This is a post in a series that focuses on the LSAT. Each post in this series contains an excerpt from our new Guide to Formal Logic on the LSAT; this focuses on contrapositives in conditional logic. If you would like to download the full guide, please use the form at the bottom of this post.
The contrapositive is a two-step process – flip the terms and then (un)negate them. Every single conditional has a valid contrapositive. It’s worth repeating: the contrapositive is the only valid inference you can make from a conditional. The LSAT will attempt to trick you with a few common and invalid inferences. We’ll look at them in more detail, but they can be summarized very quickly: as the contrapositive requires both flipping and (un)negating, incorrect inferences will do only one of these things.
Let’s look at the final example in more detail. “If I’m not in New England, then I’m not in Boston,” which we correctly contraposed to “If I’m in Boston, then I must be in New England.” That contrapositive was both flipped and negated.
The LSAT will frequently present this option as an answer/inference:
“If I’m not in Boston, then I’m not in New England.”
We call this an Incorrect Reversal, as the terms are merely switched and not negated.
EXAMPLES – are they correct contrapositives or are they fallacies?
- If someone didn’t watch the debate, then they can’t be fully caught up on political events. Jason isn’t caught up on political events, so he must not have watched the debate.
- Manny will stay in town if he accepts the position. He won’t stay in town, so he must not have accepted the position.
- Fallacy. ~Watched Debate –> ~Caught up on Events does not yield ~Caught up on Events –> ~Watched Debate. This is an incorrect reversal fallacy.
- Correct contrapositive. Accept Position –> Stay in Town is correctly contraposted as ~Stay in Town –> ~Accept Position.