ON THE GROWTH AND USE OF A SYMBOLICAL LANGUAGE. 2.25 



XXV. On the Growth and Use of a Symbolical Language. 

 By Hugh M'^Coll, Esq., B.A. Communicated by 

 the Rev. Robert Harley, F.R.S. 



Read March 2211(1, i88i. 



In an article on " Symbolical Reasoning/'' in a recent 

 number of ^ MincF (No. 17, Jan. 1880), T have described 

 the relation between symbolicaj^ reasoning and ordinary 

 verbal reasoning as analogous to that between machine 

 labour and ordinary manual labour. To trace this analogy 

 through all its various points of resemblance would take 

 too long; but there is one point which deserves some 

 notice, as it bears more especially upon the present 

 subject. 



For what kinds of operations are machines usually 

 invented ? A little reflection will show that one common 

 and prominent characteristic of such operations is same- 

 ness ; we employ machines to perform operations which 

 have to be frequently repeated, and repeated in the same 

 unvarying manner. Sewing-machines, knitting-machines, 

 reaping-machines, and, in fact, the great generality o£ 

 machines, however widely they may differ in other respects, 

 resemble each other in this. 



For what kinds of expressions and relations, mathe- 

 matical or logical, do wc usually invent symbols ? We 

 shall find, as before, that the common characteristic of 

 such expressions and relations is sameness — that they are 

 expressions and relations which have to be repeated fre- 



SER. III. vol. VII. Q 



