July 15, 2007

Weird Logic and Bayesian semantics

There are some common English expressions -- "could care less", "still unpacked", "(not) fail to miss", "cannot be underestimated" -- which are almost always used as if their meanings had a negation added or subtracted.

For example, if unpack means "to removed or undo from packing or a container", as Merriam-Webster tells us, then "still unpacked" should mean "still removed from packing", i.e. "not yet packed", or "not re-packed" or something of the sort. But if you search the web for {"still unpacked"}, you'll find that most of the examples clearly mean "still packed".

(Well, actually, the Observer's Paradox bites us on this one -- the first page of Google hits includes two Language Log posts, a Language Hat post, a Linguist List posting by Larry Horn, and a Boston Globe Brainiac column "Don't fail to miss it" by Jan Freeman. But once you get past the commentary, most of the real uses mean "still packed", e.g. "It's absolutely brand new and still unpacked.")

The standard story about this is that it's hard for our poor monkey brains to deal with the logical interaction of multiple negations. And it's especially hard when some of the negatives are implicit in word meanings (like fail or miss), or when modals (like can or possible) and scalar expressions (like less or still or underestimate) are also involved. We could call this the "semantics is hard -- let's go shopping" theory.

No question, this stuff is difficult. Quick, evaluate Catbert's statement in the middle panel of yesterday's Dilbert:

Catbert obviously intends to say that HR's sole motivation is evil, and that everyone should now recognize this -- but is this really what he said?

Yes, I think so -- but it takes a couple of seconds of conscious checking to be sure, at least for me.

But the thing is, not all combinations of negations, modals and scalar expressions are equally likely to be used illogically, in the end. "Cannot be underestimated" is a case in point. Let's use Google Scholar as our corpus, since the material ought in principle to be carefully written and copy-edited. Here are some counts:

  be overestimated be underestimated
should not
must not

The color-coding is based on my quick evaluation of the 20 examples on the first two pages of returns. My judgment is that nearly all of the "cannot be underestimated" examples are logically reversed, e.g. the first five of the "cannot be underestimated" crop:

The value of prevention in relation to these issues cannot be underestimated, yet it is not easy for physicians to learn...
...many patients have undergone an unnecessary operation whose complications cannot be underestimated...
The importance of this cannot be underestimated.
The need for abstinence from alcohol cannot be underestimated, given its documented synergistic effects on hepatotoxicity when combined with ...

(In these examples, I've read the surrounding paragraph or two in order to be sure of the intended meaning.)

By contrast, in the first 20 pages of returns for each of the other five strings, all of the uses seem to be logically correct, e.g. the first five of the "cannot be overestimated" crop (I'll spare you the other four cells, which you can check for yourself):

In short, Merleau-Ponty's importance to and influence among contemporary philosophers cannot be overestimated.
The importance of this search cannot be overestimated, because success could mean prevention of the heart failure syndrome...
The importance of this book to the development of hydrology as a geoscience cannot be overestimated and will be long-lasting ...
The significance of this condition for the individual and for the family constellation cannot be overestimated by any student of human behavior.
The importance of the boron hydride problem for valency theory cannot be overestimated.

(Thus when Barbara Landau wrote "The importance of this effect shouldn't be overestimated", meaning that its importance shouldn't be underestimated, she committed a very unusual error. In contrast, when Lila Gleitman wrote "The importance of this position cannot be underestimated", meaning that its importance cannot be overestimated, she was behaving the way English speakers usually do.)

The pattern of errors here shows that our monkey brains are not just responding randomly to combinations of negation, modality and scalar expressions. The responses are not always logically correct, according to our analysis at least, but they're far from random.

A second hypothesis that doesn't help is that English, deep down, is still a negative concord language. According to this view, our linguistic DNA yearns to amplify every no into a chorus of negation ("ain't never got nothing from nobody nohow"). Again, the "nothing nohow" theory may be true in general, but it doesn't help predict the specific "cannot be underestimated" pattern.

And a third true but unhelpful hypothesis is that some illogical expressions have simply become idioms or additional word senses. In the case of "still unpacked", this hypothesis is enshrined in the OED's entry for unpacked, which balances the first sense "Not made up in, or put into, a pack" with a second, opposite sense "Not taken out of a pack or parcel". This is no doubt correct, but it fails to explain why the same development occurs spontaneously with some other words, e.g. unwrapped, uncorked, unsealed, unveiled -- but not others, e.g. undressed, uncovered, unplugged.

In the case of "cannot be underestimated", the "illogical idiom" idea fails because other semantically-similar phrases show the same apparent illogic. Maybe it's not a surprise that the active-voice versions work the same way as the passive-voice cases do (data also from Google Scholar):

  overestimate underestimate
should not
must not

But the same thing happens with phrases like "impossible to over/underestimate", "difficult to over/underestimate":

  overestimate underestimate
impossible to
difficult to
hard to
easy to

And likewise if we replace overestimate and underestimate with overrate and underrate, or overstate and understate:

  be overrated be underrated be overstated be understated
should not
must not

OK, so we've disposed of three theories, which may be true but don't predict the facts in this case: "Semantics is Hard", "Nothing Nohow", and "Illogical Idioms". This leaves (at least) two hypotheses still standing, which I'll call "Weird Logic" and "Bayesian Semantics".

The "Weird Logic" theory was discussed and found wanting, perhaps prematurely, in an earlier Language Log post: "We cannot/must not understate/overstate ... ?", 5/6/2004. Its basic idea is that according to what we might call natural or psychological logic, "it is not possible to underestimate the greatness of X" really means that X is really great.

The "Bayesian Semantics" theory was proposed for the expression "fail to miss" in another old Language Log post, "Why are negations so easy to fail to miss?", 2/26/2004. The basic idea is that Nature (or at least the Speech Community) abhors a semantic vacuum:

...you can fail to do something only if you first intended to do it. It's relatively rare for people to intend to miss something, but missing things is generally easy to do, so when you try to miss something, you usually succeed (and you might describe what you did as avoiding rather than missing, anyhow). Therefore, failing to miss things just doesn't come up very often. Perhaps this hole in the semantic paradigm leaves a sort of vacuum that bad fail to miss rushes to fill?

So the claim here would be that the literal meaning of "it is not possible to underestimate X" is something that people are extremely unlikely to intend to convey, and therefore the form is susceptible to adoption by other, more probable meanings.

My breakfast hour is over, and this post is already too long, so evaluation of these theories will have to wait for another day.

Posted by Mark Liberman at July 15, 2007 09:06 AM