USE OF A SYMBOLICAL LANGUAGE. 231 



represented by symbols, simpler in the smallness of the 

 number of symbols employed, and simpler in the mecha- 

 nical operations that have to be performed. In claiming 

 this advantage for logic over mathematics, I speak solely 

 of that scheme of symbolical logic which I, rightly or 

 wrongly, consider the simplest and most effective, namely 

 the scheme which I have explained and illustrated in 

 ' Mind,^ in the ' Proceedings ' of the London Mathematical 

 Society, in the ' Educational Times,' and in the ' Philo- 

 sophical Magazine.' According to this scheme the whole 

 and sole duty of the logician is to investigate the relations 

 in which statements [i. e. assertions and denials) stand 

 towards each other. For all practical reasoning-piu'poses 

 a statement may be defined as anything that conveys directly 

 through a bodily sense (as the eye or ear) any information 

 (true or false) to the mind. In this sense a nod or a 

 shake of the head is a perfectly intelligible statement. 

 The Union-Jack fluttering from the mast of a ship con- 

 veys as clear and definite information as the words " This 

 is a British ship " shouted through the captain^s speaking- 

 trumpet ; and therefore the flag is as much a statement 

 in the logical sense as the words ; and, like the words, it 

 may (as we know by experience) be a true or a false 

 statement. 



Logic, then, being concerned with statements, the 

 analogy of ordinary algebra suggests the propriety 

 of denoting simple statements by single letters, and 

 the relations in which statements stand to each other 

 either by the relative positions of the statement-letters, 

 or by separate and distinct symbols. Therefore a very 

 important inquiry in laying the foundation of a prac- 

 tical symbolical calculus for solving logical problems is 

 this : — What are tlie characteristics and relations which 

 most frequently distinguish or connect the statements of 



