The Dynamics of Non-Belief (with Modesty)

Abstract “Suspension of judgment” is an ambiguous term that may refer either to a doxastic state (“suspended judgment”) or to a doxastic action (“suspending judgment”). Based on a simple non-belief account, this paper presents a formal study of both aspects of suspension. We first introduce the notion of a suspension set (a set of non-beliefs) and determine its logical structure. Then we present the classical AGM operations of belief revision and belief contraction and give characterizations of them that refer to suspension sets rather than belief sets. Finally, we study the suspension operation, a symmetric cousin of belief contraction, and characterize it both in terms of belief sets and in terms of suspension sets. Belief contraction and belief suspension thereby get reinterpreted as two different forms of the expansion of suspension sets. The project is interesting because in contrast to belief revision and belief contraction, the suspension operation is symmetric with respect to negation: suspending judgment on A is the same as suspending judgment on $$\lnot A$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>¬</mml:mo> <mml:mi>A</mml:mi> </mml:mrow> </mml:math> . Most of our results are premised on an assumption of modesty: For every person with consistent beliefs, there is always at least one proposition on which she suspends judgment.