Uncanny

Mark Liberman's recent posting on the different meanings of can depending on how wide a scope it takes reminds me of my first brush with a scope ambiguity (though at the time I didn't know what it was called). It was back in my sophomore year in high school, in Linda Misenhimer's 6th period biology class. We were having a multiple-choice exam on our genetics unit, and one of the questions went something like this:

John has type AB blood, and Marsha has type B. What blood-type child can they not have?
a. AB
b. B
c. A
d. O

OK, I thought. If John contributes an A gene, and Marsha contributes a B, then their kid will be AB, so that's not the answer. If John contributes an B, and Marsha contributes a B, then their kid will have type B, so that's not the answer. What about type A? Well, John can certainly contribute an A gene, but the rest depends on Martha. If her genotype is BB, then their child will have to have type AB. On the other hand, if her genotype is BO, then she can contribute an O, and their kid will have genotype AO, and type A blood. So item C isn't the answer. That leaves item D, type O. For that to happen, both parents have to contribute an O gene, and since John is AB, that can't happen. Regardless of Marsha's unknown gene, they cannot possibly have a child with type O blood. The answer is D.

I did well on the test, but I noticed that I'd lost two points on that question. After class, I asked why.

"You should have marked both C and D," Mrs. Misenhimer told me.

"But they can have a child with type A, if Marsha's genotype is BO," I said.

"Yes, but if Marsha's genotype as BB, then they cannot have a child with type A."

I didn't understand why this mattered. Until Martha's unknown gene was known, we could not rule out them having a type A kid, so why was I supposed to mark that answer? I asked. Mrs. Misenhimer clarified with her intonation:

"If Marsha's genotype is BB, then they can ... NOT-have a type A child!"

"But ... but ..." was all I could say.

I thought about it some more at home. I came to the realization that the problem was in how we were interpreting the can and the not. Like any other native speaker of English, I was interpreting them to mean, "not able to have," or using parentheses to represent it, NOT(CAN-HAVE). (As semanticists put it, not has wide scope over can.) But it was also possible to interpret them as "able to not have" (or if you don't like split infinitives, "able not to have"); using parentheses, CAN(NOT-HAVE). (In other words, not has narrow scope, and can has wide scope.) A less common interpretation, but sensible enough in context (for example, "Here's what I can do to annoy Jim. I can not laugh when he tells that joke he always tells."). The problem was that Mrs. Misenhimer wanted to have it both ways. She wanted the "not able to have" meaning to say that it was impossible for John and Marsha to have a type O kid, and the "able not to have" meaning to say that it was possible for John and Marsha to have a kid that was not type A. It all seemed so simple now! Geez, using her logic, I should have marked all the options, since it was also possible for John and Marsha NOT to have a type AB kid (if John contributed a B), and NOT to have a type B kid (if John contributed an A).

I went to Mrs. Misenhimer again the next day to point out the ambiguity, so she could see why her question was unfairly graded, and I could reclaim my two points. I wasn't grade-grubbing, you understand; this was an important semantic principle. Unless you're making a pun, you can't just claim every possible meaning of an ambiguous phrase as the one you intended. Imagine someone saying, "I could care less" and meaning both that they didn't care at all AND that they did care!

"I think I see where the confusion came from on this question," I said. "First, you agree that 'not able to' and 'able not to' mean different things, right?"

"No."

I couldn't argue any farther. I had to accept my grade of a 96 on the exam instead of a 98.

UPDATE: I've been thinking about it some more, and I realized that actually it's just barely possible that Mrs. Misenhimer was not trying to interpret the question two ways. The bizarre CAN(NOT-HAVE) interpretation of the question not only allows "type A" as an answer, but also my choice of "type O." That is, if it's impossible for John and Marsha to have a type O child, then it is trivially possible for them to not have a type O child. They CAN(NOT-HAVE) a type O child! But there's still a problem. Not only does the CAN(NOT-HAVE) interpretation allow choices C and D as answers; as I remarked above, it allows every choice as an answer!

So why was Mrs. Misenhimer looking for just answers C and D instead of all of them? The only interpretation I can come up with that requires "type O" and "type A" as answers but not "type AB" or "type B" is this:

What blood-type child is it possible for it to be impossible for John and Marsha to have?

