Makes are ranked according to price category. There are three such categories: lower-priced, mid-priced, and luxury. [...]
One of the results of the existence of ranks is that makes can be compared, regardless of manufacturer. Chevrolet and Ford are thus equivalent, as are Cadillac and Lincoln. Mercury is higher than Chevrolet, etc. The ranks form a value system, and each make can be placed within this system.7
7 The importance of rank in the significance of a make cannot be underestimated. Two phenomena of recent years show this clearly. The first example is that of the Oldsmobile with the Chevrolet engine. Several years ago, it was discovered that some full-size Oldsmobiles were being sold with Chevrolet engines, without the customer's knowledge. The Chevy and Olds engines were approximately the same, the only major difference being the make. Many of the people who had bought these "hybrids" were furious. There were numerous court cases against GM for the deception, and the affair was finally settled with GM paying millions of dollars in compensation. All along, GM expressed puzzlement, for the interchange of components among different makes is standard practice and is becoming more and more widespread. There was no qualitative difference between the two engines, they said. But the customers and the courts would not buy this. After all, those of us who watched TV in the fifties knew all about being behind the wheel of a Rocket Oldsmobile with its famed Rocket V-8 engine. Chevrolet is OK, but a Chevy is not an Olds, nor is its engine. [emphasis added]
As Tim Zingler has pointed out to me, the context of Aronoff's footnote 7 makes it clear that "the importance of rank in the significance of an [automobile] make" can indeed be underestimated, as demonstrated by the fact that GM did in fact underestimate it.
But I suspect that some readers are still unsure about the logic of cases like this. Google Scholar has more than a thousand hits for "cannot underestimate the importance of" X, and inspection of a sample suggests that they all interpret the expression in the same way that Mark did, to mean that X is of paramount importance.
So let's play the Estimation Game.
We have an oracular Importance Meter, which give us the true (or at least official) importance of anything that we hook it up to, measured on a scale of 0.0 Importance Units to 10.0 Importance Units. In order to play the game, a contestant estimates the importance of something — call it X — and then we connect X to the Importance Meter, and compare the contestant's estimate to the official answer.
There are three possible outcomes:
- The contestant's estimate is less than the meter reading, in which case the importance of X has been underestimated;
- The contestant's estimate is exactly equal to the meter reading (down to the precision of measurement, which is 0.2 Importance Units), in which case the importance of X has been correctly estimated;
- The contestant's estimate is greater than the meter reading, in which case the importance of X has been overestimated.
Each of the three outcomes is announced with characteristic flashing lights and blaring noises, and there's a board for keeping score of each contestant's mean squared estimation error, and there are prizes, and so on.
OK, now let's imagine a round of the Estimation Game where the CEO of General Motors estimates the importance of tail-light design. Her guess is 5 Importance Units, right in the middle of the scale. We connect "tail-light design" up to the Importance Meter, and behold, the importance is actually 6:
So the CEO of GM has underestimated the importance of tail-light design.
If she had guessed 7, she would have overestimated.
In this situation, it's easy to guess too low or two high. There are 30 possible guesses that are under-estimates (0 to 5.8, incrementing by 0.2), and 20 possible guesses that are over-estimates (6.2 to 10.0 by 0.2), and just one guess (6.0) that's exactly correct.
Now the same contestant is asked to estimate the importance of "rank in the significance of a make". And when we hooked up the Importance Meter to "rank in the significance of a make", we get the maximum possible reading of 10.0:
At this point, it almost doesn't matter what her guess was. All the 50 estimates from 0.0 to 9.8 are under-estimates; one guess is exactly correct (10.0); and there are no possible guesses that are over-estimates. It is literally impossible to over-estimate the importance of X in this case. We literally cannot overestimate it.
Alternatively, if the Importance Meter reads 0.0, there are 50 guesses that are over-estimates, and one guess that's exactly correct, but it is literally impossible to underestimate the importance of X. We literally cannot underestimate it. The importance of X cannot be underestimated.
So when we say that, as Mark Aronoff did, that "The importance of rank in the significance of a make cannot be underestimated", we (should) mean that no estimate of importance can possibly be too low, in this case, because the Importance Meter's reading is as low as it can possibly be.
But this is clearly the opposite of what Mark meant.
He's not alone — this is one of many cases where the interaction of negation, modality, and scalar predication causes smart people to say or write the opposite of what they mean:
"We cannot/must not understate/overstate", 5/6/2004
"Overstating understatement", 6/22/2004
"Multiplex negatio ferblondiat", 7/14/2007
"Weird logic and Bayesian semantics", 7/15/2007
"'Cannot underestimate' = 'must not underestimate'?", 11/6/2008
"Gov. Cuomo and our poor monkey brains", 1/21/2011
"… not understating the threat", 6/5/2012
"(Not) Underestimating the Irish Famine", 9/16/2012
"Overestimating, underestimating, whatever", 1/11/2013
"CIA unable to underestimate the effect of drone war", 4/7/2013
"Misnegation of the week", 5/17/2013
"'Impossible to understate' again", 3/1/2014
"'Hard to understate'", 3/19/2014
This state of affairs should make descriptivists stop and think. Can the authors of a thousand Google Scholar hits — and innumerable other speakers and writers — be wrong? In this case, I think, the answer is "yes".
But I've argued that "could care less", where modality and scalar predication seem similarly to point in the wrong direction, has simply become an idiom. Shouldn't the same be said for "cannot underestimate the importance"?
I don't think so. As I've argued before, there's a crucial difference.
Whatever is happening with "cannot underestimate" applies equally to "cannot understate", "impossible to underestimate/understate", "hard to underestimate/understate", "difficult to underestimate/understate", "cannot be underestimated/understated", "hard to underrate", "cannot be undervalued", and many other common ways to re-express the same idea.
In contrast, alternative formulations of "could care less" are rare, and can only be understood as bad jokes, to the extent that they're not simply puzzling. Thus one semantic equivalent to "could not care less" might be "could not possibly have less concern" — and we find this in a published translation of Montaigne's sentence
Si toutefois ma postérité est d'autre appétit, j'aurai bien de quoi me revancher: car ils ne sauraient faire moins de compte de moie que je'en ferai d'eux en ce temps-là.
However, if my descendants have other tastes, I shall have ample means for revenge: for they could not possibly have less concern about me than I shall have about them by that time.
But in this case, Montaigne means to imply that his concern-meter will be pegged at zero, not at its maximum value. And more generally, we don't see things like "I could possibly have less concern" used with the meaning idiomatically assigned to "I could care less". This is the behavior that we expect from an idiom; and the different behavior of "cannot underestimate/understate/underrate/undervalue" is what we expect from a psychologically probable error.