48 SCIENTIFIC METHOD IN PHILOSOPHY 



relations. So are before, after, greater, above, to the right 

 of, etc. All the relations that give rise to series are of 

 this kind. 



Classification into symmetrical, asymmetrical, and merely 

 non-symmetrical relations is the first of the two classifica- 

 tions we had to consider. The second is into transitive, 

 intransitive, and merely non-transitive relations, which 

 are defined as follows. 



A relation is said to be transitive, if, whenever it holds 

 between A and B and also between B and C, it holds 

 between A and C. Thus before, after, greater, above are 

 transitive. All relations giving rise to series are transi- 

 tive, but so are many others. The transitive relations 

 just mentioned were asymmetrical, but many transitive 

 relations are symmetrical for instance, equality in any 

 respect, exact identity of colour, being equally numerous 

 (as applied to collections), and so on. 



A relation is said to be non-transitive whenever it is not 

 transitive. Thus " brother ' is non-transitive, because 

 a brother of one's brother may be oneself. All kinds of 

 dissimilarity are non-transitive. 



A relation is said to be intransitive when, if A has the 

 relation to B, and B to C, A never has it to C. Thus 

 " father " is intransitive. So is such a relation as " one 

 inch taller " or " one year later." 



Let us now, in the light of this classification, return 

 to the question whether all relations can be reduced to 

 predications. 



In the case of symmetrical relations i.e. relations which, 

 if they hold between A and B, also hold between B and 

 A some kind of plausibility can be given to this doctrine. 

 A symmetrical relation which is transitive, such as equality, 

 can be regarded as expressing possession of some common 

 property, while one which is not transitive, such as 



