The purpose of this paper is to clarify the presuppositions implied in a recent debate about the possibility of economic planning using computing models and to provide additional arguments relevant to the economic calculation debate.
Recalling the fundaments of the classical debate on economic calculation (L. von Mises in 1990, O. Lange in 1936, 1937) and using Cantor's theorem from the set theory the arguments proposed by Robert R. Murphy are reformulated and refined, sustaining the thesis that, in an economic system based on collective forms of property, the central planner must necessarily resort to an infinite uncountable list of prices.
The paper provides additional arguments supporting the thesis that computation in a planned economy implies computation with infinite uncountable domains. In addition, this paper rejects the objections raised by some earlier researchers in 2007 in response to Murphy's theses.
The possibility of computation and calculation in an economic system is of great practical importance. Institutional settlements and policies are not indifferent to the economic calculation problem. Different institutional settings can hinder the very possibility of economic calculation and rational allocation of resources. From this perspective, the conclusions of economic calculation debate are crucial. The economist's and philosopher's criteria used to define institutions and policies must take into account this important question of the possibility of computation and calculation in an economic system.
The paper is of value in providing additional argumentation concerning the economic calculation debate.
