72 THE PRINCIPLES OF SCIENCE. 



leaves out some of the information afforded in the premises ; 

 it even leaves us open to interpret the some metals in a 

 wider sense than we are warranted in doing. From these 

 distinct defects of the syllogism the process of substitution 

 is free, and it only incurs the possible objection of being 

 tediously minute and accurate. 



Miscellaneous Forms of Deductive Inference. 



The more simple and common forms of deductive 

 reasoning having been exhibited and demonstrated on 

 the principle of substitution, there remain many, in fact 

 an indefinite number, which may be explained with nearly 

 equal ease. Such as involve the use of disjunctive propo- 

 sitions will be deferred to a later chapter, and several of 

 the syllogistic moods which include negative terms will be 

 more conveniently treated after we have introduced the 

 symbolic use of the second and third laws of thought. 



We sometimes meet with a chain of propositions which 

 allow of repeated substitution and form an argument called 

 in the old logic a Sorites. Take, for instance, the premises 

 Iron is a metal (i) 



Metals are good conductors of electricity (2) 



Good conductors of electricity are useful for 



telegraphic purposes. (3) 



It obviously follows that 



Iron is useful for telegraphic purposes. (4) 



Now if we take our letters thus 



A = Iron, B = metal, C = good conductor of 

 electricity, D = useful for telegraphic purposes, 

 the premises will assume the form 



A = AB (i) 



B = BC (2) 



C = CD (3) 



For B in (i) we can substitute its equivalent in (2), and 



