No wug is too dax to be zonged

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Yesterday I mentioned Wason and Reich's 30-year-old paper on sentences like No head injury is too trivial to be ignored ("A Verbal Illusion", The Quarterly Journal of Experimental Psychology 31(4):591-97, 1979), and promised to sketch their argument. Here's their basic analysis, in their own words:

There would appear to be at least three sources of potential difficulty in the target sentence. First, its syntax is permeated with negativity. Clark (personal communication) has pointed out that it probably contains four negatives, and this number might be expected simply to overload the channel capacity of the individual and render the sentence incomprehensible. In particular, there are intuitive grounds for supposing that the final negative (the verb ignored) presents the greatest obstacle to the correct interpretation.

Second, the construction, too x to be y-ed, is associated with a relation between x and y such that the more x the less y . Thus, it makes sense to argue that the more small (smaller) a missile, the less it should be banned, the more convincing an alibi the less it should be doubted, the more serious a head injury the less it should be ignored. But No head injury is too trivial to be ignored, presupposes the more trivial a head injury the less one should ignore it. Thus it implies that only trivial head injuries require treatment and serious ones may be ignored. Hence a more consistent version might be: No head injury is too serious to be ignored. However, this sentence is still not easily understood. In fact, like the target sentence, it differs from the missile-banned sentence and the head injury-noticed sentence in yet another way.

This third factor may best be illustrated by considering the injunction that is conveyed by each sentence. No missile is too small to be banned and No head injury is too trivial to be noticed may be construed to mean Ban all missiles and Treat all head injuries respectively. Both these injunctions are consistent with current views on missiles and head injuries. However, the injunction, Ignore all head injuries, which follows from the sentence, No head injury is too serious to be ignored, is unusual if not actually incredible. Although it is possible to construct a sensible context for such a sentence, it is not easy to do so. The sentence, as it stands, is inconsistent with most of our beliefs and opinions about head injuries and their treatment. For this reason it may be difficult to understand, and may be termed a non-pragmatic sentence. In contrast, information that is consistent with our opinions and beliefs about the world, such as the missile sentence, may be termed pragmatic.

A number of letters from psychologists and linguists, as well as face to face encounters, showed that the target sentence is almost invariably misconstrued. Individuals were shown the target printed on one side of a card and the sentence, No head injury is too trivial to be noticed, printed on the other side. Not only was there a pronounced tendency to misconstrue the target in the expected way, but it was also often claimed that the other sentence was in some way ill-formed. Rational attempts to correct this error frequently seemed to generate some affect on the part of the respondents.

Another way to express their theory, I think, is that certain kinds of sentences are so difficult  to process that we often (unconsciously) abandon compositional semantics and jump directly to an interpretation that puts the pieces together in a sensible way. They focus on negation as the difficulty, but their "target sentence" has two other common sources of strain, namely a scalar predicate ("too trivial") and an implicit (deontic) modal.

They ran a couple of pilot experiments to verify that people (presumably, in this case, UCL undergraduates) have trouble with sentences of this kind.  For example, when presented with the sentence No WUG is too DAX to be ZONGED, six out of ten subjects felt that this implies WUGS should be ZONGED (which is correct, according to Wason and Reich), while four out of ten concluded that WUGS should not be ZONGED.

Having demonstrated that misconstrual of such sentences is "a robust phenomenon", they designed an experiment to "[compare] the understanding of sentences which expressed pragmatic information and sentences which expressed non-pragmatic information", where by pragmatic they mean something like "common-sensical".

Their "pragmatic sentences" were:

1. No missile is too small to be banned.
2. No government is too secure to be overthrown.
3. No dictatorship is too benevolent to be condemned.
4. No weather forecast is too plausible to be mistrusted.

And their "non-pragmatic sentences" were

1. No error is too gross to be overlooked.
2. No message is too urgent to be ignored.
3. No film is too good to be missed.
4. No book is too interesting to be put down.

Each subject was given one sentence of each type to paraphrase, based on these printed instructions:

I am going to give you a sentence which may express a point of view on a particular topic. You are to disregard your point of view, or the point of view you think you ought to hold on the issue, and merely put the sentence into your own words as it stands.

