Two distinct features of the Keynes-Kyburg conception of probability are: (i) probability represents a logical relation that is objective, and (ii) not all probabilities are comparable. The non-comparability of probability is the starting point for this work in progress, which is a study of conjunction and disjunction for rationally accepted propositions understood to be an event’s lower probability. An abstract appears below the fold. Comments welcome!
Abstract: A bounded formula (φ, e) is a pair consisting of a propositional formula φ in the first coordinate and a real number within the unit interval in the second coordinate, interpreted to express that e is the lower-bound probability of φ. Converting conjunctive/disjunctive combinations of bounded formulas to a single bounded conjunctive/disjunctive proposition consisting of the propositions occuring in the collection of bounded formulas along with a newly calculated lower probability is called absorption. This paper introduces two inference rules for effecting conjunctive and disjunctive absorption and discusses their applicability to the lottery paradox and the paradox of the preface.