## Conditional Imperfection

Posted by Neal on November 15, 2013

“Rocco was doing it again today,” Adam told Doug at supper one night. His classmate Rocco has a habit of making contrarian claims, seemingly just for the purpose of arguing about them. “He was saying that Jews can be atheists.”

Maybe Rocco had some kind of idea that an atheist Jew would be something like a fasting carnivore, or a celibate homosexual (or heterosexual or bisexual), and hadn’t quite grasped the concept of criterial definitions. Or maybe he was thinking of *Jew* in a more cultural sense, like I just read about in this Wikipedia article. Whatever he had in mind, Doug and Adam weren’t buying it.

Adam tried to explain Rocco’s argument, not very satisfactorily, but that was because of the material he had to work with. He and Doug were laughing as they tried to dissect Rocco’s reasoning.

“You’re a Jew,” Doug said, “if and only if you believe in God!”

Well, you can’t say “if and only if” to a semanticist and expect it to pass unexamined. “So … Muslims are Jews?” I asked.

“No, Dad,” Doug explained. He then summarized for me the concept of *only if*, concluding, “You’ve out-literaled yourself!”

Later on, I drew a truth table for *if* and one for *only if*, and showed them to Doug. He found that, after all, he and I agreed about the meaning of *only if*. So what’s the difference between *only if* and *if and only if*, I asked.

“I don’t think there is one,” Doug said.

I drew up the table for *if and only if*, and Doug understood it, but in his opinion, in ordinary conversation, *if and only if* was just an emphatic way of saying “only if”.

“I’m with Doug on this one,” my wife offered. In a casual, dinner-table conversation, I shouldn’t have taken Doug’s *if and only if* in this technical sense.

Technical sense? This was my first inkling that there was more than one sense!

This weakening of *if and only if* to mean just *only if* is an interesting opposite to a pragmatic effect that Mike Geis and Arnold Zwicky named **conditional perfection**. Here’s the canonical example:

“I’ll give you $5

ifyou mow the lawn” taken to mean “I’ll give you $5if and only ifyou mow the lawn.”

Now, in the opposite direction, we have

“You’re a Jew

if and only ifyou believe in God” to mean “You’re a Jewonly ifyou believe in God.”

I’m not totally convinced it’s real yet, though. I checked the spoken segment of COCA for *if and only if* and got a measly three hits. For what it’s worth, they all seem to have been used in the technical sense:

- Republicans in the house are embarking on their own effort, promising to cut spending and raise the debt ceiling
**if and only if**both Houses of Congress vote for a balanced budget amendment in the coming days. - We simply should never have been in the business of saying to a 16-year-old girl,’
**If and only if**you have a child out of wedlock, we’ll send you a check in the mail.’ - we may have now a normative principle that that action is legitimate
**if and only if**it proceeds on this model through the U.N.

What do you think? Have you used, or heard others use, *if and only if* to mean *only if*?

## Hao Ye said

Well, I’m a math/CS guy, so I have to disagree with this watering down of iff.

I’m also not sure I buy the idea of conditional perfection: “p if and only if q” necessarily implies “if not q then not p”, and it’s hard to imagine, in your given example, that “I’ll give you $5 if you mow the lawn” means “I’ll never give you $5 unless you mow the lawn”.

## Ellen K. said

“I’ll give you $5 if you mow the lawn” doesn’t means “I’ll never give you $5 unless you mow the lawn”, but it does often in effect mean mean “I won’t give you $5 right now unless you mow the lawn”. There’s no reason to expand the time from infinitely as you do.

## Conuly said

He’s wrong. Quite aside from ethnic and cultural definitions of Judaism, there is such a thing as humanistic Judaism. Being an atheist does not necessarily preclude being Jewish.

Oh, you mean about if and only if? I think you’re wrong on that one, but since he’s still wrong about atheism and Jews, pound on that.

## Jan Freeman said

Neal, your first graf has “He was saying that Jews can be atheists.” Didn’t you mean “that Jews *can’t* be atheists”?

I think of “if and only if” as merely an emphatic “if,” but I don’t think I would know if someone used it in the “technical” sense, since I lack that reading.

## Jan Freeman said

Or am I not following you because I can’t imagine Doug arguing that Jews can’t be atheists?

## dw said

“I’ll give you $5 if you mow the lawn” taken to mean “I’ll give you $5 if and only if you mow the lawn.”Really? So you think it implies that he won’t give me $5 if I wash the dishes? If I buy something costing $5 and pay with a $10?

## dainichi said

I’m wondering why it’s “if and only if” and not “if but only if”. “if” and “only if” form a contrast, so “if but only if” seems to get the idea across better…

## dw said

@Dainichi: To a Boolean logician, “and” is a more satisfactory term than “but”. “But” brings in more connotations about speaker’s expectations; that may be undesirable in a mathematical or logical context.

## dainichi said

@Dw

Yep, so maybe it’s a mistake to begin with to expect mathematical/logical lingo to work in everyday English.