Liars, Lotteries, and Prefaces: Two Paraconsistent Accounts of Belief Change

  • Edwin Mares
Part of the Outstanding Contributions to Logic book series (OCTR, volume 3)


In this paper two closely related systems of paraconsistent belief change are presented. A paraconsistent system of belief change is one that allows for the non-trivial treatment of inconsistent belief sets. The aim in this paper is to provide theories that help us investigate responses to paradoxes. According to the strong system of paraconsistent belief change, if an agent accepts an inconsistent belief set, he or she has to accept the conjunctions of all the propositions in it. The weak system, on the other hand, allows people to have beliefs without believing their conjunctions. The weak system seems to deal better than with the lottery and preface paradoxes than does strong system, although the strong system has other virtues.


Paraconsistent belief change Paraconsistent consequence relation Relevance logic Lottery paradox Preface paradox Liar paradox Russell’s paradox Reject set 



David Makinson suggested to me that I write a paper for this volume and for this he is in part responsible for my rethinking my views on paraconsistency and belief revision. I am very grateful to David for his close reading of a draft of this paper and his extremely helpful suggestions. I am grateful to Rob Goldblatt, Patrick Girard, Jeremy Seligman, and Zach Weber for listening to and commenting on an earlier version of this paper. I am also indebted to Sven Ove Hansson and his two referees for very helpful comments. They saved me from some very embarrassing errors.


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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Centre for Logic, Language, and ComputationVictoria University of WellingtonWellingtonNew Zealand

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