Critical Thinking: Definitions Pt. 2: Intensional vs Extensional Definitions, Genus and Differentia, Four Rules for Good Definitions

Introduction
Definitions play important roles in arguments.  To see why, let's consider the abortion debate.  Both sides agree that killing an innocent person is morally wrong.  So, what's the ruckus about?  Often, those who are anti-abortion define human life and personhood as beginning at conception while those in the other camp say human life and personhood begin at some later stage of development. So, it seems that the abortion debate isn't so much about the moral significance killing an innocent person, rather it is about what the definition of "person" is.  For our purposes, the key idea is to notice the important role a definition can play in argument.

Last time we looked at some ways in which definitions can be a weakness in an argument.  Now we're going to start to look at the flip-side:  What are some different ways to use and construct definitions in our own arguments?  And of course, how can we do this well?

Extensional and Intensional Definitions
Let's learn a some phancy philosophy talk.  Philosophers often talk about two different kinds of definitions.  An extensional definition is one that identifies the members of the class it names by indicating instances of the thing being defined.  It's giving definitions by example.

Let's consider some examples:  "That" (pointing to the cup on my desk) "is a cup."  In this example I name an instance of a larger set--"cups".

We can also give extensional definitions without pointing.  In this type of extensional definition we define something by listing instances that are contained in the set of the term being defined. Suppose someone asks me what a carbonated beverage is.  I might answer that "Pepsi", "Coke", Sprite", and "Root Beer" are "carbonated beverages."  Notice in this definition I'm defining "carbonated beverage" by indicating members (instances) of the set of things included in "carbonated beverage."

Here's another example:  Suppose someone asks me what a primate is.  To answer I would list all the different species of primate.

When we give an intensional definition we list the essential properties of the term being defined. Usually, this means defining one concept in terms of more familiar ones.  For example, a "pen" is an instrument used for writing.  A "human" is a creature that has 2 legs and the capacity for rational thought.  "Politics" is the study of who gets what and how much.

The Gold Standard:  Intensional Definition by Genus and Differentia
In most arguments we can assume the conventional meaning of a term but if we are composing an argument that depends heavily on a certain understanding of a particular term we will want to give as clear and as unambiguous a definition as possible.  Often common terms have vague meanings so it's important to qualify them for your reader.

In the gun control debates we often hear "it's our right to own guns."  It's not clear whether by "right" the arguer means "legal" right or if they mean something more grandiose like "natural" or "divine" right.  When using such terms we need to carefully identify the specific meaning (both as arguers and as evaluators).

To do this we give what's called an intensional definition by genus and differentia.  Genus tells us the class of things to which the term belongs and differentia distinguishes it from other things in that class.  Lets look at some examples:

A "fork" is an eating utensil (genus) which has pointy prongs and is often used to penetrate the food morsels to facilitate eating (differentia).

"Humans" are primates (genus) that walk upright and are capable of moral reasoning and algebra (differentia).

In order to further clarify our definition we might also want to give some specific examples of things that qualify as being an instance of what we are defining; that is, give some extensional definitions.   Eg.  "Humans are primates (genus) that walk upright and are capable of moral reasoning and algebra (differentia) and all Americans are humans (extensional definition).

Specific Guidelines for Formulating Good Definitions
Up until now we've discussed what we are generally trying to accomplish when giving a definition. Now let's look at some specific guidelines to help make to process easier to evaluate and follow.

Rule 1: Equivalence
The definition of the term should not contain anything more or less than the term being defined.  For example, if I were to define "mug" as "something from which one drinks" this definition would fail to meet rule 1's stipulations.  The definition is too broad and also could contain wine glasses, sippy cups, and guitar- shaped margarita cups.  In other words, the definition phrase contains more than the term being defined.

On the other side of the equation I might say "'furniture' is something you sit on."  This is too narrow and excludes things that are included in the concept of "furniture" like desks and tables.

Rule 2:  Essential Characteristics
The definition must identify the essential properties of the thing being defined not the accidental properties.  For example: cars are yellow and red four-wheeled vehicles designed for transportation.  "Yellow" and "red" are accidental features of cars, they are not essential to a car being a "car."

Essential properties are the properties that are necessary for a thing or concept to be that thing or concept.  Something cannot be a cup unless it holds liquids and can be raised and drunk from.  The materials out of which a cup are made, however,  are accidental qualities.  It's not an essential property of a cup that it be made of ceramic.  Cups can also be made of plastic or even wood.

Rule 3:  Clarity
The definition should make the audience's understanding of the term clearer (rather than more vague).  For instance, "philosophy" is a walk on slippery rocks.  This definition doesn't add to our understanding of the term.   Pseudoscience and alt-med are rife with violations of rule 3.  Here's an example:

"Quantum-Touch" is a powerful, yet easy to learn, method of natural healing (or energy healing). Everyone has the innate ability to help ourselves and others. The Quantum-Touch techniques teach us how to focus and amplify life-force energy (or Chi, Bioenergy, Prana) by combining various breathing and energy awareness exercises.

I still have no clue what quantum touch is...

A common violation of the rule of clarity is the use of circular definitions.  This is when the defined word appears in the definition or there is a definition by synonym.   For example, a "definition" is an attempt to define a term.  Notice we use a closely related word (define) in the definition of what we are trying to define (definition).   An example of a circular definition by synonym is:  A "mug" is type of cup or "fast" means "speedy."  Neither of these definitions tell me what the unknown term actually is.  I am only given a synonym.  A better definition would be intensional, one that explains the essential properties and perhaps what a mug is used for (functional definition).

Rule 4:  Neutrality
The rule of neutrality says we should avoid emotional language from definitions.  In political arguments it's important to make sure definitions are neutral.  For example "'Atheists' are godless heathens who don't have any moral sense."  Clearly the definition is biased.  Other examples are "communism" is the equal distribution of poverty; "teachers" are those who can't do.

Concluding Thoughts on Constructing Definitions
Just as with everything in this course, we can use these rules in two different ways.  The first is to apply them as a standard against other people's definitions in an attempt to make a critical evaluation.  The second is to see the rules as guidelines for how you might go about constructing your own definitions for your arguments.

Recall that a good arguer takes into account what his audience already accepts and constructs his argument with those things in mind.  The same applies to constructing definitions.  A good definition should take into account what the intended audience already accepts and should be built from those beliefs.