Deck 6: Categorical Logic: Syllogisms

Question 1

The predicate term of the conclusion in a standard form categorical syllogism is called the

A) major premise.
B) minor term.
C) middle premise.
D) major term.

Answer 1

D

Question 2

Which of the following is not required in order for a categorical syllogism to be in standard form?

A) The premises and the conclusion are true.
B) The first premise contains the major term.
C) The second premise contains the minor term.
D) The conclusion is stated last.

Answer 2

A

Question 3

The mood of a standard-form categorical syllogism whose major premise is universal affirmative, minor premise is particular affirmative, and conclusion is particular affirmative would be

A) IAI.
B) IIA.
C) AII.
D) III.

Answer 3

C

Question 4

The figure of a standard-form categorical syllogism whose middle term is the subject term of the major premise and subject term of the minor premise would be

A) 1.
B) 2.
C) 3.
D) 4.

Question 5

The form of a categorical syllogism is completely specified by

A) its mood.
B) its figure and mood.
C) its figure.
D) its mood, figure, and validity.

Question 6

Which of the following categorical syllogisms is in standard form?

A) All dogs are mammals. Cats are not dogs.
So, no cats are mammals.
B) All dogs are mammals. No fish are mammals.
So, no dogs are fish.
C) Some mammals are small. No whales are small.
So, no whales are mammals.
D) No whales are mammals. Some whales are fish.
So, some fish are not mammals.

Question 7

Identify the mood and figure of this standard-form categorical syllogism:
Some turncoats are not confederate soldiers. No confederate soldiers are abolitionists. So, some turncoats are abolitionists.

A) OEI-4
B) OEI-1
C) IEO-1
D) IAO-4

Question 8

Identify the mood and figure of this standard-form categorical syllogism:
All excellent teachers are people who care about students.
All University 101 instructors are people who care about students. So, all University 101 instructors are excellent teachers.

A) AAA-3
B) AAA-2
C) EEE-2
D) EEE-3

Question 9

The Venn diagram representation of "All sailors are pirates" is which of the following?

Question 10

The Venn diagram representation of "No sailors are pirates" is which of the following?

Question 11

The Venn diagram representation of "Some sailors are pirates" is which of the following?

Question 12

The Venn diagram representation of "Some sailors are not pirates" is which of the following?

Question 13

Identify the Venn diagram representation of the following syllogism:
All minerals are rocks. All diamonds are rocks.
So, all minerals are diamonds.

Question 14

Identify the Venn diagram representation of the following syllogism:
Some ultraviolet radiation is not harmful to humans. All ultraviolet radiation is a carcinogen.
So, some carcinogens are not harmful to humans.

Question 15

Identify the Venn diagram representation of the following syllogism:
Some violinists are percussionists. Some trombonists are percussionists. So, some trombonists are violinists.

Question 16

A categorical statement has existential import if and only if

A) it is a particular statement.
B) it implies that one of its terms denotes a nonempty class.
C) it implies that its subject term denotes a nonempty class.
D) it has importance for the nature of human existence.

Question 17

Which of the following relations on the Square of Opposition is valid, according to modern categorical logic?

A) contradictories
B) subcontraries
C) subalterns/subalternation
D) contraries

Question 18

Which of the following immediate inferences is invalid according to modern categorical logic?

A) conversion
B) obversion
C) contraposition
D) contraposition by limitation

Question 19

An enthymeme is an argument that

A) is found to be valid when tested with a Venn diagram.
B) has missing or unstated steps.
C) is a standard form categorical syllogism.
D) has the mood and figure AAA-1.

Question 20

When supplying unstated steps, the principles of fairness and charity require that we

A) make the invalidity of the argument more apparent.
B) add only true (or at least plausible) steps.
C) supply premises that would improve the argument.
D) not make any critical remarks.

Question 21

Which of the following is not a feature of standard-form sorites?

A) Each statement in the argument is a standard-form categorical statement.
B) Each premise (except the first) has a term in common with the immediately preceding premise.
C) The predicate term of the conclusion occurs in the last premise.
D) Each term appears twice-once in each of two different statements.

