Disbelief as the dual of belief

Abstract
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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DOI 10.1080/02698590701589536
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References found in this work BETA
What Conditional Probability Could Not Be.Alan Hájek - 2003 - Synthese 137 (3):273--323.
A Mathematical Theory of Evidence.Glenn Shafer - 1976 - Princeton University Press.
A Material Theory of Induction.John D. Norton - 2003 - Philosophy of Science 70 (4):647-670.

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Citations of this work BETA
Ignorance and Indifference.John Norton - 2008 - Philosophy of Science 75 (1):45-68.
Cosmic Confusions: Not Supporting Versus Supporting Not.John D. Norton - 2010 - Philosophy of Science 77 (4):501-523.
The Bayesian Who Knew Too Much.Yann Benétreau-Dupin - 2015 - Synthese 192 (5):1527-1542.
Contradictory Information: Too Much of a Good Thing. [REVIEW]J. Michael Dunn - 2010 - Journal of Philosophical Logic 39 (4):425 - 452.
Deductively Definable Logies of Induction.John Norton - 2010 - Journal of Philosophical Logic 39 (6):617 - 654.

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