What happens if you use the Negation Test on a sufficient assumption?

lookingforanswers

I know we're supposed to use the negation test to confirm the right answer for a necessary assumption question but....

If we negate trap answers -- aka sufficient assumption answer choices -- doesn't it still pass the test?

Example:
"Because we locked the door, no one can break into our house."
- necessary assumption: one cannot break into the house going through the chimney.
- sufficient assumption: the door is the only way in and out of the house, and the lock is impenetrable.

• negate the necessary: one can break into the house going through the chimney (great, this wrecks the argument and passes the negation test!)
• negate the sufficient: the door isn't the only way in and out of the house, and the lock is penetrable (great? this also wrecks the argument and passes the negation test...)

So... how can I reliably use the negation test as a tool for confirming a necessary assumption, and NOT a sufficient one?

KevinLin7Sage

Many assumptions are both sufficient and necessary.

The sufficient assumption you describe happens to be necessary, too. That's why the negation of that statement hurts the argument.

Whether a statement is NA and whether it's SA are simply separate inquiries that have no relationship to each other.

Does the negation of the statement weaken the argument? If yes, it's a necessary assumption. (And whether yes or no, this doesn't tell us anything about whether the statement is also a sufficient assumption.)

Does adding the statement to the premises make the argument valid? If yes, it's a sufficient assumption. (And whether yes or no, this doesn't tell us anything about whether the statement is also a necessary assumption.)

In many cases, on both NA questions and SA questions, the correct answer happens to be both NA and SA.