I’m trying my hand at teaching Philosophy of Economics, which led me to rereading Milton Friedman’s ‘The Methodology of Positive Economics’.
In some ways I believe this essay to have received an unfairly bad rap from methodologists. But in rereading it I noticed something that I hadn’t noticed before, which is a footnote in which Friedman takes Gödel’s theorem to assert ‘the impossibility of a comprehensive self-contained logic.’
That’s not just wrong; it is virtuosically wrong. Gödel’s first ‘incompleteness’ theorem asserts that any intuitively correct formal system for arithmetic will contain at least one recognisably true statement that is expressible yet not provable within the system. The second generalises this somewhat. Neither says anything about logic in general and certainly not that no logic can be ‘comprehensive’ and ‘self-contained’. This is just as well, since there demonstrably are formal systems for, say, first-order logic that are both sound and complete.
While Friedman’s comment is contained within a footnote making a peripheral point, I believe that its wrongness should cast out a warning beacon across the rest of his work. Nobody who understood Gödel’s theorem would state what Friedman states, even as a throwaway comment. It’s no use arguing that Friedman accidentally wrote ‘logic’ when he meant ‘formal system for arithmetic’; people don’t make slips of the pen on that order. It is thus worrying, first of all, that Friedman should make such bold proclamations about something he doesn’t seem to understand. But it is also worrying that he should lack the understanding. Logic and mathematics are, after all, fairly central to what neoclassical economists do. It is telling that an economic theorist of Friedman’s stature should be deficient in the simple curiosity that would have led him to learn what he needed to avoid such an egregious howler. It reveals something, I suspect, about the dismissive attitude some neoclassical economists take towards other disciplines, even those that lie at the very foundations of the theoretical systems they typically employ.
It’s also not at all clear what point Friedman is trying to make in mentioning Gödel’s theorem. His comment occurs in a passage in which he aims to explain why ‘[t]he interaction between the observer and the process observed that is so prominent a feature of the social sciences’ is just as much a feature of other sciences. But how does Gödel’s theorem reveal any such interaction? The best answer I can come up with is something like the following: Gödel’s theorem shows that any formal system for arithmetic contains an unprovable statement, which means that there could be models of such a system in which that statement is true and others in which it is false. In recognising it as true when it occurs in the system, we must therefore have in mind some particular intended model – presumably the natural numbers. Thus our (‘the observer’s’) intentions play some role in determining the truth-values of statements contained in the system. But it is debatable whether that really is the moral we ought to draw from the theorem, and in any case Friedman says nothing like this.
This is pedantry, I know, but if you want to know my less niggling disagreements with Friedman you’ll have to enroll on my course!