If we think of a certain Class, and imagine that we have picked out from it a certain smaller Class, it is evident that the _Remainder_ of the large Class does _not_ possess the Differentia of that smaller Class. Hence it may be regarded as _another_ smaller Class, whose Differentia may be formed, from that of the Class first picked out, by prefixing the word "not"; and we may imagine that we have _divided_ the Class first thought of into _two_ smaller Classes, whose Differentiæ are _contradictory_. This kind of Division is called '=Dichotomy='. [For example, we may divide "books" into the two Classes whose Differentiæ are "old" and "not-old."] In performing this Process, we may sometimes find that the Attributes we have chosen are used so loosely, in ordinary conversation, that it is not easy to decide _which_ of the Things belong to the one Class and _which_ to the other. In such a case, it would be necessary to lay down some arbitrary _rule_, as to _where_ the one Class should end and the other begin. [Thus, in dividing "books" into "old" and "not-old," we may say "Let all books printed before A.D. 1801, be regarded as 'old,' and all others as 'not-old'."] Henceforwards let it be understood that, if a Class of Things be divided into two Classes, whose Differentiæ have contrary meanings, each Differentia is to be regarded as equivalent to the other with the word "not" prefixed. [Thus, if "books" be divided into "old" and "new" the Attribute "old" is to be regarded as equivalent to "not-new," and the Attribute "new" as equivalent to "not-old."] pg004 After dividing a Class, by the Process of _Dichotomy_, into two smaller Classes, we may sub-divide each of these into two still smaller Classes; and this Process may be repeated over and over again, the number of Classes being doubled at each repetition. [For example, we may divide "books" into "old" and "new" (i.e. "_not_-old"): we may then sub-divide each of these into "English" and "foreign" (i.e. "_not_-English"), thus getting _four_ Classes, viz. (1) old English; (2) old foreign; (3) new English; (4) new foreign. If we had begun by dividing into "English" and "foreign," and had then sub-divided into "old" and "new," the four Classes would have been (1) English old; (2) English new; (3) foreign old; (4) foreign new. The Reader will easily see that these are the very same four Classes which we had before.] pg004½ CHAPTER IV. _NAMES._