I wish to start a discussion on these topics:
- Is there any difference between the methodology of physics and mathematics?
- Who the hell is Bourbaki? Is there anybody out there who cares?
- Who the hell is Debreu? Is there anybody out there who cares?
Let us consider each of these questions in turn:
Nicola Giocoli denounces “economists’ decision to pursue the mathematicians’, rather than the physicists’, route.” The way he talks, you would think that physicists and mathematicians spit at each other as they pass in hallways, so acrimonious is their methodological dispute. Yet I have studied both subjects in depth and I do not recall any conflict. This recent paper includes several examples of the work of physicists that fly in the face of Giocoli’s thesis.
If Euclid and Newton were resurrected and brought together, would there be any dispute between these two founders over method? Are Newton’s laws of motion not an axiomatic system in the same spirit as Euclid’s geometry?
I call bullshit on the idea that there is any difference between the methodology of physics and mathematics!
I have a degree in mathematics and, while I remember hearing my professors mention the name David Hilbert, I am sure that I do not recall any mathematician paying tribute to Bourbaki. It was only after I published Axiomatic Theory of Economics in 1999 that I heard the name Bourbaki, and then only from economists. With spittle flying, they accuse anybody who employs the axiomatic method in economics of being a follower of this person/committee or whatever the hell it is. My response was, “Who?”
I call bullshit on the idea that Bourbaki is anything but a whipping boy for economists!
I minored in economics (1992) and yet I am sure that I never once heard the name Debreu. It was only after I published Axiomatic Theory of Economics in 1999 that I heard of Debreu. People who had not read past the title were accusing me of being a follower of this guy, who published in 1959, forty years earlier. I was told that he personifies mainstream economics. I responded, “What does the word mainstream mean if it is possible to get a minor in the subject without having ever heard of Debreu?”
I call bullshit on the idea that Debreu represents mainstream economics!
It is a rite of passage for mainstream economists (in the literal sense of the word; e.g. the 99% majority) to dig up Debreu’s moldering corpse and stick yet another knife in its skeletal ribs. Giocoli should get a Nebula Award for his use of the header, “Beware the Underdog.” This is a stunningly inaccurate appellation for the editor of the Journal of Economic Methodology! Yet Giocoli is actually a moderate. He writes:
With the benefit of hindsight, can we be so sure that our old pal Boccardo would have placed Hilbert in his black list of the supporters of a purely formal view of mathematics in the social sciences?
The Journal of Economic Methodology is enforcing a much weaker blacklist than that of the Journal of Philosophical Economics. Their mission statement makes it clear that it is the axiomatic method they blacklist, not just specific references to any particular mathematician:
This journal eschews monolithic perspectives and seeks innovative work that is intellectually pluralist.
Deirdre McCloskey is furious that Giocoli made a concession to Hilbert, as she would blacklist anybody who employs the axiomatic method, regardless of whether they cite Hilbert or Bourbaki. Indeed, it matters not to her what their axioms are; consistency/inconsistency proofs are beyond her ken. It is the method that she despises.
Slaying a straw man, turning “I hate math” into a philosophy and calling a 99% majority “underdogs” is really all that economists have accomplished in the last thirty years. How sad.