In-Class Quizzes 2

Mon., Apr. 21
3 points

Fill in the chart below, for the two given categorical propositions (answers in bold).

Given proposition	Quantifier	Subject Term	Copula	Predicate Term
No fish are mammals.	No	fish	are	mammals
Some birds are not penguins.	Some	birds	are not	penguins

Tue., Apr. 22
5 points

Fill in the table below, for the following categorical proposition (answers in bold).

M: persons identical to Michael Moore
D: shooters of documentaries

Given proposition: All M are D.

Letter Name	A
Quantity	Universal
Quality	Affirmative
Terms Distributed	Subject term (M)
Change quality only	No M are D.
Change quantity only	Some M are D.
Change both	Some M are not D.

Wed., Apr. 23
2 points

Using the modern square of opposition, what conclusion may be validly derived from the following premise?

Some S are P.

Answer: It is false that no S are P

(or to put it another way, "No S are P" is false).

Thu., Apr. 24
4 points

Using the modern square of opposition, what conclusion may be validly derived from the following premise?

All S are P.

Answer: It is false that some S are not P

(or to put it another way, "Some S are not P" is false).

Given the following statement and truth value, perform the indicated operation, showing the resulting statement and its truth value.

Given statement	Truth Value	Operation
No S are P.	(F)	Conversion

Answer: No P are S. (F)

Mon., Apr. 28
3 points

Given the premise, "All tigers are mammals," what conclusion follows validly via the following operations (answers in bold)?

Conversion	N/A
Obversion	No tigers are non-mammals
Contraposition	All non-mammals are non-tigers

Tue., Apr. 29
3 points

Translate the following English statements into standard-form categorical propositions.

1. Not all horses race.
2. 3 p.m. is a good time for naps.

Examples of correct answers:
1. Some horses are not racers.
2. All times identical to 3 p.m. are times good for naps.

Wed., Apr. 30
2 points

State whether the following argument is valid or invalid. Explain.

All tooth fairies are nice beings.
Therefore, some tooth fairies are nice beings.

Answer: Invalid (from any standpoint).

Explanation: The argument is an example of subalternation correctly done, with a subject term that denotes nonexistent things. Subalternation is always invalid from the Boolean standpoint, always committing the existential fallacy from the Boolean standpoint. Subalternation is conditionally valid from the Aristotelian standpoint, with the condition being that the subject term denotes existent things. In this case the condition is not fulfilled (since tooth fairies don't exist), hence this argument is invalid from the Aristotelian standpoint and commits the existential fallacy from the Aristotelian standpoint.

Thu., May 1
2 points

State whether the following argument is valid or invalid. Explain.

Some unicorns are not fighters.
Therefore, it is false that all unicorns are fighters.

Answer: Valid (from any standpoint; i.e., unconditionally valid).

Explanation: This is a correct application of the contradictory relation. It is impossible for the premise to be true while the conclusion is false. The O proposition in the premise necessarily has the opposite truth value from the A proposition embedded in the conclusion. (By the way, with the contradictory relation, the question of existence never arises, and the existential fallacy cannot be committed.)

Fri., May 2
4 points

Construct the syllogistic form from the following combination of mood and figure: AEO-4.

Answer:
All P are M.
No M are S.
Some S are not P.

Tue., May 6
3 points

Construct the following syllogistic form, which is given as invalid, and state what fallacy or fallacies it commits: OAI-3.

Answer:
Some M are not P.
All M are S.
Some S are P.

Fallacy: Drawing an affirmative conclusion from a negative premise (i.e., Rule 4 is broken).

Wed., May 7
3 points

Given the categorical proposition, "Some F are non-E," state which two of the three operations (conversion, obversion, contraposition) performed on this statement yield logically equivalent statements. Show the resulting logically equivalent statements.

Answer:

Operation	Logically Equivalent Result
Conversion	Some non-E are F.
Obversion	Some F are not E.

Explanation: Conversion yields logically equivalent results for E and I propositions, and the given statement is an I proposition. Obversion yields a logically equivalent result for any categorical propostion. (Contraposition yields logically equivalent results for A and O propositions, not applicable in this case.)

Thu., May 8
3 points
(From p. 272, 5.6, I, 11)

For the following enthymeme, say whether the missing statement is a premise or conclusion. Then supply the missing statement (which need not be expressed as a standard-form categorical proposition).

Wherever water exists, human life can be sustained, and water exists on the moon.

Answer: Conclusion - Human life can be sustained on the moon.

Mon., May 12
3 points

State whether the following argument is valid or invalid, and why (i.e. what relation or operation is applicable?).

Some C are not D.
Therefore, some D are not C.

Answer: Invalid, illicit conversion.

Tue., May 13
2 points

Which theory of probability is used to determine the likelihood that an Ajax Truck will develop transmission problems within the first two years?

Answer: Relative Frequency Theory

Wed., May 14
2 points
(From p. 234, 4.7, I, 42)

Translate the following into a standard-form categorical proposition:
Monkeys are mammals.

Answer: All monkeys are mammals.

Compare to p. 230, "Emeralds are green gems." Translation: "All emeralds are green gems."