Interpreting a statement with a negative quantifier In "Mathematics and the Real World" by Z. Artstein a sentence is stated:
There is no head injury too minor for you to ignore.
Throughout the text, the author expresses reservations regarding quantifies, especially negative ones.
I would (incorrectly in the eyes of the author) interpret the medical directive to have every head injury checked out.
Yet the author claims the sentence expresses the opposite, further supporting his thesis that "the brain has difficulty in analyzing [statements] that contain a negative."
So what is the correct interpretation of the italicized sentence?
Thanks 
 A: The misinterpretation can be derived from an analogy to examples like

No beverage is too cold to drink

which would intuitively be interpreted as  

Any beverage, no matter how cold it is, can be drunk.

Applying the same paraphrasing to the sentence

No head injury is too minor to ignore

-- which is syntactically completely identical to the first one -- leads to the author's claim

Any head injury, no matter how minor it is, can be ignored.

Of course one could switch things around and claim that the logical paraphrase of 

No head injury is too minor to ignore

is 

No head injury, no matter how minor it is, can be ignored

but this just shifts the problem because then 

No beverage is too cold to drink

becomes

No beverage, no matter how cold it is, can be drunk  

So in any case, we get an inconsistency. Luckily, the human brain is sophisticated enough to be able to figure out the intended interpretation for these to particular sentences so the problem might not seem obvious at first, but the inconsistency is there, and it is not difficult to imagine that there could be sentences whose intended interpretation is indeed unclear, as both (completely opposite) readings are in principle possible as can be seen from the examples. This is why the author concludes that "the brain has difficulty in analyzing [statements] that contain a negative."
(Personally I find that more "logical", direct paraphrase of "No X is too Y to Z" is indeed "Any X, no matter how Y it is, can be Z", which gives the head injury sentence the undesired interpretation -- but the sentence and its intended interpretation does not at all seem unnatural on first sight as the comments to your answer prove, which is precisely what seems to confirm the point that natural language does not always behave "logically".)

Re. your comment:
It is true that "ignore" has an implicit negation in its semantics, but this doesn't solve the problem. Paraphrase "ignore" as "not treat" to make the negation visible. If we want to avoid 

Any head injury, no matter how minor it is, can be not treated

and instead end up with

Any head injury, no matter how minor it is, should be treated

how could we justify that 180° turn in which the negation just magically disappeared? If we were to establish a rule that cancels out any implicit negations in the Z part ("not treat" --> "treat"), we again just shifted the problem, because then we also have translate

No expired meat is too tasty to be avoided

-- in which "avoid" is an implicitly negative word that can be paraphrased as "not eat" -- as

Any expired meat, no matter how tasty it is, can be eaten

with the negatoin cancelled away, which is not what we want -- wheras the translation we used for the beverage sentence gives us the right meaning, namly

Any expired meat, no matter how tasty it is, is to be avoided

So again, no matter how we twist and turn things, our interpretations are inconsistent, and that is exactly the problem.
