Case One:
W: Do you want X?
H: Only if you want it.
>> I don't want it.
*>> I do want it.
Case Two:
W: Do you want X?
H: Not if you don't.
>> I do want it.
*>> I don't want it.
What is strange about this case is that, presumably, the husband H's responses in both cases are logically equivalent to each either; assuming I'm parsing them right, they both say "I want X only if you want X" or, equivalently, "I do not want X if you do not want X." (***See bottom of page for an explanation, if this isn't clear.)
But the response in Case One (at least sometimes) implies something different than the response in Case Two. (I say 'at least sometimes', because, as with many implicatures, it may depend somewhat on the sonic properties of one's utterance too -- i.e., the way one pronounces the words.) But this seems to imply that the implicature is "detachable" in Grice's sense (see the bottom of p.57 and ff., here).
However, according to classical Gricean pragmatics, conversational implicatures are non-detachable; hence, if these were conversational implicatures, they would both imply the same things (which they don't). So it seems that they must be conventional implicatures. (See here on that distinction.) That's sort of weird though, because conventional implicatures are usually associated with syncategorematic expressions that do not contribute any additional truth-conditional meaning to the sentence (for instance, "however," "but," "even though," "nevertheless," etc.).
Also, these implicatures seem to be more like conversational implicatures than conventional ones, since they do seem to sort of follow from something like Grice's Maxim of Manner (or, better, Levinson's M-Principle); i.e., saying something in an equivalent but roundabout way implies a non-standard meaning. For depending on whether one uses the double negation form or not you get a different implicature. However, it doesn't *quite* fit this rule I think, because it doesn't seem like either of the response from Case One or Case Two is more "roundabout" than the other; in other words, the responses in both cases seem to be symmetric as far as the "oddness" of their phrasing goes.
Anyway, kind of an interesting case. FYI, in the actual situation, I *did* want it, but I didn't want it if she didn't. : - )
***
To see the equivalence, note that all of the following are equivalent:
- I want it only if you want it.
- I only want it if you want it.
(These are clearly equivalent. For consider the following:
x goes to the store only if x is hungry.
x only goes to the store if x is hungry.)
- If you do not want it, I do not want it.
- I do not want it if you don't want it.
