Abstract

Recently, several writers have independently proposed similar solutions to the quantum-mechanical measurement problem. This dissertation examines the conception of physical properties implicit in these proposals, which are known as modal interpretations of quantum mechanics. The dissertation focuses on Richard Healey's interpretation, which I regard as the most promising of the proposals. ;Chapter One reviews the measurement problem and the way in which modal interpretations address the problem. ;Chapter Two discusses certain mathematical theorems that impose strict limits on the number of properties that a system can possess at any instant. I examine a number of inferences that interpreters have drawn from these theorems, and argue that some of these inferences are misguided. This discussion leads to the recognition that, despite overarching similarities between Healey's interpretations and several of the other modal interpretations, the interpretations differ in fundamental respects. ;Chapter Three presents several desiderata on the set of properties possessed by a quantum system at an instant. One of these desiderata concerns the relation between a system's properties and the properties of that system's subsystems. To borrow Frank Arntzenius's illustration, the desideratum demands, for instance, that the left-hand leaf of a table be green if and only if the table has a green left-hand leaf. Unfortunately, most modal interpretations fail to satisfy this demand. Using mathematical arguments, I show that Healey's interpretation satisfies the demand. ;Chapter Four turns to a problematic feature of Healey's interpretation, namely its violation of a desideratum called Property Intersection. Property Intersection demands that if a variable's value is restricted to a set $\Delta$ and is also restricted to a set $\Gamma,$ then the value is restricted to the intersection of $\Delta$ and $\Gamma.$ I propose two strategies for amending Healey's interpretation so that it respects Property Intersection, but I find both of these strategies unsatisfactory, since each creates new problems. I then consider several possible reasons for imposing Property Intersection as a requirement, and I argue that none of these reasons is compelling; thus, I claim, Healey's violation of Property Intersection is defensible