"If" vs. "only if"

Imagine you invited me to a party. I could be a polite guest and simply say "Yes, I'll be there," or "I'm sorry, I have a prior obligation." Either of those responses would make it easy for you--you'd know for sure whether or not you should plan on me. But I could also be a pain in the ass and put a condition on my attendance. I could say, "I'll go if Miguel Angel Jimenez goes." Or I could say, "I'll go only if Miguel Angel Jimenez goes." In real life, those two statements might sound like the same thing--you'd try to figure out whether Miguel is coming, and then you'd know whether or not I'll be there. But on the LSAT, it's more complicated than that. The two statements do not mean the same thing on the LSAT--they mean subtly, yet concretely, different things. The purpose of this post is to explain that difference, because it's a critical concept.

 

 

 

 

 

 

 

 

 

Miguel Angel Jimenez:  The most interesting golfer in the world.

If I say "I'll go if Miguel goes," what I'm telling you is that Miguel is a "sufficient condition" for my attendance. If Miguel is there, that's sufficient information for you to know that I will also be there. Memorize this: The word "if," on the LSAT, indicates a sufficient condition. So "I'll go if Miguel goes" looks like this:

M --> N

This does not, of course, mean that if I go Miguel must also go. The arrow only goes one way! What it does mean is that if I'm not there, Miguel can't be there:

N -->M

(What I just did there is called the "contrapositive." If you're having any trouble following so far, please check out my posts on the sufficient and necessary conditions.)

Now, I need you to carefully consider what this actually means:

  • It's okay for Miguel and Nathan to both be at the party.
  • It's okay for neither Miguel nor Nathan to be at the party.
  • It's okay for Nathan to be there without Miguel. (I said I'd go if Miguel goes... but I didn't say I wouldn't go without him!)
  • But it's NOT okay for Miguel to be there without Nathan. I told you that I'd be there if Miguel was there. So if Miguel is there and I'm absent, then I've broken my promise to you.

This might all seem obvious so far. But the next step is where your mind will be blown, so please pay careful attention.

If I say "I'll go only if Miguel goes," (or "I'll only go if Miguel goes,") I'm no longer telling you that Miguel is a sufficient condition for my attendance, like I was in the discussion above. Rather, I'm telling you that Miguel is a necessary condition: If I'm there, then Miguel is also going to be there. Memorize this:  "Only" indicates a necessary condition. So "I'll go only if Miguel goes looks like this:

N --> M

This does not mean that if Miguel goes I must also go. The arrow only goes one way! What it does mean is that if Miguel is not there, I can't be there:

M -->N

(I just did the contrapositive again. And, reminder, if you're having trouble following the discussion it really might help to check out my posts on the sufficient and necessary conditions.)

Now, I need you to carefully consider what this actually means:

  • It's okay for Miguel and Nathan to both be at the party.
  • It's okay for neither Miguel nor Nathan to be at the party.
  • It's okay for Miguel to be there without Nathan. (I said I'd only go if Miguel goes... but that doesn't preclude me from skipping the party even if he's there!)
  • But it's NOT okay for Nathan to be there without Miguel. I told you that I'd only be there if Miguel was there. So if Miguel is absent and I'm there, then I've broken my promise to you.

To recap:

In both scenarios, it's okay for both Miguel and Nathan to be at the party.

In both scenarios, it's okay for both Miguel and Nathan to be absent from the party.

In the "I'll be there if Miguel is there" scenario, it's okay for Nathan to be there without Miguel, but it is not okay for Miguel to be there without Nathan.

In the "I'll only be there if Miguel is there" scenario, it's okay for Miguel to be there without Nathan, but it's not okay for Nathan to be there without Miguel.

Please note the difference between the last two outcomes. This is a departure from how people tend to talk in everyday life, so it's something that you might just need to memorize for the LSAT.

One last note, if your head is spinning: This concept is a lot easier than it might look at first! Please email me with questions, or talk to me in class, and I'll be happy to walk you through it and provide additional examples. As always, I'm here to help.

Best,

--nathan