**Paul Samuelson Cleaning Out The Stables**

Paul Samuelson Economic

It is often said that PhD dissertations come and go, but that some live on for ever. The latter is certainly the case with Samuelson's prize-winning dissertation, completed in 1941 at Harvard, and published as Foundations of Economic Analysis in 1947. Samuelson's own affection for this piece of work has not diminished through the years, not surprisingly, since it remains a classic statement of the mathematical foundations of economic theory. It is worth noting here that Samuelson has cautioned against the view that accomplished mathematics necessarily implies accomplished economics. However, the presentation of an economic argument in laboured prose, instead of simple mathematical concepts, involves 'mental gymnastics of a peculiarly depraved type' (1947).

The objective of Foundations was to cleanse economic analysis of errors perpetuated through economic theorems which are imprecisely formulated and operationally meaningless. This is the crux of Samuelson's scientific work and since controversy has surrounded the notion of operationally significant (i.e. empirically verifiable) theorems, it will be useful to examine this issue in some detail a little later on. Undeniably, the mathematical revolution swept all before it. Instruction at undergraduate and graduate level in the USA and UK has increasingly emphasised a knowledge of differential and integral calculus and linear algebra as a prerequisite for the understanding of micro-economic and macro-economic theory. Although a substantial time lag can exist, this trend reflects the increasing use of mathematics in articles in professional economic journals, particularly American ones. The intellectual osmosis that has brought this about is clear: the current generation of professors and lecturers were schooled by mathematical revolutionaries such as Samuelson and, accordingly, conduct their own teaching and research in the lingua franca of mathematics. Hence, each new cohort entering the economics profession exhibits more and more sophisticated technical skills in mathematics (and statistics), thereby increasing the average level of competence and likelihood of mathematical methods being employed. The desirability of this state of affairs can be called into question on a number of grounds:

(i) Mathematical symbolism may disguise inadequate economics. Samuelson holds no brief for mathematical skills that are not accompanied by sound economic reasoning.

(ii) Those economists who, for reasons of age, fear or lack of opportunity, have not acquired mathematical fluency, have been confronted with serious problems of technical obsolescence. Insofar as this has resulted in such economists seeking sanctuary in the less technically demanding regions of the discipline, the breakdown of communication between the mathematically and non-mathematically inclined has intensified, (iii) The extent to which mathematics imposes rigour rather than relevance, has been a much-debated question in the 1970s (Leontief, 1970; Gordon 1976). It is argued that the rigour of sophisticated mathematical formulation is inappropriate to a discipline such as economics, where the datum is incomplete and experimental methods are unreliable. This contrasts with the natural sciences where the 'hardness' of data and consistency of experimental method, permit the sophisticated use of mathematics.

Samuelson is well aware of criticisms of this kind and his work constitutes a spirited defence of the role of mathematics in economics. Mathematical formulation, argues Samuelson, can clarify the essential structure and properties of a model or argument. Keynes, with his suspicion of mathematical economics, avoided the mathematical presentation of complex ideas in the General Theory of Employment, Interest and Money (1936). In contrast, Samuelson reasons that subsequent mathematical interpretation probably assisted Keynes as much as anybody in understanding the significance of this book. Unlike the work of many mathematical economists, Samuelson's writings combine mathematical analysis with geometric and verbal clarity in such a way as to keep open (in all but his most recondite papers) the channels of communication to readers with little mathematical ability. Concerning the question of rigour and relevance, Samuelson has argued that the rigour of mathematical argument is appropriate insofar as it facilitates the development of propositions or theorems in economic theory that are meaningful in the sense of being empirically refutable. Unlike Physics and Chemistry, where the logic of scientific procedure is well established, economics has need of careful methodological discussion. As far as Samuelson is concerned, it is vital that the classification of procedures accompanying the construction of operationally meaningful propositions in economics, should be as clear and unambiguous as possible.

Insofar as mathematics, as language, can sharply define such propositions, it is fully justified. Samuelson understands that the refutation of these propositions involves considerable philosophical problems as well as, perhaps, only being possible under certain ideal experimental conditions. He, himself, has not entered into the world of econometrics in order to specify suitable tests that might establish the relevance of the rigorous propositions he has advanced; by responding to intellectual comparative advantage, Samuelson is prepared to practise what he preaches! Although this has, undoubtedly, disappointed those who, with regard to his stature as an economist, have enjoined him to enter the statistical fray, Samuelson's failure to satisfy such aspirations cannot diminish the importance of his contributions to the development of a logical and consistent scientific method in economics.