Vagueness and Ambiguity

Univocal, Equivocal, and Analogical

Intensional and Extensional Definitions

Principles for Definitions

Objects and Essential Natures

Common Sense LogicChapter 1.4—1.6

Some objects are discrete; others exist on a continuum.

Chairs vs. Clouds

Question: when is a word vague? Answer: when the range of things on a continuum to which it refers is not precisely defined.

Huh? That’s somewhat “vague”

What is Vagueness?

How precise must a definition be?

Old growth forests vs. New growth forests

Reality consists of discrete objects and continuums

How do we distinguish between rich people and poor people?

Possible implication: are all divisions, along a continuum, arbitrary?

Reality is (Partially) Vague

Ambiguity=when there are two or more unrelated kinds of things to which a word refers

For example, “Key” has several possible meanings

“Please count the number of keys in the room”

Some words can be both vague and ambiguous

For example, “Bank” is vague because, when referring to the sides of a river, it’s not obvious where it begins and ends; it can be ambiguous because it can refer to several objects

What is Ambiguity?

EquivocationAll factories are plants

All plants are made of organic material

Therefore, all factories are made out of organic material

Analogy“Spinach is a healthy food; Fred’s complexion is looking healthy”

“Bad” and “Good” Ambiguity

There are few words that are completely unambiguous (i.e. univocal)

Most words are either equivocal or analogical

Analogical words help us better understand reality

Newton: the solar system is like a giant clock

Is it contradictory to say of two things that they are both different and not different?

Maybe yes, maybe no

The Necessity of Analogy

Intension=all the characteristics, traits, and properties of the word which makes it what it is

For example, “television”

An electronic instrument capable of receiving electromagnetic radiation and turning it into pictures and sounds

The intension is the concept

What is Intension?

Extension=all the things to which the word refers

For example, “television”

All past, present, and future television sets

The extension is the thing

What is Extension?

The intension of a word increases as the list of characteristics included in the meaning of the word increases

For example, “Irish Setter” is more specific than “dog,” and “dog” is more specific than “animal”

As the intension of a word increases, the extension typically decreases

The number of things referred to by “Irish Setter” is fewer than is referred to by “dog”

A Principle for Intension

However, sometimes increasing the intension has no effect on the extension

“Female President of the United States” vs. “Republican Female President of the United States”

The second has a greater intension; yet the extension is identical, since there is neither a female President of the United States, nor a Republican female President of the United States

Note: this is philosophically significant. The meaning of words can never be reduced to their reference (i.e. extension)

An Exception to the Rule

1) Genus and specific difference

Genus=the next larger or more general category to which a term belongs (e.g. Irish Setter, dog, animal, living thing)

Specific difference=that which distinguishes the word being defined from other members of the genus (e.g. having long, reddish hair, slender bodies, big chest, and long ears are differences that distinguish Irish Setters from other dogs)

Species=the word being defined (e.g. Irish Setter)

Intensional Definitions

2) Operational

Provides a test or procedure for determining what something is

For example, cookbooks often define “done” like this: “A cake is done if a toothpick placed into the middle comes out without dough sticking”

Intensional Definitions

3) Precising

Sets quantifiable limits to the range on a continuum to which a word is to be applied

The lines being drawn are somewhat arbitrary, but must still be reasonable

For example, we know when someone is intoxicated, but it’s difficult to identify the line of demarcation

Intensional Definitions

4) Stipulative

A specific meaning is assigned to a word in order to make a distinction or clarify a discussion

Words must be “public” in order to be useful for communication

Sometimes semi-private words are allowed (e.g. “fish”)

Necessary to avoid wholly verbal disputes

For example, the use of the word “freedom” in political debates

Intensional Definitions

Three ways of specifying the extension of a word

1) Demonstrative definitionsFor example, pointing to a television set in the room, to define “television”

2) Enumerative definitionsFor example, “baseball player” defined as Babe Ruth, Joe Dimaggio, Mickey Mantle, etc.

3) Definition by subclassFor example, defining “insects” by listing ants, spiders, and flies.

Extensional Definitions

1) Avoid definitions that are too broad

“An automobile is a vehicle with wheels”

2) Avoid definitions that are too narrow

“An automobile is a vehicle designed to transport up to four people with comfort and convenience”

Principles for Definitions

Why precise definitions matter

Because if there is confusion regarding what is being discussed, miscommunication is inevitable

Some examples: 1) In what sense is Jesus Christ divine? 2) What does it mean to know something? 3) What is evolution?

An entire branch of contemporary philosophy (i.e. the “analytic” tradition) is concerned with the precise use of language and the meaning of terms.

For example, “the present King of France is bald”

Why Precision Matters

3) If possible, avoid circular and negative definitions

Circular: “An A paper is a paper which the instructor says deserves an A”; “God is a divine being”

Negative: “An organic substance is a substance which is not organic”

4) Definitions shouldn’t be needlessly figurative/obscure

“Architecture is frozen music”; “A bunny is a mammalian of the family Leporidae of the order Lagomorpha that are furless and blind”

More Principles…

5) Definitions shouldn’t be argumentative

“Democrats are pointy-headed liberals who always have their hands in other people’s pockets”

“Abortion is the intentional murdering of an innocent human person”

Most of us will agree that this is what abortion entails, but it’s argumentative (and question begging) to include this entailment in the definition.

Avoid Argumentative Definitions

Keep in mind the different purposes of definitions and arguments

Arguments: to reveal what is true, good, or beautiful

Definitions: to serve as preliminaries to arguments by specifying what something is

Once we know what something is, then we can rationally discuss whether it’s true, good, or beautiful

The Role of Good Definitions

6) Must specify the essential nature of the thing being defined

Problem: do things even have an essential nature?

For example: 1) what is a human being? 2) what is morality? 3) what is beauty? 4) what is the soul?

Necessary and sufficient conditions

Heraclitus: “All is flux”

The Metaphysics of Definitions

We’ll be looking more closely at the metaphysics of Aristotelian realism, emphasizing the distinction between substances and attributes, the importance of contingency and necessity, and the difference between real and nominal definitions.

We’ll also highlight how a proper understanding of these issues is essential for refuting positivism and relativism.

Looking Forward to Next Week…