Determinism in physics means that the state of a real system at a given time is fixed by its prior states. This presumes time and a notion of system. The state of the system is expressed by an equation as a function of time. But it is the equation that is “deterministic,” not the real system. The notion of physical determinism confuses the logical relationships of variables in the equation with some physical or metaphysical force of one state to “fix” another. After all, the word determine is ambiguous, meaning either to fix or to ascertain. One is an ontological claim, presuming some causally continuous process relating one state and a later one. The other is an epistemological claim, presuming a conscious agent, such as a scientist. The equation enables such claims, but only at the cost of describing an idealized fiction.

The obvious advantage of determinism in physics is that one can predict the future or retrodict the past. In order to be calculable in the required way, the system must be well defined and follow mechanical rules. In other words, it must be a deductive system, an idealization, which can only correspond approximately to a natural system. The ability to accurately predict the future of planetary motions, for example, results from the fact that such real systems coincide, for all practical purposes, with deductive systems. (In such massive systems, deviations on a micro scale cancel out to yield a statistically precise averaged macroscopic pattern, which is then codified as a law.) A deterministic system always evolves the same way from a given starting point. The equations involved in the early studies of dynamics were linear, and well-behaved phenomena were deliberately selected for study that could be expressed by such equations. The notion of determinism afforded a point of view outside the system under study, from which to regard change without being affected by it. But this has obvious limits in dealing with the universe as a whole.