Over the centuries, the doctrine of determinism has been understood, and assessed, in different ways. Since the seventeenth century, it has been commonly understood as the doctrine that every event has a cause; or as the predictability, in principle, of the entire future. To assess the truth of determinism, so understood, philosophers have often looked to physical science; they have assumed that their current best physical theory is their best guide to the truth of determinism. Most have believed that classical physics, especially Newton’s physics, is deterministic. And in this century, most have believed that quantum theory is indeterministic. Since quantum theory has superseded classical physics, philosophers have typically come to the tentative conclusion that determinism is false.
In fact, these impressions are badly misleading, on three counts. First of all, formulations of determinism in terms of causation or predictability are unsatisfactory, since ‘event’, ‘causation’ and ‘prediction’ are vague and controversial notions, and are not used (at least not univocally) in most physical theories. So if we propose to assess determinism by considering physical theories, our formulation of determinism should be more closely tied to such theories. To do this, the key idea is that determinism is a property of a theory. Imagine a theory that ascribes properties to objects of a certain kind, and claims that the sequence through time of any such object’s properties satisfies certain regularities. Then we say that the theory is deterministic if and only if for any two such objects: if their properties match exactly at a given time, then according to the theory, they will match exactly at all future times.
Second, this improved formulation reveals that there is a large gap between the determinism of a given physical theory, and the bolder, vague idea that motivated the traditional formulations: the idea that the world as a whole, independent of any single theory, is deterministic. Admittedly, one can make sense of this idea by adopting a sufficiently bold metaphysics: namely, a metaphysics that accepts the idea of a theory of the world as a whole, so that its objects are possible worlds, and determinism becomes the requirement that any two possible worlds described by the theory that match exactly at a given time also match exactly at all future times. But this idea cannot be made sense of using the more cautious strategy of considering determinism as a feature of a given physical theory.
Third, according to this more cautious strategy, the traditional consensus is again misleading. Which theories are deterministic turns out to be a subtle and complicated matter, with many questions still open. But broadly speaking, it turns out that much of classical physics, even much of Newton’s physics, is indeterministic. Furthermore, the alleged indeterminism of quantum theory is very controversial: it enters, if at all, only in quantum theory’s account of measurement processes, an account which remains the most controversial part of the theory. These subtleties and controversies mean that physics does not pass to philosophers any simple verdict about determinism. But more positively, they also mean that determinism remains an exciting topic in the philosophy of science.
Examples of Non-Constructive Proofs in Quantum Theory