USE OF A SYMBOLICAL LANGUAGE. 235 



other method^ but also for the complete solution of many 

 problems which, I think, it would be diflficult to solve by 

 any other method with which I am at present acquainted. 



The rules which I have proposed for observance in 

 introducing new symbols are, I believe, sound, and. I have 

 followed them myself to to the best of my ability. As the 

 science advances, other symbols will, no doubt, become 

 necessary ; but they should be introduced slowly, and not 

 till their utility is made clearly manifest. 



My statement in ' INIind,' that though a : h implies 

 a' -{-b, it is not equivalent to it, has been called in ques- 

 tion, my critics maintaining that there is no real difference 

 between the conditional statement " If a is true, b is 

 true,'"" and the disjunctive statement "Either a is false or 

 b is true.^^ Now, I admit at once that, in the ordinary 

 language of life, disjunctive statements are often made 

 which convey, and are intended to convey, a conditional 

 meaning, and, further, that the example which I gave in 

 illustration, namely "He will either discontinue his 

 extravagance, or he will be ruined,'^ is one of them. 

 Many statements, however, are made in common life 

 which are tacitly understood to convey a stronger meaning 

 than logically and literally belongs to them. Take, for 

 instance, the well-known expression, " He will never set 

 the Thames on fire.^^ In its literal sense this very harm- 

 less-sounding statement does not commit one to much ; it 

 may, with equal safety, be applied to the cleverest man 

 living and to the most incapable idiot. What the practical 

 reasoner would be concerned with in making use of any 

 evidence conveyed to him in such terms would be the 

 intended meaning of the speaker; and if his argument 

 should be of such a nature as to necessitate the employ- 

 ment of symbols, the symbol for the statement should 

 denote its intended and not its literal meaning. The real 



