3. LOGICAL DIVISION AS PARTITION.
Partition is the process of separating an individual thing into its parts.
The partition is quantitative or mathematical when the separation is in terms of space or time, but when otherwise the partition becomes qualitative or logical. Or to put it in another way, the partition is mathematical when the separation gives parts and logical when the separation gives ingredients.
To illustrate:
| (1) Tree |  | quantitative or mathematical | | branches leaves roots trunk |
| qualitative or (logical) | | woody fibre capillary attraction sap chlorophyll | ||
| (2) House | | quantitative or mathematical | | roof frame-work foundation |
| qualitative or (logical) | | wood iron stone plaster |
An easy way to determine that the separation involves logical division proper and not partition is to affirm the connection between a class and a sub-class. To wit: A man is a biped; a square is a rectangle; a Caucasian is aman, etc. If such an affirmation cannot be made then the separation involved is not properly logical division but probably partition. For example it cannot be said that a roof is a house, or that sap is a tree. It is seen, then, that a logical division of any genus may be summarized in the form of a series of judgments of which a species is the subject and the genus is the predicate. For example, by a logical division quadrilaterals may be divided into trapeziums, trapezoids and parallelograms; this process may then be summarized in a series of three judgments: (1) A trapezium is a quadrilateral; (2) A trapezoid is a quadrilateral; (3) A parallelogram is a quadrilateral.