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ideal-type concepts which they define, and then on the basis of these definitions they construct a priori the whole framework of their theorems and proofs. After that they go back to experience not to confirm but to apply their conclusions.’ This is how geometry deals with triangles, circles and so on, and reality confirms its definitions and demonstrations only approximately, and ‘yet reality admits of a very wide and fruitful application of these propositions’. Following the same procedure, the pure theory of economics ought to take over from experience certain type concepts, like those of exchange, demand, market, capital, income, productive services and products. From these ... [it should] ... define ideal-type concepts in terms of which it carries on its reasoning. The return to reality should not take place until the science is completed and then only with a view to practical applications. In other words, pure economics could investigate the concept of a market economy even though there may be nothing in the world which may strictly speaking be called a market economy and the conclusions of pure economics, like those of geometry, need not be tested. Walras regretted ‘the absence of philosophy among French economists which offsets and nullifies’ their intellectual qualities of ‘clarity and precision’. 7.4. Pareto: equilibrium as hypothesis Writing of Walras and Pareto, Schumpeter said: Their common ground was confined to pure theory and specifically to Walras’ equations of equilibrium. But in every other respect they were as different as two men can be, and even their companionship in arms in the fight for mathematical economics and Pareto’s obligation to Walras in the matter of the Lausanne professorship did not prevent their deep-seated mutual dislike from asserting itself or even from spilling over in conversation with third persons. While their pure theories are cast in the same mould, their systems of thought taken as wholes and their visions of the social process are not. And all those economists who are not disposed to neglect a man’s philosophy and practical recommendations completely  ... THE HAND BEHIND THE INVISIBLE HAND 78 will, for this reason alone, consider the Paretian structure to be something completely different from that of Walras. Although the word Walrasian is nowadays applied quite generally to an important segment of neoclassical economics, the word Paretian would be more accurate as a description of the most usual form of this kind of economics. That the Walrasian and Paretian ‘structures’ are ‘completely different’ and stem from quite different ‘systems of thought taken as wholes’ is a matter which is not easy either to set out or to comprehend. Nevertheless, some indication of the difference will be attempted in this section. There was first of all Pareto’s disdain of Walras’s preoccupation with social policy and with economics as not only a pure science, but also an art and a moral science. As Schumpeter again puts it: Walras presented his immortal theory in the garb of a political philosophy that is extra-scientific in nature and, moreover, not to everyone’s taste. I am afraid that there is no better way of conveying what that philosophy was than to call it the philosophy of petty-bourgeois radicalism. He felt called upon to preach an idéal social that hails from the semi-socialist French writers of the first half of the nineteenth century or, as we may say with equal justice, from utilitarianism. Schumpeter was merely unsympathetic towards such an outlook; Pareto held it in utter contempt. The man who spoke of ophelimity to avoid the possible moral connotations of utility simply despised any talk of welfare or the common good. That Pareto became (once more in Schumpeter’s words) ‘the patron saint of the “New Welfare Economics” ... [and] ... came to render a service to a cause with which he was – or would be – completely out of sympathy is not without its humor’. However, this difference of temperament was only one manifestation of a much more deep-seated discord. Walras and Pareto were separated by the ancient philosophical divide between realism and nominalism, in their case between Walras’s rationalism and Pareto’s positivism. One cannot avoid touching on the often abstruse and difficult ideas involved in this schism if one is to understand how the general equilibrium analysis of Walras and even of Smith has become something very different in this century despite maintaining a resemblance in its outer form. What is important in our context is that realists, in the sense in which they are contrasted with nominalists, are committed to the view that significant scientific conclusions may be drawn from what others would

The Hand Behind the Invisible Hand