Conditional imperfection

[Laurence Horn]

I've tried dealing with this conflation of "only if" with "if and only if" when I teach logic, and I agree it's tricky.  My approach is to concede that in saying "only if p, q" a speaker is conceding "if p, q", in the same way that "only" statements generally presuppose their "prejacent" (a medieval term for what you get when you take away the "only").  So "Only Pat passed the test" presupposes Pat passed, "Only on high holy days does he go to shul" presupposes he goes to shul on high holy days", "Only then will A-Rod testify" presupposes A-Rod will testify.  This isn't just a suggestion (or implicature), since people *generally* reject sentences like

"Only Pat passed, and (maybe) even Pat didn't", "Only Pat passed, and (maybe) nobody did"
"Only then will A-Rod testify, and (maybe) not even then", "Only then will A-Rod testify, and (maybe) he never will"

So in the same way, "Only if Selig shows up will A-Rod testify" presupposes "if Selig shows up A-Rod will testify", and the assertion (only if…) and presupposition (if…) together gives you the "if and only if". So there's a commitment to "if and only if", but still an asymmetry to the way the speaker is committed to each conjunct: one is asserted, the other presupposed.  So I try, with mixed success, to convince the students of this by bringing up

(i) the fact that for some speakers, the presupposition but not the assertion can be suspended by a "maybe", "perhaps", or "it's possible that".  So compare:

"Only if Selig shows up will A-Rod testify, and maybe not even then"
"If and only if Selig shows up A-Rod will testify, and maybe not even then"

--the first of these sounds better than the second (to some of us, anyway), because only in the latter is the "if" part being explicitly asserted.  (Notice also that the subject inversion in the consequent is more likely with the "negative" only-if than the positive-and-negative if-and-only-if, while being ruled out completely in an ordinary if-then conditional.)

(ii) Similarly, in contexts like "It's too bad that only if Selig shows up will A-Rod testify", what's too bad is that A-Rod won't testify under other conditions (i.e. that Selig's showing up is a necessary condition for Alex's testifying), while in "It's too bad that if and only if Selig shows up will A-Rod testify" that's less clear.  Here, what the speaker is saying is too bad is that the two events are causally linked, i.e. that Selig's showing up is both a necessary and sufficient condition for A-Rod's testifying.

It's a subtle distinction but I think a real one, even for (at least some) ordinary, non-logic-trained speakers. That's my story, and I'm sticking to it.

Certainly "only if", by virtue of its presupposition, is a lot closer to "if and only if" than simple "if" conditionals are.  Even though we often move from e.g. "If you mow the lawn I'll give you $5" to "If and only if you mow the lawn I'll give you $5" (Geis & Zwicky's "invited inference", which Neal will recall my discussing at OSU at a talk in Arnold's honor back in the previous millennium), this if-->iff "conditional perfection" (whence Neal's subject line) amounts to a context-dependent implicature rather than a presupposition and is much easier to slough off.

LH



On Nov 20, 2013, at 11:50 PM, Neal Whitman wrote:

> From my latest blog post:
>
>   "You're a Jew," Doug said, "if and only if you believe in God!"
>   ...
>
>   "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!
>
>
>   http://literalminded.wordpress.com/2013/11/15/conditional-imperfection/
>
>
>
> Is this new to anyone else?
>
> Neal
>
> ------------------------------------------------------------
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The American Dialect Society - http://www.americandialect.org