lad·derNoun - Mathematics

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Lesson 3
______________________ is taking a term and all objects to which the term applies (including all
species and and subspecies of the term.)
Give examples in the extension of the term ‘book’.
______________________ is taking a term and all objects in which the term itself is an example
(including all possible genus of the term.)
Give examples in the intension of the term ‘book’.
Which has greater extension? Beverage or Coca Cola?
Which has greater intension? Mozzarella or Cheese ?
Two terms must be related in order to talk about extension or intension!!
Printer
Candy Bar are ___________________________.
A term has greater extension if it is more : Specific
General
(circle one)
A term has greater intension if it is more : Specific
(circle one)
General
One can think they are adding intension without actually doing so.
People Alive Today
People Alive Today less than 1,000 years old.
At first it appears that ‘People Alive Today’ is more general (greater ____________________________)
But these both refer to the same set of people!! (why?)
Lesson 4 Ways of Defining
Terms may be defined by ______________________________,
________________________________, or __________________________________________.
1. By Synonym: Defining a term by using another term or terms.
newsNoun/n(y)o͞oz/ Newly received or noteworthy information
Trouble/Difficulty:
2. By example: (how children are primarily taught) Defining a term by listing all possible examples
of the term.
e.g. How is a child taught the word ‘cereal’?
Trouble/Difficulty: Suppose we define metals by example by saying that metals are iron, gold,
silver, copper, or bronze?
3. By genus and difference: Explaining the genus of the term and what distinguishes the term from
the rest of the genus.
lad·derNoun/ˈladər/ 1. A structure consisting of a series of bars or steps
between two lengths of wood, metal, or rope, used for climbing up or down
something.
What is the genus here?
What distinguishes ‘ladder’ from other structures?
Trouble/Difficulty: What if the genus is unclear/unknown?
What is the trouble with the following?
en·do·mor·phism. noun \ˌen-də-ˈmȯr-ˌfi-zəm\. a homomorphism that maps a mathematical set
into itself.
What is the genus in this definition?
Lesson 5 Rules for Defining Genus and Difference
A definition should:
1. state only the essential attributes of term.
What is inessential in the below?
An adult is a person over 18 years of age and who was born.
2.
not be circular. (Not be defined in terms of itself)
Canada is country whose name is Canada.
3. not be too broad or narrow. (all aspects of the term need to be included)
A square has four sides. (Is this too broad or too narrow?)
A sailor is someone who is a captain of a boat. (Is this too broad or too narrow?)
4. not be unclear or figurative.
Death is the golden key that opens the palace of eternity. (nice poetry, poor definition)
5. be stated positively, if possible. (definitions should avoid ‘not’ if possible)
Lunch is not the meal we eat in the morning or evening.
(some definitions must be negative (bankrupt, dark, cashless) )
6. should be the same part of speech as the term. (Don’t define a verb in as a noun)
winning: when a person is victorious.
Winning is a ____________________________ (part of speech)
‘When a person is victorious’ describes a time so it is a ____________________________ (part
of speech)
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