Question 22

A sorites is

A) a chain of syllogisms in which the final conclusion is stated but the subconclusions are unstated.
B) an argument with an unstated premise or an unstated conclusion.
C) an argument comprised entirely of categorical statements.
D) a chain of inferences moving from the particular to the general.

Question 23

When removing term-complements, which of the following is not a permissible change?

A) changing "No S are P" to "No P are S"
B) changing "All S are P" to "Some P are S"
C) changing "Some S are not P" to "Some non-P are not non-S"
D) changing "Some S are P" to "Some S are not non-P"

Question 24

When removing term-complements, which of the following is a permissible change?

A) changing "Some S are P" to "Some non-P are non-S"
B) changing "All S are P" to "Some P are S"
C) changing "Some S are not P" to "Some non-P are not non-S"
D) changing "No S are P" to "Some S are not P"

Question 25

A term is distributed in a statement when

A) it occurs in the subject position.
B) it occurs in the predicate position.
C) the statement says something about every member of its class.
D) the statement denies something about its class.

Question 26

A fallacy of the undistributed middle is a violation of which of the following rules for evaluating categorical syllogisms? In a valid standard-form categorical syllogism¼

A) there are exactly three terms, and each term must be used with the same meaning throughout the argument.
B) the middle term is distributed in at least one premise.
C) a term must be distributed in the premises if it is distributed in the conclusion.
D) if the conclusion is particular, then at least one of the premises must be particular.

Question 27

A fallacy of illicit minor is a violation of which of the following rules for evaluating categorical syllogisms? In a valid standard-form categorical syllogism¼

A) there are exactly three terms, and each term must be used with the same meaning throughout the argument.
B) the middle term is distributed in at least one premise.
C) a term must be distributed in the premises if it is distributed in the conclusion.
D) if the conclusion is particular, then at least one of the premises must be particular.

Question 28

Which fallacy is committed by the following categorical syllogism?
All cats are soft and furry animals.
Some amphibians are not soft and furry animals. So, no cats are amphibians.

A) fallacy of the undistributed middle
B) fallacy of the illicit middle
C) fallacy of the illicit major
D) fallacy of the illicit minor

Question 29

The predicate term of the conclusion is the major term of a standard form categorical syllogism.

Question 30

The term that occurs once in each premise is called the bridge term.

Question 31

The minor term is the subject term of the conclusion.

Question 32

In a standard-form categorical syllogism, the minor premise always comes first.

Question 33

In a standard-form categorical syllogism, the conclusion always comes last.

Question 34

The figure of a standard-form categorical syllogism indicates the position of the middle term.

Question 35

The mood of a standard-form categorical syllogism is an indicator of the position of the middle term in the premises.

Question 36

Two different categorical syllogisms cannot have the same mood and figure.

Question 37

The form of a categorical syllogism is completely specified by its mood and figure.

Question 38

To show that an area of a Venn diagram is empty, we use an "x" in that area.

Question 39

When an area of a Venn diagram is shaded, it indicates that there is at least one thing in that area.

Question 40

When a syllogism contains both a universal and a particular premise, you should always diagram the universal first.

Question 41

A categorical statement has existential import when (and only when) it implies that its subject terms only denote classes that have at least one member (i.e., are nonempty).

Question 42

Aristotelian and modern logicians agree that universal categorical statements have existential import.

Question 43

According to modern logicians, "All elves are people with infrared vision" is equivalent to "If anything is an elf, then it is a person with infrared vision."

Question 44

The only relationship on the Square of Opposition that both Aristotelian and modern logicians accept is contradictories.

Question 45

An enthymeme is an argument with a

Question 46

All enthymemes are valid.

Question 47

When forced to choose between adding a false premise and making an enthymeme clearly invalid, we adopt the practice of adding a false premise and thereby making the syllogism valid.

Question 48

A sorites is a chain of syllogisms in which the final conclusion is stated but the subconclusions are unstated.

Question 49

In a standard form sorites, the subject term of the conclusion must occur in the first premise.

Question 50

Evaluating the validity of a sorites requires that we identify all its subconclusions.

Question 51

When reducing the number of terms (removing term complements) in a categorical syllogism, we are not permitted to use conversion by limitation nor contraposition by limitation.

