[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.
The word “Thing”, which conveys the idea of a Thing, without any idea of an Adjunct, represents any single Thing. Any other word (or phrase), which conveys the idea of a Thing, with the idea of an Adjunct represents any Thing which possesses that Adjunct; i.e., it represents any Member of the Class to which that Adjunct is peculiar.