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Journal of Logic and Computation Advance Access published online on March 4, 2008
Journal of Logic and Computation, doi:10.1093/logcom/exm096
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© The Author, 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original papers

Degrees of Belief

Isaac Levi

John Dewey Professor of Philosophy Emeritus, Columbia University, New York, USA.

E-mail: levi{at}columbia.edu


  Abstract

This article surveys various accounts of degrees of belief and the relation between degrees of belief and full belief or absolute certainty. Corresponding to each notion of degree of belief is a conception of evidential support. Three different kinds of degrees of belief and the corresponding notions of evidential support are considered: probability, evidential support in the maximizing sense and in the satisficing sense. It is argued that probability cannot be the degree of belief or evidential support in either the maximizing or satisficing sense. Reconstructions of maximizing and satisficing degree of belief are proposed, which show that they are ways of evaluating potential answers to questions that demand the inductive expansion of a state K of full belief. These reconstructions are based on an account of inductive expansion briefly summarized in the text that understands inductive expansion to be the choice of a potential answer that maximizes a weighted average of the risk of error and the value of the information acquired. Thus, maximizing this weighted average is an index of degree of evidential support in the maximizing sense. It is explained how an index of evidential support in the satisficing sense can be constructed that achieves the same result. Finally, it is argued that several so called ‘qualitative’ notions of belief other than full belief are deprived of useful application in deliberation and inquiry because they lack the relevance to inductive expansion that maximizing and satisficing evidential support (or degree of belief) has. The discussion should be of interest to students of measures of uncertainty, inductive or non-monotonic reasoning and decision making.

Keywords: Inductive expansion; full belief; credal probability; maximizing evidential support; satisficing evidential support; plain belief


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