u.J TERMS. 



We are logically weak and imperfect in respect of the fact 

 that we are obliged to think of one thing after another. We 

 must describe metal as " hard and opaque," or " opaque and 

 hard," but in the metal itself there is no such difference of 

 order ; the properties are simultaneous and coextensive in 

 existence. 



Setting aside all grammatical peculiarities which render 

 a substantive less moveable than an adjective, and dis- 

 regarding any meaning indicated by emphasis or marked 

 order of words, we may state, as a general law of logic, 

 that- AB is identical with BA, or AB = BA. Similarly, 

 ABC = ACB = BOA = &c. 



Boole first drew attention in recent years to this pro- 

 perty of logical terms, and he called it the property of 

 Coinnmtativeness. 1 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 this work to show how the necessary im- 

 perfection 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 crystalliza- 

 tion of water." All relations which involve differences of time 

 and space are inconvertible ; the higher must not be made to 

 change places with the lower, nor the first with the last. For 

 the parties concerned there is all the difference in the world 

 between A killing B and B killing A. The law of com- 

 mutativeness simply asserts that difference of order does 

 not attach to the connection between the properties and 

 circumstances of a thing to what I call simple logical 

 relation. 



1 Laws of Thought, p. 29. It is pointed out in the preface to this 

 Second Edition that Leibnitz was acquainted with the Laws of 

 Simplicity and of Cominutativeness. 



