Mr. Bertrand Russell[1] gives the following definition in this connection. A system is said to be 'deterministic' when, given certain data, e1, e2 ... en, at times, t1, t2 ... tn respectively, concerning this system, if Et is the state of the system at any time t, there is a functional relation of the form
Et = f(e1, t1, e2, t2 ..., en, tn, t).
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."
Mr. Russell goes on to consider the possibility that such a formula may be applicable to the Universe, in which case the latter would be a deterministic system. Leaving aside for the moment the general question as to whether the Universe is in any sense deterministic or not, and if so in what sense, let us consider what determinism, in the above use of the term, implies. In the first place it is evident that the given functional relation is equivalent to a description in general terms. Now the fundamental characteristic of the Universe is the particularity of its facts. The individuals which, at least in part, compose it, and their experiences, are essentially unique, and therefore are in no way susceptible to description in general terms. This fact is of the first importance when we are endeavoring to form a final conception of the nature of the Universe and not simply attempting to formulate a partially adequate general description of certain aspects of it. If they are to take account of the uniqueness in the Universe, the data contained in our functional relation would have to comprise every individual in the Universe, and the experience of each at every instant of his history, were this possible in a relation of the given type. It is true that Mr. Russell admits that the relation may be of strictly infinite complexity, but if it must necessarily be of the order of complexity we have indicated, it would simply be a recital of the whole history of the Universe. That is, it would have to contain explicitly all the information which it might have been hoped to contain implicitly. There is, in fact, no room in it for a variable at all, for it contains
- ↑ "Notion of Cause." Scientia, pp. 331 ff.
