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30 Aug 2011
Logical questions behind the lottery and preface paradoxes: lossy rules for uncertain inference
 David Makinson
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We reflect on lessons that the lottery and preface paradoxes provide for the logic of uncertain inference. One of these lessons is the unreliability of the rule of conjunction of conclusions in such contexts, whether the inferences are probabilistic or qualitative; this leads us to an examination of consequence relations without that rule, the study of other rules that may nevertheless be satisfied in its absence, and a partial rehabilitation of conjunction as a ‘lossy’ rule. A second lesson is the possibility of rational inconsistent belief; this leads us to formulate criteria for deciding when an inconsistent set of beliefs may reasonably be retained.
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 Title
 Logical questions behind the lottery and preface paradoxes: lossy rules for uncertain inference
 Journal

Synthese
Volume 186, Issue 2 , pp 511529
 Cover Date
 20120501
 DOI
 10.1007/s1122901199972
 Print ISSN
 00397857
 Online ISSN
 15730964
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Lottery paradox
 Preface paradox
 Uncertain inference
 Conjunction
 Rationality
 Inconsistency
 Lossy rules
 Industry Sectors
 Authors

 David Makinson ^{(1)}
 Author Affiliations

 1. Department of Philosophy, Logic & Scientific Method, London School of Economics, Houghton Street, London, WC2A 2AE, UK