Let's go through the choices one by one. Type AB: it is not possible for it to be impossible for John and Marsha to have a type AB child, since it is a fact that John can contribute an A gene, and Marsha can contribute a B. Type B: it is not possible for it to be impossible for John and Marsha to have a type B child, since it is a fact that John can contribute a B, as can Marsha. Type A: it is possible for it to be impossible for John and Marsha to have a type A child; it is impossible in the case in which Marsha's genotype is BB. Type O: it is impossible for it to be possible for John and Marsha to have a type O child, since it is a fact that John's genotype is AB.

But seriously, that's not how can works, is it? No, the bottom line is this: Mrs. Misenhimer should have given me full credit on that question!

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Weight a Minute...

Is this a contradiction?

1. The nannies tell us that overweightness and obesity are on the rise. More than 60% of Americans are overweight or obese, they say.

2. The nannies (perhaps a different group of nannies) also tell us that the media have distorted the American vision of a desirable body. While the average model is 5’ 11” and 117 pounds, the average American woman is 5’ 4” and weighs 140 pounds.

Obviously, the height of models – and hence the height to weight ratio – is far out of reach for most people. But if the nannies are correct about overweightness, then the average weight for American women must be too high – so what business do they have using it as the appropriate benchmark when talking about body images?

On a related note, are these the same nannies who get huffy about fat jokes and consider it discrimination to charge fat people for two seats on an airplane? I try not to make fat jokes myself (though I admit that I’ve occasionally succumbed) because I consider other people’s eating and exercise choices their own damn business. But the food-nazis have been pressing the line that your weight is not your own business, but a pressing social issue. If they really believe that, shouldn’t they be encouraging more fat jokes, and higher airfares for fat people, as a means of increasing the psychological and economic costs associated with overweightness?

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Healthcare and the Tax Code

Tyler is puzzled by the usual economic argument against the tax treatment of health insurance. In a nutshell, the current system allows health insurance to be bought with pre-tax dollars, but direct purchases of healthcare products and services must be made with post-tax dollars. The usual economic argument, as stated by Glenn Hubbard, is that this system encourages a system of third-party payment in which consumers are rarely confronted with the true cost of their choices at the point of sale.

Tyler raises some tough questions about this line of argument. I’ll try to respond, while admitting that I (like Tyler) am not an expert in this field.

If the argument is that tax deductibility leads to too much health care, I can see the logic. But then the problem is in the pretzels and beer markets; health care should be doing fine, albeit in bloated form.

A bloated healthcare market is indeed part of the problem. It seems likely that many Americans do purchase more healthcare services than they really need. But the bigger issue is that greater expenditures don’t necessarily translate into more health services. The fact that consumers cannot use untaxed dollars to buy healthcare directly creates a strong incentive to have as much of our healthcare as possible purchased through middlemen (the insurance companies), which at a minimum drives up administrative costs. Instead of you just handing a check to your doctor, your employer has to pay an insurance company, you and/or your doctor have to fill out reimbursement forms, and bureaucrats at the insurance company have to process the claims and payments. (Lest it seem like I’m arguing against insurance in general, I’m not – for low-risk high-consequence health events, insurance makes perfect sense for purposes of risk-spreading, despite the administrative costs. But for small and routine expenses, out-of-pocket payment is more sensible.)

In addition, there is an incentive problem created by third-party payment. Patients have no incentive to economize on their health purchases when someone else is paying at the point of sale. They tend to purchase more doctor visits, more hospital days, more name-brand medicines, more pain medication in the hospital, more physical therapy, etc., and they have no reason to ask if the price is right. More on this below.

Alternatively, it might be argued that buying health insurance involves a negative externality on others. Maybe insurance companies are intrinsically bad monitors, and more insurance corrupts the system as a whole.

Tyler’s point, I think, is that the problem of uneconomical health purchases, brought on by third-party payments, could be solved through better cost monitoring. That’s true, but it creates problems of its own. First, the enforcement itself is costly, because it involves having insurance companies regularly reviewing and sometimes overruling the decisions of doctors and patients. Second, it engenders the animosity of doctors and patients, who don’t like having their decisions second-guessed. The essential purpose of an HMO is to ration healthcare by means of lines and bureaucracy instead of by price; hence the recent vilification of HMOs. Facing such resistance, the insurance companies can either (a) continue their monitoring and face the public’s wrath, (b) raise premiums, or (c) a little of both, which is what we’ve in fact observed.

