Question 1

What would the following proposition be in standard form? My keys are somewhere in my office.

Accepted Answer

The proposition can be translated as "There exists a place in my office where my keys are located," which is equivalent to option E.

Question 2

If an argument has a categorical conclusion, that suggests that the argument is:

Accepted Answer

The form of an argument (categorical, hypothetical, disjunctive, etc.) is determined by the structure of its premises, not just by the nature of its conclusion. A categorical conclusion alone does not specify the form of the entire argument.

Question 3

If an argument uses words like unless, if, or without, that suggests that the argument is:

Accepted Answer

The use of words like unless, if, or without in an argument suggest that the argument is hypothetical, meaning it puts forward a possible scenario or condition rather than stating a fact outright.

Question 4

If an argument uses the word either or or, that suggests that the argument is:

Accepted Answer

The use of "either or" indicates that the argument is presenting two mutually exclusive options, which is the definition of a disjunctive argument.

Question 5

If an argument has a disjunctive conclusion, that suggests that the argument is:

Accepted Answer

If the conclusion of an argument is disjunctive, it means that it presents a choice between two or more alternatives. This makes the argument a disjunctive argument.

Question 6

What would the following proposition be in standard form? The mail always arrives late on Saturdays.

Accepted Answer

The standard form of the proposition "The mail always arrives late on Saturdays" is "All Saturdays are days when the mail arrives late." This is because the proposition makes a universal claim that every Saturday is a day when the mail arrives late. Therefore, choice (D) is the best answer.

Question 7

If two logicians are putting an argument into standard form, is it possible that they would use two different syllogism types? (E.g., one would make it a categorical syllogism and the other would make it disjunctive.)

Accepted Answer

Some syllogisms can be represented equally well by more than one type of syllogism. Therefore, it is possible for two logicians to use different syllogism types when putting an argument into standard form.

Question 8

If an argument has an affirmative premise and an affirmative conclusion, that suggests that the argument is:

Accepted Answer

The answer of If an argument has an affirmative premise...

Question 9

What would the following proposition be in standard form? No one has ever managed to finish our famous eight-pound burger.

Accepted Answer

The proposition "No one has ever managed to finish our famous eight-pound burger" can be translated into standard form as "No person is a person who has managed to finish our famous eight-pound burger."

Question 10

If an argument repeats terms rather than whole propositions, it is most likely:

Accepted Answer

A categorical argument consists of categorical propositions, which have a subject term and a predicate term. Repeating these terms in the argument is a characteristic of a categorical syllogism.

Question 11

What would the following proposition be in standard form? There is strawberry jam in this sandwich.

Accepted Answer

The proposition states that there is some strawberry jam in the sandwich, but it does not necessarily state that all of the jam in the sandwich is strawberry. Therefore, choice A, "Some strawberry jam is an ingredient of this sandwich," is the best option.

Question 12

If a categorical proposition begins with "there is," then will that proposition be universal, particular, or singular?

Accepted Answer

The answer of If a categorical proposition begins with "there...

Question 13

If an argument has a negative premise and an affirmative conclusion, that suggests that the argument is:

Accepted Answer

A negative premise and an affirmative conclusion indicate that the argument is disjunctive. Disjunctive arguments present two or more alternatives and assert that only one of them is true.

Question 14

An extended argument is valid if:

Accepted Answer

An extended argument is valid only if all of its steps are valid, meaning that the conclusion logically follows from the premises. Even if the conclusion is true, if the steps leading up to it are not logically sound, the argument is not valid.

Question 15

If a proposition uses a word like always, sometimes, never, everywhere, somewhere, or nowhere, that suggests that it should be formalized as what type of proposition?

Accepted Answer

Words like always, sometimes, never, everywhere, somewhere, or nowhere are often used in categorical propositions that make a claim about all, some, or none of the members of a particular category. For example, "All dogs are mammals" is a categorical proposition that uses the word "all" to assert something about the entire category of dogs. Such propositions can be represented using the standard form of categorical syllogisms, with a subject term, a predicate term, and a copula (i.e., "are" or "are not").

Question 16

If two logicians are putting a syllogism into standard form, but they choose two different types of syllogism (e.g., one makes it categorical and the other hypothetical), could both of the resulting syllogisms be valid?

Accepted Answer

The type of syllogism chosen to represent the premises does not determine the validity of the conclusion. The validity of the syllogism depends on whether the truth of the premises is sufficient to guarantee the truth of the conclusion, regardless of the type of syllogism. Therefore, both syllogisms could be valid as long as they meet this criterion.

Question 17

An extended argument is an argument that:

Accepted Answer

An extended argument is one that involves more than one syllogistic step. This means that it is not just a simple logical process but rather involves multiple steps and may have several premises leading to a conclusion.

Question 18

What would the following proposition be in standard form? There is a lid for every pot.

Accepted Answer

The answer of What would the following proposition be in...

Question 19

What would the following proposition be in standard form? Only S is P.

Accepted Answer

The proposition "Only S is P" means that S is the only thing that can be P, which translates to "All P are S" in standard form.

Question 20

What would the following proposition be in standard form? Only people with self-esteem are happy.

Accepted Answer

The original statement implies that having self-esteem is a necessary condition for being happy. Therefore, if someone is happy, they must have self-esteem, which is accurately reflected in option B.

Quiz 8: Reasoning With Syllogisms