There were 64 subjects (16 pairs X 2 orders X 2 replications).

The results are consistent with their hypothesis (numbers in each cell are correct/incorrect):

No. 1 No. 2 No. 3 No. 4 Total
Pragmatic sentences 16/0 16/0 11/5 8/8 51/13 (80%)
Non-pragmatic sentences 3/13 4/12 9/7 11/5 27/37 (42%)

[Their choice of sentences is open to question, it seems to me. For example,  bookish children are often told that they should put down what they're reading, no matter how interesting it is, and go out to play. (At least, this would have been true back in the childhood of 1979 undergraduates, when children still went out to play.)  So the correct reading of No book is too interesting to be put down is far from "non-pragmatic" — as their results suggest.  And I suspect that (especially where British weather forecasts are concerned) many people retain some traces of the old meaning of plausible as "having a false appearance of reason or veracity; specious", which would move No weather forecast is too plausible to be mistrusted into the non-pragmatic category.]

Wason and Reich conclude with some observations about the peculiar difficulty of the original example, No head injury is too trivial to be ignored:

There may be still another reason why the non-pragmatic sentences were less resistant to a correct construal than our original target sentence … [T]he target presupposes that the more trivial a head injury the less we should ignore it, and it enjoins us to ignore all head injuries. But by merely dropping the negative on the verb, both these implausibilities are simultaneously removed: No head injury is too trivial to be noticed. Hence if the processor fails to handle this negative verb correctly, he reaches an apparently satisfactory interpretation. But suppose that the target were to be presented so that it is implausible in just one of these ways. No head injury is too serious to be ignored, has a plausible presupposition (the more serious a head injury the less it should be ignored), but an implausible injunction (ignore all head injuries). Conversely, No head injury is too serious to be noticed, has an implausible presupposition (the more serious a head injury the less it should be noticed), but a plausible injunction (notice all head injuries).

As a result, they argue, it's paradoxically easier to see the problem with these other sentences, precisely because their problems are less pervasive.

They also connect their target example's peculiar difficulty ("When the correct interpretation was explained it was often adamantly rejected …, as if the informants literally could not see an alternative view. […] [This] is analogous to the susceptibility to the Ames Illusion which, unlike most illusions, also does not fluctuate. Like the Ames Illusion the sentence appears to be normal and regular, and this tempts us into a plausible but wrong interpretation.

This case also helps to bring out the reasons why I feel that the terms "prescriptive" and "descriptive" are misleading.  If Wason and Reich are right, then  the intuitions of the overwhelming majority of native English speakers are wrong.  But few if any "descriptive" linguists would take that as a knock-down argument against Wason and Reich's analysis.

A final note: I haven't found any work on analogies to this illusion in other languages.  The details would generally need to be different, but the basic ingredients should all be there. Does anyone know of any cross-linguistic work on such things?

[Update — there seems to be some confusion, perhaps also on my part, about exactly what W & R's terminology means.  So let me try to explain, diagrammatically, what I think they were getting at.

Behind the phrase No missile is too small to be banned there is a background assumption that we can diagram something like this:

banned not banned
————— |T| —————
← less small more small →

In other words, on the scale of missile smallness, we presuppose that there is a threshold T such that missiles smaller than T (i.e. farther to the right in the diagram) are (or should be) not banned, while missiles less small than T are (or should be) banned.

Against this background, we assert that T is in fact so far along the scale of smallness that there are no missiles "too small to be banned", i.e. on the not-banned side of T:

———————————– |T|
← less small more small →

It follows that all missiles should be banned.

Now consider No error is too gross to be overlooked. The presupposition is exactly analogous:

overlooked not overlooked
————— |T| —————
← less gross more gross→

That is, there's a threshold T on the scale of error grossness, such that errors less gross than T are (or should be) overlooked, and errors more gross than T are not overlooked.  But now the analogous assertion can be diagrammed as

———————————– |T|
← less gross more gross →

This means that T is so far along the scale of grossness that there are no errors below T on this scale, and therefore all errors are (or should be) overlooked. This assertion is (in W&R's terminology) non-pragmatic, in the sense that it's contrary to common sense.

