A World Ruled by Number: William Stanley Jevons and the Rise of Mathematical Economics

A World Ruled by Number: William Stanley Jevons and the Rise of Mathematical Economics

by Margaret Schabas


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If any single characteristic differentiates current, neoclassical economics from the classical economics of Adam Smith and David Ricardo, it is the use of mathematics. Pointing to the critical role of William Stanley Jevons (1835-1882), Margaret Schabas demonstrates that the advent of mathematical economics in late Victorian England resulted more from new currents in logic and the philosophy of science than from problems specific to the classical theory of value and distribution.

Jevons's Principles of Science (1874) was the first book to take issue with John Stuart Mill's faith in inductive reasoning, to assimilate George Boole's mathematical logic, and to discern many of the limitations that beset scientific inquiry. Together with a renewed appreciation for Bentham's utility calculus, these philosophical insights served to convince Jevons and his followers that the economic world is fundamentally quantitative and thus amenable to mathematical analysis.

Originally published in 1990.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Product Details

ISBN-13: 9780691634807
Publisher: Princeton University Press
Publication date: 04/19/2016
Series: Princeton Legacy Library , #1134
Pages: 206
Product dimensions: 6.40(w) x 9.30(h) x 1.00(d)

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A World Ruled by Number

William Stanley Jevons and the Rise of Mathematical Economics

By Margaret Schabas


Copyright © 1990 Princeton University Press
All rights reserved.
ISBN: 978-0-691-08543-2


Mathematical Pursuits

Mathematical economics is riding high. It seems much longer ago than 1871 that Jevons should feel compelled to offer a variety of defences for his primitive symbols.

—George Stigler

Even a brief perusal of a shelf of contemporary economics journals would convince someone unfamiliar with the field that economics is a subject steeped in mathematics. But this was not always the case. Although political economy emerged by the mid-eighteenth century as a distinct discipline, it was not until the last third of the nineteenth century that mathematics took hold within it, and much later, somewhere in the 1930s or 1940s, that economic theorists began to study the calculus as a matter of course.

For some, mathematical renditions of economics are nothing more than attempts to dress the subject in the garb of the more revered science of physics, and thereby mask what are essentially apologetics for capitalism. There may be a grain of truth in this, in that all knowledge is imbued with the ideology of its time and its practitioners may be said to seek ways, perhaps unwittingly, to sustain the power that comes with expertise. No one would deny that economic thought of the last three or four centuries is by and large a product of the rise of Western capitalism and, insofar as much of the subject matter is drawn from extant economic phenomena such as banking, private property, and labor markets, is undoubtedly a reflection of the specific characteristics that mark this epoch in world history. Prima facie, this seems to be the case far more than in the natural sciences. But it does not follow that economists of the past one hundred years have conspired to dupe the public, or even that they have been engaged in self-deception with regard to their scientific credentials. Mathematics might appeal for its scientific sheen, and as a barrier to entry into the profession, and yet nonetheless enrich our understanding of the economy, capitalist or noncapitalist.

If mathematics offers the allure of a hard science, why did economists take so long to enlist its aid? Since Hobbes, social theorists have sought to emulate the exact sciences of astronomy and mechanics. In many respects, the human sciences were the focal point of Enlightenment thought, particularly in France and Scotland. Starting in the eighteenth century, one finds various attempts to infuse the moral sciences with elements of geometry, algebra, or the theory of probability; the example of Condorcet is legendary, but there were many others. Each attempt, however, either failed to gamer a following or was explicitly denounced by such prominent figures as Jean-Baptiste Say and Auguste Comte. Perhaps what was lacking was a judicious use of mathematics, although the case of Augustin Cournot (1838) suggests otherwise. Or perhaps few economists knew enough mathematics to make significant inroads. It so happens, however, that a number of prominent nineteenth-century economists, such as Thomas Robert Malthus and John Stuart Mill, had studied mathematics without succumbing to its charms. A knowledge of mathematics, while a necessary condition for the transformation under consideration here, was clearly not a sufficient one.

The most important figure in shifting the tide was William Stanley Jevons (1835–1882), and much of this study will focus on his contributions to the rise of mathematical economics. Trumpeting the virtues of mathematics was easy. What set Jevons apart from numerous predecessors, and enabled him to secure a following where others before him had failed, were his analyses of logic and scientific methodology, his assimilation of new ideas in mathematics, and the concrete details of his economic theory. Other factors, which will only be touched on here and there, also helped his cause: advances in mathematical education and the growth of universities, stagnation and strife among economists of the post-Millian era, and the more widespread shift to professionalization starting in the 1880s.

Jevons is usually discussed within the context of the so-called Marginal Revolution, which is said to have begun in 1871 with the publication of Jevons's Theory of Political Economy and Carl Menger's Grundsätze der Volkswirtschaftslehre. Subsequent reinforcement purportedly came in 1874 with Léon Walras's Éléments d'économie politique pure. Each of these professors of political economy—Jevons at Manchester, Menger at Vienna, and Walras at Lausanne—had independently arrived at the principle of diminishing marginal utility and proclaimed this insight to be the cornerstone of a significantly new science of economics. For this reason, the Marginal Revolution has traditionally been characterized as a recasting of the theory of value. Whereas the classical theory of Smith, Ricardo, and Mill had focused upon costs as the determinant of exchange-value, the early neoclassical theory emphasized utility. Or so the story is told in countless texts on the history of economic thought.

