John V. Burke wrote to draw my attention to a phrase in Walter Kaiser's "Saving the Magic City", NYRB, 12/3/2009 (emphasis added):
Roeck's book, for which he has done an impressive amount of research, tries to be a number of things at once: it is an account of the social and intellectual world of the expatriate community in fin-de-siècle Florence; it continues the biography of Aby Warburg he began with his earlier book; it is a history of late-nineteenth-century Florentine urban development; it is a cultural history; it addresses a wide variety of ancillary topics such as anti-Semitism, anarchism, labor conditions, and economic trends; and it discusses the various aesthetic theories being formulated at the turn of the century. No detail is too small to escape Roeck's net, not even the plans formed in 1898 to produce artificial ice commercially in Florence.
This echoes the classic example "No head injury is too trivial to ignore", discussed by Peter Wason and Shuli Reich, "A Verbal Illusion", The Quarterly Journal of Experimental Psychology 31(4):591-97, 1979.
Something interesting is going on here, as Wason and Reich observed, but it's not entirely clear what it is. The most striking aspect of the problem is that it's so hard for people to recognize that it exists.
Let's start with some real-world instances of the pattern No NOUN is too small to VERB:
No business is too small to play a role.
No donation is too small to make a difference.
No amount is too small to benefit from compounding interest.
No country is too small to make it as a sovereign nation.
No exposure is too small to intitiate cellular damage.
No news item is too small to be lampooned in the blogosphere.
No occasion is too small to warrant a gift.
You could translate these as something like All NOUNs, however small, [can or should] VERB. Thus the last one comes out "All occasions, however small, warrant a gift".
To understand how this works, consider the positive statement "This occasion is too small to warrant a gift". This presupposes that we can set a value on the scale of occasion size, such that larger occasions warrant a gift, while smaller ones don't; and it asserts that the designated occasion is below the threshold. Now if we say that "No occasion is too small to warrant a gift", we're asserting that the gift-warranting threshold is so low, in the context under discussion (which was Japanese culture), that no occasion worth mentioning is below it.
One additional wrinkle: In the pattern NOUN is too ADJECTIVE to VERB, the initial NOUN might either be the subject of the VERB ("The patient is too weak to eat") or the object ("The soup is too hot to eat"). All the examples that we've seen so far are subject-type cases; but object-type cases exist as well:
No service is too small to render to the King.
No problem is too small to obsess over.
But now consider these examples:
No pavement irregularity is too small to overlook.
No social injustice is too small to ignore.
No risk is ever too small to disregard.
No convenience is too small to forget.
No precaution is too small to be omitted.
No detail is too small for you to discard it as insignificant.
No expense is too small to escape the finance chief's attention
No worthy cause was too small to escape his generosity.
These can't be translated in the same way as the earlier batch. "All worthy causes, however small, escaped his generosity" — no, that's not what the writer meant at all.
And the corresponding positive assertions are already problematic in the same way, e.g. "This expense is too small to escape the finance chief's attention". To make them make sense, we want to flip something: "This expense was too large to escape the finance chief's attention"; "This expense was too small to attract the finance chief's attention".
But examples like "No detail is too small to overlook" are very common. You see them all the time, even in the work of careful writers like Walter Kaiser, in well-edited publications like the New York Review of Books. Legend has it that "No head injury is too trivial to ignore" was posted on the walls of London hospitals for decades. I suspect that this is untrue, but it's a good story — certainly versions of this same apparently incoherent phrase, attributed to Hippocrates, have been published many times in reputable books, journals, and other places, e.g. here, here and here.
So what's going on here? As discussed in many earlier LL posts, these puzzles tend to arise from interactions among negatives, scalar predicates, modals. And explanations include variants on "it's a mistake", "it's an ambiguity", and "it's an idiom".
There are many different types of what we've called misnegation (also overnegation and undernegation), and different explanations may be appropriate for different examples. In this case, though, I think that Wason and Reich's 1979 account has held up pretty well. I'll lay out their hypotheses and their experimental results in another post.
[Note -- Francis Adams' translation of Hippocrates On Injuries of the Head has nothing that seems likely to be the source of the phrase "No head injury is too severe to despair of, nor too trivial to ignore". If you know where in the Hippocratic Corpus this comes from, please let us know in the comments.]