60 THE PRINCIPLES OF SCIENCE. [CHAP. 



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 old syllogism the process of substitution is 

 free, and the new process only incurs the possible objection 

 of being tediously minute and accurate. 



Miscellaneous Forms of Deductive Inference. 



The more common forms of deductive reasoning having 

 been exhibited and demonstrated on the principle of 

 substitution, there still remain many, in fact an indefinite 

 number, which may be explained with nearly equal ease. 

 Such as involve the use of disjunctive propositions will be 

 described in a later chapter, and several of the syllogistic 

 moods which include negative terms will be more con- 

 veniently 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, G = good conductor of 

 electricity, D = useful for telegraphic purposes, 

 the premises will assume the forms 



A = AB, (i) 



B = BC, (2) 



C = CD. (3) 



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

 obtaining, as before, 



A = ABC. 



Substituting for C in this intermediate result its equivalent 

 as given in (3), we obtain the complete conclusion 



A = ABCD. (4) 



The full interpretation is that Iron is iron, metal, good 

 conductor of electricity, useful for telegraphic purposes, which 