Since the 1970s, however, scholars have begun to question this account. The impetus for their reinterpretation derived more, it appears, from careful historical research than from collateral debates on the structure of scientific revolutions, though these have also left their mark. Studies of various pre-1870 economists established quite conclusively that the principle of diminishing marginal utility had been discovered several times throughout the last century, and recognized as a central concept from which to derive an explanation of market prices. Other scholars have challenged the received view since Joseph Schumpeter that "Jevons, Menger, and Walras taught essentially the same doctrine." William Jaffé, for one, has argued that each of these economists, working in isolation from one another, built upon distinct intellectual traditions and drew different implications from the principle of marginal utility. Erich Streissler has also done much to separate Menger from Walras and Jevons, primarily because of his disdain for mathematics. The difficulties in treating Jevons, Menger, and Walras as a united front have led some historians, such as Mark Blaug, to deny categorically that a revolution happened at the time.

If one looks only at Britain, however, a strong case can be made for a "Jevonian Revolution." As Terence Hutchison has argued, "in the space of a few years in the late 1860s and early 1870s the classical structure of 'theory' underwent a remarkably sudden and rapid collapse of credibility and confidence, considering how long and authoritative had been its dominance in Britain." Until Jevons, British economic thought from Locke to Mill formed one long, unbroken tradition. Even the occasional injection of foreign notions, Say's law most saliently, grew from seeds planted by Adam Smith. For the most part, nineteenth-century British economists wrote in a state of "splendid isolation," bolstered by appeals to such indigenous philosophical currents as utilitarianism. Jevons's own allegiance to British thought and exposure to foreign works is a case in point. Although he read French well and German poorly, he was schooled almost exclusively on British texts and was totally unaware of explorations similar to his own on the Continent. With time, he came to realize that the "truth lay with the French" rather than the British, and helped to foster intellectual trade across the channel.

Jevons never learned of Menger's existence and, although their work was subsequently lumped together, more probing scholarship has tended to set them apart. Certainly, the Austrian School that Menger spawned has retained a distinct identity well into this century. Although Walras corresponded with both Jevons and Menger, he failed to establish a close rapport with either man and was relatively unappreciated within French-speaking circles until the second or third decade of this century. He will be treated here as part of the Jevonian Revolution, as one who, like Alfred Marshall, helped to secure the practice of mathematics within economics. Not that he was a subordinate theorist. If anything, late twentieth-century economists hark back to Walras rather than to Jevons. But the movement depicted here, the emergence of mathematical economics in the late nineteenth century, is one in which Walras's role was that of supporter rather than leader.

There is little doubt that Jevons regarded mathematics as the means to further the scientific standing of economics. A reading only of the introductory sections to his Theory of Political Economy certainly gives the impression of unfettered opportunism. Yet, as our study of his Principles of Science will demonstrate, he was acutely aware, far more than previous economists, of the many limitations of scientific knowledge. The contrast with John Stuart Mill is particularly striking. Jevons, by and large, marks the shift toward fallibilism and conventionalism that preoccupied the fin-de-siècle methodologists Ernst Mach, C. S. Peirce, and Henri Poincaré. During the nineteenth century, mathematics lost its supreme epistemological standing and came to be seen more as a convenient tool than as an essential key to unlock the mysteries of the universe. Jevons was one of the first in Britain to appreciate and disseminate these findings. In fact, he was the first to respond to Helmholtz's celebrated paper on non-Euclidean geometry and one of the first to assimilate Boole's contributions to mathematical logic. All of this, we shall see, placed him in the timely position to argue that mathematics had as legitimate a place in economics as it did in the physical sciences.

One implicit aim of this book is to assess from an historical perspective the extent to which economic theory is amenable to mathematical analysis. A priori, there is no obvious reason why economists should ever have adopted mathematics. For many it is still difficult to understand how numbers link up with human behavior. But one might make a similar case for the behavior of physical objects. It is possible to imagine, albeit with more difficulty, a history of physics in which mathematics does not appear. The physics that we do possess, however, is fundamentally mathematical. Its central concepts of matter and force are only fully explicable in the language of mathematics. Merely recognizing that this is the cumulative result of independent actors does not render it accidental. Similarly, economics could hardly have become the densely mathematical discipline it is at present were it not for some fruitful anchoring of mathematics at the theoretical level. To suppose otherwise is to assume a widespread conspiracy on the part of thousands of seemingly intelligent men and women. No doubt, the majority of economists might admit that at times they are excessive in their use of mathematics, often at the expense of empirical relevancy. At least, such indulgences have been a frequent source of humor, even from within the ranks. But there are now numerous instances where mathematics has yielded interesting results, and recent cases where economists have contributed to certain branches of mathematics, such as set theory and topology. The use of geometry or curves, which also dates back to Jevons, has become so much a part of the economist's craft as rarely to be noticed when the subject of mathematics is broached.