Question 52

The only requirement when removing term complements is that the changes we make to each statement must produce a logically equivalent statement.

Question 53

A term is distributed in a categorical statement if the statement says something about every member of the class that term denotes.

Question 54

In "Some dogs are mammals," the subject term is distributed.

Question 55

In a universal negative statement, both terms are distributed.

Question 56

In a valid standard-form categorical syllogism, the middle term must be distributed in at least one premise.

Question 57

Any categorical syllogism with two negative premises is invalid.

Question 58

Any categorical syllogism with two affirmative premises is valid.

Question 59

From the standpoint of modern logic, a valid standard-form categorical syllogism with a particular conclusion can have two universal premises.

Question 60

Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and figure: All hyperventilating iguanas are bungee-jumpers since all bungee-jumpers are pencil-pushers and some pencil-pushers are hyperventilating iguanas.

Question 61

Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and figure: No drowsy dromedaries are prized prodigies since all prized prodigies are shameless sheiks and no shameless sheiks are drowsy dromedaries.

Question 62

Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and figure: No tragic actors are idiots. But some comedians are not idiots. So, some comedians are not tragic actors.

Question 63

Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and figure: No coal tar derivatives are nourishing foods, because all artificial dyes are coal tar derivatives and no artificial dyes are nourishing foods.

Question 64

Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and figure: Some spaniels are not good hunters, though all spaniels are gentle dogs. Thus, no gentle dogs are good hunters.

Question 65

Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and figure: All professional wrestlers are good actors, because some good actors are not powerful athletes and all professional wrestlers are powerful athletes.

Question 66

Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and figure: All patriotic citizens are mindless followers of the government, and all soldiers are mindless followers of the government, so all soldiers are patriotic citizens.

Question 67

Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and figure: Since some science professors are absent-minded persons and all philosophers are absent-minded persons, some scientists are not philosophers.

Question 68

Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and figure: No knights are shrubberies, since no shrubberies are jousters and all jousters are knights.

Question 69

Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and figure: Whereas all Klingon warriors are ferocious opponents and some Klingon warriors are not male, it must be that some ferocious opponents are not males.

Question 70

Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and figure: Some tax-exempt organizations are religious associations and no tax-exempt organizations are profitable businesses. Thus, some religious associations are not profitable businesses.

Question 71

Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and figure: Since all aardvarks are CB radio operators, and no CB radio operators are Olympic champions, no Olympic champions are aardvarks.

Question 72

Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and figure: Some Tibetan monks are bookstore junkies, because no Ronald Reagan movie fans are bookstore junkies and some Tibetan monks are Ronald Reagan movie fans.

Question 73

Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and figure: All cartographers are Martians from outer space, and some cartographers are not agents for the CIA, whence it follows that some agents for the CIA are not Martians from outer space.

Question 74

Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and figure: Some Swedish water volleyball team members are not beer drinkers, because some molecular biologists are Swedish water volleyball team members and some molecular biologists are not beer drinkers.

Question 75

The following categorical argument form has more than three terms: "Some non-P are non-M. All non-S are M. So, some S are not P." Reduce the terms to three by removing term-complements via applications of conversion, obversion, and/or contraposition.

Question 76

The following categorical argument form has more than three terms: "No non-M are P. Some S are non-M. So, no S are non-P." Reduce the terms to three by removing term-complements via applications of conversion, obversion, and/or contraposition.

Question 77

The following categorical argument form has more than three terms: "No non-P are non-M. Some M are non-S. So, some S are P." Reduce the terms to three by removing term-complements via applications of conversion, obversion, and/or contraposition.

Question 78

The following categorical argument form has more than three terms: "All non-P are M. Some S are non-M. So, no non-S are P." Reduce the terms to three by removing term-complements via applications of conversion, obversion, and/or contraposition.

Question 79

The following categorical argument form has more than three terms: "All P are M. Some non-S are M. So, no non-S are non-P." Reduce the terms to three by removing term-complements via applications of conversion, obversion, and/or contraposition.

Question 80

Which of the five rules for evaluating syllogisms can you use to determine whether the following form is valid?
All M are P. No S are M. So, no S are P.