138 THE PRINCIPLES OF SCIENCE. 



kind, the concrete. But inference probably enters when 

 we pass from either of the above propositions to the 

 assertion that the class of immortal men is zero, or con- 

 tains no objects. 



It is really a question of words to what processes we 

 shall or shall not apply the name ' inference/ and I have 

 no wish to continue the trifling discussions which have 

 already taken place upon the subject. We shall not 

 commit any serious error, provided that we always bear 

 in mind that two propositions may be connected together 

 in four different ways. They may be 



1 . Tautologous or identical, involving the same relation 

 between the same terms and classes, and only differing in 

 the order of statement ; thus ' Victoria is the Queen of 

 England' is tautologous with 'The Queen of England 

 is Victoria/ 



2. Grammatically equivalent, in which the classes or 

 objects are the same and similarly related, and the only 

 difference is in the words ; thus ' Victoria is the Queen 

 of England' is grammatically equivalent to 'Victoria is 

 England's Queen/ 



3. Equivalent in qualitative and quantitative form, 

 the classes being the same, but viewed in a different 

 manner. 



4. Logically equivalent, when the classes and relations 

 are different, but involve the same knowledge of the 

 possible combinations. 



