A World Ruled by Number

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

Margaret Schabas
Copyright Date: 1990
Pages: 204
  • Cite this Item
  • Book Info
    A World Ruled by Number
    Book Description:

    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.

    ThePrinceton Legacy Libraryuses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback 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.

    eISBN: 978-1-4008-6151-4
    Subjects: Economics

Table of Contents

  1. Front Matter
    (pp. i-viii)
  2. Table of Contents
    (pp. ix-x)
  3. Preface
    (pp. xi-2)
  4. CHAPTER ONE Mathematical Pursuits
    (pp. 3-11)

    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...

  5. CHAPTER TWO Jevons’s Life
    (pp. 12-30)

    William Stanley Jevons was born in Liverpool on September 1, 1835. Both his parents were Unitarian and solidly middle-class. His paternal grandfather, William Jevons, had established an iron trade in Liverpool at the beginning of the century and by the time of Jevons’s birth the firm of Jevons & Sons was prospering.¹ Jevons’s father Thomas was the oldest of these sons and a steadfast member of the family firm. He also wrote two short pamphlets on political reform and was one of the first to launch a seaworthy iron boat.

    Jevons’s maternal grandfather, William Roscoe, had risen from humble beginnings...

  6. CHAPTER THREE The Mathematical Theory of Economics
    (pp. 31-53)

    Jevons’s work in economic theory has, more often than not, been discussed and judged in terms of contemporary theory rather than on its own terms. This may be attributed in part to the Whiggish tendencies of many commentators and in part because he was, after all, one of the first to set down the basic components of what became neoclassical economics. Like other pathbreakers, however, his exposition left many loose ends. In his analysis of Jevons’s theory of capital and interest, Ian Steedman has demonstrated that the entire system is indeterminate. But he is only one of a long line...

  7. CHAPTER FOUR Logic and Scientific Method
    (pp. 54-79)

    Jevons’s philosophical writings fall squarely within the tradition of British empiricism, the tradition of Bacon, Locke, Berkeley, and Hume. But the century that separates Hume from Jevons spawned several new schools of thought. Without question, the most influential of these was utilitarianism, ably developed by Jeremy Bentham, William Paley, and the two Mills. Mid-nineteenth century Britain also witnessed a major revival in logic. With the publication of works by John Herschel, William Whewell, and John Stuart Mill in the period 1830-1843, new ground was broken in the philosophy of inductive logic, or what is now known as the philosophy of...

  8. CHAPTER FIVE Markets and Mechanics
    (pp. 80-97)

    We are now in a position to examine the extent to which Jevons’s program for mathematical economics was shaped and justified by his philosophical convictions. Like many before him, he firmly believed that a unified method held for all of the sciences and that nature itself was ultimately uniform and law-governed. Hence, the economist was free to explore analogies to the natural sciences and to read them as meaningful clues to more fundamental harmonies. Where Jevons differed from his predecessors was in discerning more detailed similarities at the conceptual level that went beyond simple appeals to abstraction and the hypothetico-deductive...

  9. CHAPTER SIX Response to the Theory
    (pp. 98-118)

    Jevons was disappointed with the initial response to hisTheory of Political Economy.To Walras he wrote in 1874 that his theory of exchange had been “either neglected or criticized” in England.¹ But it is fair to say that Jevons overreacted, probably because the reviews appeared while he was hard at work on thePrinciples of Science.By May 1872, he was so strained and exhausted by this project that his doctor insisted he take a three-month holiday.² We know from his “sad reverse” on the university examination in political economy that Jevons had, in his own words, set out...

  10. CHAPTER SEVEN Mathematical Economics Takes Hold
    (pp. 119-134)

    During the 1870s, Jevons regarded George Darwin as one of his strongest British supporters. In addition to his distinction as the son of the famous naturalist, Darwin had placed Second Wrangler at Cambridge, thus putting him in the company of such notables as James Clerk Maxwell, W. K. Clifford, and Lord Kelvin. Although he published only one article in economics, his command of the subject was sufficient to undertake an essay review of Cairnes’Leading Principlesfor theFortnightly Review.Entitled “The Theory of Exchange Value,” the review read as a promotion for Jevons’s new program. Jevons was clearly heartened...

  11. CHAPTER EIGHT Mathematical Hegemony
    (pp. 135-140)

    We have seen throughout that Jevons’s reformulation of the content and methods of economic theory was rooted in a rich appreciation of logic and natural philosophy. It is not too far-fetched to argue that the rise of mathematical economics was as indebted to his assimilation of the philosophical insights of Boole, De Morgan, Herschel, Whewell, and Mill, as to the specific assertions on value and distribution put forth by the classical economists. Certainly Jevons’s program to mathematize economic theory owed more to his broader conception of scientific reasoning than to any single problem in the theory of production or consumption....

  12. Notes
    (pp. 141-176)
  13. Select Bibliography
    (pp. 177-186)
  14. Index
    (pp. 187-192)