94 THE PRINCIPLES OF SCIENCE. 



instance. A very common process of reasoning consists in 

 the determination of the name of a thing by the successive 

 exclusion of alternatives, a process called by the old name 

 abscissio infiniti. Take the case : 



Red-coloured metal is either copper or gold (i) 

 Copper is dissolved by nitric acid (2) 



This specimen is red-coloured metal (3) 



This specimen is not dissolved by nitric acid (4) 

 Therefore this specimen consists of gold. (5) 



Assigning our letter-symbols thus 

 A = this specimen 

 B = red-coloured metal 

 C = copper 

 D = gold 



E = dissolved by nitric acid, 

 the premises may be stated in the form 



B = BCrf + BcD (i) 



C = CE (2) 



A = AB (3) 



A = Ae. (4) 



Substituting for C in (i) by means of (2) we get 



B = BCdE | BcD. 

 From (3) and (4) we may infer likewise 



A = ABe, 



and if in this we substitute for B its equivalent just 

 stated, it follows that 



A = ABCdEe -I ABcDe. 



The first of the alternatives being contradictory, the result 

 is A = ABcDe 



which contains a full description of ' this specimen/ as 

 furnished in the premises, but by ellipsis indicates that 

 it is gold. It will be observed that in the symbolic 

 expression (i) I have explicitly stated what is certainly 

 implied, that copper is not gold, and gold not copper, 

 without which condition the inference would not hold good. 