Grant this premise, but where do we end up?
1. We would have a good argument for taxing insurance purchases. Yet the insurance point is rarely raised with this conclusion in mind. We might have (yikes!) an argument for greater government involvement in health care.

Actually, the argument is for equalizing the tax treatment of health insurance and direct healthcare expenditures. One way to do this is to tax health insurance; the other is to remove the taxes on direct health expenditures. The latter approach would continue to subsidize healthcare relative to other goods and services, but it would get rid of the perverse incentive to get all healthcare through insurance companies. Either approach would be preferably to the status quo.

2. If insurance companies are such poor cost monitors, why doesn't this raise premia accordingly? The poor monitoring of the company would be reflected in policy price and thus would be internalized by the people or institutions who buy the policies. The externality should vanish or at least significantly diminish.

See above points about cost monitoring. The bottom line is that even if there is substantial competition among insurance companies for institutional customers, the competitive price is still higher than it would be otherwise. Even the most efficient health insurance company can’t eliminate the administrative and enforcement costs entirely.

3. Why should insurance subsidies lead to "low copayments and deductibles"? Insurance with high copayments and deductibles is favored by the tax system as well. That being the case, why do we blame the tax system for how insurance is (perhaps) poorly structured?

It’s not exactly true that the tax system favors high-copayment/low-deductible policies as well, because in general, such copayments and deductibles must by paid out of consumers after-tax dollars. Recent change in the tax code have made it possible to have limited Medical Savings Accounts (MSAs), which allow you to put aside some pre-tax dollars for copayments and deductibles. This is a move in the right direction. But my understanding – again, limited by lack of expertise – is that such MSAs have been hobbled by a variety of restrictions. For them to create the proper incentives, it must be possible to “roll over” any unused dollars into your general income, which to my knowledge is not possible in the status quo. The patient’s incentive is to use the dollars before they disappear.

All these points collapse into a more simple query: how can a simple relative price, whether a distortion or not, corrupt the cost control practices of an entire industry?

The issue is not the distorted relative price between healthcare and other products and services. It’s the distorted relative price between health insurance and directly purchased healthcare. That, as outlined above, leads to higher administrative and enforcement costs.

And if government provision of health care is ineffective and costly, isn't there a positive externality from the purchase of private health insurance?

Certainly, private insurance is better than government provision. But what would be even better is a combination of private insurance and private direct payment.

For more commentary on healthcare, much of it inspired by Gephardt’s plan, see my previous posts here, here, and here.

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Giving Credit Where It's Due Department

The Doonesbury strip from the Sunday before last featured a reporter calling Bush to task for supporting so many constitutional amendments:

Mr. President, you have always said you believed in strict constitutional constructionism … and yet you favor amending the Constitution to prevent gay marriage … and you favor another amendment to outlaw abortion, and another to criminalize flag-burning … and another one to balance the budget … and yet another to enshrine victims’ rights.

With the possible exception of the balanced-budget amendment, I oppose all those proposals. But there is absolutely no contradiction between supporting constitutional amendments and favoring strict constitutional constructionism. The strict constructionist opposes reading one’s own opinions into the existing Constitution, not changing it. If you want the government to do something not specifically authorized, according to the strict constructionist view, proposing a constitutional amendment is the right way to go about it. I wish I could say this Bush administration was always this respectful of constitutionalism.

To be fair to Gary Trudeau, Bush is being disingenuous. He claims to believe in the principles of our Constitution – a claim belied by his willingness to (for instance) create a special loophole in freedom of speech to punish flag burners. But this contradiction has nothing to do with strict constructionism.

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Fecal Meter

Columbus (Ohio) Dispatch reporter Barbara Carmen had a story in the Metro section yesterday about a notorious apartment complex just south of the airport. I’m always interested in stories about these apartments, since I lived in one of them for about a week back in 1993. It looks like the latest attempts at renovation aren’t going so well; Carmen had this to say about one tenant’s unit:

(1) Feces float on her living room floor when it rains.

That sentence almost jumped off the page at me, it was such a poetic line in a column filled with ordinary prose. I even went to Poetry Daily and checked out a few poems there, to compare what “real” poetry looked like these days, and I’m telling you that Carmen’s one sentence had more poetry in it than the entire first two poems I read at Poetry Daily.

First, notice the [f] alliteration at the very beginning, in “feces float.” Effective metrical composition, too: “Feces” is two long syllables, both stressed, giving us a spondaic foot, encouraging the reader to slow down and dwell on the words. This effect is amplified by the long, stressed syllable of “float,” followed by a caesura—that is, a pause instead of the rest of a metrical foot.

