Ekonomi TEK
Yazarlar: Hasan ERSEL
Konular:İktisat
Anahtar Kelimeler:Axiomatic approach,Debreu,Formal axiomatic approach,Von Neumann,Soft axiomatic approach
Özet: The modern axiomatic approach was developed by David Hilbert, the prominent German mathematician of the last century, who first applied it to geometry and then to physics. His concept evolved over time, exhibiting considerable differences between its application in mathematics and in physics. Motivated by his deep interest in demonstrating the consistency of mathematics, Hilbert decided on pursuing the so-called “formalist axiomatic approach” for that field. However, realizing that this strict interpretation would not do for use in physics, Hilbert came up with a more relaxed scheme for the latter, which was later termed the “soft axiomatic approach.” Hilbert had an enormous influence on the scientific community, and his axiomatic approach was adopted widely throughout the mathematics community. This was notably due to Nicholas Bourbaki’s work, which drew the attention of researchers involved in physics and other sciences, including economics. Economists learned of the axiomatic method through the publications of three distinguished scientists: John von Neumann, Gerard Debreu, and Kenneth J. Arrow. Following Bourbaki’s formal axiomatic approach, Debreu aimed to formalize Walrasian general equilibrium theory and proved its consistency. Von Neumann and Arrow, on the other hand, used the same approach to develop completely new fields of research, i.e., game theory and social choice theory, respectively. Despite the similarity of their applications of the axiomatic method to economics, von Neumann distinguishes himself from both Debreu and Arrow with his criticism of the axiomatic approach’s use in science in general. Despite never having explicitly referred to economics, he warned of the vulnerability of the formalist axiomatic approach to capture by what he called the “aesthetics of mathematics.” Von Neumann’s solution was to introduce an explicit and effective trade-off between the strict formalism of the mathematical reasoning and the requirements of the scientific field of research. Obviously, this requires rather strong cooperation between the scientist and the mathematician.