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I was looking at the book Introduction to Mathematical Thinking by Keith Devlin, and came across a question where the reader is asked to reformulate this sentence to avoid the unintended second reading:

No head injury is too trivial to ignore.

However, I couldn't really find any alternative meaning.

Any ideas about what the “unintended second meaning” might be?

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I've taken the liberty to touch up this question, but, given that this is a site for language enthsiasts, I'd advise you to be more careful when submitting future questions. (Faux pas such as lower-case names and book titles won't make it easy for your question to be taken seriously.) –  J.R. Nov 18 '12 at 7:02
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Since you do not say what meaning you have found, it is very difficult for anyone to give you the "other" one. I suggest that you look at the possible interpretations of No X as either "X does not exist" or "Not one of the instances of X". –  Fortiter Nov 18 '12 at 7:13
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So the sentence might mean "The head injury does not exist which is too trivial to ignore," or "Not one of the instances of head injury which do exist are too trivial to ignore." Those are identical. –  Andrew Leach Nov 18 '12 at 9:26
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The phenomenon is called Overnegation and is quite common, enough to generate some work from Larry Horn. –  John Lawler Nov 18 '12 at 15:29
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Compare: "No head injury is too complicated to treat" means we can treat all head injuries. "No head injury is too trivial to ignore" does not mean that we can ignore all head injuries. –  Peter Shor Nov 18 '12 at 17:23

6 Answers 6

up vote 4 down vote accepted

The basic meaning is litotes, reversal of the sentence:

Every head injury is serious enough to pay attention to it.

But you can completely twist the meaning, reading it in a straightforward manner that only after you finish parsing the sentence starts appearing as making no sense:

Lack of head injury is so trivial that you can't ignore it.

Only after you notice "triviality of issue rather encourages ignoring it" - the relation is reverse, the more trivial something the more prone to ignore it you are - that's when you stop and notice this way of parsing the sentence makes no sense and you must re-parse.

The ambiguity comes from no head injury meaning none of head injuries and an absence of head injury.

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No, the meaning you get at first glance is "you should pay attention to every head injury", but if you parse out the sentence more carefully, and suspend your knowledge of head injuries and triviality, you get "you can ignore all head injuries, because none of them are so trivial that their triviality precludes ignoring them". I think that's the duality the OP was after. –  interfect Jul 27 at 5:26

The ambiguity seems to be that taking the words "no head injury" , indicating an absence of a head injury, "is too trivial to ignore", which makes no sense, at least to me. If it is that trivial, it seems to me it should be ignored. At first I thought this would require that the answer read "All head injuries ARE serious". However, this statement is not what the original intended and is not even true. As I thought about it further, I realized the statement was not about the severity of injuries, but was actually addressed to the attitude of the person injured or initially consulted about the injury. My suggestion is "All head injuries should be taken seriously.

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The ambiguity is whether "too" modifies "trivial" or "trivial to ignore." The latter is very, very weak, so to illustrate the idea more clearly, consider these examples:

"The diamond is too hard to cut." "The diamond is too hard to see." Now it should be clear that the first one has "too" modifying "hard" but the second has it modifying "hard to see."

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One could imagine two meanings by inserting hyphens:

No head-injury is too trivial to ignore.

and

No-head injury is too trivial to ignore.

I’m having trouble coming up with an example of a No-head injury, though.

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A broken arm is no head injury. Thus a broken arm is too trivial to ignore. –  David Schwartz Nov 19 '12 at 10:48

What is meant is No head injury is trivial enough to ignore (or possibly Any head injury is too important to ignore). The original actually means that all head injuries should be ignored.

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No head injury is too trivial to ignore.

The phrase No head injury could potentially mean either of the following:

  • Not a single (type/kind of) head injury (or, in other words, the presence of any head injury)
  • Having no head injury (or, in other words, the absence of a head injury)

These two interpretations are contradictory.

A similar ambiguous construction is, "No news is good news".

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I would argue that "no head injury..." as a subject is distinctly different than "having no head injury...". One would not reasonably substitute one for the other, so the chance of a misinterpretation seems unlikely. –  Lynn Nov 18 '12 at 13:49
    
@Lynn I'm suggesting that the misinterpretation is centred around the word no rather than Lymington's enough. A similar ambiguous statement is, "No news is good news". –  coleopterist Nov 18 '12 at 16:00
    
I see. Personally I find that there's no ambiguity in the "No head injury" phrase and that the "No news is good news" idiom is the weirdly confusing one. But I get what you're saying. –  Lynn Nov 19 '12 at 2:55

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