CHAPTER 10. DIVISION

10. DIVISION
Logical division - rules and fallacies of division - division by dichotomy.

Logical division:

Logical division is a simple method of dividing a class into its sub-classes in order to explain the or describe any class. This type of division is useful in explaining many concepts and making the understanding clear.

Division is useful for;

a] determination of exact relationships among related things,

b] formulation of definitions

When we divide, we use two main criteria. These are, Physical division and metaphysical division.

Physical division divides a whole into its parts
• e.g., a complex machine into its simple mechanical parts

Metaphysical division divides an entity into its qualities,

• e.g.,a species into its genus & difference
– man into animality & rationality

• a substance into its attributes
– sugar into color, texture, solubility, taste, etc.

• a quality into its dimensions
– sound into pitch, timbre, volume

Understanding Division:

Division is another way to explain any class by talking about its sub-groups and dividing the class into its sub groups. Here are its basic qualities:

• Logical Division

– begins with a summum genus
– proceeds through intermediate genera
– ends at the infimae species
– NB: It does not continue to individuals

• The results of division should meet these criteria:

1. The subclasses of each class should be coextensive with original class.
2. The subclasses of each class should be mutually exclusive.
3. The subclasses of each class should be jointly exhaustive.
4. Each stage of a division should be based on a single principle.

Kinds of Classification

Classification is the technique of inquiry in which similar individuals and classes are grouped into larger classes.

e.g., how are steam, diesel, & gasoline engines related to one another?

Natural Classification:
• Natural classification is a scheme that provides theoretical understanding of its subject matter e.g. classification of living things into monerans, protistans, plants, fungi and animals
• The concept “monerans” is now obsolescent because it does not provide sufficient theoretical clarity.

Artificial Classification:
• Artificial classification is a scheme established merely to serve some particular human purpose e.g. classification of plants as crops, ornamental, and weed

Classification and Division Compared

• The result of a classification will look like the result of a division.
• Classification begins with a individuals or small classes and works
towards a summum genus. It works in the direction opposite to that of division
• Classification begins with a set of apparently related things found in
the world based on experience and builds from there. Hence, it is well-suited to natural objects. But it will work with any kind of object.

Two Overly Ambitious Ideals

the divisions by a few things can never encounter any fallacy.

In logic as well as in any reasoning, if we are using division to explain something, we all aim at making divisions that will have no fallacies. In order to have a perfect flawless division we must divide using one of the following methods.

• Pure division
– begins with the summum genus and
– divides on the basis of a priori considerations
• i.e., it is based on logical possibility, not experience

• Dichotomous division
– divides on the basis of the presence or absence of a particular feature
• Classification can also be dichotomous.
• Striving for these ideals
– works well with mathematical objects,
– does not work well with natural objects
– guarantees a division that meets criteria
– sometimes provides more insight than alternative divisions.
• But “ dichotomous division is often difficult and often impracticable”
• Sometimes, class Rules notification is more practical.

RULES OF DIVISION:

When we are using logical division, we need to follow certain rules. thesde are as follows:

1. One division must follow only one criteria. It must be either physical or metaphysical.
2. The division criteria must be mutually exclusive and collectively exhaustive.
3. All the parts of an entity being explained must be covered by the division.
4. No extra members must be suggested as parts of the entity explained during the process of division.

FALLACIES OF DIVISION:

When we fail to follow above rules, we end up in committing following fallacies:

1. Division by cross criteria: When we divide something by using two or more criteria at the same time, we commit this fallacy. e.g. when we divide Indians into "Hindus, Muslims, Christians, Sikh, Rich, poor, Tall, short, Fair, Dark, introverts and extroverts"; we are committing this fallacy as we are using many criteria, both of physical as well as metaphysical divisions at the same time. at the same time.
2. Too narrow division: when we exclude some of the members from the group or some qualities of the entity being explained, we commit this fallacy. e.g. Quadrilateral into, square and rectangle. Here we exclude many other types of quadrilaterals and so the division becomes too narrow as it leaves out many other members that actually belong to this group.
3. Too wide division: when we include some members that actually do not belong to the group as we are dividing, our division becomes too wide. e.g. birds into single coloured & multicolored. Here, many other single coloured and multicolored things and beings get indicated as part of the group of bird, so it is a too wide division.