The Transcendental Character of Determinism

DETERMINISM in philosophical discussions of determinism I believe it is fair to say that there is not ordinarily a sharp separation of a process being deterministic and a process being predictable. Much of the philosophical talk about determinism proceeds as if it is understood that a deterministic process is necessarily predictable. Here is a typical quotation, taken from A. J. Ayer's essay " Freedom and Necessity: " " Nevertheless, it may be said, if the postulate of determinism is valid, then the future can be explained in terms of the past: and this means that if one knew enough about the past one would be able to predict the future. " Without attempting quite general definitions for arbitrary systems, it will still be useful to examine in somewhat more detail how we ordinarily think about these two related but different concepts of determinism in prediction. One formulation of determinism grows naturally out of the theory of differential equations. If a set of differential equations is given for a phenomenon, then we say that the phenomenon is deterministic if there is exactly one solution as a function of time of the differential equations satisfying the given initial and boundary conditions. There is no general conceptual reason, of course, for restricting ourselves to differential equations. We can easily say that a system of equations for discrete time intervals is deterministic in the same sense. Sometimes in formulating what we mean by deterministic systems we put the emphasis rather differently. For example, in asserting the claim that classical mechanics is deteministic we may formulate the condition along the following lines. The history of an isolated system of particle mechanics is determined by the masses and forces acting on the particles, together with'appropriate initial conditions. Âs is weil known, these appropriate initial conditions give for some particular instant of time the position and velocity of each of the particles. When