Disbelief as the dual of belief

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
John D. Norton (2003). A Material Theory of Induction. Philosophy of Science 70 (4):647-670.

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John Norton (2008). Ignorance and Indifference. Philosophy of Science 75 (1):45-68.
John Norton (2010). Deductively Definable Logies of Induction. Journal of Philosophical Logic 39 (6):617 - 654.

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