Once we get past the caesura, the line quickly runs to its end in three anapestic feet: three sequences of two unstressed syllables and one stressed one, as shown here (note also the continued [f] alliteration):

(2) on her LIV/ing room FLOOR / when it RAINS

Alliteration and a detectable meter, neat! I’ll have to be on the lookout for more of Barbara Carmen’s journalistic poetry.

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Language as Signaling Mechanism

I’ve defended a mild form of linguistic prescriptivism in the past, but a distinct argument for linguistic prescriptivism has been running around in my head for a few weeks now, and Neal’s post below helped me finally pin it down. Neal said, among other things:

Ultimately, I had to concede to my wife that criticizing someone for thinking that “beg the question” means “induce one to ask the question” is little more than saying, “Ha, ha! I’ve read books on logic and you haven’t! I know the code and you don’t!”

This reminded me of something Bill Poser said about a month ago:

Prescriptive grammar has very little to do with maintaining the clarity and precision of the language. What it really has to do with is maintaining the dominance of the upper classes and enforcing social norms. It used to be that only the wealthy had access to the kind of education that would provide knowledge of the particular type of English enshrined in the prescriptive standard, so discriminating against people who did not command this type of English helped to preserve class distinctions and to keep the lower classes in their place by making them believe that because they spoke differently they were inferior. This isn't as true as it once was, but the idea persists. Prescriptive grammar is a tool of the kleptocracy.

Whoa, that’s harsh. The general message one might glean from Neal’s and Bill’s posts together is that many rules of grammar and style have no purpose but to keep certain people down while privileging the elite. (I should recognize that Neal’s position is not as extreme as Bill’s.)

I wonder if there might be a more charitable way of saying the same thing. Perhaps the rules of grammar and style perform a useful social function by providing signals about the educational backgrounds and effort levels of communicators. Consider the analogy to university education. One popular theory about such education is that it actually imparts useful knowledge to students and increases their productivity. That is, I hope, at least true to some extent. But another theory about education – one that I find increasingly plausible – is that it simply helps us to distinguish the more and less capable students. Someone who has graduated from college with a good GPA has (at least with some colleges) demonstrated a combination of native talent, work ethic, and persistence – all virtues that future employers value. Your degree is thus a signal of your productivity, even if getting the degree did not actually make you more productive.

For a signaling mechanism like education to work efficiently, there must be some cost of acquiring the positive signal, and the cost must be greater for the low productivity person than for the high productivity person. To put it simply, it must be harder for a low-talent person than for a high-talent person to graduate or get a good GPA. The valuable output of the signaling process is information about talent levels. I suspect that rules of grammar and style may perform a similar signaling role. To learn the rules, you need reasonably good instruction, and you must apply yourself to learn them. When you speak and write, listeners and readers acquire information about your education and work ethic.

It would be silly, of course, to judge a person ignorant or stupid on the basis of a single infraction of the rules. There are too many idiosyncratic rules for every person to learn every single one. I would not assume, for instance, that someone who uses “beg the question” to mean “induce one to answer the question” is uneducated. I might, however, infer (as Neal indicates) that the speaker had probably never studied logic. That inference might be buttressed by his reference to “ad homonym attacks.” The more errors (deviations from traditional usages) a person makes, the more confidence I have in my conclusions. This is similar to how I grade essays for style. I realize that style is unavoidably subjective, so I don’t subtract a standard number of points for each stylistic problem. Instead, I mark every stylistic problem I see, and then I make a holistic judgment of how badly written the paper was, taking into account the total number of red marks I see.

If my argument sounds elitist, that’s because it is. But it is an elitism grounded in information inferred from behavior, as opposed to irrelevant factors like sex or skin color. Most Americans do have the opportunity, if they apply themselves, to learn the basics of good writing and speaking. Indeed, learning to speak and write clearly, and in line with traditional rules, is probably one of the most accessible means of crossing class boundaries. Listeners should, of course, make exceptions for immigrants and others who cannot reasonably be expected to have fully absorbed the rules of the language. But the fact that a mechanism is imperfect does not imply that it has no use at all.

