Page:Our knowledge of the external world.djvu/159

 mathematical theory of motion is applicable to the data of sensation as well as to the supposed particles of abstract physics.

There are a number of distinct questions which are apt to be confused when the mathematical continuum is said to be inadequate to the facts of sense. We may state these, in order of diminishing generality, as follows:—


 * (a) Are series possessing mathematical continuity logically possible?


 * (b) Assuming that they are possible logically, are they not impossible as applied to actual sense-data, because, among actual sense-data, there are no such fixed mutually external terms as are to be found, e.g., in the series of fractions?


 * (c) Does not the assumption of points and instants make the whole mathematical account fictitious?


 * (d) Finally, assuming that all these objections have been answered, is there, in actual empirical fact, any sufficient reason to believe the world of sense continuous?

Let us consider these questions in succession.

(a) The question of the logical possibility of the mathematical continuum turns partly on the elementary misunderstandings we considered at the beginning of the present lecture, partly on the possibility of the mathematical infinite, which will occupy our next two lectures, and partly on the logical form of the answer to the Bergsonian objection which we stated a few minutes ago. I shall say no more on this topic at present, since it is desirable first to complete the psychological answer.

(b) The question whether sense-data are composed of mutually external units is not one which can be decided by empirical evidence. It is often urged that, as a