“If” vs “Only if” vs “If and only if”

Question

If I said:

Yell only if I fall.

Would the person have to yell once I fell?

---

Sources of confusion

Wikipedia
This guy

Answer 1

Recall that in formal logic, your expressions are used as follows:
A if B means that B implies A.
A only if B means that A implies B
A if and only if B means that A is equivalent to B.

For example if in the morning I tell my wife "I'll buy that shirt we saw yesterday only if it costs less than 40 dollars" and she sees me wear it in the evening, she can deduce that I paid less than 40 dollars.
So, logically speaking, in your example, the deduction is that if a yell is heard, necessarily you fell: no notion of obligation is involved.
However, human beings are not computer programs and the use of "only if" in real life is more subtle than what logicians might decree:
it would be cruel for a father to tell his daughter "I'll buy you this dress only if you get good grades at the end of the year" and then buy nothing even though she had only A's. You wouldn't have committed a logical error but would have shown you are a lousy parent!

Answer 2

No :P

"Only If" is not a stronger version of "If" that keeps what it implies.

This is the illustration for the two equivalent statements:

• Yell only if I fall.
• If you yell, I must have fallen. (Notice the subtlety. I didn't say "I fall if you yell". This is logical deduction, not cause-effect.)

Each circle represents a set of instances of "I fall" or "Yell".

Disclaimer: English is not my first language. I'm only talking about the mathematical sense.

Answer 3

Practically speaking, it's an ambiguous command, and if you really want to be clear in your request, you would phrase it in an unambiguous way.

Technically speaking... well, who cares? The goal of language is to communicate with humans. There may be some arcane rules of language that provide for a definitive answer to your question, but since few people are familiar with it, knowing the rule won't do you any good.

Edit: First time visiting/posting so I'm not sure how this community leans between looking for technical grammar rules as opposed to practicality. In real life and in a lot of writing I find "Just say what you mean in a way that people will understand you!" to be the underlying answer to a lot of grammatical questions. Since I've been downvoted already, I can see that at least one person prefers the former.

Answer 4

Question:

Would the person have to yell once I fell?

Yes, the person would yell once you fell, but only if you fell.

"If" and "Only if" used in the same way means the same thing, except that "only if" is more forceful, more compelling.

"If and only if" is the most obligatory of the three, in which the action has been distinguished and emphasised, "If, and only if" It's the most forceful of the three