232 H. M'^COLL ON THE GROWTH AND 



an argument ? Foremost among distinctions we shall find 

 that of truth and falsehood. All intelligible statements 

 may be divided into two great classes_, the true and the 

 false. Every statement must belong to one or other of 

 these two classes, though we may not always know to lohich. 

 If it were not for this element of uncertainty, reasoning 

 would be purposeless, and logic would have no raison d'etre. 

 This uncertainty (sometimes real, and sometimes only 

 hypothetical) suggests the convenience of dividing the 

 statements of any argument upon which we happen to be 

 engaged into three distinct classes, the admittedly true, the 

 admittedly false, and the doubtful. Borrowing a hint from 

 mathematical probability, we may denote any statement 

 belonging to the first class by the symbol i, and any 

 statement belonging to the second class by o, while any 

 doubtful statement (whether the doubt be real or hypo- 

 thetical) may be denoted by any symbol we choose except 

 these. Now, generally speaking, in the course of any 

 consistent argument or investigation the boundaries of 

 these three classes will be found to be gradually changing ; 

 the first two classes, the admittedly true and the admit- 

 tedly false, though never encroaching upon each other's 

 ground, will both constantly encroach upon the ground of 

 the third, the doubtful. 



Statements may also, independently of their truth or 

 falsehood, be divided into two distinct classes, namely 

 assertions and denials. Every assertion either claims or 

 has already obtained admission into the class denoted by 

 the symbol i ; while its denial contests its right to this 

 symbol, which it claims for itself, and seeks to brand it, 

 as an impostor, with the symbol o. As long as these two 

 claimants belong to the class of doubtful statements, all 

 that we can say about them is, that the one (either the 

 assertion or its denial) must be true, and the other false. 



