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.
4. RULES OF LOGICAL DIVISION.
When the logical division of a genus is under consideration there are four rules which should be observed.
FIRST RULE. There must be but one principle of division (fundamentum divisionis). To divide mankind into white man, Australian, yellow man, African and red man is a violation of this rule as the two principles of color and geographical location are involved. A division in which more than one principle is used is sometimes referred to as cross division because the various species cross each other. For example in the foregoing there are many white men who are Australians.
This rule applies only to one division. Where there is a series of divisions a new principle may be employed in each division. For example, in dividing triangles into scalene, isosceles and equilateral, the equality of sides isthe principle involved, but, in subdividing isosceles triangles into right angled and oblique angled, the principle employed concerns the nature of the angle.