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 qualitative 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 inferrible 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-- 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 related*, when 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. *Equivalents* in qualitative and quantitative form, the classes being the same, but viewed in a different manner. 4. *Logically inferrible*, one from the other, or it may be *equivalent*, when the classes and relations are different, but involve the same knowledge of the possible combinations. CHAPTER VII. INDUCTION.