Talk:only if

RFV discussion

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Does this meet our CFI (it needs formatting anyhow)? I know we have if and only if and if only. SemperBlotto 08:05, 26 July 2007 (UTC)

This is definitely a set phrase with a specific, technical meaning in mathematics (my field): if its being a sum of parts is your worry, that should (à la prior knowledge) alleviate your concern. Otherwise, I'm not sure what's wrong with it, as there are countless hits in books, etc., with the meaning that's listed in the entry. —msh210 15:34, 26 July 2007 (UTC)

I think I just contradicted my own stance in the discussion, above, on genuine issue of material fact. Ah, well, a foolish consistency is the hobgoblin of little minds. —msh210 15:40, 26 July 2007 (UTC)

In mathematics, only if is idiomatic, because (unlike other uses of only) it doesn't imply if; P only if Q means Q if P, and in particular, it does not mean the same is P if and only if Q. —Ruakh_TALK 18:04, 26 July 2007 (UTC)

P only if Q means Q if P ? Surely you mean P only if Q means ~P if ~Q ! Robert Ullmann 17:11, 27 July 2007 (UTC)

You're right that P only if Q more narrowly means ~P if ~Q, but this seems like a distinction without a difference? :-/ —Ruakh_TALK 01:01, 28 July 2007 (UTC)

I think Robert means that "Q if P" is incorrect. You meant to say "Q implies P", I think. No, I'm not sure what you meant. --EncycloPetey 01:13, 28 July 2007 (UTC)

By "Q if P" I mean "if P, Q" i.e. "P → Q" i.e. "P implies Q" i.e. "Q ← P" i.e. "Q is implied by P" i.e. "~Q → ~P" i.e. "~P ← ~Q" i.e. "Q is true if P is" i.e. "if P is true, Q is" i.e. "if Q is false, P is" i.e. "P is false if Q is". (I'm not just being crazy, am I? I really think all of those are the same. It hasn't been that long since I've used a contrapositive.) —Ruakh_TALK 01:38, 28 July 2007 (UTC)

For purposes of this discussion then, are you distinguishing betwen "P if Q" and "P only if Q"? Those aren't the same to me, but your discussion implies they are synonymous. In particular, "P only if Q" shluld not mean the same as "Q if P". Yes? --EncycloPetey 01:50, 28 July 2007 (UTC)

By my understanding — which I was really pretty sure of until this discussion — "P only if Q" and "Q if P" are exactly equivalent (and hence might as well be synonymous), and neither is equivalent to "P if Q". —Ruakh_TALK 02:46, 28 July 2007 (UTC)

Drat, I can't find the nice litle book I used to have on symbolic logic (and can't remember the last time I had it). Most of my mathematical texts are either too general for this, or cover the wrong subdisciplines. --EncycloPetey 03:36, 28 July 2007 (UTC)

Unfortunately, the only textbook of mine that I can remember covering this sort of basic terminology is one that wasn't actually a published work yet (it later became this book), so I don't think it's a good idea to put it in the references section without being sure the published version had the same text in the same place. What it says is:

We have already mentioned that the implication P ⇒ Q can be expressed as both “If P, then Q” and “P implies Q”. In fact, there are several ways of expressing P ⇒ Q in words, namely:

If P, then Q.
Q if P.
P implies Q.
P only if Q.
P is sufficient for Q.
Q is necessary for P.

It is probably not surprising that the first three of these say the same thing, but perhaps not at all obvious that the last three say the same thing as the first three. […]

(That's from Gary Chartrand, Albert D. Polimeni, and Ping Zhang, Mathematical Proofs: A Guide to Understanding the Basics of Abstract Mathematics and Constructing and Writing Proofs of Your Own, as it stood at the end of 1999, Chapter 2: Logic, pages 27–28.)

—Ruakh_TALK 14:15, 28 July 2007 (UTC)

OK, but it needs hammering into some sort of proper format. SemperBlotto 07:21, 27 July 2007 (UTC)

I'm marking this RFV passed under the "clearly widespread use" clause, and adding {{rfquote}}. —Ruakh_TALK 02:02, 28 October 2007 (UTC)

an additional hedge may be added to the main clause: "The company can succeed only if it has sufficient backing."

Why is the change of will by can "an additional hedge"? what meaning of hedge is used here? --Backinstadiums (talk) 16:56, 19 February 2020 (UTC)