Negation is a gloriously complicated thing to keep straight, as the Language Log brain trust has been busy pointing out these days (here, here, and here, not to mention a hysterical story from Sally Thomason). The examples which are causing such consternation are largely of the forms:
"no X is so Y that we (normatively or habitually) Z it", or "no X is so Y that it (normatively or habitually) Zs" (formulation due to Mark Liberman)
Prof. Liberman's considered opinion is that these things are misinterpreted because "the interaction of negation, scalar direction and infinitival control doesn't work out right, but it's hard to calculate these things, and so the result passes muster." SC thinks that Prof. Liberman overestimates the capacity of either the grammar or the average speaker, but it's hard for him to decide which. Why? Because there are English phrases where the behavior of negation is so hopelessly difficult that their interpretations as positive or negative polarity items are practically gibberish. For the non-linguistically tutored or the gainfully employed (they work out nearly identically), the jargon about "polarity" refers to whether or not a word's semantics include negation.
Consider, for example, questions of the forms "Do you mind if X?" or "Would it bother you if I Y?". If someone asks you "Do you mind if I smoke?", both the answers "Yes, go right ahead", and "No, it's fine" convey the requested permission, even though they have opposite polarity. SC has no idea about the relative frequencies of these usages, but he's heard both of them enough to be sure that they're both acceptable (note: your host is referring to the question/answer frames; he doesn't actually smoke). Given that both "yes" and "no" answers can be acceptable, this suggests that "mind"/"bother" are words which can be understood as either positive or negative in meaning.
Tag questions, which are supposed to be reasonably well-defined in polarity, are also a pain in practical usage. Everyone has been to a department or office potluck at some point, and thought to themselves, "Boy, I hope that X's family eats out every night, because this casserole/salad/nuclear waste dip is so bad that I think I'd want a VX chaser afterwards!" Well, SC has thought so, at any rate. But then X makes your life difficult by walking up and saying "My sewage souffle's pretty good, don't you think?" The "correct" answer, at least socially, is "yes", but SC analyzes the proposition being agreed to as "yes, I don't think your souffle's good". If the reader is disinclined to accept this, consider reorganizing the sentence to "Don't you think my souffle's pretty good?"; SC claims that this is the same proposition, and more clearly demonstrates that the negation takes scope over a logical form which is something like "(X = you) AND (Thinks my souffle is good(X))". If other people don't agree, well, at least this relieves SC's conscience of the thought that anybody is suspicious when he praises their cooking while turning green.
Reams of papers have been written on both the intrinsic polarity of various vocabulary items and the question of how to analyze the scope of negation. But SC is not aware of anything which treats the question of words which can apparently function as either positive or negative polarity items, and for which both positive and negative answers can have the same interpretation, which is what seems to be going on with "do you mind...". Negation is simply quite difficult to deal with, especially when the social conventions surrounding it don't line up with the logic. However, this is an area where SC is far from current with the academic literature, and unlikely to have the time to research it in the near future, so if a reader is able to point your host to a paper which deals with this point, SC won't mind.
(Edited @ 7:28 am on 2/23/04 to reinsert an accidentally deleted clause.)
The 'mind' examples are probably heard as a whole idiom: 'Do you mind if X' = 'Is it all right to X' = 'Do I have permission to X', without analysis of the components.
No wait, that can't be right. If I answered 'yes' or 'no' tout court I'd be answering the 'mind', so I'd have to add 'yes, go ahead'.
Posted by: NW | February 23, 2004 at 12:21 AM
An relevant recent paper:
Romero, Maribel and Chung-hye Han (to appear), On Negative Yes/No Questions, Linguistics and Philosophy.
Posted by: Kai von Fintel | February 23, 2004 at 03:50 AM
I think the post is really good but sometimes we can get into discussions with that topic because a lot of people don't agree with that, just look at the first comment he already has a mess in his brain.m10m
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