WORLDS OF PHYSICS AND OF SENSE 125 



But many relations are transitive without being sym- 

 metrical for instance, such relations as " greater," 

 " earlier," " to the right of," " ancestor of," in fact all 

 such relations as give rise to series. Other relations 

 are symmetrical without being transitive for example, 

 difference in any respect. If A is of a different age from 

 B, and B of a different age from C, it does not follow that 

 A is of a different age from C. Simultaneity, again, in 

 the case of events which last for a finite time, will not 

 necessarily be transitive if it only means that the times of 

 the two events overlap. If A ends just after B has 

 begun, and B ends just after C has begun, A and B will 

 be simultaneous in this sense, and so will B and C, but 

 A and C may well not be simultaneous. 



All the relations which can naturally be represented as 

 equality in any respect, or as possession of a common 

 property, are transitive and symmetrical this applies, for 

 example, to such relations as being of the same height or 

 weight or colour. Owing to the fact that possession of a 

 common property gives rise to a transitive symmetrical 

 relation, we come to imagine that wherever such a relation 

 occurs it must be due to a common property. " Being 

 equally numerous is a transitive symmetrical relation of 

 two collections ; hence we imagine that both have a 

 common property, called their number. " Existing at a 

 given instant ' (in the sense in which we denned an 

 instant) is a transitive symmetrical relation ; hence we 

 come to think that there really is an instant which confers 

 a common property on all the things existing at that 

 instant. "Being states of a given thing" is a transitive 

 symmetrical relation ; hence we come to imagine that 

 there really is a thing, other than the series of states, 

 which accounts for the transitive symmetrical relation. 

 In all such cases, the class of terms that have the given 



