George Boole's ‘Conditions of Possible Experience’ and the Quantum Puzzle

Abstract

In the mid-nineteenth century George Boole formulated his ‘conditions of possible experience’. These are equations and ineqaulities that the relative frequencies of (logically connected) events must satisfy. Some of Boole's conditions have been rediscovered in more recent years by physicists, including Bell inequalities, Clauser Horne inequalities, and many others. In this paper, the nature of Boole's conditions and their relation to propositional logic is explained, and the puzzle associated with their violation by quantum frequencies is investigated in relation to a variety of approaches to the interpretation of quantum mechanics.