85. II. Division Inseparable from Definition. -- The processes of definition and division go hand-in-hand and complete each other.

The definition says what a thing is, identifies it with the simplest components of its essence (genus and specific difference). The division shows to what special forms the generic element of the thing defined applies. The genus is the foundation, or reason, of the division.

(1) In the exact sciences the reasoning faculty sets out from generic notions, follows the progress of their specialization, and at every stage marks a new division or subdivision of the genus into subordinate species. In the example given in 83 (1) the number is first specialized as uneven, then it is individualized by the exclusion of all other uneven numbers which is involved in the attribute first.

(2) In the positive sciences the reasoning faculty at first follows the inverse process, the analytic: here division brings us to definition. We observe distinct activities in vegetable, animal and human substances; nevertheless, at the basis of these activities, there is a common activity: immanent activity, or life. The two different forms of activity -- the transitive and the immanent -- in their turn cover a common idea -- a higher genus -- activity. Step by step the mind passes from species to genera, from the members of the division to the reason of their separability. Nevertheless, when the common principle is disengaged, the mind turns back to the subjects analyzed to comprehend synthetically the formal divisions of the genus into its species.

Definition and division, then, are indissolubly joined together. In the exact sciences the definition precedes, the division follows. In the experimental sciences a first superficial division leads to the essential definition; the latter in its turn becomes the formal reason of the specific differences observed in the first instance.