It’s International Women’s Day, so let me celebrate by once again singing the praises of Joan Robinson’s wonderful book, Economic Philosophy.
After writing my last post on the logical mistakes of economists, I came across George Stigler’s review of that book. Stigler calls Robinson a “logician” and argues for the superiority of economists to logicians in the following passage:
A logician is a wondrous creature, but he cannot distinguish between the two simple errors: if A = B and B = C then (1) A = 1.01C, and (2) A = 10^65C. An economist can. (p.193)
I’m not sure why he had to use the male pronoun, but anyway his comment proves my (and Robinson’s) point about economists and logic admirably. Take Error Number 1. We have:
(a) A = B
(b) B = C, and
(c) A = 1.01C.
Substituting identicals from (a) into (b) and (b) into (c), we can derive:
(d) C = 1.01C.
Substituting back into (c), we can derive:
(c’) A = 1.01(1.01C).
Running exactly the same substitutions again, we can derive:
(c”) A = 1.01(1.01(1.01C)).
Generalizing, if we run the substitutions n times we get:
(cn) A = (1.01^n)C.
For a large enough n we can get an error of the same magnitude (or much greater) than Stigler’s Error Number 2: A = 10^65C.
So Error Number 2 is logically derivable from Error Number 1. Stigler’s implication is that 2 is a worse error than 1 and that Robinson fails to see this. But in fact 1 implies 2 as well as errors approaching infinitely greater magnitude. In a typical mathematical model, the application of 1 could easily compound into a far greater error than 2. This is precisely what a logician could help an economist to avoid, if only the economist would listen.
Thank you, Joan Robinson, for helping to expose the logical sickness of economists. I wish they would stop trying to answer back and just fill the damned prescription. But, wishes aside, without women like you the Rule of Unreason would go even more unchallenged.