ssrn-id930660 - ESHET Ninth Annual Conference (Stirling,...

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ESHET – Ninth Annual Conference (Stirling, June 9-12, 2005) B LANQUI L ECTURE In the sign of the axiomatic method: mathematics as the role model for neoclassical economics Nicola Giocoli * §1. Beware the underdog <<Mathematical analysis may deal with economic issues, like with any other scientific issue, in two different ways. The first is the method that I would like to call formal , by using which the analyst does not care at all of the intrinsic truthfulness or falseness of the theorem that he is willing to demonstrate, nor does he bother himself with investigating whether the problem’s data are based upon real or hypothetical foundations, as his only goal is that of replacing the involved and inexact forms of ordinary language with the simple and exact statements of mathematical language. On the contrary, the other method, which we can call objective , never satisfies itself with dressing up with a rigorous formula any concept whose reality and nature have not been ascertained beforehand, but rather it makes analysis subservient to the search of truth and its demonstration. The difference between these two systems is the same as that between nominalism and realism, between a vane science of words and a true and positive philosophy of things.>> <<Deductive reasoning about social phenomena invited the use of mathematics from the first. Among the social sciences, economics was in a privileged position to respond to that invitation, for its two central concepts, commodity and prices, are quantified in a unique manner, as soon as units of measurement are chosen. … As a formal model of an economy acquires a mathematical life of its own, it becomes the object of an inexorable process in which rigor, generality and simplicity are relentlessly pursued. … An axiomatized theory first selects its primitive concepts and represents each one of them by a mathematical object. … Next, assumptions on the objects representing the primitive concepts are specified, and consequences are mathematically derived from them. The economic interpretation of the theorems so obtained is the last step of the analysis. According to this schema, an axiomatized theory has a mathematical form that is completely separated from its economic content. If one removes the economic interpretation of the * Department of Economics, University of Pisa, via Curtatone e Montanara 15, 56126, Pisa, Italy; e-mail: I wish to thank the President and the members of the executive board of the ESHET and the organizers of the Stirling conference. My special gratitude goes to the three persons whose friendship and scholarship have accompanied me along the years: Marco Dardi, Riccardo Faucci and Alberto Zanni. The financial support of MIUR PRIN 2002 “Mathematics in the history of economics” is gratefully acknowledged. I bear of course full responsibility for this lecture’s content.
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This note was uploaded on 10/24/2011 for the course SCIENCE PHY 453 taught by Professor Barnard during the Winter '11 term at BYU.

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ssrn-id930660 - ESHET Ninth Annual Conference (Stirling,...

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