Thursday, August 7, 2014

Barkley Rosser Cuts Gödel's Mustard

It appears the Sandwichman has inadvertently stumbled onto Professor Rosser's inherited PRIVATE intellectual property:
"I do not disagree with your main point in this point, but please do not join the long list or [of] ignorami who spout off about Gödel inappropiatel[y], and, sorry, this post does not cut the mustard." 
Having read somewhere that Gödel's theorems are often referred to in the singular, I committed the unpardonable faux pas of assuming that I, a mere ignorami, could do the same. I also cited some folks views on Gödel that seemed reasonable to me. I must admit to having skimmed parts of a couple of articles by Professor Gödel Rosser that didn't seem wildly out of sync with the main point of my point post.

One of those articles was a review essay on a book by Weintraub on the Evolution of Mathematical Economics. The other article was titled "Belief: Its Role in Economic Thought and Action" and again I didn't see anything there that flatly contradicted my argument. Here's some of what Professor Rosser wrote there:
In the face of this Kuhnian critique, many have attempted to salvage something of the positivist apparatus. A strong response is Friedman’s emphasizing the predictive content of a theory. But a serious problem for economics arises when we see the severe disagreements over appropriate econometric techniques and methodologies that occur. It is rarely unequivocal that one model predicts better than another. 
A widely discussed middle ground was staked out by Lakatos (1970) using the concept of the 'methodology of scientific research programs.' Such a program is judged on its 'fruitfulness' in generating interesting and useful questions in a progressive manner. Within the program, positivist rules apply. But the program as a whole is a paradigm in Kuhn’s sense, ultimately judgeable only by some higher level criterion of belief. Within the program, a 'hard core' set of axioms must be accepted without question and are not testable by positivist methodologies, much like the undecidable statements in a Gödelian logical system [emphasis added]. The hard core is protected by a 'protective belt' which fends off arguments with a 'positive heuristic' that sometimes turns an attack into supporting evidence.
So where does this leave economics? At the level of crude empiricism of the instrumentalist sort, a remnant of positive economics remains. 
The problem becomes more serious in moving from raw data to generalizations and to theory. Encountered are all the issues of paradigm conflicts and the ultimate unjudgeability of scientific research programs. Despite all efforts at mathematical abstraction, normative aspects become very important in these conflicts and judgments. There is the basic question: do economists make unrealistic assumptions to generate predictions which satisfy their normative prejudices? 
A notorious example from the perspective of many non-economists is the assumption made in standard neoclassical economic theory of 'rationality' on the part of economic agents. This assumption is that people know what they want, that what they want is internally consistent, and that they act to get what they want to the best of their ability on the basis of the information available to them. But there is considerable evidence that people do not always know what they want, that even if they think they do that it is frequently internally inconsistent, and that their behavior reflects these inconsistencies.
I invite and welcome substantive criticism. I don't consider "you're over your head." "do not join the long list of ignorami," "this is family for me" or "this post does not cut the mustard" to be substantive arguments. I'm flattered to hear that the Barkster does not disagree with my main point and would dearly love to read elaboration on that, too!

Your call, Barkley.

3 comments: said...

Gosh, S-man. Guess I am hoisted on my own petard and can't even cut the mustard myself... said...

Having conceded that you have caught me in at least somewhat of a contradiction, not to mention being pompous, I will note a few points regarding what you quote by me here.

One is that I said that some of these axioms are "like" Godelian ones. That is not the same as saying that the proof of their undecidability uses the same arguments that Godel used in his theorems. Thus, while they may be "like" Godelian arguments, they are not strictly Godelian arguments, certainly not in the way Fusfield argues in another of your posts. This of course does not save me from the implicit charge of hypocrisy in citing Godel myself while having argued that he gets brought up too frequently and often inappropriately, which I still think is the case.

The other point, not unrelated, is that for most questionable axioms used by standard economists, the best way to criticize them is to show that they are empirically false, or at least do not hold widely empirically. This is most certainly not using Godelian arguments, either directly or somewhat indirectly.

Sandwichman said...

Fair enough, Barkley. I would agree with your position that this is a matter of analogy. I'm not convinced that Fusfeld makes the strict case, either, though. He's saying that Godel's theorem(s) "offer a profound challenge" and "raise epistemological problems," which they would do even by analogy. As I point out in my "math anxiety" post, it is only reasonable to take the Euclidean/non-Euclidean economics distinction metaphorically, too.

What do you mean by the "best" way to criticize questionable axioms? Intellectually purest? Most persuasive? Most enduring? I would agree that the Godel analogy is not the best but I don't think empirical evidence counts for much with people whose minds are made up.

My own hypothesis is essentially an ethnographic one and I don't have any expectation that my criticism will change anybody's mind. I just think it needs to be "on the record" for whatever purpose, I can't be sure. Maybe just to ease the troubled minds of a few other witnesses.