TERMINOLOGY AND NOMENCLATURE* 293 



tions which are to be performed upon the symbols, 

 such as squaring both sides of the equation, multiply- 

 ing or dividing by the same or by equivalent 

 symbols, and so forth. Each of these operations, it 

 is true, corresponds to a syllogism; 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 con- 

 forming to which we can make sure of finding the 

 conclusion of the ratiocination, our end can be com- 

 pletely attained without our ever thinking of any- 

 thing but the symbols. Being thus intended to work 

 merely as mechanism, they have the qualities which 

 mechanism ought to have. They are of .the least 

 possible bulk, so that they take up scarcely any 

 room, and waste no time in their manipulation; they 

 are compact, and fit so closely together that the eye 

 can take in the whole at once of almost every operation 

 which they are employed to perform. 



These admirable properties of the symbolical lan- 

 guage of mathematics have made so strong an impres- 

 sion on the minds of many philosophers, as to have led 

 them to consider the symbolical language in question 

 as the ideal type of philosophical language generally; 

 to think that names in general, or (as they are fond of 

 calling them) signs, are fitted for the purposes of 

 thought in proportion as they can be made to ap- 

 proximate to the compactness, the entire unmeaning- 

 ness, and the capability of being used as counters 

 without a thought of what they represent, which are 

 characteristic of the a and &, the x and y, of algebra. 

 This notion has led to sanguine views of the accelera- 

 tion of the progress of science by means which, as I 

 conceive, cannot possibly conduce to that end, and 

 forms part of that exaggerated estimate of the influ- 



