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Disbelief as the Dual of Belief

Norton, John D. (2007) Disbelief as the Dual of Belief. [Preprint]


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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.

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Item Type: Preprint
Norton, John D.
Additional Information: To appear in International Studies in the Philosophhy of Science
Keywords: probability duality measure belief disbelief ignorance
Subjects: General Issues > Confirmation/Induction
Depositing User: John Norton
Date Deposited: 13 Jul 2007
Last Modified: 07 Oct 2010 15:15
Item ID: 3438

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