THE THEORY OF CONTINUITY 143 



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 in- 

 stants 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 mathe- 

 matical 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. 



(F) 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 



