38. The Application of the Functional Relation.
I have already shown ([p. 34]) how the first formulation of a causal relation which experience yields can be purified and elaborated by the multiplication of the experience. The method described was based upon the fact that the necessary and adequate factors of the result were obtained by eliminating successively from the "cause" the various factors of which its concept was or could be compounded, and by concluding from the result, that is, the presence or absence of the "effect," as to the necessity or superfluity of each factor.
Obviously the application of this process presupposes the possibility of eliminating each factor in turn. Very often it is not possible, and then in place of the inadequate method of the individual case the method of the continuous functional relation steps in with its infinitely greater effectiveness. If in most cases we cannot eliminate the factors one by one, there are very few instances in which it is not possible to change them, or to observe the result in the automatically changed values of the factors. But then we have the principle that for the causal relation all such factors are essential the change of which involves a change of the result.
It is clear that this signifies a generalization of the former and more limited method. For the elimination of the factor means that its value is reduced to zero. But now it is no longer necessary to go to this extreme limit; it suffices merely to influence in some way the factor to be investigated.
It is true that here the difference in the result cannot be expressed with a "yes" or a "no," as before. It can only be said that it has changed partly, more or less. From this it can be seen that the application of this process requires more refined methods of observation, especially for measuring, that is, for determining values or magnitudes. On the other hand, we must recognize how much deeper we can penetrate into the knowledge of things by the application of the measuring process. Each advance in precision of measurement signifies the discovery of a new stratum of scientific truth previously inaccessible.