If we now examine the original "target" sentence No head injury is too trivial to be ignored, we see that there are problems at both stages. The presupposition

ignored not ignored
————— |T| —————
← less trivial more trivial →

tells us that there is a threshold T on the scale of head-injury triviality, such that injuries that are less trivial than T are (or should be) ignored, while injuries that are more trivial than T are (or should be) not ignored.  This is already backwards — simply by virtue of the meaning of the words, the scale should work in the opposite direction.

And the assertion is equally problematic:

———————————– |T|
← less trivial more trivial →

This tells us that T is so far along the scale of triviality that there are no head injuries below T on this scale (i.e. less trivial than the threshold), and therefore all head injuries are (or should be) ignored.

W&R wanted to make their test a fair one, so they crafted their "non-pragmatic" sentences to have sensible presuppositions with counter-sensical assertions. But (as they point out) the original target sentence No head injury is too trivial to be ignored is bass-ackwards in both respects. This undoubtedly makes it harder to see the problem, since one interpretive flip changes both, and leaves the interpreter with an all-around sensible sentence. In their "non-pragmatic" sentences, the analogous flip fixes one problem at the expense of creating another one.]


  1. David D. Levine said,

    November 28, 2009 @ 12:38 pm

    There are two different meanings here: "No X is too Y to be Z'd" can mean either "all Xs should be Z'd, no matter how Y" or "any X could be Z'd, no matter how Y." One is an opinion, the other a warning. All four of the second group have the latter interpretation, as well as "no government is too secure to be overthrown" in the first group.

  2. John Lawler said,

    November 28, 2009 @ 12:43 pm

    See Larry Horn's BLS 2009 talk, "Hypernegation, hyponegation: Gluts, gaps, and parole violations"; abstract on page 14 of this pdf:

    Blogged on later by a member of the audience at BLS at

    I can't find a link for Larry's handout, but on the (20-page!) pdf that I have of it are examples of some of the basic categories of multiple negation, including:

    Triplex Negatio Negat:
    We sincerely hope and insist that peaceful means should be used to solve the Taiwan issue…China has never committed to not taking nonpeaceful means to solve the Taiwan issue simply because such a commitment would make peaceful reunification impossible.
    (Chen Defu, Chinese Embassy Press Counselor, letter to editor of NYT, 7/18/89)

    Triplex Negatio Confundit:
    No detail was too small to overlook.
    New Yorker 12/14/81, Words of One Syllable Department
    People knew too little about him not to vote against him.
    Bill Moyers on why voters in 1984 primaries voted for Gary Hart

    Quadruplex negatio farblondiat:
    (btw, 'farblondiat' is apparently the Latin translation of Yiddish 'farblunjet')
    “Bernie produced what Bernie is supposed to produce”, Smith said, “but I don’t think, either, that you can single out Bernie as not a guy who is not part of the disappointment.”
    New York Rangers’ general manager Neil Smith, declining (one guesses) to absolve star forward Bernie Nicholls for his play, N. Y. Times, 4/15/91, C3

    [(myl) For some discussion of Larry's earlier work on this subject, see "Multiplex negatio ferblondiat", 7/14/2007.]

  3. Mark said,

    November 28, 2009 @ 1:57 pm

    This is an awesome topic; thank you for your great posts.

    Maybe even more than you are, I'm confused about the categorization at the end in terms of pragmatic and non-pragmatic sentences. Is a non-pragmatic sentence one whose "correct" (compositional) interpretation conflicts so much with common sense that one would be conversationally shocked to hear it asserted and so would search for other hypotheses about what the speaker is doing?

    [(myl) I've added a note at the end of the post, where I invoke some diagrams in order to try to clarify what W&R had in mind. This graphical explanation may help (on the non-trivial assumption that I got it right — this stuff is really hard to think about!)]

    If so, I would think that all of the "non-pragmatic sentences" in the list are actually pragmatic. The first two are most naturally (compositionally, I think) interpreted as involving non-deontic (alethic? epistemic?) modals:

    1. No error is too gross to be overlooked.


    1A. Any error, no matter how gross, might be overlooked.

    (Equivalently: No error is so gross that, because it is that gross, it is not the case that it might be overlooked.)

