Reply To: Confuses sufficient and necessary conditions

August 18, 2016 at 10:24 am #2440

Hi, Cecily. You probably know that you can’t just switch the order of the terms in a conditional statement. For instance, you can’t go from “If Fluffy is a cat, then Fluffy is a mammal” to “If Fluffy is a mammal, then Fluffy is a cat.” That’s often called a “mistaken reversal.” The second statement is the converse of the first, and a conditional statement doesn’t imply that its converse is true.

Or, in symbolic terms:

P –> Q doesn’t mean that
Q –> P.

When you see this answer choice, what’s going on is basically that the premises gave you a conditional statement, but the conclusion is based on its converse (or inverse, the “mistaken negation,” which is logically equivalent to the converse).

For example, here’s a simple argument where an answer choice like this would be right:

“In order to become an attorney, one must pass the bar exam. Maria passed the bar exam; therefore, she is an attorney.”

The premise gave us this:

A –> PB (necessary condition on the right side of the arrow when neither term is negated)

The conclusion, as applied to Maria, is based on this:

PB –> A

The premise, which always has to be accepted as true, is that passing the bar is a NECESSARY condition for becoming an attorney. The conclusion treats is as a SUFFICIENT condition, i.e. a condition that guarantees that anyone who accomplishes it becomes an attorney. That’s not true. There’s also a background check. There are also bar dues that have to be paid. etc.

Hope this helps.