by Roger Koppl
The term “magical thinking” has different meanings, most of them involving something like extrasensory perception or the efficacy of spells. Here I define it as an argument, one of whose steps requires something impossible. (Larry White helped me with this definition, but gets no blame for it or anything I say here.) It is not magic thinking if your argument has an unexplained piece. Darwin knew didn’t have anything like Mendelevian genetics as a mechanism. That was a hole in his theory, eventually filled by others. No magic there. Magical thinking exists when one fills the gap with something that is logically or physically impossible.
If you can show I have engaged in magical thinking, you have overturned my argument. Magical thinking in this sense is clearly to be rejected. And yet we find magical thinking often in supposedly scientific reasoning. Jacob Viner’s famous problems with the envelop theorem is a nice example. Computable economics has revealed other examples of magical thinking in economics. It turns out, for example, that best-reply strategies are not always computable, even in finite games. Computing the Nash equilibrium does not necessarily get you around the infinite regress of “you think that I think.” Imagining otherwise turns out to be magical thinking.
Following Lewis (“Some aspects of constructive mathematics that are relevant to the foundations of neoclassical mathematical economics and the theory of games,” Mathematical social sciences, 1992, 24, 209–235.) Tsuji, M., da Costa, & Doria ( “The incompleteness of theories of games,” Journal of philosophical logic, 1998, 27, 553–564) have shown that even finite games can be noncomputable. Computability issue crop up in contexts we had thought of as “finite,” because our vague descriptions allow an infinite variety of finite games to fit the description. The problem here and in the best-reply result is that an infinite set of possibilities intrudes in an unexpected way.
Tsuji et al. draw the inference that rational economic planning under socialism may be impossible. Here is what I say about that in my review of Velupillai (Computability, Complexity and Constructivity in Economic Analysis, Blackwell, 2005):
One can no longer answer Hayek (1935) and von Mises (1920), who argued that “rational” economic planning under socialism is impossible, by appealing to modern computers as have Lange (1967) and Cottrell and Cockshott (1993). Doing so turns out to be another example of magical thinking. Instead of implicitly assuming that rational agents can make impossible calculations, however, such arguments explicitly assume that magical computers can make impossible calculations. In reaching this result, da Costa and Doria have shown what advantage markets have over central planners: markets do not have to know what they are doing. Markets achieve their equilibria because the overall results are not planned and need not be computed. Needing to compute the result ahead of time, central planners have given themselves the impossible task of computing the future.
This blog’s dustup on evolutionary psychology provides another interesting example of magical thinking. I defended evolutionary psychology against Gene Callahan’s criticisms in part by raising the example of landscape preference whereby, among other things, young children show a preference for the landscapes of our biological ancestors and do so more strongly the younger they are. Gene asked, “as Bob Murphy notes, why wouldn’t evolution favor this preference arising more strongly in young adults, who actually might lead the tribe somewhere, rather than in young children?” He refers to this comment at Free Advice: “If you wanted to make a fitness story, wouldn’t it be the exact opposite? A young child has no influence over where the family / tribe sets up camp. If you wanted to give a bunch of ignorant apes an advantage, and could only program a preference for the savannah at a certain age range, then I’d stick it in the 13 – 25 year olds, not the 0 – 12 year olds.”
This is magical thinking, too. This super-Planglossian interpretation of Darwin transforms natural selection from a filtering process that explains speciation into a magic wand that creates impossible adaptations on demand. Murphy seems to basically accept Darwinism his discomfort with evolutionary psychology notwithstanding. But I do think many creationists make natural selection magic and then point to its failure to produce super-Panglossian results as counter argument to the theory.
1 Corinthians 13:11 nicely expresses why we should not engage in magical thinking. “When I was a child, I spake as a child, I understood as a child, I thought as a child: but when I became a man, I put away childish things.”