Addendum to SCIOD 4: Liar's Paradox

Gödel's Theorem illustrated with regard to Say's Law and the Theory of the Lump of Labour:

1. "...a fallacy long recognized by economists as being especially pernicious. It is based upon the old exploded 'lump of labor theory'—the theory that there is a limited amount of work to be done. The truth is, of course, that every worker turning out a salable product thereby automatically generates a demand for other products, and thus sets others to work."


2. "The theory of a wage-fund and that of a 'lump of labor' naturally cohere, and there seems to be as much truth in one as in the other."


3. "Mill's successors rejected his wages-fund theory but overlooked the fact that Mill's refutation of Malthus depended on it." -- Keynes


4. "Of all the opinions advanced by able and ingenious men, which I have ever met with, the opinion of M. Say, which states that, Un produit consommé ou detruit est un débouché fermé appears to me to be the most directly opposed to just theory, and the most uniformly contradicted by experience." -- Malthus

Daniel R. Fusfeld (1980) "The Conceptual Framework of Modern Economics."  Journal of Economic Issues, 14, 1, pp. 7-8:

Gödel's theorem offers a profound challenge to the theory of knowledge on which logical empiricism is based. Unprovable propositions compromise the completeness of theoretical models. The results depend on the assumptions made about the unprovable propositions, and since those assumptions cannot be proven to be correct (or incorrect), the results must also be unprovable. If investigators try to avoid assumptions by using casual empiricism as the foundation for their unprovable propositions, they will then find themselves testing their hypotheses with the empirical data from which their casual empiricism was drawn, and the argument becomes circular. The only alternative is to leave the entire system open and unprovable through pure assumption or faith. The knowledge derived from formal axiomatic models must be imperfect, subjective, problematic.  

Gödel's theorem has had little impact on economic method, however, and has not been discussed by economists [Sandwichman: prior to Mirowski]. They have always used the ceteris paribus assumption to close their models. The embarrassing presence of an undecidable proposition can be avoided by inserting at any convenient point in the chain of deductive reasoning the simple assumption that "everything else remains the same." This procedure closes the model at that point and allows the remaining axiomatic model to be logically complete -- qualified, of course, by the "as if" assumption made when "everything else remains the same." This procedure was traditional in economics long before the epistemological problems raised by Gödel's theorem were recognized. Economists have been able to proceed as if Gödel had never lived.

"Gödel's Theorem seems to me to prove that Mechanism is false, that is, that minds cannot be explained as machines." J. R. Lucas (1961) "Minds, Machines and Gödel." Philosophy, 36, 137.