Page:Mysticism and Logic and Other Essays.djvu/211

Rh circumstances, and would not have been true if the rest of the universe had been different though subject to the same laws.

The essential function which causality has been supposed to perform is the possibility of inferring the future from the past, or, more generally, events at any time from events at certain assigned times. Any system in which such inference is possible may be called a "deterministic" system. We may define a deterministic system as follows:—

A system is said to be "deterministic" when, given certain data, $$e_1, e_2, ..., e_n$$, at times $$t_1, t_2, ..., t_n$$ respectively, concerning this system, if $$\Epsilon_t$$ is the state of the system at any time $$t$$, there is a functional relation of the form

$$\Epsilon_t=f(e_1, t_1, e_2, t_2, ..., e_n, t_n, t).$$(A)

The system will be "deterministic throughout a given period" if $$t$$, in the above formula, may be any time within that period, though outside that period the formula may be no longer true. If the universe, as a whole, is such a system, determinism is true of the universe; if not, not. A system which is part of a deterministic system I shall call "determined"; one which is not part of any such system I shall call "capricious."

The events $$e_1, e_2, ..., e_n$$ I shall call "determinants" of the system. It is to be observed that a system which has one set of determinants will in general have many. In the case of the motions of the planets, for example, the configurations of the solar system at any two given times will be determinants.

We may take another illustration from the hypothesis of psycho-physical parallelism. Let us assume, for the purposes of this illustration, that to a given state of brain