Page:The Conception of God (1897).djvu/344

 law, but all still mutually free with a freedom that is a part of the freedom of the Whole?

It is, then, possible that the selection of an individual whole should at a stroke determine the individual parts, or that, on the other hand, an individual whole should consist of mutually contingent individuals. The conditions that determine whether the one or the other of these logical possibilities shall be realised are not difficult to state. All depends upon the nature of the system of ideas that is to be realised. In any system of ideas, in advance of realisation the ideas may be of objects which stand to each other in relations that admit of no ambiguity as to their particular expressions. Relationships of this kind are very familiar. If in the world of ideas a is a quantity, and b another quantity equal to a, no ambiguity of any sort besets the relationship. In that case, any individual embodiment of this system of ideas in actual quantities — for example, A and B — will be such that I am free to choose only one of the two quantities, the other then being predetermined. On the other hand, in the most exact sciences, nothing is more common than cases of relationships which are not inexact, but which are in one sense ambiguous. Notoriously, any quantity a has two square roots, three cube roots, etc. If, then, I know that b is the square root of a, an individual embodiment of this simple system of ideas is not such that the determination of one object A in an individual embodiment predetermines absolutely the other individual. In this case, two alternatives are left open; and when I exemplify the system by