v.J DISJUNCTIVE PROPOSITIONS. 79 



A = ABc -I- A5C ; 

 uniting B to each side we infer 



AB = ABc -I- AB&C 

 or AB = ABc ; 



that is, 



Water which is salt is water salt and not fresh. 

 I should weary the reader if I attempted to illustrate 

 the multitude of forms which disjunctive reasoning may 

 take ; and as in the next chapter we shall be constantly 

 treating the subject, I must here restrict myself to a single 

 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 inftniti. Take the case : 



Ked-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) 



Let us assign the letter-symbols thus 

 A = this specimen D = gold 



B = red-coloured metal E = dissolved by nitric acid. 

 C = copper 



Assuming that the alternatives copper or gold are 

 intended to be exclusive, as just explained in the case of 

 fresh and salt water, the premises may be stated in the 

 forms 



B = BCd-|-BcD (i) 



C = GE (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 -\- AEcDe 



The first of the alternatives being contradictory the res ait 

 is 



A = ABcDe 



