Only if & if only & conditionality

[rench.co]

Hi there,

I know that "only if" is a necessary condition indicator, but I'm wondering if "if only" would also be a necessary condition indicator or if it is a sufficient indicator? If "if only" is a sufficient indicator, then how does it differ from "only if"?

I've also been having a bit of trouble wrapping my head around the difference between sufficient and necessary conditions. I know the standard definitions and the traditional if-then explanation but none of these have lead to a click style moment of realization for me. I have gotten it down pat that if-then and such does represent a sufficient and necessary condition, but how exactly does the one differ from the other? The explanations in the Powerscore Bibles do not seem to be helping me understand the critical difference.

A recent question where I made a mistake was "the only way to achieve success is to work hard" I understand now that the "way" is referring to work hard which so work hard is the sufficient condition. If I put this statement into and if-then format I'll get "if I work hard then I will achieve success" but if I did the reverse which is incorrect I would get "if I achieve success then I will work hard." How do these differ though? I seem to be messing up then which portion is the necessary and which is the sufficient a lot even when I use if-then form to phrase things. Feel free to use other examples to explain as well!

[Beth Hayden]

Hi Rench,

The sufficient/necessary distinction seems like it should be simple but it took me a while for it to really click--you're not alone on that!

To your first question, I don't think I've seen "if only" in this context--it's definitely not an indicator you are going to see. In "only if" the only is modifying the conditional statement, but if you say "if only" the only is modifying whatever comes after that. I could say something like "if only one person comes to the show, we will cancel it," but in that case the word only doesn't indicate anything about the conditional, you could just as easily drop it entirely.

Here's how I think of conditionals--when the sufficient condition is there, it must be the case that the necessary condition is true. The sufficient condition is sufficient (good enough on its own) to prove the necessary condition. Or put another way, if the sufficient condition is there, the necessary condition must also happen (it's necessary). It's easier to see this with examples.

Driver's license 16+
If you meet someone with a driver's license, you know for sure that they are at least 16 years old.
But if you meet someone who is 16, who knows if they have a drivers license or not!

If you're a lawyer You must have taken the LSAT (but some people take the LSAT and never become lawyers)

It doesn't matter what order the two things happen in--if the sufficient condition happens it's guaranteed that the necessary condition either has happened or will happen.

So let's look at your example. Knowing that the only way to achieve success is to work hard does NOT mean that if you work hard it is guaranteed that you will achieve success. Lots of people work hard and aren't successful, but everyone who is successful had to have worked hard. Your statement is really close! I would phrase it as "if someone is successful, then it must be the case that they worked hard."

(When you see) success (you know for sure) they worked hard

The indicator words are really helpful! But when I look at a conditional statement, I don't really focus much on them. Instead I just ask myself "which one of these statements guarantees that the other one is true?" If I meet someone who is successful, it is guaranteed that they worked hard. If I meet a lawyer, it is guaranteed that they took the LSAT. This is something that takes some time to really grasp, but I promise if you look at enough examples at some point it will click!

I hope that helps!
Beth