This brief post is in response to my exasperation upon reading this blog post from Mark Perry, “In a Letter to Congress, Some Economists Refute the Law of Demand and Propose a 35% Increase in the Minimum Wage to Stimulate the Economy“. Read it and weep. All I can do is shake my head in disgust with regard to the present state of mainstream economics. This also led me to think about how economics differs from mathematics.
In math, once the proof of a theorem has been widely accepted by the mathematics community, it is set in stone. A valid proof is composed of an unbreakable chain of logic that links the first and last statements of the proof. Since math is a human endeavor, there are occasions where proofs have been accepted that were later rejected. However, mathematicians are the most skeptical and paranoid people in the world. When a new proof is presented, the first instinct of the community is to search for a mistake. Also, mathematicians are haunted by the possibility that there are mistakes in some of the foundations of the discipline. Thus, the constant urge to strengthen and verify proofs that form the superstructure of all of mathematics and serve to eliminate erroneous proofs.
While it is certainly true that there exists multiple proofs for many theorems, this does not mean that either the theorem or older proof are incorrect. The fact that mathematicians reprove theorems is part of the continuous error checking of the discipline. It also serves as a means to apply new techniques which can open up new insights.
Let us contrast the situation regarding proofs in math to that of economics. In economics, the same fallacies reappear constantly. The above article about the minimum wage prompts yet another restatement about the law of supply and demand. The fallacy that victorious wars create prosperity prompts yet another restatement of opportunity costs. Etc, etc, etc. Fundamental truths are constantly ignored and must be restated again and again. If there is any reason to refer to economics as the “dismal science”, this is it.
While mathematics proceeds from triumph to triumph, economics is mired in fallacies that were exploded decades ago yet still persist.