LOGIC AS THE ESSENCE OF PHILOSOPHY 49 



inequality, can be regarded as expressing possession of 

 different properties. But when we come to asymmetrical 

 relations, such as before and after, greater and less, etc., 

 the attempt to reduce them to properties becomes ob- 

 viously impossible. When, for example, two things are 

 merely known to be unequal, without our knowing which 

 is greater, we may say that the inequality results from 

 their having different magnitudes, because inequality is 

 a symmetrical relation ; but to say that when one thing is 

 greater than another, and not merely unequal to it, that 

 means that they have different magnitudes, is formally 

 incapable of explaining the facts. For if the other thing 

 had been greater than the one, the magnitudes would 

 also have been different, though the fact to be explained 

 would not have been the same. Thus mere difference of 

 magnitude is not all that is involved, since, if it were, 

 there would be no difference between one thing being 

 greater than another, and the other being greater than 

 the one. We shall have to say that the one magnitude is 

 greater than the other, and thus we shall have failed to get 

 rid of the relation " greater." In short, both possession 

 of the same property and possession of different properties 

 are symmetrical relations, and therefore cannot account for 

 the existence of asymmetrical relations. 



Asymmetrical relations are involved in all series in 

 space and time, greater and less, whole and part, and 

 many others of the most important characteristics of the 

 actual world. All these aspects, therefore, the logic which 

 reduces everything to subjects and predicates is compelled 

 to condemn as error and mere appearance. To those 

 whose logic is not malicious, such a wholesale condemna- 

 tion appears impossible. And in fact there is no reason 

 except prejudice, so far as I can discover, for denying the 

 reality of relations. When once their reality is admitted, 



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