DIARIO DE CAMPO N° 03 Área : Comunicación

It is maintained that this thesis is concerned with the methodology of economics and that it also has attributes that are included in the epistemological studies of mathematics and of the social sciences (cf. Cheix, 1996). By methodology, we mean the study of the methods used in a particular science and the problems occurring in a science. By epistemology, we mean the philosophical study of scientific knowledge, equivalently named the philosophy of science. The kind of epistemology this thesis claims to be relevant to is what Piaget (1976) calls 'intra-scientific' epistemology. It aims neither at being normative, nor at being unifying. It is based on the study of problems occurring in a particular science and it treats general epistemological questions only in connection with these problems. In this thesis however, we shall focus on specific problems, and only mention general epistemological questions. It is also maintained that neither methodological studies nor epistemological studies can avoid considering the history of science. This is a way to cast light upon what, in scientific practice, is based on cultural habits and what is not.

The subject matter of the thesis is mathematical economics. The first topic it analyses is mathematical economics in the theory of the Neo­ classical school of economic thought. This school has its roots in the late 19th c and prevailed in the 20th c, both within academic economics and, generally

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speaking, within Western ideology. The second topic analysed is mathematical economics, considered within in the 20th c. scientific practice of model-building. The originality of the thesis does not lie in its topics, but in the way they are approached. This approach is a critique of the use of mathematical formalism in economic theory. It is an epistemological- methodological critique that uses a semiotic framework. It is neither a teleological critique of economic science nor a critique that procédés from a Political Economy perspective. The first part of the thesis is concerned with describing both this approach and the methodology of the thesis.

A standard approach to the use of mathematical formalism in science is that of an important movement in 20thC. philosophy of science, namely logical positivism. This movement has many facets and we can only claim to convey its views in connection with our subject-matter. From a positivist point of view, the use of logico- mathematical formalism, as opposed to vernacular language, is one characteristic of a true science. In so far as a theory is formal, its logical cogency can be assessed. In so far as it is grounded on arithmetics and it formulates equations and inequalities, its statements are quantified. They can be assessed

empirically, with the aid of statistics in particular.

Logico-mathematical formalism thus guarantees the

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objectivity of both the reasoning and its results. This approach tends to focus on the role of mathematics as a conceptual and logical tool rather than as an empirical tool, as in statistics.

In this thesis, another approach to the use of mathematics in science and in economics in particular is developed. We follow Gilles Gaston Granger (cf. Bibliography) and Giorgio Israel (1996) and understand the subject-matter, namely mathematical economics, as

the mathematization process of economic science. By

mathematization, we mean the historical and epistemological relationships between the "mathematical form" and the "economic content" (cf. chapter 2, Section 1

).

This approach leads us to adopt an 'external' perspective on the history of mathematical economics for the reasons that follow. Firstly, the mathematical formalism used in economics has sometimes developed initially in other fields (cf. chapter 2, note 6) such as physics (cf. Mirowski, 1989), commercial life (see Bicquilley, 1804) and political science (cf. Armatte, 1991; Perrot, 1992). By 'external' perspective, we mean (cf. chapter 2, section 1) that we replace the history of the use of mathematical formalism in both the history of science in general, and in the history of mathematics. Authors who have adopted a similar approach to the history of economic thought are; Armatte (1991, 1995), Ingrao et al(1987), Israel (1996),

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Mirowski <1989, 1990, 1991), Mirowski et a l (1994), Perrot (1992), Punzo(1991), and Zerner (1993). Authors who adopt an 'internal' approach are: Morgan (1990), Theocharis (1961, 1983, 1993), Stigler (1954, 1964), and Zylberberg (1990). The survey of the academic corpus available on the history of mathematical economics shows first that there are not many sources on the subject (e.g. Theocharis, 1961, 1983, 1993; Baumol et al, 1968; Darnell, 1991a, b, c, d, e, f ; cf. chapter 1) and that they proceed from 'internal' historical approaches. Consequently, any general historical or epistemological statement on the development of mathematical economics must be handled with caution. Secondly, the survey of this corpus also shows that contemporary historians and epistemologists challenge the historiography of economic thought (cf. chapter 1, section 1).

From an epistemological point of view, approaching mathematical economics in terms of mathématisation does not lead us to contrast vernacular- unscientific language and mathematical-scientific language as sharply as in a positivist perspective. In economic practice, vernacular language is indeed used to relate mathematical symbols to economic ideas. This also applies to mathematics, since mathematical texts also contain vernacular language. Taking this position is also a way to avoid the layman's paradoxical position, that on the one hand, economics is not a "true" science, but on the other hand, it is scientific

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because it uses mathematics intensively. Our keeping a distance from positivist approaches to the subject matter does not contradict general concerns emerging from the literature in the epistemology and the methodology of economics (cf. Cheix, 1996, section 2 and section 3 ). One concern is that economic science and standard epistemological categories are not adequate to one another. One explanation is that standard epistemology, logical positivism included, has been strongly influenced both historically and sociologically, by the study of problems typical to physics. Our position on the epistemological status of mathematical formalism explains our choice of semiotics rather than formal logic for the study of the structure of two Neo-classical texts in mathematical economics upon which we focus, namely Jevons' Theory of Political Economy and Debreu's Theory of Value (cf. chapter 2). Because the semiotic approach to "meaning" strongly differs from that of the positivists, the semiotic perspective is explained in some details (cf. chapter 2, section 2 and Cheix, 1996, section 4).

To the extent that this thesis is concerned with the 'external' history of mathematical economics, it places the two topics it deals with (the use of mathematical formalism both within the Neo-classical tradition and also in connection with model-building), in the history of science (chapter 3; chapter 6, section

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1; chapter 9, section 1) and in the history of mathematics (chapter 4; chapter 6, section 301). In so

far as it is concerned with the

methodological/epistemological analysis of the use of mathematics in economics, first it defines the mathematics which are and have been used in economics (chapter 5, section 301; chapter 6, section 201; chapter

6

The reader may find that the foundational part of the thesis is extensive. This is justified because we are taking an unorthodox philosophical view on mathematical economics and also because comprehensive historical sources on the subject are lacking. The reader might also find that such philosophical authors such as Karl Popper, Thomas Kuhn, Imre Lakatos, Larry Laudan etc. are not referred to as often as the

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reader might expect since it is claimed that this thesis is relevant to epistemology. This lack is not a sign of ignorance. It results from the choice to refer to philosophers (e.g. Granger, 1955; Hausman, 1992; Rosenberg, 1983; Morton, 1990, 1993; Van Parijs, 1990) with specific interest in economics rather than in physics or in general epistemology, so as to avoid difficulties to which we have already alluded.

PART TWO

MATHEMATICS AND THE NEO-CLASSICAIi