v.] DISJUNCTIVE PROPOSITIONS. 79 



A = ABc -I- AbC ; 

 uniting B to each side we infer 



AB = AB6- -I- AB&C 

 or AB = ABc ; 



that is, 



Watei' "which is salt is water salt and not fresh. 

 I should Aveary the reader if I attempted to illustrate 

 the multitude of forms wliicli 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 infiniti. Take the case : 



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



Copper is dissolved by nitiic 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 



Assundng that tlie alternatives copper or gold are 

 int-ended to be exclusive, as just explained in the case of 

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

 forms 



B = BC(^-|-BcD (i) • 



C = CE (2) 



A = AB (3) 



A = Ae (4) 



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



B = BCVZE •!• Be] J 

 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 = ABCV^Ee -I- ABcDe 



The first of the alternatives being contradictory the result 

 is 



A = ABcDe 



