The Undecidability of a Computable General Equilibrium - A Contemporary Philosophical Aspect

Undecidability is a longstanding problem in mathematical logic and computability theory. Gödel, Turing, Church, Tarski and others delved into concerns and issues surrounding an algorithm capable of providing a correct decision when presented with a binary option. The article will first present different aspects of this problem and proceed to analyse the issue in the context of economic theory. Ever since economic science set itself the task of solving the recursive computability problem of a general equilibrium point, engaging the minds of scholars from Walras, Pareto, and Lange to Hayek, Arrow, and Debreu, to name but a few, the area has been the focus of much research. Kumaraswamy Vela Velupillai’s significant work has recently pointed out that the strictly constructive mathematical application of Uzawa Equivalence Theorem, successfully used as scaffolding for various economic models (CGE, DSGE, ABE) to induce a “constructed” equilibrium point, rests on the assumption that lead to its (algorithmic uncomputable) undecidability. Reliance on Zorn's Lemma (Axiom of Choice) to resolve the undecidable suggests convergence, deep implications and consequences also for contemporary philosophy. Therefore, the second part of the paper will shift the object of knowledge to the contemporary political philosophy of Alain Badiou – his life’s oeuvre proposing the “mathematics is ontology” axiom. Endorsing and innovatively reapplying his formalization – encircling the concept of undecidability, and simultaneously complementing it with the use of ZFC set theory, especially rethinking the use of the axiom of choice in Badiou’s theorizing – the article will try to show that the economic general equilibrium theory necessarily proceeds, echoing Badiou, with a decision of a subject, pushing the alleged subject-less scientificity of general equilibrium economics into an ethics of political economy. In turn, the paper will conclude that such an outcome can be directly linked to the political and ideological dimensions of presumably “neutral and objective” means-to-an-end economic theorizing.