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The phrase "if and only if" (iff) is commonly used in the field of mathematics () and computer programming, as a conditional expression in classical (Boolean) logic.

Within that scope, it might not mean the same as a simple "if:"

If it rains, I will get wet.

I will get wet if it rains, but, there are numerous ways to get wet.

I will get wet, if and only if it rains.

Only rain, exclusively, can make me wet.

Do these distinctions apply in this way (example above), outside of the aforementioned domain?

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  • On a related note, I realized the other day that "and/or" in English (and in other natural languages) is used to represent logical inclusive or, since "or" is usually taken to be the exclusive or (this or that, but not both). – Henrik N Mar 26 '11 at 17:56
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    In normal writing I would usually punctuate it: I will get wet if, and only if, it rains. – psmears Mar 26 '11 at 18:24
  • @Henrik N: Interesting, I hadn't thought of that before. Now you got me questioning all "logical operators" in the English language! Aaah! :p – Leif Mar 26 '11 at 21:39
  • @psmears: True, it should probably be punctuated in normal writing :) – Leif Mar 26 '11 at 21:41
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When you say "if and only if" in regular conversation, you are taking the mathematical construction and applying it to a general life situation. So you can say "I will get wet if and only if it rains" and mean that:

If it is raining, I am wet.

AND:

If I am wet, it is raining.

(If either condition is met, the other is also met.)

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  • Yes, that's what I thought. So, in general life situations, "I will get wet, if and only if it rains" also implies that there are no other possible ways to get wet? (Contra "if", which implicitly leaves room for other possible causes). Is the "if and only if" statement void if I get wet from somebody throwing a waterballon at me? :) – Leif Mar 26 '11 at 21:48
  • That's right; If you get wet because of a water balloon and it's not raining, then your if-and-only-if statement was a false statement. (On the other hand, if someone hit you with a water balloon while it was raining on you, you'd still be okay.) – Hellion Mar 26 '11 at 22:01
  • Thanks for the clear answer! You confirmed what I thought to be the case. You must be a programmer too? :p – Leif Mar 26 '11 at 22:09
  • Can "if an only if" be shortened to just "only if" and mean exactly the same thing? – Paul J. Lucas Jan 12 '15 at 17:35
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    @PaulJ.Lucas, that's one of those gray areas; some people may take it that way, others may argue that "only if" implies necessity but not sufficiency--that is, "I will get wet only if it rains" means that "it rains" is the only condition under which I can get wet, but it does not mean that I must get wet when it rains. – Hellion Jan 12 '15 at 17:49
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Yes, it does work (though it sounds a little technical) in common language because by saying:

I will get wet if and only if it rains.

you are saying both

I will get wet if it rains.

(meaning that if it rains there is no chance I will not be wet) and

I will get wet only if it rains.

(there is no way I will get wet unless it rains).

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  • Okay, so I guess the term is a bit more "loose" when it comes to general life situations then :) – Leif Mar 26 '11 at 21:36

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