TI;eE PROBABILISTIC ARGUMENT FOR A NON-CLASSICAL LQGIC OF QUANTUM MECHANICS"

The aim of this paper is to state the single most powerful argument for use of a non-classical logic in quantum mechanics. In outline the argument is the following. The working logic of a science is the logic of the events and propositions to which probabilities are assigned. A probability should be assigned to every element of the algebra of events. In the case of quantum mechanics probabilities may be assigned to events but not, without restriction, to the conjunction of two events. The conclusion is that the working logic of quantum mechanics is not classical. The nature of the logic that is appropriate for quantum mechanics is examined. 1, The argument. The aim of this paper is simple. I want to state as clearly as possible, without a long discursion into technical questions, what I consider to be the single most powerful argument for use of a non-classical logic in quantum mechanics. There is a very large mathematical and philosophical literature on the logic of quantum mechanics, but almost without exception, this literature provides a very poor intuitive justification for considering a non-classical logic in the first place. A classical example in the mathematical literature is the famous article b