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MajorIronMouse30
4.4 1. Term Complements – Simple Terms The class complement is…
4.4
1. Term Complements – Simple Terms
The class complement is the set of objects consisting of everything outside the class. For example, the class complement of the class of fish consists of everything that is not a fish. The term complement is a term that denotes the class complement. Single-word terms usually have a term complement that is formed by attaching the prefix “non-” to the term. For example, the term complement for the term “fish” is “non-fish.” You can see the relationship between a term and its term complement in the following diagram, where the area inside the circle represents the class of fish, and the area outside the circle represents the class of non-fish.
Example:
The relationship between a term and its term complement is reciprocal. The term complement for “fish” is “non-fish,” and the term complement for “non-fish” is just “fish.” A term complement is still a term, which means that it can be used as the subject or the predicate of a categorical proposition, such as “Some non-fish are mammals.”
Indicate the correct term complement for each term.
Given Term: non-blessings
Term Complement:
Given Term: non-virtues
Term Complement:
Given Term: agencies
Term Complement:
Given Term: non-deer
Term Complement:
Given Term: cousins
Term Complement:
Given Term: capitalists
Term Complement:
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2. Term Complements – Complex Terms and Scope of Discourse
Term complements are more difficult to formulate for complex terms than for simple terms because the correct term complement for a complex term is often determined by the chosen scope of discourse. The scope of discourse is a restriction on the total set of objects that are relevant to a discussion. A scope of discourse is either restricted (reduced) or unrestricted (not reduced). A term complement must denote the correct class complement for a given term out of the total set of objects from the scope of discourse.
For example, consider the term “people who are single.” If you restrict the scope of discourse so that you are just talking about people, then the proper term complement is “people who are not single,” because this term would denote everything within the scope of discourse that is not denoted by the original term.
If, however, you do not restrict the scope of discourse, then the proper term complement must denote everything (not just people, but anything at all) that is not denoted by the given term. So the proper term complement for “people who are single” is “things that are not single people.”
Identify the correct term complement for each of the following terms, assuming the given reduction in the scope of discourse.
Given Term: soups that are not cream-based
Which of the following terms is the correct term complement for the term just given if you assume a scope of discourse that is restricted to soups?
soups that are cream-based
non-soups that are cream-based
non-soups that are not cream-based
non-soups
Given Term: professors who have published books
Which of the following terms is the correct term complement if you assume a scope of discourse that is restricted to professors?
professors who have not published books
non-professors who have not published books
non-professors who have published books
professors with tenure
Given Term: Granny Smith apples
Which of the following terms is the correct term complement if you assume an unrestricted scope of discourse?
apples that are not Granny Smiths
non-apples
things that are not Granny Smith apples
Red Delicious apples
Given Term: wines that are not made from red grapes
Which of the following terms is the correct term complement for the term just given if you assume an unrestricted scope of discourse?
wines made from red grapes
non-wines that are made from red grapes
things that either are not wines or are wines made from red grapes
white grape juice
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4. Conversion – Practice
Performing the operation of conversion on a type E or type I categorical statement yields a new categorical proposition with a truth value identical to that of the original statement. Converting a type A or type O categorical statement yields a new categorical proposition whose truth value is logically undetermined with respect to the truth value of the original statement.
Suppose that each of the following categorical propositions has the stated truth value. First, indicate the converse of each statement using the provided selection lists. Then indicate whether the converse must be true or false, or whether the truth value of the new statement is logically undetermined by the truth value of the original statement.
Given Statement: Some S are not P.
Truth Value of Given Statement: False
Converse of Given Statement: .
Truth Value of Converse:
Given Statement: No non-S are P.
Truth Value of Given Statement: True
Converse of Given Statement: .
Truth Value of Converse:
Given Statement: Some S are P.
Truth Value of Given Statement: True
Converse of Given Statement: .
Truth Value of Converse:
Given Statement: All non-S are P.
Truth Value of Given Statement: False
Converse of Given Statement: .
Truth Value of Converse:
Given Statement: All non-S are non-P.
Truth Value of Given Statement: True
Converse of Given Statement: .
Truth Value of Converse:
Given Statement: Some S are P.
Truth Value of Given Statement: False
Converse of Given Statement: .
Truth Value of Converse:
Given Statement: Some non-S are not non-P.
Truth Value of Given Statement: True
Converse of Given Statement: .
Truth Value of Converse:
Given Statement: No non-S are non-P.
Truth Value of Given Statement: False
Converse of Given Statement: .
Truth Value of Converse:
