260 OPERATIONS SUBSIDIARY TO INDUCTION. 



Whenever the nature of the subject permits our reasoning 

 processes to be, without danger, carried on mechanically, the 

 language should be constructed on as mechanical principles 

 as possible ; while in the contrary case, it should be so con- 

 structed that there shall be the greatest possible obstacles to a 

 merely mechanical use of it. 



I am aware that this maxim requires much explanation, 

 which I shall at once proceed to give. And first, as to what 

 is meant by using a language mechanically. The complete or 

 extreme case of the mechanical use of language, is when it is 

 used without any consciousness of a meaning, and with only 

 the consciousness of using certain visible or audible marks in 

 conformity to technical rules previously laid down. This ex- 

 treme case is nowhere realized except in the figures of arith- 

 metic and the symbols of algebra, a language unique in its 

 kind, and approaching as nearly to perfection, for the purposes 

 to which it is destined, as can, perhaps, be said of any creation 

 of the human mind. Its perfection consists in the complete- 

 ness of its adaptation to a purely mechanical use. The symbols 

 are mere counters, without even the semblance of a meaning 

 apart from the convention which is renewed each time they 

 are employed, and which is altered at each renewal, the same 

 symbol a or x being used on different occasions to represent 

 things which (except that, like all things, they are susceptible 

 of being numbered) have no property in common. There is 

 nothing, therefore, to distract the mind from the set of mecha- 

 nical operations which are to be performed upon the symbols, 

 such as squaring both sides of the equation, multiplying or 

 dividing them by the same or by equivalent symbols, and so 

 forth. Each of these operations, it is true, corresponds to a syl- 

 logism; represents one step of a ratiocination relating not to 

 the symbols, but to the things signified by them. But as it has 

 been found practicable to frame a technical form, by conform- 

 ing to which we can make sure of finding the conclusion of 

 the ratiocination, our end can be completely attained without 

 our ever thinking of anything but the symbols. Being thus 

 intended to work merely as mechanism, they have the quali- 

 ties which mechanism ought to have. They are of the least 



