Newton and economic methodology
... Newton had insisted on the certainty of an approach founded on rigorous method. (Westfall, 2008, p. 346)
Like most of his fellow moral philosophers, Hume thought it was worth a try to make all sciences as rigorous as Newtonian physics ... (Redman, 1997, p. 111)
But what is important is that the entire topic had become a scandal in the eighteenth century. If scientific method could institute some degree of order in chemistry, in physics, in astrophysics, in astronomy and so forth, why did we have to be plunged into this dreadful chaos of conflicting opinions, with not a thread to guide us? ... so that nobody is able to institute the kind of order which Newton established in the great realm of nature? Naturally enough, men’s wishes began to move towards the delineation of some simple single principle which would guarantee just such order and yield truths of just such an objective, general, lucid, irrefutable kind as had so successfully been obtained concerning the external world. (Berlin, 2002, p. 9)
So impressive were the accomplishments of Newtonian physics that eighteenth-century philosophers, including the founders of political economy, never questioned the suitability of transferring Newton's methods to moral philosophy. After all, as they saw it, philosophy, science, social science, and ethics were all the same kind of activity. (Redman, 1997, p. 109)
His [Adam Smith’s] method is always the method of Newton, which we have already seen applied to psychology and morals: to attain, by generalization, certain simple truths, from which it will be possible to reconstruct, synthetically, the world of experience. (Halévy, 1960, pp. 100, 494), see also (Hollander, 1977)
For Edgeworth, to apply mathematical reasoning to the science of political economy is to look to mathematical physics to see how mathematics can aid in the construction of propositions within the science. ... In the land of Newton, and in the century of science, how could it be otherwise? (Weintraub, 2002, p. 30)
Walras’s early reading consolidated his boundless admiration for Newtonian astronomy and the solid edifice of classical mechanics, which he regarded as unequaled models of scientific knowledge throughout his life. (Ingrao and Israel, 1990, p. 88)
Now there is simply no doubt that whatever was the source of inspiration for Jevons, Menger and Walras, all three invoked whatever physics they knew to lend prestige to their theoretical innovations. Unfortunately, with the exception of Jevons, that was the physics of Newton, not the physics of Helmholz, Joule and Maxwell; Adam Smith, Ricardo, James Mill and McCulloch had been just as eager in earlier days to invoke the name of Newton to legitimise their theoretical claims. (Blaug, 1989, p. 1226)
Today's economics, in fact, comes closer to using Newton's approach than Smith's did: his system neither strived for logical consistency nor boasted a fancy axiomatic foundation. (Redman, 1997, p. 357)
Could all the phaenomena of nature be deduced from only thre [sic] or four general suppositions there might be great reason to allow those suppositions to be true. (Newton, quoted in Westfall, 2008, p. 642)
This, then, is the Newtonian style:
The Principia begins with an idealized world, a simple mental construct, a “system” of a single mathematical particle and a centrally directed force in a mathematical space. Under these idealized conditions, Newton freely develops the mathematical consequences of the laws of motion that are the axioms of the Principia. At a later stage, after contrasting this ideal world with the world of physics, he will add further conditions to his intellectual construct – for example, by introducing a second body that will interact with the first one and then exploring further mathematical consequences. ... In this way he can approach by stages nearer and nearer to the condition of the world of experiment and observation, introducing bodies of different shapes and composition and finally bodies moving in variant types of resistant mediums rather than in free space. (Cohen, 1994, p. 77)
Economics, too, starts with an idealized world but then it does not move nearer and nearer to the world of experiment and observation but in the opposite direction in order to rationalize an unsuccessful initial idealization. Thus idealization, which is indispensable, becomes counterproductive. There is only a thin line between fruitful abstraction and barren absurdity. To assume that the moon is a mass point is unrealistic but fruitful, to assume that it is made of green cheese is unrealistic but nothing else. Most assumptions of conventional microeconomics fall into the green cheese category.
In the most fruitful applications of mathematics to the physical world, some nonmathematical axioms also enter. The Newtonian system of mathematical mechanics depends as much on the Newtonian laws of motion and gravitation as it does on the axioms of mathematics. (Kline, 1981, p. 469)
It is often said that axioms must be self-evident. This is a slight misunderstanding. Axioms may turn common sense on its head:
We may, therefore, agree with Ernst Mach, who very wisely pointed out that the law of inertia could hardly be “obvious” or “self-evident” since throughout most of recorded history men believed in a quite different law and would have denied the Cartesian-Newtonian inertial principle. (Cohen, 1977, p. 328 fn. 57)
As clueless epigones the social scientists, and economists in particular, borrowed a lot from Newton but did not grasp the Newtonian style. By consequence, it cannot be said that Newton's method has failed in the social sciences. It has never been applied properly but was soon made redundant by Hamilton’s reformulation of rational mechanics (Cohen, 1994, p. 71-75). With this, if anything, the misunderstandings grew even worse (Mirowski, 1995).
