TERMINOLOGY AND NOMENCLATCTRE. 429 



subordinate to the mode of aiTaiif^insr those Kinds into larger classes. 

 With respect to the minor n'<iuisitos of Tenninology, some of them 

 are well stated and copiously iUustrated in the "Aphorisms on the 

 Language of Science," included in Mr, Wlievveirs Philos02>hu nf the 

 Inductive Sciences. These, as being of secondary, importance in the 

 peculiar pouit of view of Logic, we shall leave the reader to seek in 

 Mr. Whewell's pages, and shall confine our own observations to one 

 more quality, which, next to the two already treated of, appears to be 

 the most valuable which the language of science can possess. Of this 

 quality a general notion may be conveyed by the following aphorism: 



Whenever the nature of the subject permits our reasoning process 

 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 constructed that there shall be the greatest 

 possible obstacles to a merely mechanical use of it. 



I am conscious 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 mo 

 chanical use of language, is when it is used without any consciousness 

 of eP meaning, and with only the consciousness of using certain visible 

 or audible marks in conformity to technical rules previously laid down. 

 This extreme case is, so far as I am aware, nowhere realized except 

 in the figures of arithmetic and the symbols of algebra, a language 

 unique in its kind, and approaching as nearly to perfection, for the pur- 

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

 of the human mind. Its perfection consists in the completeness of its 

 adaptation to a purely mechanical use. The symbols are mere coun- 

 ters, without even the semblance of a meaning apart from the conven- 

 tion which is renewed each time they are employed, and which is al- 

 tered at each renewal, the same symbol a or x being used on diflbrertt 

 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 mechani- 

 cal operations which are to be perft)rmed upon the symbols, such as 

 squaring both sides of the equation, multiplying or dividing by the 

 same or by equivalent symbols, and so forth. Each of these opera- 

 tions, it is true, coiTesponds 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 -jiracticable to frame a techirical form, 

 by conforming 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 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 wliich they are employed to perfoiTn. 



These admirable properties of the symbolical language of mathe- 

 matics have made so strong an impression on the minds of many phi- 

 losophers, 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 



