Given a set of entities, any property that distinguishes one set from another can be used as the basis for constructing a **CATEGORY**. For example, we find that there exist organisms composed of a single cell, and others composed of more than one cell. We set up a category called ‘UNICELLULAR’ and define it as follows:

*An organism is unicellular if and only if it is composed of a single cell. *

Drawing on an idea from Vignesh, let us try the same strategy for the property black, set up a category of ‘BLACKOID’, defined as follows:

*An organism is a blackoid if and only if its colour is black. *

Once we make that move, we can set up many such categories: blackoid, greenoid, pinkoid, … And we can also set up sub-categories like semi-blackoid, semi-greenoid, and so on. Within each of these, we can set up black-pinkoid, white-brownoid, and so on. The possibilities are endless.

Intuitively, you would agree that it makes sense to set up UNICELLULAR as a category in biology, but not BLACKOID. Another way of expressing this intuition is to say that unicellular is a legitimate category, but blackoid is not. The question then is:

** What makes a category legitimate in academic knowledge?**

**CATEGORIES** are special cases of concepts. Other types of concepts include units of organization like ‘atom’ and ‘molecule’ in the physical world, or ‘organism’ and ‘community’ in the biological world; **PROCESSES** like ‘development’ and ‘evolution’; and **ABSTRACT CONCEPTS** like ‘justice’ and ‘theory’. So we may generalize our question as:

**Under what conditions do we accept a concept as legitimate in academic knowledge?**

This question is parallel to the question:

**Under what conditions do we accept a proposition as true in academic knowledge?**

Now, it makes sense to ask: “Is this conjecture true?” But it is strange to ask, “Is this axiom true?” “Is this definition true?” Truth is not a property that is relevant for axioms and definitions. However, we can ask:

** Does this definition/axiom serve a purpose? Is it legitimate? **

To combine these questions into a general one:

On what basis do we decide whether or not

A. conjecture X is true, and

B. definition/axiom/concept Y serves a purpose?

These are important questions that a theory of knowledge (called *epistemology*) must address.

**[You must have guessed by now that an important theme that runs through all the LTs in IIE is epistemology. Epistemology is the study of knowledge. "What is knowledge? What is the nature of knowledge? How is it constructed?" These are some of the questions that epistemology explores. We will not be able to go into further details about epistemology in this course. But if this is something that interests you, a Google search will help you get started with exploring it.] **

Consider the generalizations on angles in polygons. Let us begin by refreshing our memory of the geometry that we all learnt in school:

1. *An equi-angular polygon is one whose angles are equal/congruent. *

2. *The sum of angles in a (convex) polygon is 2 (n-2) right angles* (where n is the number of sides).

3. Vocabulary:

Triangle: three-sided polygon

Quadrilateral: four-sided polygon

Pentagon: five-sided polygon

Hexagon: six-sided polygon

Heptagon: seven-sided polygon

Octagon: eight-sided polygon

Nonagon: nine-sided polygon

Decagon: ten-sided polygon

Now, given the formula 2(n-2), we can calculate the sum of angles in

a triangle as: 2(3 – 2) = 2 right angles;

a quadrilateral as: 2(4 – 2) = 4 right angles;

a pentagon as: 2(5 – 2) = 6 right angles;

a hexagon as: 2(6 – 2) = 8 right angles;

and so on. (You can do the rest of the calculation on your own.)

Now consider the following generalizations:

(Note: For convenience, we use the convention of dividing a full rotation into 360 units, as done by a standard protractor.)

1. If a triangle is equi-angular, then its angles are 60 degrees. (180/3)

2. If a quadrilateral is equi-angular, then its angles are 90 degrees. (360/4)

3. If a pentagon is equi-angular, then its angles are 108 degrees. (540/5)

4. If a hexagon is equi-angular, then its angles are 120 degrees. (720/6)

5. If a heptagon is equi-angular, then its angles are128 4/7 degrees. (900/7)

(You can do the calculation for an octagon, nonagon, decagon… and state similar generalizations for equi-angular polygons with 11, 12, 13 sides, *ad infinitum*.)

Given these generalizations, should we use the following terminology of angles?

Alpha angle: 60 degrees

Right angle: 90 degrees

Beta angle: 108 degrees

Gamma angle: 120 degrees

Delta angle: 1284/7 degrees

Epsilon angle: … degrees.

Zeta angle: … degrees

Eta angle: … degrees

and so on.

Why is the above categorization ridiculous? Notice that there are no inferences to be made from knowing what one of the angles of a polygon is, whether it is alpha, beta, gamma… Notice also that there are no inferences to be made from knowing that a triangle is alpha-angled, a quadrilateral is right-angled, or a pentagon is beta-angled… The only useful category from which we can make inferences is that of** right-angled triangles**.

Given this lesson, we can define justified concepts (or legitimate concepts) as follows:

*In academic knowledge, a justified concept is one that can be shown to allow us to make a number of inferences by acting as a hub for a number of generalizations.*

Alpha-angled triangle, gamma-angled triangle, alpha-angled quadrilateral, beta-angled quadrilateral, alpha-angled pentagon, right-angled pentagon, and so on, are not legitimate concepts because they don’t yield any inferences.

To take another example, if we are told that something is a triangle, we can infer a large number of its properties. So TRIANGLE is a legitimate concept in geometry. So are the concepts of QUADRILATERAL and POLYGON. Are pentagon, hexagon, heptagon, octagon, nonagon, and decagon legitimate concepts in geometry? What inferences can we draw by knowing that something is a heptagon or octagon? We leave it to you to address that question.

Moving to another domain, we can infer a number of properties of an organism if we know that it is male or female. So we conclude that MALE and FEMALE are legitimate concepts in biology. But what about the concepts of masculine and feminine? What can we infer from the statement that someone is masculine or feminine? We leave it to you to decide whether masculine and feminine are legitimate concepts in human cultural studies.

If we know that an organism has vertebrae (= is a vertebrate), we can infer that it has an alimentary canal, that it has a brain, that it has eyes, and lungs, and so on. But if a given organism doesn’t have vertebrae (= is an invertebrate), what can we infer about the organism? Bacteria, amoeba, fungi, coconut trees, worms, ants, snails, and butterflies do not have vertebrae. What properties do these groups of organisms have in common such that we can infer those properties if we know that the organism doesn’t have vertebrae?

But you may ask: what if we define invertebrate not as an *organism* that does not have vertebrae, but as an *animal* that does not have vertebrae? or as a chordate that does not have vertebrae? (For ‘chordate’, see https://en.wikipedia.org/wiki/Chordate) We leave you to gnaw on that question, and figure out where that question takes you.

Are the concepts of noun, verb, and adjective legitimate academic concepts in linguistics? Is the concept of ideology a legitimate academic concept?

Do start looking at school textbooks, make a list of the terms they use, and ask yourself how many of them are legitimate academic concepts.