March 12, 2003: Letters

The big think

Only her hairdresser knows for sure

Honoring Hargadon

Correction, war deaths

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The big think

“Thinking about Thinking” (cover story, January 29) poses a pair of philosophical questions — the trolley dilemma and the footbridge dilemma — and suggests that they are morally equivalent. In the first, the reader must imagine that she can save five lives from a runaway trolley by hitting a switch that will turn the trolley to a side track, thereby killing one other unfortunate person. In the second, the reader imagines she is standing over the trolley track on a footbridge next to “a large stranger.” With a timely push, she can shove the stranger onto the track, so that his body will prevent the train from reaching the other five. People who have been posed these dilemmas are said to respond “yes” to the first, and “no” to the second, and philosophers are said to be puzzled as to why the responses should be different.

Perhaps the academic study of philosophy and morality has changed since my undergraduate days at Georgetown University. However, I suspect that morality has not changed so dramatically in people’s minds. In the second problem, the morally correct answer is for the reader to jump onto the track herself. Pushing another person would indeed be murder. This option would surely occur to many hearers of the

situation, and its absence in the formal problem shows that moral philosophers will forever be handicapped in their research if they negate the presence of love and self-sacrifice in the world. In contrast, it is clear in the first problem that you cannot offer your own life for that of the poor unsuspecting victim on the side track. No wonder those few people who agreed to murder in the second question took a long time to think about it.

Canice Lawler *91
North Potomac, Md.


In “Thinking about Thinking,” Professor Johnson-Laird’s logic problem, which trips up smart people, is described as follows: “In a hand of cards, only one of the following three assertions is true: There is a king or an ace or both in the hand. There is a queen or an ace or both in the hand. There is a jack or a ten or both in the hand. Is it possible that the hand contains an ace?” Smart people answer “Yes,” and they are wrong. But PAW’s explanation for why the answer is “No” is not clear.

Readers with middling logical abilities (such as myself) will be misdirected by the explanation: “If the first assertion is true, the second and third must be false — so there is no ace. The same reasoning applies if the second assertion is true.” The proper explanation is different.

First off, if the first assertion is true, it does not follow that the second is false. Indeed, if the first is true by virtue of there being an ace in the hand, it follows that the second is true. That’s the problem for the “Yes” answer. If the ace possibility is realized by the truth of the first assertion, then this makes the second true as well, contradicting the initial assumption that only one of the three is true. The same reasoning applies to the supposition that only the second assertion is true by virtue of the hand containing an ace. That supposition leads, in the same way, to contradiction.

Tony Brueckner ’74
Goleta, Calif.


I want to question the analysis of the “restaurant” puzzle and the “Linda” problem, both of which appeared in your article about thinking.

Regarding the restaurant puzzle, I think there is an internal inconsistency in your explanation. Your answer on page 31 states, “If you were told that you could have ‘the fish or else the meat,’ you could have one or the other, not both.” This seems to me a correct interpretation of the words “or else,” particularly in a restaurant setting. (I note that “or else” does not have the same meaning as “or” in pure logic, because — at least in that realm — “or” does not imply “not both.”)

Your explanation goes on to deduce that if the diner were offered “the fish or else not the meat,” the diner could have both fish and meat. If “or else” means “not both,” however, it would not be permitted for the diner both to have fish and to have non-meat. If the diner has fish, then he is having both fish and non-meat, which contradicts the meaning of “or else.”

It seems to me as a layman that what is going on here is not a failure of the listener to apply logic in analyzing the question, but rather a failure of language (at least in these laconic phrases) to be sufficiently precise to express the nuances of choice that the waiter is offering. I suspect that many people, upon hearing the waiter’s offer, instinctively reject it, not because they are “befuddled” or incapable of understanding simple logic, but because they recognize the confusion and potential logical inconsistency embedded in the waiter’s words.

In a somewhat similar vein, I question the analysis of the “Linda” problem. The test subject is offered, among others, the choices that (X) Linda is a bank teller active in the feminist movement and (Y) Linda is a bank teller. Given the juxtaposition of these two choices, an intelligent subject who is aware of the imprecise way in which most writers and speakers use language might very well assume that (Y) means “Linda is a bank teller who is not active in the feminist movement” (or, perhaps, “Linda is just a bank teller”). If, as I believe, that assumption is a reasonable (albeit not uniquely valid) interpretation of the words given, ranking (X) as more likely than (Y) is also quite reasonable. The “Linda” problem thus seems to me to reveal something about how the brain makes assumptions in interpreting the meaning of language. It does not seem to me to reveal, as your article suggests, that people “failed to reason proficiently” or that people are “blind.”

Although the analogy is not perfect, the assumption above reminds me of experiments in which a baby who already knows the word “cup” hears the word “plastic” while being shown a plastic cup. Those experiments show that the baby assumes that the word “plastic” refers to the material rather than the cup itself, because he assumes that the new word means something different from the word “cup” that he already knows. In a somewhat similar light, the “Linda” subject appears to assume that (Y) is meant to be an opposite to (X), even though the test does not say that in so many words.