    2. No message is too urgent to be ignored.


    2A. Any message, however urgent, might be ignored.

    The latter two involve deontic modals in what seems a straightforward way, compositional way. They seem easy to interpret "correctly", even if the interpretations are somewhat controversial opinions.

    3. No film is too good to be missed.


    3A. No film is so good that because it is that good it should not be missed.


    4. No book is too interesting to be put down.


    4A. No book is so good that because it is that good it should not be put down.

    If I follow your explanation of their view, Wason and Reich seem mistakenly to equate "not-ought-not" with "ought". There is no implication that all books ought to be put down, for instance, but merely that no book is such that it ought not to be put down (owing to its interest). Any book might (reasonably, permissibly) be put down, its interest notwithstanding.

    The availability of non-deontic interpretations may help explain the divided verdicts about whether

    No WUG is too DAX to be ZONGED

    "implies" that WUGs should or should not be ZONGED. In the most easily imagined use of:

    2. No message is too urgent to be ignored.

    the speaker is bemoaning how easily-ignored even urgent messages are; and so the presupposition is that urgent messages should not be ignored.

    Back to "No head injury is too trivial to be ignored." It seems to me the allegedly incorrect interpretation is:

    No head injury should be ignored because it is too trivial.

    Maybe this really is incorrect, or maybe the orignal sentence literally means something with a relevant ambiguity, like

    No head injury, with respect to the question whether to ignore it, is too trivial.

    Then the hearer is left to decide on pragmatic grounds whether what the speaker is denying is that "too trivial" might imply "should be ignored" or rather "should not be ignored". Probably this is one of the "ambiguity" hypotheses you alluded to in an earlier post. Sorry for the length of this comment!

  4. Benjamin Zimmer said,

    November 28, 2009 @ 2:42 pm

    Ah, good ol' wugs.

  5. JT said,

    November 28, 2009 @ 2:44 pm

    When I come across these kinds of sentences, I find it helpful to consider them the response to some claim. E.g., no head injury is too trivial to ignore as a response to this head injury is too trivial to ignore. Imagining this kind of dialog makes it clear to me why too trivial should have been trivial enough. No WUG is too DAX to be ZONGED would be a response to this WUG is too DAX to be ZONGED, [so I won't ZONG it], but the response indicates that every DAX should be ZONGED (or more correctly, no DAX shouldn't be ZONGED on account of its DAXitude).

  6. Peter Taylor said,

    November 28, 2009 @ 4:47 pm

    FWIW, I consider "No head injury is too trivial to be noticed" to be "non-pragmatic". It works neither as injunction (Notice all head injuries! But what if they're not visible?) nor as observation: a small cut to the head caused by flying glass could easily fail to be noticed in the face of other injuries sustained. Surely the intended meaning of "No head injury is too trivial to ignore" is "No head injury is too trivial to check out".

    (As an aside, I'm not sure even that one is rigidly adhered to in the British hospital system. The last time I went to the hospital, having come off my bike, I wanted my hand stitched up. I was asked by everyone whether my head had hit the ground, but they all accepted my assertion that although my helmet had hit the ground it had not been with sufficient force to cause concern).

  7. Mark said,

    November 28, 2009 @ 5:07 pm

    Thanks for the clarification, Mark. And thanks, JT for that test; it convinces me that the ambiguity hypothesis I sketched above is wrong.

  8. Gregory Bryce said,

    November 28, 2009 @ 5:08 pm

    Here too:
    «(the serious a head injury the less it should be ignored), »

    What a fascinating discussion, most thought-provoking for the layman who aspires to write clearly! Thank you.

  9. Rubrick said,

    November 28, 2009 @ 6:16 pm

    I'd think time constraints would be very important when gathering subjects' interpretations. When I encounter such a sentence in the real world, I'll often stop in my tracks and try to puzzle out its "true" meaning in the same way I would a complex expression in a line of computer code.

    The densest such impenetrable expression I know is "That's not unmeaningless." In this case the difficulty is purely a matter of multiple-negation. Obviously you'd never expect to find "unmeaningless" in a news article, but if you're a decent actor you can toss it into conversation pretty naturally.

