Generalized Probability Measures and the Framework of Effects

Abstract

This paper is dedicated to the memory of Itamar Pitowsky. It develops the idea that the generalized probability measures of quantum mechanics are the probabilities of “effects.” As explained below, effects are included among measurement outcomes but are not exhausted by them. They also differ in key respects from propositions which attribute dynamical properties to the systems that are probed by measurements. These differences are elaborated, and an interpretation of the implicit probability theory of quantum mechanics in terms of effects is outlined. A central feature of this interpretation is that it supports a form of realism that accommodates the no hidden variable theorem of Kochen and Specker, and it does so without appealing to any notion of contextuality.