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:
giocoli@mail.jus.unipi.it
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.