Spherical Cows and Repugnant Conclusions

Spherical Cows

One day, the new chairman of the Mathematics department decided they should be doing more to help the local community. An offer of expert advice placed in the newspaper was taken up by the county Dairy Association. The mathematics faculty spent a day touring farms and discussing with the farmers how to best improve the efficiency of their businesses. The mathematicians returned to the university and worked on the problem for a month. At the end of this period, the farmers were invited to a lecture hall on campus. The chair went to the front of the room, welcomed the gathering, and then turned to the blackboard: “Assume cows are spherical…” he began.

There are endless versions of this joke involving physicists, mathematicians, and other theorists. The point isn’t simply that theorists are impractical; it is that a seemingly completely logical argument with indisputable results is completely worthless if it starts from a flawed premise, and that the mere act of abstracting or simplifying the premise can introduce a fatal flaw.

For the errours of Definitions multiply themselves, according as the reckoning proceeds; and lead men into absurdities, which at last they see, but cannot avoid, without reckoning anew from the beginning; in which lyes the foundation of their errors. — Thomas Hobbes, the Leviathan

I find myself thinking about Spherical Cows every time I see a discussion of one of the problems of theoretical ethics. The most famous of these are the various Trolley Problems, but population ethics, longterm-ism, and virtually all abstract discussions of utilitarianism remind me of this joke.

These are thought experiments and, like other simple, abstract models, can lead to insights. Or to absurdities. I think part of the reason they are so unintuitive and so often lead to Repugnant Conclusions is that they are spherical cows treated as if they are regular cows.

Trolley Problems

Consider the basic Trolley problem: we are given the choice between diverting a Trolley and killing one person or not diverting the Trolley and killing five people. Reluctantly, naive consequentialists draw the conclusion that they should divert the Trolley and then go on to push fat men from bridges and perform other similar gyrations in the name of saving the largest number of lives. Worse, they then extend these insights to real-world problems.

These problems have the same relationship to real-world ethics that Spherical Cows do to real ones. In real life, the person at the switch does not have perfect information; they do not know all the options, what others may be doing to solve the problem, what the actual chances are of the people on the tracks being injured or killed, or anything about those people.

Repugnant Conclusions

Many, many others have pointed out these flaws and others with Trolley problems. Thinking about these as Spherical Cows, it becomes obvious that they are flawed from before the argument begins.