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Carrots, Sticks, and the Begging of Questions

Frequent commentator trumpit sent me the link to this LA Times article by Peter Garrison. In it, Garrison complains about how the idiom “to beg the question” has almost entirely lost its original meaning. These days, it is mostly used to mean, “to induce one to ask the question,” as in this typical example:

The Twins are up by five runs, and Lohse can't be sent back out there, and the real bullpen pitchers need a rest, but this still makes me nervous. Which begs the question, if you can't use him now, when can you use him? Which begs the question why is he in the major leagues? Which begs the question, what are Terry Ryan and Ron Gardenhire thinking? link

Originally, “begging the question” meant to use a circular argument, i.e., one whose conclusion is sneakily used as one of the premises. Garrison is not alone in this complaint. These guys here make the same one, and I’ve been bugged by the newer usage for years.

I even complained about it to my wife one day, but she was not sympathetic. She had several points. First of all, “beg the question” in its original sense is certainly not a semantically transparent phrase. What connection is there between “begging a question” and “using an argument’s conclusion as one of its premises”? Actually, there is one, which Evan Morris (aka The Word Detective) states concisely:

It means to bypass or avoid an essential question, but to proceed as if it had already been answered.

Even so, the semantic connection between begging and bypassing or avoiding is pretty tenuous, and not likely to be made by someone encountering this idiom for the first time.

Second: When someone does hear the phrase for the first time, they have every reason to treat it like any other English pharse, and create a meaning for it using their already-existing definitions for “beg” and “question.” Since you can’t actually beg a question to do something, guessing that it means to practically beg someone to ask some question is a pretty reasonable course to take.

Third: Of course, if they looked up the idiom, they’d find out what it meant, but as Geoff Pullum argues, you can’t look up everything . And why would you look up this phrase, anyway, once you’ve figured out a plausible meaning? It’s like when you get a bad grade because of some misunderstanding, and the teacher says, “If you didn’t understand, you should have asked me”—dammit, until I got this grade, I thought I understood perfectly! If someone says to you, “I eat bologna sandwiches,” are you going to look up the phrase “eat bologna sandwiches” to see if it’s an idiom?

Ultimately, I had to concede to my wife that criticizing someone for thinking that “beg the question” means “induce one to ask the question” is little more than saying, “Ha, ha! I’ve read books on logic and you haven’t! I know the code and you don’t!”

Returning to the LA Times article... Garrison generalizes his complaint, arguing that when terms for specific concepts lose their meaning, people are less likely to be aware of the concepts they denote. I have three things to say here. One: maybe, and maybe not. This claim is a version of what linguists call the Sapir-Whorf hypothesis, whose validity has not been established. Second: in this particular case, Garrison needn’t worry, because there’s another, more semantically transparent term for the concept--circular argumentation. And third, what would he say in a case where the goals of preserving a term’s original meaning and having a term for a useful concept were in opposition? This brings me to the other topic of this post: carrots and sticks.

My dad has brought to my attention the rampant misinterpretation of “carrot and stick.” Whenever you read the phrase in editorials or hear people use it, they mean “simultaneous use of rewards (carrot) and punishment (stick) to produce a desired behavior.” A typical example:

Jeb Bush is proposing a carrot-and-stick approach: reward school districts that have already tried and punish those that fail. link

But the phrase seems to have come from the image of dangling a carrot in front of a mule or donkey in order to get it to move forward in an attempt to get the carrot which is always just out of reach, as illustrated here and here. So the carrot is a reward (albeit an unreachable one), but the stick is just what keeps the reward out of reach, not an instrument of punishment. Evan Morris comments on the commonly used meaning for this phrase, too, here. In fact, it seems that even knowing of the origin of the phrase is not enough to keep the newer meaning at bay, as this cartoon shows.

Now I can definitely see Dad’s point, but what I haven’t had the heart to tell him is this: I think the phrase “carrot and stick” is more useful where it is now. First of all, you can’t look up everything. If you’re not familiar with the image of a carrot and stick used with a donkey, what are you going to think when you hear about motivating someone with a carrot and stick? I’d probably think of Teddy Roosevelt’s “Speak softly and carry a big stick,” and get the rest from context. Second, if everyone were to start using “carrot and stick” strictly in its original sense tomorrow, we would lose a convenient, short way of referring to a simultaneous use of rewards and punishment to produce a desired behavior, a concept that is useful in describing many situations. What would we gain in return? A convenient, short way to refer to one particular means of motivating a donkey or mule.

Which meaning would you rather have for "carrot and stick"?

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