SPACE, TIME 299 



correlation of the private spaces and private times is pos- 

 sible only through the discovery of common events. The 

 theoretical difficulties arising in this discovery constitute 

 one of the foundations for the theory of relativity. 



From discreteness to continuity. Only one of the meanings 

 of "continuity' will be considered here, viz., 'linear con- 

 tinuity." The problem is to determine the operational route 

 by which a finitely divisible space and time are made infi- 

 nitely divisible. This problem is sometimes formulated in 

 terms of the empirical derivation of points and instants. 

 Two closely similar views as to the nature of this derivation 

 may be presented. One is that of Russell and is called the 

 method of logical construction; the other is that of White- 

 head and is called the method of extensive abstraction. 



Russell's illustration is taken from time, but a similar 

 procedure is applicable to space. 'Let us take a group of 

 events of which any two overlap, so that there is some time, 

 however short, when they all exist. If there is any other 

 event which is simultaneous with all of these, let us add it 

 to the group; let us go on until we have constructed a group 

 such that no event outside the group is simultaneous with 

 all of them, but all the events inside the group are simul- 

 taneous with each other. Let us define this whole group as 

 an instant of time." 1 A somewhat less empirical point of 

 view would be inclined to define 'point" not as the class 

 of such events but rather as the property possessed in com- 

 mon by all of the events. 2 This method of defining "point" 

 seems preferable to the traditional one which considers it 

 as the limit of a series of gradually decreasing volumes. 

 Since the limit cannot be certainly known to exist, an opera- 

 tional route which defines the construct in terms of an 

 abstract feature which is known to exist retains a closer 

 empirical reference. 



Not altogether unlike this is Whitehead's method of 



1 Our Knowledge of the External World, p. 118. 



2 This empirical tendency has been noted before in connection with Russell's 

 definition of number as the class of all classes rather than as the properly of classes. 

 See above, p. 264 n. 