  10. Nathan Myers said,

    November 28, 2009 @ 6:41 pm

    I was surprised to find that they took the opposite of "ignore", in the case of head injuries, to be "notice" rather than "treat" or "examine" or some other medical response. We all notice our own head injuries, unavoidably, but it's completely normal not to notice somebody else's concussion unless some attention is called to it.

    Others mentioned the book problem. Such lapses call into question the care taken in conducting the research, and thus the results.

  11. Aaron Davies said,

    November 28, 2009 @ 9:31 pm

    I find "Rational attempts to correct this error frequently seemed to generate some affect on the part of the respondents." to be one of my favorite sentences from a scholarly work, ever.

    [(myl) Indeed. It was my first choice for the title of the post, but in the end I concluded it was too long to fit.]

  12. Jerry Friedman said,

    November 28, 2009 @ 10:46 pm

    My first thought when I read that sentence was laughter, but my second was, "Does Language Log need a motto?"

  13. J. Goard said,

    November 29, 2009 @ 4:35 am

    As Clark p.c. (Herbert Clark? "Dogmas of understanding" is a great paper) noted in the first quote, the negative orientation in the semantics of both "trivial" and "ignored" is too conspicuous to dismiss. Thus, although they have a positive association (we tend to ignore trivial things), this may be overwhelmed by the negative orientation each word has to other concepts.

    So, I'd want to test straightforward examples of positively-associated pairs in this construction, to see whether they continu. Something like:

    (1) No food is too delicious to eat.

    Does that confuse anybody?

  14. Sven said,

    November 29, 2009 @ 4:50 am

    I have no linguistic background (I'm a physicist) and I can't even recall when and why I subscribed to the LL rss feed but I often find myself in a position where I'm too scared to read up on a new post, because I regularly end up in a web of links with ten browser pages open, all about interesting, funny, and thought provoking topics in need of being followed.

    Today, again, I read something that sounded trivial (trivial enough to be ignored?) and only at the end I find out that it sounded trivial, because I didn't get the initial problem. It's very enriching to try and look past your own preconceptions.

    Although I often don't know the linguistic terms (and I'm *not* going to look those up, there's enough tab-opening going on already!) I find the LL posts very well written, such that it's even possible for the layman and non-native speaker (I'm German) to follow. This is, by the way, also true for the comments which (like today) often add a lot to a topic.

    So while I can't add anything to said topic itself I can at least let you all know how much I enjoy reading about it :)

  15. Sven said,

    November 29, 2009 @ 5:14 am

    Actually, there may be something I can add after all. You were wondering if this has been studied in other languages. Googling "keine Kopfverletzung ist zu trivial, sie zu ignorieren" turns up with the first hit:

    which seems to be on topic. (I haven't had time to read it.) Maybe that's of interest.

  16. Dominik Lukes said,

    November 29, 2009 @ 5:42 am

    These examples really do your head in. I would suggest that testing them as quadruplets might clarify the difficulties somewhat. Consider the following:

    1. No stain is too small to be ignored.
    2. No stain is too small to be cleaned.
    3. No stain is too large to be ignored.
    4. No stain is too large to be cleaned.

    I find that only 3. causes me significant problems but it would be interesting to test is there is a progressive scale of interpretive difficulty or a cut off point.

    It might also be interesting to compare some of the related constructions:
    1. No stain is too large to ignore/clean.
    2. No stain is so large as to ignore/clean.
    3. No stain is too large for us to ignore/clean.
    4. No stain is too large for ?ignoring/cleaning.

    Here I find 3. produces the clearest difference between negative (ignore) and positive (clean) description of the agent by making it explicit. But not as much as in "We find that no stain is too large for us to overlook as we go about cleaning." or even "We find that no stain is too large for our cleaners to overlook as they go about cleaning." The more clearly we describe an agent with a state of mind to which we can attribute a process, the easier the interpretation is. But even in the last sentence to potential paradox large/ignore requires an ironic interpretation to reconcile. At least to me. Perhaps another way to test the original dilemma would be to ask subjects to not paraphrase but provide enough context until the statement is clear. Having them do this in pairs and record the discussion would probably reveal quite a bit about the possible interpretations, as well.

