Man Believes Everything He Believes Is True and Also Believes That Can't Possibly Be the Case

MADISON, Wis. — I have, over the past sixty years, received a considerable volume of correspondence from people who believe they have solved the paradox I identified in 1965. I have received rather less correspondence from people who believe they are living inside it. Noel Stettner is, to my knowledge, the first person to contact me not because he thinks he has found a solution, but because he would like to confirm that no solution exists, so that he can, as he put it in his email, “plan accordingly.”

Mr. Stettner, 53, is a database administrator for the Dane County Department of Public Works. He is not a philosopher. He has not, until recently, had occasion to think about the formal properties of rational belief. He describes himself as “a pretty straightforward thinker.” I do not doubt this. It is, I think, precisely the problem.

The difficulty, as I have noted elsewhere, is structural. A person who holds a set of beliefs and considers each one individually will find, upon inspection, that he believes each one to be true — because if he believed any of them to be false, he would, presumably, stop believing it. At the same time, a rational person recognizes that he is fallible: that some of his beliefs are, statistically and historically, almost certainly wrong. He believes each item on the list. He also believes the list contains errors. The two positions are individually reasonable and jointly incoherent. I described this in a four-page paper in Analysis in 1965. The literature it has generated is not four pages.

Mr. Stettner arrived at the problem in January, during a conversation with his daughter, Megan, a philosophy sophomore at the University of Wisconsin, who mentioned the concept of epistemic humility. Mr. Stettner agreed with the concept immediately. He then went home and attempted to identify one of his own beliefs that might be wrong. He could not find one. He has been looking since. He has filled eleven legal pads.

“I went through them methodically,” he told me by phone. He had organized his beliefs by category: politics, science, personal finance, sports predictions, and a section labeled “Gut Feelings, Strong.” Every entry had a checkmark beside it. “Every single one of these is correct,” he said. “I’m sure of it. And I’m also sure that can’t be right.”

I told him that this was, in formal terms, exactly the paradox.

“Right,” he said. “So what do I do?”

I told him that this was, in formal terms, exactly the question.

Dr. Arthur Goode, a senior research fellow at the Center for Computational Epistemology at Carnegie Mellon University, with whom I have discussed Mr. Stettner’s case, confirmed what I suspected: the man is not confused. He is correct twice, in two directions that cannot be simultaneously occupied. Dr. Goode noted that the center’s database of formally cataloged epistemic failures contains more than four hundred entries related to the paradox, including several submitted by researchers who acknowledged, in their cover letters, that their own analyses might contain errors. “The unusual thing about Mr. Stettner,” Dr. Goode said, “is that he appears to be taking it seriously.”

I have some sympathy for this. Most people, upon encountering the paradox, do what any rational person would do: they acknowledge it abstractly and continue to believe everything they believe with undiminished confidence. This is, practically speaking, the correct response. It is also, logically speaking, the problem. Mr. Stettner has declined to take the practical route. He is, instead, sitting at his kitchen table in Madison, Wisconsin, checking his beliefs against themselves, one by one, with the methodical persistence of a man who administers databases for a living and is accustomed to finding the error in the table.

His wife, Laura Stettner, told me the situation has been manageable but persistent. “He’s fine at work. He’s fine at dinner. But if you ask him a question — any question — you can see him sort of check it twice now,” she said. “He told me yesterday he believes the dishwasher is running. And then he just stood there for a minute.”

Mr. Stettner has considered the possibility that the belief causing the problem is the belief that not all his beliefs can be true. If he abandoned that belief, the paradox would collapse. But he believes that belief is also true. He is, by his own assessment, stuck.

I understand the feeling. I identified the paradox sixty-one years ago. I have not resolved it. I believe my identification was correct. I also believe, as I noted in the original paper, that a rational person should expect some of his work to contain errors. I have been asked, at more than seventy conferences, whether this constitutes a personal instance of my own paradox. I have answered, each time, that it does. I have then been asked what I intend to do about it. The answer has not changed.

“The worst part,” Mr. Stettner told me, “is that I believe I’ll figure this out eventually.” He paused. “And I also believe that I won’t.”

I told him I believed he was right about both.