Please explain the difference between intension and extension of terms. Use your own words. Give your own examples.
Also, please explain the difference between vagueness and ambiguity.
This is not a discussion, so no need to respond to another student here. You should be able to do this in a couple of paragraphs.
CHAPTER 2, Sec!on 2, Covers
1. Intension of Terms 2. Extension of Terms
Language meaning also has to do with the way we create defini!ons. There are different kinds of defini!ons and different ways to construct defini!ons. This sec!on will introduce you to two of the basic concepts about terms and their meaning, the intension versus the extension of terms.
When we use the word, “term,” we basically mean a noun. We will see later in Chapter 4 that Tradi!onal Logic uses terms in the subject posi!on and the predicate posi!on of a categorical claim. Here the term could be either a noun or a noun phrase.
A noun is a word that stands for a person, place, animal, thing, idea, or concept. A noun phrase, also called a descrip!ve phrase, can be used as a subject or a predicate of a categorical claim. Here are examples of nouns and noun phrases, or descrip!ve phrases.
Car (This is a noun.)
Cat (This is a noun.)
Dog (This is a noun.)
Car that ran in the Indianapolis 500 (This is a descrip!ve phrase.) Cat that was just born (This is a descrip!ve phrase.)
Dog that escaped the dog pound (This is a descrip!ve phrase.)
No!ce that a descrip!ve phrase clarifies or makes something more explicit. We were not talking about just any car, but a car that ran in that specific race. We were not talking about just any cat, but a cat that was just born. We were not talking about just any dog, but a specific dog that escaped from the dog pound.
I know that we will not be learning about Tradi!onal Logic or Categorical Logic un!l Chapter 4, but the informa!on I have given you here is a clue. It is not just a clue to what is coming in Chapter 4. It is a clue to what we will be discussing next.
Intension versus Extension of Terms
Intension has to do with quali!es or a#ributes that a term connotes. Ask yourself, “what does something have to be like in order to be a cat?’ A cat could be a furry feline with four legs or a purring creature. A cat could be wild or domes!c. A cat could be a ki#en or a grown animal. There are any number of quali!es or a#ributes that give us, as ordinary speakers of English, an idea of what a cat is, and what that term means.
Extension is different. It denotes the members of the class. Once we know the connota!on or intension of the term, we can point out members of the class. In other words, if we know the intension or connota!on of a term, that is, the a#ributes that make it a member of the class called, “cats,” then we could point out any animal that could belong to that class.
Let’s think about some quali!es that members of the class, “cats” might have. Here is a possible list.
Cats
Domes!c cats
Wild cats
White cats
Black cats
Calico cats
Furry animals
Animals belonging to the species called, “felines” Striped cats
Animals that purr
Animals that are loveable
So$ ki%es
Warm ki%es
Li#le balls of fur.
I am sure you can think of many more a#ributes. Maybe we could disagree about those a#ributes. A cat lover might think cats are loving and adorable. Someone who does not like cats might think that cats are arrogant and selfish. Pu%ng those differences aside, we can all recognize that there are some characteris!cs that pertain to cats.
If I were to ask you to point out all members of the class of animals called “cats,” you might point to the following animals.
Lions
Tigers Panthers Bob Cats House Cats Pet Cats Black Cats White Cats Male Cats Female Cats
All of these would be examples of cats. When you point out specific kinds of cats, you are deno!ng the members of the general class called, “cats.” The act of deno!ng has to do with extension. The a#ributes or characteris!cs of the members of the class connote the meaning of the term, “cat,” and have to do with the intension of the term. Please note the spelling of the word,”I N T E N S I O N.”
Rela!onship between Intension and Extension
Suppose we had a group of cats in front of us. All members of this group of cats were either black or white. Now suppose I gave you not just the word, “cats,” but said the descrip!ve phrase, “black cats.” I made the defini!on of the kind of cats more specific. That means I increased the intension of the term, “cats” by specifying only black cats. The connota!on or intension of the term was changed. It was given more specific a#ributes or quali!es.
If I told you now to point to the black cats, you would have to exclude the white ones from that act of poin!ng out cats. No!ce that when you get more specific or increase the intension of the term, you have fewer members in the class to point at. This means that when you increase intension, you decrease extension, or the number of cats that you can point out.
Here is an example of increasing intension, that means making the term more and more specific.
1. Felines
2. Wild felines
3. Wild felines that are solid black in color 4. Black panthers.
As you progress from 1 to 4 in the list, there are fewer and fewer kinds of felines that you are able to actually point to. Moving from 1 to 4 in the list increases the intension, that is, things get more specific. That makes fewer individuals you can point at, which means that the extension is decreased.
All you have to do is remember this to figure out the other rela!onships.
If you decrease intension, you increase extension. Try moving from 4 to 1 in the list. By being less specific, you increase the number of individuals you can actually point to.
If you increase extension, you increase the number of individuals you can point to, so you must be ge%ng less specific, and that means you are decreasing intension.
If you decrease extension, you decrease the number of individuals you can point to, so you must be ge%ng more specific, and that means you are increasing intension.
Here is a list of those rela!onships.
Increasing intension decreases extension. Increasing extension decreases intension. Decreasing intension increases extension. Decreasing extension increases intension.
Another way to say you could denote or point out the members allowed in the class is to say you can enumerate them. If you enumerate the cats in the class, you are using extension.
Empty Extension
This means that there are no members of the class. Suppose I ask you to point out all members of the class, “living dodo birds.” You could look all over the place, but you would not be able to point to a single living dodo bird because they are all ex!nct. There are no living dodo birds in existence. This means that the class, “living dodo birds,” is empty. It is an empty set. That means that its extension is empty.
How about this class. Point out all the current kings of France. Empty set again. There are no current kings of France, so the extension is empty. Maybe there were kings of France hundreds of years ago, but not now. You could point out all the kings of France that ever were, but at some point in !me, probably a$er the French Revolu!on, when they decapitated the king and queen, there were no more kings of France. So, the extension of a class can be said to change over !me, in certain instances.
Things to Remember
Intension is connota!on. It connotes a#ributes, quali!es, and characteris!cs of a term. Extension is denota!on. It denotes the members of a class defined by the intension of a term. Increasing Intension decreases extension.
Increasing extension decreases intension.
Decreasing intension increases extension.
Decreasing extension increases intension.
Empty Extension means there are no members of the designated class.
Enumera!on is another way to point out members of a class.
Some Vocabulary from The Book
Ambiguous expression: An expression that can be interpreted as having more than one dis!nct meaning in a given context.
Cogni!ve meaning: The meaning by which terminology conveys informa!on.
Connota!on: Intensional meaning or intension
Conven!onal connota!on: The intensional meaning conven!onally agreed upon by the members of the community that speak the language in ques!on.
Decreasing extension: The order of decreasing class size.
Decreasing intension: The order of decreasing specificity or increasing generality.