I saw a sticker on the lid of a pedal-operated hospital waste bin that said this:
|THIS SACK HOLDER IS SPECIFICALLY DESIGNED TO BE FOOT OPERATED ONLY. THE LID MUST NOT BE HAND OPERATED AND PUSHED PAST THE POINT WHERE IT WILL NOT AUTOMATICALLY RETURN TO THE CLOSED POSITION.|
Everyone who uses the bin sees this notice; maybe some even read it and try to respect it; but perhaps only Language Log readers will notice that it contains a misnegation — another sign that the number of negations within a sentence that our poor monkey brains can successfully handle averages out at little more than 1.
Lifting the lid by hand and pushing it back all the way beyond the vertical is apparently likely to either break it or lock it in a position where the automatic quiet-closing action will fail. So what the sticker should have said is that you shouldn't push it past the point where the automatic closing mechanism will still work. In other words, you shouldn't push it to the point where the automatic closing mechanism will not work. (This still isn't helpful, since the user will not know where that point is, which means this is a case of nerdview; but at least it has the right semantics.)
I might be the first person in human history to notice that this sign doesn't say what it was meant to say, and you might be the second. But we belong to a small minority. When ordinary people read signs at all (and mostly they don't, as an examination of the contents of almost any recycling bin will show) they typically just grab a quick sense of what it probably means. They don't parse with care, and they don't analyse much.
Even in speech, this is a perfectly normal way of responding to language. If you remark "That's not necessarily not untrue" at some point in a conversation with someone who isn't a linguist or a logician, your interlocutor is likely to take you to mean "That's probably true" if that's plausible in the context or "That's probably false" otherwise.
The people who work in factories writing the text for warning labels on products are very much like the rest of the hairless bipedal primates roaming the planet. They can handle a negation on a fair day if the wind is in the right direction. They can seldom handle a second or a third within a single sentence.
[UPDATE: I should add that a number of people have written to me to defend the wording of the sticker, or to suggest alternative interpretations. I'll spare you the details, and just say this: I have a PhD in English syntax and six decades of experience reading the language, and read the sticker with the best will in the world, and couldn't make it coherent. Possibly the deep and complex interaction of English grammar, semantics, and pragmatics allow it to be interpreted as saying something sensible. But couldn't someone have written it in a way that allowed me, and people with far less experience of reading complex material, to understand it? Wouldn't it have sufficed to say "DON'T PULL THIS LID UP. IT'LL BREAK. USE THE PEDAL."? Of course it would. All that stuff about sack-holding (it's just a bin!) and hand-operation and automatic return and the point past which the automatic-return mechanism will no longer function is, as I mentioned above, pure nerdview. People are just hopeless at writing signs to warn the general public about things. That's my secondary point, and should perhaps have been my primary one.