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Disbelief as the dual of belief

Norton, JD (2007) Disbelief as the dual of belief. International Studies in the Philosophy of Science, 21 (3). 231 - 252. ISSN 0269-8595

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The duality of truth and falsity in a Boolean algebra of propositions is used to generate a duality of belief and disbelief. To each additive probability measure that represents belief there corresponds a dual additive measure that represents disbelief. The dual measure has its own peculiar calculus, in which, for example, measures are added when propositions are combined under conjunction. A Venn diagram of the measure has the contradiction as its total space. While additive measures are not self-dual, the epistemic state of complete ignorance is represented by the unique, monotonic, non-additive measure that is self-dual in its contingent propositions. Convex sets of additive measures fail to represent complete ignorance since they are not self-dual. © 2007 Inter-University Foundation.


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Item Type: Article
Status: Published
CreatorsEmailPitt UsernameORCID
Norton, JDjdnorton@pitt.eduJDNORTON
Date: 1 December 2007
Date Type: Publication
Journal or Publication Title: International Studies in the Philosophy of Science
Volume: 21
Number: 3
Page Range: 231 - 252
DOI or Unique Handle: 10.1080/02698590701589536
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > History and Philosophy of Science
Refereed: No
ISSN: 0269-8595
Date Deposited: 21 May 2009 20:54
Last Modified: 02 Feb 2019 15:56


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