Deck 9: A Little Categorical Logic

Question 1

"Some" statements, in contrast to "all" or "no" statements, are understood to assert _____.

A) that something actually exists
B) that something exists if something else exists
C) None of the answers are correct
D) that something may exist

Answer 1

that something actually exists

Question 2

In a Venn diagram, placing an X precisely on the line between Area 1 and Area 2 means that _____.

A) neither Area 1 nor Area 2 is empty
B) None of the answers are correct
C) both Area 1 and Area 2 are empty
D) we can't tell whether the class of things signified by X belongs in Area 1 or in Area 2

Answer 2

we can't tell whether the class of things signified by X belongs in Area 1 or in Area 2

Question 3

To diagram statements of the form "Some S are not P," we place an X in that portion of the S circle that overlaps with the P circle.

Answer 3

False

Question 4

Which of the following is a rule of thumb for translating categorical statements containing the words "only," "only if," and "the only" into standard categorical form?

A) If "the only" occurs in the middle of a sentence, the subject and predicate terms should generally be reversed.
B) If "only if" occurs at the beginning of a sentence, the subject and predicate terms should generally not be reversed.
C) If "only if" occurs in the middle of a sentence, the subject and predicate terms should generally be reversed.
D) If "only" occurs at the beginning or in the middle of a sentence, the subject and predicate terms should never be reversed.

Question 5

Use a Venn diagram to evaluate the following argument: "Sherman is a Star Wars fan. All Star Wars fans are nerds. Therefore, Sherman is a nerd." This argument is _____.

A) None of the answers are correct
B) invalid but has true premises and a true conclusion
C) valid but there is no way to know whether all the premises are true
D) valid and has true premises
E) invalid and has at least one false premise

Question 6

Use a Venn diagram to evaluate the following argument: "Shakespeare is a famous author. Shakespeare wrote Macbeth. Therefore, a famous author wrote Macbeth." This argument is _____.

A) valid but has false premises
B) valid and has true premises
C) invalid and has at least one false premise
D) None of the answers are correct
E) invalid but has true premises and a true conclusion

Question 7

In the English language, the phrases "only," "only if," and "if only" are interchangeable.

Question 8

To diagram statements of the form "No S are P," we shade that portion of the S circle that overlaps with the P circle.

Question 9

If a categorical syllogism contains one "no" premise and one "some" premise, the "some" premise should be diagrammed first.

Question 10

In standard-form categorical statements, a word or phrase that names a class and is represented by the letter " S" is known as a _____.

A) subject term
B) prerogative term
C) syllogism
D) copula

Question 11

In standard-form categorical statements, a word or phrase that names a class and that serves as the subject complement of a sentence is known as a(n) _____.

A) quantifier
B) predicate term
C) additive term
D) copula

Question 12

In logic, "some" always means "_____."

A) a few
B) many
C) at least one
D) at least one but not all

Question 13

All standard-form categorical statements have a predicate term.

Question 14

Use a Venn diagram to evaluate the following argument: "The moon is made of green cheese. Green cheese often stinks. So, the moon definitely stinks." This argument is
_____.

A) invalid but has true premises and a true conclusion
B) valid but has false premises
C) invalid and has at least one false premise
D) None of the answers are correct
E) valid and has true premises

Question 15

All standard-form categorical statements have a _____.

A) quantifier and a copula
B) quantifier
C) copula
D) None of the answers are correct

Question 16

Use a Venn diagram to evaluate the following argument: "No penguins can fly. Penguins are birds. Therefore, some birds cannot fly." This argument is _____.

A) valid and has true premises
B) invalid but has true premises and a true conclusion
C) invalid and has at least one false premise
D) None of the answers are correct
E) valid but has false premises

Question 17

In a Venn diagram, placing an X in an area means _____.

A) None of the answers are correct
B) that the area is not empty
C) that the area has at least one member and that the area is not empty
D) that the area has at least one member

Question 18

Use a Venn diagram to evaluate the following argument: "Dogs are mammals. No mammals are reptiles. So, no dogs are reptiles." This argument is _____.

A) invalid but has true premises and a true conclusion
B) valid but has false premises
C) invalid and has at least one false premise
D) None of the answers are correct
E) valid and has true premises

Question 19

Use a Venn diagram to evaluate the following argument: "No Presidents have been Popes. Hilary Clinton is not the U.S. President. So, Hilary Clinton is not the Pope." This argument is _____.

A) valid and has true premises
B) invalid but has true premises and a true conclusion
C) invalid and has at least one false premise
D) None of the answers are correct
E) valid but has true premises and a false conclusion

Question 20

"Only alphas are betas" should be translated as "_____."

A) All alphas are betas
B) None of the answers are correct
C) Some betas are not alphas
D) All betas are alphas

Question 21

If, after the premises have been diagrammed, inspection of a Venn diagram shows that the diagram contains all the information stated in the conclusion, then the argument is valid.

Question 22

Consider the following Venn diagram:
Which of the following statements best describes what this diagram conveys?

A) "All musicians are talented individuals."
B) "Some musicians are talented individuals."
C) "No musicians are talented individuals."
D) None of the answers are correct.
E) "Some musicians are not talented individuals."

Question 23

To diagram statements of the form "Some S are P," we place an X in that portion of the S circle that does not overlap with the P circle.

Question 24

Which of the following techniques used in testing the validity of simple categorical arguments involves drawing a series of overlapping circles and associated markings?

A) a Hasse diagram
B) a thematic map
C) a Venn diagram
D) a graduated circle map

Question 25

There are four types of standard-form categorical statements.

Question 26

A categorical statement is one that makes a claim about the relationship between _____.

A) two or more classes or categories of things
B) a thing and its properties
C) one subject and another
D) None of the answers are correct

Question 27

In Venn diagrams, we should never diagram the information in an argument's conclusion.

