A couple of days ago, I cited a quotation with an apparently extra or redundant not: "I challenge anyone to refute that the company is not the most efficient producer in North America." It's occurred to me since then that the speaker may have been confused not only by "three phones going nonstop for more than 12 hours each day" for "39 consecutive days", but also by the fact that challenge can function as a sort of negative. Phases of the form "I challenge anyone to X" are often used to mean "No one can X" or "No one will X".
Looking for "I challenge anyone" on the web, we find some (perhaps more basic) cases where the anyone means "anyone at all": "I challenge anyone that's willing to a Mechasummon duel." However, there are other cases where anyone seems to be the negative polarity version, and may be followed by other polarity-sensitive items:
"I challenge anyone to find a school or department at UF or any other major Florida state supported university that comes anywhere close to the decadence of this law school."
"I challenge anyone to find another net company that offers this great of a net at an affordable price.
I don't think this really makes the original quotation semantically balanced. "No one can deny that the company is not the most efficient producer" is still not what the speaker meant -- he meant "no one can deny that the company is the most efficient producer." But it helps explain why it was hard for him to figure out whether he needed another not or not. The difficulty of calculating the meaning of sentences with multiple negations and a scalar predicate or two is hard to underestimate.
[Update: Kai von Fintel writes:
I posted a related item on my blog on the old example "No head injury is too trivial to ignore", which illustrates your point rather well, I believe.
Kai's post is here.]
Posted by Mark Liberman at January 23, 2004 06:03 AM