DEDUCTIVE REASONING. 71 



The great importance of this process of inference arises 

 from the fact that the conclusion is more simple and 

 general than either of the premises, and contains as much 

 information as both of them put together. It is on this 

 account constantly employed in inductive investigation, 

 as will afterwards be more fully explained, and it is the 

 natural mode by which we arrive at a conviction of the 

 truth of simple identities as existing between classes of 

 numerous objects. 



Inference of a Limited from Two Partial Identities. 



We have just considered arguments which are of the 

 type treated by Aristotle in the first figure of the 

 syllogism. But there are two other types of argument 

 which employ a pair of partial identities. If our premises 

 are, as shown in these symbols, 



B = AB (i) 



B = CB, (2) 



we may substitute for B either by (i) in (2) or by (2) in 

 (i), and by both modes we obtain the conclusion 



AB = CB, (3) 



a proposition of the kind which we have called a limited 

 identity (p. 51). Thus, for example, 



Potassium = potassium metal (i) 



Potassium = potassium floating on water ; (2) 



hence 



Potassium metal = potassium floating on water. (3) 

 Now this is really a syllogism of the mood Darapti in the 

 third figure, except that we obtain a conclusion of a much 

 more exact character than the old syllogism gives. From 

 the premises ' Potassium is a metal ' and ' Potassium floats 

 on water,' Aristotle would have inferred that ' Some 

 metals float on water.' But if inquiry were made what 

 the some metals are, the answer would certainly be ' Metal 

 which is potassium.' Hence Aristotle's conclusion simply 



