LOGIC AS THE ESSENCE OF PHILOSOPHY 47 



the best results. Everyone knows that to read an author 

 simply in order to refute him is not the way to understand 

 him ; and to read the book of Nature with a conviction 

 that it is all illusion is just as unlikely to lead to under- 

 standing. If our logic is to find the common world 

 intelligible, it must not be hostile, but must be inspired 

 by a genuine acceptance such as is not usually to be 

 found among metaphysicians. 



Traditional logic, since it holds that all propositions 

 have the subject-predicate form, is unable to admit the 

 reality of relations : all relations, it maintains, must be 

 reduced to properties of the apparently related terms. 

 There are many ways of refuting this opinion ; one of 

 the easiest is derived from the consideration of what are 

 called " asymmetrical ' relations. In order to explain 

 this, I will first explain two independent ways of classify- 

 ing relations. 



Some relations, when they hold between A and B, also 

 hold between B and A. Such, for example, is the relation 

 "brother or sister." If A is a brother or sister of B, 

 then B is a brother or sister of A. Such again is any 

 kind of similarity, say similarity of colour. Any kind of 

 dissimilarity is also of this kind : if the colour of A is 

 unlike the colour of B, then the colour of B is unlike 

 the colour of A. Relations of this sort are called sym- 

 metrical. Thus a relation is symmetrical if, whenever it 

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



All relations that are not symmetrical are called non- 

 symmetrical. Thus " brother " is non-symmetrical, because, 

 if A is a brother of B, it may happen that B is a sister 

 of A. 



A relation is called asymmetrical when, if it holds 

 between A and B, it never holds between B and A. 

 Thus husband, father, grandfather, etc., are asymmetrical 



