Formal limitations in economic theory and the alternative set theory AFA- + AD + AC

TOHMÉ, FERNANDO

Denver, CO

Otro; Graduate Colloquium, Department of Mathematics, University of Denver; 2006

Department of Mathematics, University of Denver

Many authors in the discipline as well as outsiders have claimed that the main results from Mathematical Economics are far removed from real world phenomena. A more elaborated version of this position is that one of the main reasons for this unrealistic stance is the use of the wrong formal tools. So, for example, it has been pointed out that the computability of choice functions as well as the existence of economic equilibria and of states of the world may not be ensured in general if the assumed set theory is ZFC. While we agree in that these claims are true up to certain point, we will show that there exists a very natural form of overcoming the formal limitations of contemporary economic theory. A switch to an alternative set theory helps to get rid of some of the negative results. While this procedure seems a facile form to solve analytical problems, we think that it may have a legitimate importance for economic theory. In fact, alternative set-theoretical frameworks convey different intuitions about how agents behave when solving problems. We end this paper discussing the advantages of AFA− +AD+DC as an alternative set-theoretical universe for economic theory.ZFC. While we agree in that these claims are true up to certain point, we will show that there exists a very natural form of overcoming the formal limitations of contemporary economic theory. A switch to an alternative set theory helps to get rid of some of the negative results. While this procedure seems a facile form to solve analytical problems, we think that it may have a legitimate importance for economic theory. In fact, alternative set-theoretical frameworks convey different intuitions about how agents behave when solving problems. We end this paper discussing the advantages of AFA− +AD+DC as an alternative set-theoretical universe for economic theory.AFA− +AD+DC as an alternative set-theoretical universe for economic theory.