Conditionalizing on knowledge

A theory of evidential probability is developed from two assumptions:(1) the evidential probability of a proposition is its probability conditional on the total evidence;(2) one's total evidence is one's total knowledge. Evidential probability is distinguished from both subjective and objective probability. Loss as well as gain of evidence is permitted. Evidential probability is embedded within epistemic logic by means of possible worlds semantics for modal logic; this allows a natural theory of higher-order probability to be developed. In particular, it is emphasized that it is sometimes uncertain which propositions are part of one's total evidence; some surprising implications of this fact are drawn out.
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Brian Weatherson (2005). Should We Respond to Evil with Indifference? Philosophy and Phenomenological Research 70 (3):613–635.
Hannes Leitgeb (2013). Reducing Belief Simpliciter to Degrees of Belief. Annals of Pure and Applied Logic 164 (12):1338-1389.
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