vi.] THE INDIRECT METHOD OF INFERENCE. 119 



identical in their signification, I fail to see any difference 

 between the statements whatever. As well might we say 

 that x = y and y = x are different equations. 



Another point of difficulty is to decide when a change 

 is merely grammatical and when it involves a real logical 

 transformation. Between a table of wood and a wooden 

 table there is no logical difference (p. 31), the adjective 

 being merely a convenient substitute for the prepositional 

 phrase. But it is uncertain to my mind whether the 

 change from " All men are mortal " to " No men are not 

 mortal" is purely grammatical. Logical change may 

 perhaps be best described as consisting in the determination 

 of a relation between certain classes of objects from a 

 relation between certain other classes. Thus I consider 

 it a truly logical inference when we pass from " All men 

 are mortal" to "All immortals are not-men," because the 

 classes immortals and not-men are different from mortals 

 and men, and yet the propositions contain at the bottom the 

 very same truth, as shown in the combinations of the 

 Logical Alphabet. 



The passage from the qualitacive to the quantitative 

 mode of expressing a proposition is another kind of change 

 which we must discriminate from true logical inference. 

 We state the same truth when we say that "mortality 

 belongs to all men," as when we assert that " all men are 

 mortals." Here we do not pass from class to class, but 

 from one kind of term, the abstract, to another 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 contains no objects. 



It is of course 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. What we need to 

 do is to define accurately the sense in which we use the 

 word " inference," and to distinguish the relation of in- 

 ferrible propositions from other possible relations. It 

 seems to be sufficient to recognise four modes in which 

 two apparently different propositions may be related. 

 Thus two propositions may be 



i. Tautologoiis or identical, involving the same relation 

 between the same terms and classes, and only differing in 



