In the June issue of the Atlantic Magazine (not on line yet), Barbara Wallraff proposes a new explanation for the use of phrases like we cannot understate the importance of X when the writer seems to mean we cannot overstate the importance of X. At least, her explanation is new to me. When I first read it, her analysis didn't seem to make sense. But on reflection, I think she may be on to something.
In an earlier post, I related examples like cannot understate the importance of... to the hypothesis that it's hard for people to calculate the meaning of phrases involving negatives in combination with modals, scalar thresholds and so on. This interpretive difficulty explains why some phrases with semantically-backwards interpretations are hard to edit out -- it's hard to calcuate what they actually mean, and they include pretty much the right words, and they're syntactically correct. In order to explain why the erring phrases are constructed in the first place, I suggested combining this interpretive difficulty with a sort of lego-block model of sentence construction -- take out an assortment of relevant tree-fragments from the lexicon, and fit them together until it looks OK. Sometimes another factor may be a sort of semantic gap, created by the fact that there is hardly ever any reason to want to express the idea that corresponds to the correct interpretation of the phrase in question.
Wallraff's explanation (The Atlantic, v. 293 no. 5, June 2004, p. 154) is completely different. She suggest that phrases like cannot understate are genuinely ambiguous, not just confusing:
Cannot understate and cannot overstate are like architectural elements in an M.C. Escher drawing: if you like, you can flip-flop them in your mind. The trick is done by cannot, which has two meanings. Think of Parson Weem's tale in which the young George Washington delared, "I can't tell a lie". Of course Washington was physically capable of uttering a false statement; by can't, he meant he chose not to. Can't, or cannot, can mean something very much like must not -- and if it means that, cannot understate the importance of makes sense.
This is a bit unclearly expressed, at best. I couldn't find a dictionary that gives must not as an alternative meaning for cannot, nor do I believe that it has such a meaning in general. When I say "I cannot jump 50 feet", there's no way to construe that as meaning "I must not jump 50 feet."
And I don't buy the analysis that when George Washington mythically confessed his guilt by saying "I cannot tell a lie", he really meant "I choose not to tell a lie." That turns a claim of essential moral character into an expression of situated existentialist choice.
However, a version of Wallraff's analysis can work. First, the George Washington quote points us helpfully towards the modality of moral obligation in place of the modality of logical necessity. And second, it's true of modal logics, of whatever kind, that ~◊A → □~A (if it's not possible that A, then it's necessary that not-A). I believe that this is the connection between can and must -- with interchanging scope of negation -- that Wallraff has in mind.
How does this help? Well, we can interpret "X cannot underestimate Y" as "it is not possible that X underestimate Y". This in turn is equivalent to "it is necessary that X not underestimate Y".
If this is logical necessity, we're right back where we started. If it's necessarily true that X is not underestimating Y, that means that no estimate X could be making of Y's value could possibly be too low, and that means that Y's value is negligible. This is just a more elaborate explanation of why expressions like "we cannot underestimate..." actually mean exactly the opposite of what people who use them usually think that they mean.
However, if we're talking about deontic necessity -- the logic of what ought to be -- then things are different. When we say that "it's morally imperative not to underestimate Y", we may mean that Y in fact has considerable value, and therefore it would be untruthful and even unfair to assign Y too low a value.
This still doesn't solve the whole puzzle. It applies only to cases involving "cannot" or "impossible", and not to the many other types of apparent overnegation, such as "fail to miss". And it doesn't seem to be the whole story even in the "cannot" or "impossible" cases, because when people say "we cannot understate the importance of X" (the phrase Wallraff is discussing), they seem to mean "we cannot overstate the importance of X" (because it is so great), not just "we're obliged not to understate the importance of X" (because it is not negligible). So I think we still need to appeal to the kind of explanation I (and others) have offered earlier, which depends crucially on the fact that it's psycholinguistically difficult to calculate the meaning of phrases combining negatives, modals and scalar predicates. However, the fact that phrases like "cannot overstate..." have an interpretation that is close to what is meant, rather than being completely the opposite of what is meant, may play a role as well..
[While we're on the subject, Alessandra Staley wrote in today's NYT:
The challenge of creating weekly scripts that move seamlessly among six clearly defined principal characters cannot be underestimated.
[Note also that this discussion has nothing to do with the question of whether can can be used to mean "is permitted to". It's sometimes prescribed that may should refer to permission, and can should only refer to ability. This doesn't correspond to current usage, and in the discussion above, I assumed that can can refer to permission as well as ability, possibility and other forms of modality.]Posted by Mark Liberman at May 6, 2004 12:27 AM