THE THEORY OF CONTINUITY 149 



different shades in the spectrum, and so on, are all in 

 the nature of unverifiable hypotheses perfectly possible 

 logically, perfectly consistent with the known facts, and 

 simpler technically than any other tenable hypotheses, 

 but not the sole hypotheses which are logically and em- 

 pirically adequate. 



If a relational theory of instants is constructed, in 

 which an " instant ' is defined as a group of events 

 simultaneous with each other and not all simultaneous 

 with any event outside the group, then if our resulting 

 series of instants is to be compact, it must be possible, 

 if x wholly precedes y y to find an event z, simultaneous 

 with part of x y which wholly precedes some event which 

 wholly precedes y. Now this requires that the number 

 of events concerned should be infinite in any finite 

 period of time. If this is to be the case in the world 

 of one man's sense-data, and if each sense-datum is to 

 have not less than a certain finite temporal extension, it 

 will be necessary to assume that we always have an 

 infinite number of sense-data simultaneous with any given 

 sense-datum. Applying similar considerations to space, 

 and assuming that sense-data are to have not less than a 

 certain spatial extension, it will be necessary to suppose 

 that an infinite number of sense-data overlap spatially 

 with any given sense-datum. This hypothesis is possible, 

 if we suppose a single sense-datum, e.g. in sight, to be a 

 finite surface, enclosing other surfaces which are also 

 single sense-data. But there are difficulties in such a 

 hypothesis, and I do not know whether these difficulties 

 could be successfully met. If they cannot, we must do 

 one of two things : either declare that the world of one 

 man's sense-data is not continuous, or else refuse to 

 admit that there is any lower limit to the duration and 

 extension of a single sense-datum. I do not know what 