William H. Weigel ’71
Brooklyn, N.Y.

Editor’s Note: Professor Johnson-Laird’s response is online in Letterbox and will appear in our next issue.


Your cover story on thinking was fascinating, and the story reports some potentially significant work about what parts of the brain do what sorts of thinking. The (seemingly) purely emotional difference between the “tram” and “footbridge” problem are striking evidence of a physical explanation for an emotionally understandable difference in reaction to logically equivalent situations.

But the article also illustrates a serious problem about many such “logical” problems — the role of ambiguity in the question. As a litigator and sometime student of public opinion polls on difficult public policy issues, I often have been struck by the difficulty of asking truly clear questions about complicated issues, if the objective is to get meaningful answers. The “Linda” question illustrates less about logic or the brain than about the problem of imprecision in questions.

The “Linda problem” concerns a bright, but also idealistic woman. Her stated career choices are “that she is active in the feminist movement, that she is a bank teller, or that she is a bank teller active in the feminist movement.” We are asked to pick Linda’s most likely choice. To most people, the proffered set of choices implies that the first two choices are mutually exclusive, i.e., that Linda chooses to be only a bank clerk with no broader cause that she seeks to advance or that she decides to be only an impractical activist with no visible means of support.

The supposed “logical” answer is “teller.” The basis for this allegedly logically correct conclusion is that Linda could be a teller and at the same time also be an activist, and therefore, “logically,” it must be true that “teller” is more likely than “teller plus activist” since “teller” includes not only whatever chance there is of Linda being only a teller but also the combination of teller and activist.

But this “correct” answer is not necessarily right even as a matter of logic. It is equally true that the answer “activist” includes both the combined roles of teller from 9 to 5 and activist the rest of her waking hours, but also whatever chance there is of Linda being just an activist.

The real point is that if one understands the “pure” options (“teller” and “activist”) as alternatives that exclude being both gainfully employed and socially conscious, they are exposed as highly unlikely alternatives, compared to the “balanced” choice of working at a bank and seeking justice in her “spare” time. And most normal, highly logical people would so understand the problem.

Walter B. Slocombe ’63
Washington, D.C.


In your article “Thinking About Thinking,” I, like most Princeton undergraduates, instantly jumped to the conclusion that the answer to problem #4 was $1, which proves that the part of my brain that predominated as an undergraduate won out over the other part of my brain that I mistakenly thought had taken control when I entered graduate school.

Warren J. Wittreich ’51 *54
Bethlehem, Pa.


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Only her hairdresser knows for sure

I would like to point out to Anne Margaret Daniel *99 (Perspective, January 29) that although “when someone says redhead . . . we think of the dizzy and dazzling Katharine Hepburn, or Lucille Ball, or the lavish and lustful Rita Hayworth,” neither Lucille Ball nor Rita Hayworth were natural redheads. Even Katharine Hepburn, whose hair was never more floridly described than “reddish brown” by contemporary sources, didn’t appear on screen in color until The African Queen in 1951, some two decades into her film career. Thus, these three Hollywood legends might not be the best examples to choose. Consider instead Maureen O’Hara (“That red head of hers is no lie,” says Barry Fitzgerald in The Quiet Man [1952]), Susan Hayward, Greer Garson, Ann Sheridan, Deborah Kerr, Moira Shearer, or even Angela Lansbury.

Elizabeth Anthony ’99
Oklahoma City, Okla.

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Honoring Hargadon

It was with great disappointment that I learned that President Tilghman had invited Dean of Admission Hargadon to speak at Baccalaureate (Notebook, February 26). When Dean Hargadon’s office embarrassed the university community on a national level by abusing information it had been given in trust, President Tilghman said that everyone involved would be disciplined. Not so. Although he apologized, Dean Hargadon was subject to no disciplinary penalty. Instead, a retirement that was already fast approaching was accelerated.

Now, one of the great honors the university can bestow is being given to him. Given the nature of the Baccalaureate (an interfaith ceremony meant to emphasize the great ethical weight upon the graduates as they enter the world) and the nature of the offense (a failure to recognize an obvious ethical responsibility), the choice is particularly upsetting.

Christopher Beha ’02
New York, N.Y.

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Correction, war deaths

I suspect that Professor James M. McPherson was ill-served by an editor when the following sentence appeared in “The Crossroads of History” (feature, February 12): “(He notes that the death toll amounted to 2 percent of the population, which would be equivalent to about 5.5 million people today.)”

There were 6,000 deaths in the Battle of Antietam, which would put the population of the U.S. at 300,000, when it was actually about 30,000,000 at the time. What the professor presumably meant was that the deaths on both sides during the entire Civil War came to about 2 percent of the population. That concept would be about right, and it illuminates the tragedy of that conflict.

David S. North ’51
Arlington, Va.

Editor’s Note: Professor McPherson was referring to the death toll of the Civil War. We apologize for the error.

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