42 THE PRINCIPLES OF SCIENCE. 



The late Professor Boole first drew attention, so far as 

 I know, to this property of logical terms, and he called 

 it the property of Commutativeness 6 . He not only stated 

 the law with the utmost clearness, but pointed out that 

 it is a Law of Thought rather than a Law of Things. 

 I shall have in various parts of the following pages to 

 show how the necessary imperfection of our symbols 

 expressed in this law clings to our modes of expression, 

 and introduces complication into the whole body of 

 mathematical formulae, which are really founded on a 

 logical basis. 



It is of course apparent that the power of commutation 

 belongs only to terms related in the simple logical mode 

 of synthesis. No one can confuse 'a house of bricks/ 

 with * bricks of a house/ ' twelve square feet' with * twelve 

 feet square/ 'the water of crystallization' with 'the 

 crystallization of water.' All relations which involve 

 differences of time and space are inconvertible ; the 

 higher must not be made to change place with the 

 lower, or the first with the last. For the parties con- 

 cerned there is all the difference in the world between A 

 killing B and B killing A. The law of commutativeness 

 simply asserts that difference of order does not attach to 

 the connection between the properties and circumstances 

 of a thing to what I shall call simple logical relations. 



e 'Laws of Thought,' p. 29. 



