"Cannot underestimate" = "must not underestimate"?
As recently noted, people often get confused about English phrases involving negatives combined with other negatives, modals, or scalar predicates, and there's a series of Language Log posts that collectively offer several (non-exclusive) hypotheses for why this confusion is so easy to fail to miss:
- Our poor monkey brains just can't deal with complex combinations of certain logical operators;
- The connection between English and modal logic may involve some unexpected ambiguities;
- Negative concord is alive and well in English (or in UG);
- Odd things become idioms or at least verbal habits ("could care less"; "fail to miss"; "still unpacked").
Yesterday's post specifically involved expressions like "cannot underestimate X" or "X cannot be underestimated", as a way of saying that "X is very large or important"; and I followed Lila Gleitman and many others in assuming that these phrases are examples of the class of common logical errors involving negation, modality, and scalar predication. We seem to be saying that X is so large that it's impossible for us to underestimate it — that is, our estimate of X will always be greater than X, no matter how large our estimate is. And this will be true if X is rather small, which is not what we're trying to say.
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