Question 28

In logic, "some" means "at least one but not all."

Question 29

Consider the following Venn diagram:
Which of the following statements best describes what this diagram conveys?

A) "All musicians are talented individuals."
B) "Some musicians are talented individuals."
C) None of the answers are correct.
D) "No musicians are talented individuals."
E) "Some musicians are not talented individuals."

Question 30

In categorical logic, the statement "Some dogs are mammals" can be interpreted as "All dogs are mammals."

Question 31

All standard-form categorical statements begin with the quantifiers _____.

A) None of the answers are correct
B) "all," "no," or "some"
C) "most," "none," or "almost all"
D) "any," "no," and "many"

Question 32

No standard-form categorical statement begins with the word "if."

Question 33

The statement "Not a single romantic novel is intellectually stimulating" means the same thing as "If anything is a romantic novel, then it is not intellectually stimulating."

Question 34

In a Venn diagram, a shaded area means that the _____.

A) area is empty or has no members
B) None of the answers are correct
C) area is not empty but has at least one member
D) area is indeterminate

Question 35

_____ is a linking verb that serves to join the subject term with the predicate term in a standard-form categorical statement.

A) A copula
B) A quantifier
C) A determiner
D) A hedge

Question 36

The correct standard-form translation of "Not every person who is a lawyer is wealthy" is "_____."

A) None of the answers are correct
B) Some lawyers are not wealthy persons
C) No lawyers are wealthy
D) All lawyers are not wealthy persons

Question 37

Which of the following is not a standard-form categorical statement?

A) Some bears are not carnivores.
B) All dogs are not cats.
C) Some dentists are musicians.
D) No coeds are men.

Question 38

In modern logic, statements beginning with "all" or "no" _____.

A) are treated as purely conditional statements and are not interpreted as asserting the existence of anything
B) None of the answers are correct
C) are not interpreted as asserting the existence of anything
D) are treated as purely conditional statements

Question 39

Use a Venn diagram to evaluate the following argument: "Some fruits are apples. Some apples are red. So, some fruits are red." This argument is _____.

A) invalid and has at least one false premise
B) valid and has true premises
C) valid but has false premises
D) invalid but has true premises and a false conclusion
E) None of the answers are correct

Question 40

The correct standard-form translation of "Something is a fish only if it has gills" is "_____."

A) Anything that is a fish does not have gills
B) All fish have gills
C) No fish has gills
D) If anything is a fish, then it does not have gills

Question 41

The statement "Whoever is the president is a United States citizen" means the same thing as "Presidents are all United States citizens."

Question 42

Use a Venn diagram to evaluate the following argument: "If something is an oak, then it's a tree. Roses aren't trees. So, roses aren't oaks." This argument is _____.

A) valid and has true premises
B) invalid but has true premises and a true conclusion
C) None of the answers are correct
D) invalid and has at least one false premise
E) valid but has false premises

Question 43

When placing an X in a two-part area, if one part of the area has been shaded, the X should be placed in the unshaded part.

Question 44

Consider the following Venn diagram:
Which of the following statements best describes what this diagram conveys?

A) "No musicians are talented individuals."
B) "Some musicians are not talented individuals."
C) "Some musicians are talented individuals."
D) None of the answers are correct.
E) "All musicians are talented individuals."

Question 45

The statement "Several candy bars are bad for you" means the same thing as "Some candy bars are not bad for you."

Question 46

Use a Venn diagram to evaluate the following argument: "Some Republicans are conservatives. Some conservatives love Ronald Reagan. Therefore, some Republicans love Ronald Reagan." This argument is _____.

A) valid and has true premises
B) invalid but has true premises and a true conclusion
C) invalid and has at least one false premise
D) None of the answers are correct
E) valid but has false premises

Question 47

Consider the following statement: " Doctor Who is the greatest sci-fi series of all time." What would be the best way to rephrase this ordinary English statement into standard categorical form?

A) "If the series is Doctor Who, then it is the greatest sci-fi series of all time."
B) "Some show that is the greatest sci-fi series of all time is Doctor Who."
C) "If a series is the greatest sci-fi series of all time, then it is Doctor Who."
D) None of the answers are correct.
E) "All shows identical with Doctor Who are shows that are the greatest sci-fi series of all time."

Question 48

To diagram statements of the form "All S are P," we shade out that portion of the S circle that does not overlap with the P circle.

Question 49

Which of the following choices is a common stylistic variant of the statement "No Democrats are Republicans"?

A) "Most persons who are Democrats are not Republicans, and Democrats are not Republicans."
B) "Most persons who are Democrats are not Republicans."
C) None of the answers are correct.
D) "Democrats are not Republicans."

Question 50

Which of the following choices is a common stylistic variant of the statement "All bachelors are males"?

A) "Bachelors are always males."
B) None of the answers are correct.
C) "Whoever is a bachelor is a male, and Bachelors are always males."
D) "Whoever is a bachelor is a male."

Question 51

Use a Venn diagram to evaluate the following argument: "Not everyone who likes football watches the Super Bowl. Not everyone who watches the Super Bowl likes football. So, some people who like football watch the Super Bowl." This argument is _____.

A) invalid but has true premises and a true conclusion
B) valid and has true premises
C) invalid and has at least one false premise
D) None of the answers are correct
E) valid but has false premises

Question 52

If I say it's true that "All of Santa's reindeer can fly," I am committed to saying it's true that Santa exists and has flying reindeer.

Question 53

Consider the following Venn diagram:
Which of the following statements best describes what this diagram conveys?

A) "Some musicians are not talented individuals."
B) "Some musicians are talented individuals."
C) "No musicians are talented individuals."
D) None of the answers are correct.
E) "All musicians are talented individuals."