The crucial point of the Newtonian style is the undissolvable combination of axiomatics and empiricism. Despite heavy borrowing, this point never got across:
Did anyone ever attempt to found a system of social science or economics on the level of identity with Newtonian rational mechanics or the Newtonian system of the world? In my research I have never found such an example. (…) In the Newtonian system, furthermore, there is no equilibrium, no balancing of contrary forces as in the case of a lever. (Cohen, 1994, p. 61)
An amusing point is that Newton was not Newtonian. He, on the contrary, believed in an evolving world. The world would go into ‘confusion’ and the ‘agent’ (God?) would have to repair it. (Prigogine, 2005, p. 63), original emphasis
According to one widely held viewpoint in the history of ideas, eighteenth-century thought was dominated by the concept of the "Newtonian world-machine." God had been assigned the role of master clockmaker who designed a universe so perfect that it could run indefinitely without any need for divine tinkering. Closer inspection of Newton's own writings shows that he was actually quite firmly opposed to this concept which had been popularized by earlier writers such as Robert Boyle. Newton's objections were both physical and moral: he pointed to the existence of irreversible processes tending to dissipate motion and gravitational perturbations that seemed to threaten the stability of the solar system, and he warned that restricting God to the creation and design of the world while denying His continual supervision was a step on the road to atheism. (Brush, 1976, p. 605)
Equilibrium theorists completely missed the point:
As we shall see, general economic equilibrium theory originated and developed in the context of a project put forward in varying forms by different scholars to repeat Newton’s titanic achievement – i.e., the fulfillment of Galileo’s program for a quantitative (mathematical) study of physical processes – in the field of the social sciences. (Ingrao and Israel, 1990, pp. 33-34), original emphasis
Newton was quite explicit about the difference between theory (hypotheses non fingo) and storytelling (assumptions don't matter):
Those who take the foundations of their speculations from hypotheses, even if they then proceed most rigorously according to mechanical laws, are merely putting together a romance, elegant perhaps and charming, but nevertheless a romance. (Roger Cotes, Preface to the second edition of Newton’s Principia, Newton, 1999, p. 386)
Under the perspective of Newton's methodology, utility maximization, equilibrium, or diminishing returns, for instance, are feigned hypotheses.
According to his [Helvétius's] principle, the only thing which men wish is pleasure, and the only things which men wish to avoid are pains. The pursuit of pleasure and the avoidance of pain are the only motives which in fact act upon men, as gravitation and other physical principles are said to act on inanimate bodies. (Berlin, 2002, pp. 12-13)
Generally speaking, “equilibrium” is simply the solution of a system of equations. (Ingrao and Israel, 1990, p. 263)
Virtually every concept in neoclassical microeconomics depends on diminishing marginal productivity for firms on the one hand, and diminishing marginal utility for the community on the other. If both these foundations are unsound, then almost nothing else remains standing. (Keen, 2011, p. 127)
As a consequence
... we know little more now about "how the economy works," or about the modus operandi of the invisible hand than we knew in 1790, after Adam Smith completed the last revision of The Wealth of Nations. (Clower, 1999, p. 401)
Newton's method works, of course, but only with an applicable set of axioms. After a long detour this becomes progressively clear:
To repeat, starting from individuals with standard preferences and adding them up allows one to show that there is an equilibrium but does not permit one to say that it is unique nor how it could be attained. With such severe drawbacks, one might wonder why we have persisted with our models based on the General Equilibrium approach. The idea that the economy is essentially in an equilibrium state or on an equilibrium path from which it is sometimes perturbed seems simply to be the wrong departure point. (Kirman, 2010, p. 511)
Newton's most important methodological message is: hypotheses non fingo. Economists have done the opposite with much alacrity but little success. To criticize economics as Newtonian is a gross unfairness towards Newton. Despite incessant copying there is not one iota of Newton's scientific spirit in economics. His axioms have nothing in common with the green cheese assumptionism of conventional economists.
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