The General Impossibility of Neoclassical Economics

AutorBen Fine
Páginas1-22
Ensayos Revista de Economía–Volumen XXX, No. 1, mayo 2011, pp. 1-22
Ben Fine
Fecha de recepción: 28 IX 2010 Fecha de aceptación: 22 II 2011
Abstract
This article recalls how neo-classical economics prides itself both on its
mathematical rigour and on the universal applicability of its principles, and
how, on this basis, “economics imperialism” is colonising the subject matter
of the other social sciences. Critics of the mainstream have emphasised the
conceptual and theoretical weaknesses of reliance upon axiomatic
deductivism and methodological individualism of a special type, as well as
denying the image that the mainstream has of itself as emulating the natural
sciences. In a complementary critique, this article demonstrates, by drawing
upon Russell’s logical paradoxes, how results from within mathematics
itself, as opposed to its application, impose unnoticed limitations upon the
scope and consistency of the mainstream.
Keywords: individualism, holism, mathematical foundations.
JEL Classification: B41.
Resumen
En este artículo, se destaca que la economía neo-clásica enaltece el rigor
matemático y la aplicabilidad universal de sus principios; también, el hecho
de que el “imperialismo económico” se ha establecido como tema central de
las demás ciencias sociales. Los críticos de la corriente principal han hecho
hincapié en las debilidades conceptuales y teóricas de la dependencia hacia
el deductivismo axiomático y el individualismo metodológico; al mismo
tiempo, estos niegan la imagen que tiene la corriente neo-clásica de sí misma
Department of Economics, School of Oriental and African Studies, University of London.
Address: Thornhaugh Street, Russell Square, London, WC1H 0XG, United Kingdom.
Email: bf@soas.ac.uk
Thanks to my brother Kit, a leading expert in these matters, for pointing to some relevant
references in the philosophy of mathematics, to Costas Lapavitsas, Roberto Veneziani and
anonymous referees and other for comments on earlier drafts. Originally, there was a
subtitle, “Or Does Bertrand Russell Deserve a Nobel Prize for Economics?”
Ensayos Revista de Economía
2
como una emulación de las ciencias naturales. En una crítica
complementaria, este artículo demuestra, tomando como base las paradojas
lógicas de Russell, cómo los resultados que vienen de las matemáticas en sí,
a diferencia de su aplicación, imponen limitaciones desconocidas sobre el
alcance y la coherencia de la corriente principal.
Palabras Clave: individualismo, holismo, fundamentos matemáticos.
Clasificación JEL: B41.
Introduction
Today, mainstream economics prides itself on its mathematical rigour and
deploys mathematics to an enormous extent as indicative of disciplinary
acceptability, thereby policing the exclusion of other forms of economics to
an extraordinary degree. In the following section, I highlight the extent to
which the use of mathematics has promoted a particular content within
economics, one that has shifted only in its expanding scope of application
since the formalist revolution of the 1950s. This sets the context for the main
goal of this contribution: to assess the extent to which formal problems
within, and not of, mathematical reasoning itself set constraints on what can
be achieved within mainstream economics. In particular, mathematics has
found it necessary to negotiate the consequences of Russell’s paradoxes, laid
out in Section 2. Placing mathematics on sound foundations is found to have
potential implications for, or limitations on, what can be achieved by
mathematics in its applications. These limitations have been totally and
unconsciously ignored within economics despite its heavy use of
mathematics. In particular, as argued in Section 3, for an economic theory
based on methodological individualism, there are severe limitations upon the
extent to which social properties can be consistently addressed – whether
micro can be fully and legitimately extrapolated to macro. This raises
questions over whether what have now become increasingly standard
concepts within mainstream (micro)economics, such as institutions, liquidity
and the state, can be properly or fully addressed given its methodology and
the requirements of mathematical logic. One or other of the latter has to give,
and the final section draws the conclusion that methodological holism needs
to take precedence over methodological individualism if the social is to be
able to be fully addressed in principle, consistently and without limitations.
As misunderstandings have arisen in comments on earlier versions of this
paper, it makes sense to emphasise what it does not seek to do. It does not
seek to resolve Russell’s paradoxes, to provide a contribution to the
philosophical foundations of mathematics (or, indeed, to assert that these are

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