That said, I think real research economists know the meaning of a model. My concern is more with people who take Econ 115, stop there, and start screaming “markets will solve all our problems!” or “government regulation is the only answer!” Silliness.

Similarly, I have always found it funny that “the economy” (reified, because reifying abstractions may be terrible intellectual method, but it makes for great politics, c.f. the war on terror) is always a huge issue in elections. Perhaps I really am the only one who doesn’t understand precisely what politicians mean when they talk about “the economy,” but I highly doubt it. They imply, of course, that they mean each individual voter’s economic well-being (again, because such an implication makes for good politics), but of course that’s not what economic policy necessarily addresses. How many voters really have a deep understanding of the meaning of mortgage rates, unemployment, or inflation? Given the number who fall prey to various mathematically fallacies, I’d say not many.

Furthermore, about Chaitin, its been said that the majority of mathematicians never cite an axiom once in their work. There is plenty of work left to be done in even the simplest axiomatic systems, just as Schoenberg once said there was plenty of music left to be written in C major. One can work in the analog of C major or 12 tone serialism, and one chooses based on which produces what one considers nicer results. I would also say that we pick our axioms based on what theorems we want them to prove (e.g. Zermelo’s use of the axiom of choice to prove the well ordering theorem.). We already have intuitions of how we want things to behave, and the axioms we choose reflect this. There is nothing arbitrary, and it is indeed the theorems which our axioms can prove that are the final goal.

1) Mathematics is a game we play. The work of mathematics is the construction of arbitrary definitions (axioms) of abstract structures, and we then prove theorems that tell us how these structures relate.

2) Some axioms are true (in a transcendent way outside of any logical system) and some are false.

Gregory Chaitin, among others, has pointed out that the real work of mathematics is not that of proving theorems from axioms, but of deciding which axioms to accept.

I also have quibbles with your objection to blending form and content, but that’s the subject for a much longer conversation.