Reply To: Difficulty understanding "required assumption" questions

August 20, 2016 at 2:23 pm #2454

The mountain sickness question is a tough one that stumps a lot of students. In terms of advice, I’d say to keep working through them, but here’s a simplified example that might help.

My roommate loves maple bars. He went to the donut store this morning. He will buy a maple bar if he can afford one. I happen to know that maple bars only cost 25 cents today, so he will buy a maple bar.

Conclusion: He will buy a maple bar today.

Here’s a possible answer choice:

A) My roommate has three dollars.

Notice that this is great as a sufficient assumption answer – if he has 3 dollars, then we know the conclusion is true: He will buy a maple bar. How do we know? Because they’re only a quarter, so he can afford one with his 3 dollars, and we have a premise that if he can afford one, he will buy one.

But it’s a wrong answer as a necessary assumption question. The argument doesn’t DEPEND on his having three dollars. He’s not REQUIRED to have three dollars in order for the conclusion to follow. Even if he only has two dollars, he might still buy a maple bar.

His having three dollars is sufficient, but not necessary.

Now the reverse:

In order to become an attorney, one must pass the bar exam. Rhonda has been studying hard for the bar exam, so Rhonda will become an attorney.

Conclusion: Rhonda will become an attorney.

Answer choice:

A) Rhonda will pass the bar exam.

This is a good answer for a NECESSARY assumption question – if she doesn’t pass the bar exam, then she won’t be an attorney. So the conclusion that she’ll become an attorney DEPENDS on her passing the bar exam.

But it’s a wrong answer for a sufficient assumption question – passing the bar doesn’t guarantee that the conclusion is true. It doesn’t automatically make you an attorney. You still have to pay bar dues. You have to pass a background check.

Basically, necessary assumptions aren’t sufficient because there might be OTHER necessary conditions. For instance, if beer costs $5, then it’s necessary to have five dollars to buy one. But that’s not sufficient – you still have to be 21 years old or older. There’s more than one necessary condition.