u.] TERMS. :35 



We are logically weak and imyerfect in respect of the fact 

 tJiat we are uhliyed to think of one thing after another. We 

 miu-it describe luttal as " hard and opaque," or " opaque and 

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

 order ; the properties are simultaneous and coextensive in 

 existence. 



Setting aside all grammatical peculiarities whicli 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. Sindlarly, 

 ABC = AUB = B< A = &c. 



Boole first drew attention in recent years to this pro- 

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

 Oomiuutativeness.^ 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 tlie necessary im- 

 perfection of our synibols expressed in this law clings to 

 our modes of expression, and intioduces complication into 

 the whole body of mathenuitical formulae, which are really 

 founded on a logical basis. 



It is of cour.se 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 dilference in the world 

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

 mutativeness simply asserts that difference of order doc^s 

 not attach to the connection between the properties and 

 circumstances of a thing — to what 1 call simple logical 

 reiatiun. 



' Laws of Thouijht, p. 29. It is poiiitt'J out in the preface to this 

 Second Eililiun Ihat Leibnitz was acquainted with the Lavvs ol 

 Simplicity and of Commutativeness. 



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