Posts Tagged ‘logic’

Formal Logic – The Unless Dilemma

By: Christopher Cosci - posted May 18th 2009 at 2:12 PM    

Given a statement in "if X, then Y" format, most people are perfectly comfortable writing it down in shorthand (X → Y) and forming the contrapositive (No Y → No X). However, there’s one formal logic keyword that distracts and confuses more test takers than any other: unless.

While some people continually struggle with "if" vs. "only if" (remember, "if" indicates a sufficient condition; "only if" indicates a necessary condition), "unless" is a virtually universal stumper. However, like with any concept on the LSAT, dealing with this issue comes down to understanding it.

To help, let’s use an analogy from the world of politics: Unless you were born in the United States, you cannot become President of the United States.

So, what does that mean? Just like on the LSAT, the word "unless" indicates a necessary condition; a person needs to be born in the United States. What is that necessary for? It’s necessary to be the president. However, does being born in the United States guarantee one becoming president? Of course not.

Remember that necessary conditions are just that – necessary. They will not guarantee results. However, what happens if a person was not born in the U.S.? That guarantees something: that person cannot be president. So, how does this translate into formal logic? Like so:

Not born in U.S. → Not president
President → Born in the U.S.

Many people will offer the following quick tip: cross out the word "unless" and replace it with "if not." Then, start with that "if not" and go from there. It works perfectly because you’re negating the necessary condition. And when you don’t have the necessary condition, you can’t possibly have the condition for which it’s necessary.

Take one more quick example for practice: The television show will be canceled unless viewers draft a petition.

In this case, drafting a petition is necessary to save the television show, but even the best petition isn’t guaranteed to save it. However, change that "unless" to "if not," and you have a definite statement: if viewers don’t draft a petition, the show will be canceled. And, by the contrapositive: If the show is not canceled, then viewers must have drafted a position. (Note how drafting a petition is the necessary condition in this logic.)

Now, go find your hardest "unless" statement and don’t let it stump you again.