Part IV: Exercises

1. For each of the following collections of things, stipulate a term with an intension such that the collection becomes the extension of the new term. Choose as specific an intension as possible.

Ex. Oak, Pine, Maple, Cedar

Best Answer: “Tree” (all of the things above are part of the extension of the standard intension of “tree.”)
Worse Answer: “Plant” (while it is true that all of those things are plants, this is not the most specific intension).

a.) California, Michigan, Kentucky, Pennsylvania
b.) Monday, Tuesday, Saturday
c.) Apples, bananas, mangos, oranges
d.) California, Paris, Yellowstone National Park, Russia
e.) Chairs, tables, cabinets, dressers
f.) Mars, the Sun, Neptune, Earth
g.) Rutgers University, New York University, Columbia University
h.) Rutgers University, Frederick Douglass Elementary School, Allentown High School

For each of the intensions given below, list 5 things that would fit the relevant extension.

Ex. Companies

Answer (could vary): Nike, McDonald’s, Target, Hackett Publishing Company, Facebook

a.) People in your classroom
b.) Holidays which take place between the beginning of January and the end of July
c.) Presidents of the United States
d.) Polygons which have more than 3 sides
e.) Polygons which have fewer than eight sides
f.) Subjects taught in your school
g.) Places
h.) Places in the United States
i.) Places in your city

Notice: if you answered questions (a)-(i) correctly, you will see that the extensions are decreasing as the intension becomes more specific.

Make a case for why the following definitions (intensions) are too broad or too narrow.

Ex. Lions – large cats

Answer: This definition is too broad. There are many large cats that we would not consider lions
(tigers or cougars for instance). Thus, there are members of the extension of “large cats” that are not
lions – the definition is too broad.

a.) Humans – things that at a given moment are featherless bipeds (2 legged animals that have no
feathers)
b.) Humans – rational featherless bipeds that weigh more than 50 pounds
c.) Squares – four-sided polygons
d.) Squares – four-sided polygons with equal side lengths and four right angles, where each side is
longer than 10 inches
e.) Mathematics – a boring thing to study
f.) Sandwich – a type of food that has ham, cheese, and other things between two pieces of bread
g.) School – a place where someone eats lunch, takes some classes, learns from teachers, and
brings a backpack
h.) Aristotle – A philosopher from Ancient Greece

Evaluate each of the following arguments, and write whether or not the terms being used have been defined correctly, or if their definitions are too broad or too narrow.

1. Humans can be defined as “animals.”
   Some animals have four legs.
   Therefore, some humans have four legs.
2. Triangles can be defined as “three-sided polygons.”
   Each side face of the pyramids was roughly a three-sided polygon.
   Therefore, each side face of the pyramids was roughly a triangle.
3. Computers can be defined as “electronic devices.”
   Power tools are electronic devices .
   Therefore, power tools are computers.
4. Countries can be defined as “areas of land greater than 50,000 square miles with a legitimate
   government.”
   Austria has a land area less than 50,000 square miles.
   Therefore, Austria is not a country.

Distinguish these four terms:

a.) Categorematic Term
b.) Category
c.) Intension
d.) Extension