  17. Coby Lubliner said,

    November 29, 2009 @ 2:56 pm

    What I find missing from this discussion (as well as the one on the preceding post), unless it has escaped my notice, is any mention of the fact that the opposite of "too [Adj]" is "[OppAdj] enough," where [OppAdj] is the opposite of [Adj]. So, the opposite of "too big" is "small enough" and vice versa. Now, in the original sentence analyzed in the previous post, "too small to escape" doesn't make sense, not so much in terms of logic but of physical reality: something (e.g. a fish) is either (1a) small enough or (1b) too big to escape a net. Conversely, it's either (2a) too small or (2b) big enough to be caught by the net. Clearly, 1a and 2a are equivalent, as are 1b and 2b. What Walter Kaiser really (by "really" I mean pragmatically, or consistently with general usage outside of set expressions or snowclones) meant to say was that "no detail was too small to be caught" or, equivalently, "no detail was small enough to escape," and somehow, as often happens with overnegation, the two meaningful phrases, "too small to be caught" and "small enough to escape" got short-circuited. I would suspect that most of the other examples follow this pattern, and I believe that this confusion has already been analyzed on LL, by myl, amz and gkp. The reason why most people aren't bothered by them is probably the context: if the tone of the article is laudatory, then our interpretive mind will supply the laudatory interpretation, and so on.

  18. Tim K said,

    November 29, 2009 @ 3:54 pm

    It seems pretty clear what is going on: the writer obviously meant one thing, and that interpretation was taken.

    Now, a very careful parsing of the language shows that the *opposite* was actually written.

    We have idioms like this that are very common: "I could care less" is one. The speaker means, literally, the opposite of what they said. Beyond one negation, and few readers or listeners seem to attempt to apply them logically. They instead rely on context.

    Our ability to understand language is very impressive. But carefully parsing such a sentence is difficult, and one generally only has seconds to do so. Since what was meant is pretty obvious from context, the reader/listener takes the obvious interpretation and moves one.

    Which points out a major flaw in this very interesting study: giving sentences in isolation takes away the common compulsion to get past the sentence in question, and instead forces the reader/listener to focus on the suspect sentence. So actual "correct" interpretation of the odd sentence will be more common in practice than the study would indicate. [With 'correct' here meaning what the author meant, rather than what a very careful parsing indicates.]

  19. Ben said,

    November 29, 2009 @ 4:02 pm

    Following JT, I found it helpful to imagine these sentences as a response to a similar assertion beginning with "this", as in "This missile is too small to ban."

    I also found it helpful to rewrite "too X to Y" as "so X that it can't/shouldn't be Yed"

    too big to eat –> so big that it can't be eaten
    too small to ban–>so small that it shouldn't be banned
    too secure to be overthrown–> so secure that it can't be overthrown
    too trivial to ignore –> so trivial that it can't be ignored [already doesn't make sense]

  20. Sili said,

    November 29, 2009 @ 5:04 pm

    Thanks for the update.

    Those diagrams really help drive the point home for me.

  21. Kenny V said,

    November 30, 2009 @ 12:14 am

    having wracked my brain about this all weekend, I think I'm finally beginning to understand what the heck is going on here.

    I initially was misconstruing the head injury sentence, and I could not see why it meant the opposite of what I thought it did. Obviously, I figured that I must be wrong and LL right. But now I understand: All the negations were so hard to process for my brain that it just reworked the meaning of the phrase into "no head injury is so trivial that it should be ignored."

  22. Dave said,

    December 4, 2009 @ 3:25 pm

    Um, "No business is too big to fail"?

  23. flug said,

    February 3, 2010 @ 3:53 pm

    This reminds me of an open source project I've done a little work on.

    They had a fairly complex SQL query to find records. I had (say) 10000 records in my database. I did a query and got 3000 records. I did the "not" of that query and got 4000 records.

    What about the other 3000?

    Well, the previous programmers had forgotten a few of the more obscure possibilities that can happen when you negate a logical statement.

    Coming up with the negative of a statement is not that easy for the human mind to handle, and even more so if it is a complex statement with a few exceptions, caveats, or negatives of negatives thrown in.

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