WORLDS OF PHYSICS AND OF SENSE 119 



first must be before the third. Secondly, every event 

 must be at a certain number of instants ; two events are 

 simultaneous if they are at the same instant, and one is 

 before the other if there is an instant, at which the one 

 is, which is earlier than some instant at which the other 

 is. Thirdly, if we assume that there is always some 

 change going on somewhere during the time when any 

 given event persists, the series of instants ought to be 

 compact, i.e. given any two instants, there ought to be 

 other instants between them. Do instants, as we have 

 defined them, have these properties ? 



We shall say that an event is " at " an instant when it 

 is a member of the group by which the instant is con- 

 stituted ; and we shall say that one instant is before 

 another if the group which is the one instant contains an 

 event which is earlier than, but not simultaneous with, 

 some event in the group which is the other instant. 

 When one event is earlier than, but not simultaneous 

 with another, we shall say that it "wholly precedes" the 

 other. Now we know that of two events which are not 

 simultaneous, there must be one which wholly precedes 

 the other, and in that case the other cannot also wholly 

 precede the one ; we also know that, if one event wholly 

 precedes another, and the other wholly precedes a third, 

 then the first wholly precedes the third. From these 

 facts it is easy to deduce that the instants as we have 

 defined them form a series. 



We have next to show that every event is " at " at least 

 one instant, i.e. that, given any event, there is at least 

 one class, such as we used in defining instants, of which 

 it is a member. For this purpose, consider all the events 

 which are simultaneous with a given event, and do not 

 begin later, i.e. are not wholly after anything simultaneous 

 with it. We will call these the " initial contemporaries 



