Negation Test - Conditional Answer Choices? (NA)

[daniel]

I've been trying to practice the negation test on answer choices in Necessary Assumption questions, but I'm not sure about the proper way to negate conditional statements.

I understand that adding "It's not true that ..." to the beginning of the statement is probably a safe bet, but what's the best way of negating answer choices like the following:

1) If the new building is constructed, then the city's jobless rate will decrease.

2) If Jane doesn't go to the store, then we won't have food to cook for dinner.

In negating these, is it just the necessary conditions that should be negated? For example,

1) If the new building is constructed, then the city's jobless rate will NOT decrease.

2) If Jane doesn't go to the store, then we WILL have food to cook for dinner?

[ohthatpatrick]

Great question.

Negating conditionals is tricky, if not worth avoiding altogether.

Here is the short answer:
Don't try to negate a conditional on Necessary Assumption. Just ask yourself if the conditional matches some move the author made from Prem --> Conc (or Prem --> Subsidary Conc). Beware that the answer may be in contrapositive form (~Conc --> ~Prem).

If the conditional matches the logic/strength of the argument, then it's going to be correct. If not, it won't. So these are easier to judge as you would a Sufficient Assumption answer, i.e. by making sure that the two halves of the conditional statement match concepts in the arguments and reflect their proper logical ordering.

I've rarely picked a conditional answer as the correct answer on Necessary Assumption, and when I have, it has simply mimicked the argument core.

Longer answer:
If you were to negate a conditional, you would not negate the sufficient OR the necessary.

Let's use your examples.
1) If the new building is constructed, then the city's jobless rate will decrease.

If we negate that, we're saying " it is not true that if the new building is constructed, then the jobless rate will decrease".

All we're saying is that there is NOT some guaranteed connection between those two ideas. (If anything, what you're really negating is the arrow).

Basically, we're saying that if the new building is constructed, the jobless rate may decrease, increase, or stay the same.

2) If Jane doesn't go to the store, then we won't have food to cook for dinner.

Negation: If Jane doesn't go to the store, then maybe we will have food, maybe we won't have food.

It's easier to see how this works with quantity-conditional statements.

"All girls love Justin Bieber" = Girl --> Love JB

If I negate "all girls love Justin Bieber" I get "NOT ALL girls love Justin Bieber", i.e. "at least one girl does NOT love JB".

If I negate "If you're a girl, you love Justin Bieber", we're getting "If you're a girl, you may or may not love JB ... there's no definite connection between being a girl and loving JB".

So if I'm forced to negate
X --> Y

I'm going to say it in my head as "if X is true, then Y or ~Y could still happen."

Let me know if any of this is confusing. Hope it helps.

[daniel]

Thanks, Patrick. Your explanation is both clear and helpful.