494 OPERATIONS SUBSIDIARY TO INDUCTION. 



of distinction, while tlie word, still continuing to denote the same group or 

 things, is not considered to have changed its meaning. For this is no more 

 than may happen in the case of any other general name ; we may, in re- 

 forming its connotation, leave its denotation untouched ; and it is general- 

 ly desirable to do so. The connotation, however, is not the less for this 

 the real meaning, for we at once apply the name wherever the characters 

 set down in the definition are found ; and that which exclusively guides 

 us in applying the term, must constitute its signification. If we find, con- 

 trary to our previous belief, that the characters are not peculiar to one spe- 

 cies, we cease to use the term co-extensively with the characters ; but then 

 it is because the other portion of the connotation fails ; the condition that 

 the class must be a Kind. The connotation, therefore, is still the meaning ; 

 the set of descriptive characters is a true definition ; and the meaning is 

 unfolded, not indeed (as in other cases) by the definition alone, but by the 

 definition and the form of the word taken together. 



§ 6. We have now analyzed what is implied in the two principal requisites 

 of a philosophical language ; first, precision, or definiteness; and, secondly, 

 completeness. Any further remarks on the mode of constructing a nomen- 

 clature must be deferred until we treat of Classification ; the mode of naming 

 the Kinds of things being necessarily subordinate to the mode of arranging 

 those Kinds into larger classes. With respect to the minor requisites of 

 terminology, some of them are well stated and illustrated in the "Aphorisms 

 concerning the Language of Science," included in Dr. Whewell's Philosophy 

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

 peculiar point of view of Logic, I shall not further refer to, but shall confine 

 my observations to one more quality, which, next to the two already treat- 

 ed 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 follow- 

 ing aphorism : 



Whenever the nature of the subject permits our rensoning processes to 

 be, without danger, carried on mechanically, the language should be con- 

 structed on as mechanical principles as possible; while, in the contrary 

 case, it should be so constructed that there shall be the greatest possible ob- 

 stacles to a merely mechanical use of it. 



I am aware that this maxim requires much explanation, which I shall at 

 once proceed to give. At first, as to what is meant by using a language 

 mechanically. The complete or extreme case of the mechanical use of lan- 

 guage, is when it is used without any consciousness of a meaning, and with 

 only the consciousness of using certain visible or audible marks in con- 

 formity to technical rules previously laid down. This extreme case is no- 

 where realized except in the figures of arithmetic, and still more the sym- 

 bols 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 

 completeness 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 al- 

 tered at each renewal, the same symbol a or x being used on different oc- 

 casions to represent things which (except that, like all things, they are sus- 

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

 ing, therefore, to distract the mind from the set of mechanical operations 

 which are to be performed upon the symbols, such as squaring both sides 