Historians of economic thought have often assumed that nineteenth-century science was organized along the same lines as the present. But historians of science now paint a very different picture. To be sure, the nineteenth century was a time of convergence and conceptual unification, as well as one of increasing specialization and professionalization. In many respects, however, practitioners of science had more in common with the savant of the Enlightenment than with the scientist of the mid-twentieth century. Polymaths abounded: John Herschel, Hermann von Helmholtz, and Louis Pasteur to name just a few. It would not be misleading to assert that virtually every nineteenth-century contributor to a major field recognized today—physics, astronomy, chemistry, biology, geology—left his or her mark in another, seemingly disparate, field.

This suggests an obligation on the part of the historian to resist imposing current categories on the past, even the fairly recent past of the nineteenth century. As Thomas Kuhn has argued, there were two quite separate traditions in the physical sciences—the experimental and the mathematical—up until the 1830s. And whereas the experimental tradition ranged over problems we would now readily place within chemistry (or even physiology), the mathematical tradition had long included astronomy. Similarly, there were two separate strands in the life sciences—natural history, which encompassed morphology as well as geology; and physiology, which blended seamlessly into medical practices. The two converged toward the end of the last century, but until the 1860s or thereabouts were kept quite distinct.

Political economy's flirtation with various fields, whether sociology, law, or history, was thus in keeping with much of early nineteenth-century science. In many respects, it was no more or less diffuse than any other branch of knowledge. Efforts were made to rename the field or to formulate a narrower domain of discourse, such as Richard Whately's neologism "catallactics" for a science of exchange. But by and large, there was considerable consensus over the definition and scientific status of political economy. Virtually every treatise began with a declaration to the effect that political economy is the "Science which treats of the Nature, the Production, and the Distribution of Wealth." According to J. R. McCulloch, political economy "admits of as much certainty in its conclusions as any science founded on fact and experiment can possibly do."

It is worth emphasizing the extent to which political economy, by the middle of the last century, was recognized as a legitimate, if not exemplary science, since historians have had a tendency to project current insecurities over the status of economics back into the past. One source of confusion, perhaps, are the frequent appeals by classical economists to Newtonian mechanics. But this was de rigueur of every scientific tract. Indeed, whereas political economists could readily proclaim Adam Smith as the Newton of his age, chemists were divided between Lavoisier and Davy. Another source might be the general conflation of science with technology in our century and the tendency to appraise science in terms of its engineering feats. But in the time of Smith and Ricardo, science was primarily a branch of philosophy, the search for truth rather than a technical mastery of the world.

Many in the natural sciences, John Herschel and William Whewell most notably, had a high esteem for, if not active interest in, political economy. Charles Babbage led a successful campaign in the early days of the British Association for the Advancement of Science to secure a place—the notorious Section F—for political economy and statistics. At Cambridge, the tripos in the moral sciences was established at the same time as the one for the natural sciences (1838). We have tended to lose sight of the immense impact Smith, Malthus, and Quetelet had with their insights into the social order. But there is reason to believe that Darwin and Maxwell, among others, worked under their spell. As historians are beginning to recognize, one cannot fully assess Victorian science without considering the impact and influence of political economy.

By early nineteenth-century standards, political economy was about as bona fide a science as chemistry. According to the received view, both emerged in their modem guise in the 1770s. But it was not until the 1830s that these subjects were widely recognized in the form of university professorships. Until that time, chemistry was treated as an adjunct of the medical faculty, while political economy, particularly on the Continent, was taught as a branch of law. As a factor in gaining greater autonomy, chemistry had the additional advantage of serving industry. Its rise in university curricula matched almost year for year the transformation of Britain into the workshop of the world.

A steady increase in the teaching of political economy, at the universities and Mechanics Institutes, also mirrored the commercial growth of London and the Midlands. But it had the drawback of being less overtly practical. Despite widespread concern for poverty and labor unrest, the general lesson of laissez-faire did not suggest a distinct career path. Jevons's life, quite appropriately, instantiates all of these generalizations. He studied chemistry in preparation for a career in industry but, upon switching to political economy, found himself without obvious employment. Nowadays, the two subjects are probably comparable stepping-stones into the business world.


Excerpted from A World Ruled by Number by Margaret Schabas. Copyright © 1990 Princeton University Press. Excerpted by permission of PRINCETON UNIVERSITY PRESS.
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Table of Contents

  • FrontMatter, pg. i
  • Contents, pg. ix
  • Preface, pg. xi
  • CHAPTER ONE. Mathematical Pursuits, pg. 1
  • CHAPTER TWO. Jevons’s Life, pg. 12
  • CHAPTER THREE. The Mathematical Theory of Economics, pg. 31
  • CHAPTER FOUR. Logic and Scientific Method, pg. 54
  • CHAPTER FIVE. Markets and Mechanics, pg. 80
  • CHAPTER SIX. Response to the Theory, pg. 98
  • CHAPTER SEVEN. Mathematical Economics Takes Hold, pg. 119
  • CHAPTER EIGHT. Mathematical Hegemony, pg. 135
  • Notes, pg. 141
  • Select Bibliography, pg. 177
  • Index, pg. 187

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