Validity of Argument

[jadechiagirl]

Hi there! I'm having difficulty with identifying the validity of an argument from a class. It goes as follows:

Consider the following argument: All groups or institutions that spend money are businesses. All families are groups or institutions that spend money. Therefore, all families are businesses. This argument is invalid because:

A) the conclusion is true, and thus the argument is not truth preserving.

B) the premises are true, and thus the argument is truth preserving.

C) the premises and conclusion are false; it doesn't matter if truth is preserved.

D) the premises are true, but the conclusion is false (and thus the argument is not truth preserving).

I got the question wrong and the correct answer was apparently D, but I don't understand why. The question seemed wrong to begin with because it seems like the argument is valid in the first place.

1. All groups or institutions that spend money are businesses.
2. All families are groups or institutions that spend money.
3. Therefore, all families are businesses.

Doesn't the conclusion follow from the premises and is therefore valid?

[Steve3007]

Yes, the conclusion follows from the premises as far as I can see. But the question of whether the premises are true depends on definitions. The premise "All groups or institutions that spend money are businesses" uses an odd/non-standard definition of the word "business" when it's used as a noun to denote an entity. "All families are groups or institutions that spend money" is clearly not necessarily true for all families in the world.

So I've no idea why the correct answer is deemed to be D.

[LuckyR]

Yes, the conclusion follows from the premises as far as I can see. But the question of whether the premises are true depends on definitions. The premise "All groups or institutions that spend money are businesses" uses an odd/non-standard definition of the word "business" when it's used as a noun to denote an entity. "All families are groups or institutions that spend money" is clearly not necessarily true for all families in the world.

So I've no idea why the correct answer is deemed to be D.

I'm with you, the first premise is clearly incorrect, thus of the given answers, C is best.

If the question writer feels that the first premise is clearly true, IMO they are not very talented in coming up with test questions.

[jadechiagirl]

Okay, so if I confront them with this, I should be able to generally point out that firstly, the question is misleading because the argument isn't invalid in the first place. Next, even if we say that the argument invalid (which it isn't), the given answer doesn't make sense because it's not the case that the premises are true, as the answer suggests.

[LuckyR]

Okay, so if I confront them with this, I should be able to generally point out that firstly, the question is misleading because the argument isn't invalid in the first place. Next, even if we say that the argument invalid (which it isn't), the given answer doesn't make sense because it's not the case that the premises are true, as the answer suggests.

While I don't disagree with your post, in my experience with dealing with folks in charge of my grades, I would approach it differently. I would inquire why they feel the first premise is true. Where to go will depend on their answer.

[Steve3007]

I agree with LuckyR that when you're dealing with people in a position of power over you, that should affect how you approach it. Softly softly catchy monkey.

I might start by telling them that, perhaps due to my own ignorance, I wasn't aware that the word "business" (when used to refer to an entity as opposed to an action) refers to any group or institution that spends money. I tend to think of it more specifically as the word for an entity that takes in raw materials and/or labour (in exchange for money), produces goods and/or services, and sells those goods and/or services for (ideally) more money than was spent on the raw materials and/or labour, thereby making a profit.

Not all groups or institutions that spend money do all of that.

[kaczynskisatva]

The solution to your problem is to drop the class, and change your major if necessary.

Both premises are false. The conclusion from them, is true.

Groups or institutions that spend money, but are not businesses, include governments, charities, and religious organizations.

Families which are not groups or institutions which spend money, include tribal family units existing outside of a monetized economy, and may also include some families which have no income and subsist on resources, but not money, provided to them. Two or more institutionalized sibling orphans may constitute a family, but dispose of no money.

The conclusion drawn from these premises is true, according to basic set theory. If all B's are A's, and all C's are B's, then transitively all C's are A's.