300 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



extensive abstraction. Consider it with reference to time. 

 "Durations can have the two- termed relational property of 

 extending one over the other. Thus the duration which is 

 all nature during a certain minute extends over the duration 

 which is all nature during the 30th second of that minute." l 

 "Every event extends over other events, and every event 

 is extended over by other events. Thus in the special case 

 of durations which are now the only events directly under 

 consideration, every duration is part of other durations; 

 and every duration has other durations which are parts of it. 

 Accordingly there are no maximum durations and no min- 

 imum durations." 2 "Such a set . . . has the properties of 

 the Chinese toy which is a nest of boxes, one within the 

 other, with the difference that the toy has a smallest box, 

 while the abstractive class has neither a smallest event nor 

 does it converge to a limiting event which is not a member 

 of the set." 3 The abstractive set serves to "guide thought 

 to the consideration of the progressive simplicity of natural 

 relations as we progressively diminish the temporal exten- 

 sion of the duration considered. Now the whole point of the 

 procedure is that the quantitative expressions of these 

 natural properties do converge to limits though the abstrac- 

 tive set does not converge to any limiting duration. The 

 laws relating these quantitative limits are the laws of 

 nature 'at an instant,' although in truth there is no nature 

 at an instant and there is only the abstractive set. Thus an 

 abstractive set is effectively the entity meant when we con- 

 sider an instant of time without temporal extension. It 

 subserves all the necessary purposes of giving a definite 

 meaning to the concept of the properties of nature at an 

 instant." 4 As in the case of Russell, the notion of "point" 

 is defined not as the limit of the series but as the series 

 itself, or an abstract feature of it. 



From finitude to infinity. The limits of empirical space 

 and time are extended through correlation. The essential 

 feature of an infinite series is the existence of a principle 



1 Concept of Nature, p. 58. 2 Ibid., p. 59. 3 Ibid., p. 80. 4 Ibid., p. 61. 



