholar
Bostrom, Nick. (2002). Anthropic Bias. Routledge, New York.Google Scholar
Caie, Michael. (2016). Agreement and updating for self-locating belief. (ms).Google Scholar
Degrémont, Cédric, & Roy, Oliver. (2012). Agreement theorems in dynamic-epistemic logic. Journal of Philosophical Logic, 41(4), 735–764.CrossRefGoogle Scholar
Demey, Lorenz. (2014). Agreeing to disagree in probabilistic dynamic epistemic logic. Synthese, 191(3), 409–438.Google Scholar
Elga, Adam. (2000). Self-locating belief and the sleeping beauty problem. Analysis, 60(266), 143–147.Google Scholar
Halpern, Joseph, Moses, Yoram, & Vardi, Moshe. (1995). Reasoning About Knowledge. MIT Press Cambridge, Massachusetts.Google Scholar
Lederman, Harvey. (2015). People with common priors can agree to disagree, this Review, 8(1), 11–45.Google Scholar
Leslie, John. (1997). Observer-relative chances and the doomsday argument. Inquiry, 40, 427–436.CrossRefGoogle Scholar
Lewis, David. (1969). Convention. Blackwell Publishing, Oxford.Google Scholar
Lewis, David. (1979). Attitudes de dicto and de se. The Philosophical Review, 88(4), 513–543.Google Scholar
Lewis, David. (2001). Sleeping beauty: Reply to Elga. Analysis, 61(271), 171–176.CrossRefGoogle Scholar
Lewis, David. (2004). How many lives has Schrödinger’s cat? Australasian Journal of Philosophy, 82(1), 3–22.Google Scholar
Meacham, Christopher. (2008). Sleeping beauty and the dynamics of de se beliefs. Philosophical Studies, 138(2), 245–269.Google Scholar
Rubinstein, Ariel, & Wolinsky, Asher. (1990). On the logic of ‘agreeing to disagree’ type results. Journal of Economic Theory, 1, 184–193.Google Scholar