A Primer on the Tools and Concepts of Comutable Economics.?

Abstract

Computability theory came into being as a result of Hilbert s attempts to meet Brouwer s challenges, from an intuitionistc and constructive standpoint, to formalism as a foundation for mathematical practice. Viewed this way, con- structive mathematics should be one vision of computability theory. However, there are fundamental di¤erences between computability theory and construc- tive mathematics: the Church-Turing thesis is a disciplining criterion in the former and not in the latter; and classical logic - particularly, the law of the excluded middle - is not accepted in the latter but freely invoked in the former, especially in proving universal negative propositions. In Computable Economics an eclectic approach is adopted where the main criterion is numerical content for economic entities. In this sense both the computable and the constructive traditions are freely and indiscriminately invoked and utilised in the formaliza- tion of economic entities. Some of the mathematical methods and concepts of computable economics are surveyed in a pedagogical mode. A digital economy is considered embedded in an information society and speculative methodolog- ical, epistemological and ontological notes suggest a theory of the information society.