WORLDS OF PHYSICS AND OF SENSE 121 



Instants may also be defined by means of the enclosure- 

 relation, exactly as was done in the case of points. One 

 object will be temporally enclosed by another when it is 

 simultaneous with the other, but not before or after it. 

 Whatever encloses temporally or is enclosed temporally 

 we shall call an " event." In order that the relation 

 of temporal enclosure may be a "point-producer," we 

 require (1) that it should be transitive, i.e. that if one 

 event encloses another, and the other a third, then the 

 first encloses the third ; (2) that every event encloses 

 itself, but if one event encloses another different event, 

 then the other does not enclose the one ; (3) that given 

 any set of events such that there is at least one event 

 enclosed by all of them, then there is an event enclosing 

 all that they all enclose, and itself enclosed by all of them ; 

 (4) that there is at least one event. To ensure infinite 

 divisibility, we require also that every event should enclose 

 events other than itself. Assuming these characteristics, 

 temporal enclosure is an infinitely divisible point-producer. 

 We can now form an " enclosure-series ' of events, by 

 choosing a group of events such that of any two there is 

 one which encloses the other ; this will be a " punctual 

 enclosure-series ' ' if, given any other enclosure-series such 

 that every member of our first series encloses some 

 member of our second, then every member of our second 

 series encloses some member of our first. Then an 

 " instant " is the class of all events which enclose members 

 of a given punctual enclosure-series. 



The correlation of the times of different private worlds 

 so as to produce the one all-embracing time of physics is 

 a more difficult matter. We saw, in Lecture III., that 

 different private worlds often contain correlated appear- 

 ances, such as common sense would regard as appearances 

 of the same " thing." When two appearances in different 



