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Home | Library | Sir William Petty and the Mathematics of Power

Sir William Petty and the Mathematics of Power

October 7, 2010

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[Excerpted from An Austrian Perspective on the History of Economic Thought, vol. 1, Economic Thought Before Adam Smith. An audio file of this article, read by Jeff Riggenbach, is available here.]

Since Bacon's thought fitted well into the spirit of the age, it is not surprising that he developed enthusiastic followers. One little-recognized follower was Thomas Hobbes, the philosophic apologist for monarchical absolutism who, on the eve of the Civil War, was searching for a "modern" defense of monarchical despotism that relied neither on the outworn correspondence theory of order, nor on the Grotian variant of natural law as did his friends in the Tew circle.

Grotius's conservative version of consent theory held that the right of sovereignty had indeed originated with the people, but that the people, at some murkily distant point in the past, had surrendered their sovereignty irrevocably to the king. This defense of royal absolutism had been continued in England by the Tew circle, Hobbes's only disagreement being that each individual, in the last analysis, had the "right of self-preservation" and therefore had the right to disobey any orders from the king that were tantamount to the particular individual's murder.1

But more importantly, Hobbes's political theory forswore scholastic natural-law methodology for a "modern" mechanistic, scientistic methodology far more in keeping with Francis Bacon. This shift is not surprising, considering that Hobbes served his philosophic apprenticeship as secretary to Bacon himself. Later on, in addition to a life in service to the royalist Cavendish family, Hobbes served as a mathematical tutor to the future King Charles II.

The leading Baconian in political economy, who was also, fittingly, a pioneer in statistics and in the alleged science of "political arithmetic," was the fascinating opportunist and adventurer Sir William Petty (1623–1687). Petty was the son of a poor rural cloth-worker from the county of Hampshire. He learned Latin at a country school, and was put to sea as a cabin boy at 13. When his leg was broken at sea, he was put ashore in France by the captain. Petty got himself admitted to the Jesuit university at Caen by applying for admission in Latin. There he received an excellent education in languages and mathematics, supporting himself by tutoring and trading in custom jewelry. Soon, Petty was off to Holland to study medicine; there he became friendly with Dr. John Pell, professor of mathematics at Amsterdam.

Traveling to Paris to study anatomy, Petty was armed with an introduction by Pell to Thomas Hobbes. Soon, Petty became Hobbes's secretary and research assistant, and from Hobbes imbibed Baconian and Hobbesian empiricism, mechanism, and absolutism. Through Hobbes, Petty also joined advanced circles, including new scientists plus the philosophic friends of science. We must remember that science did not yet enjoy the professional specialization of the 20th century, and new scientific discoveries were often made in an atmosphere of scientists surrounded by dilettantish philosophical cheerleaders. Through Hobbes, Petty participated in the Parisian circle of Father Marin Mersenne, which included scientists such as Fermat and Gassendi as well as philosopher-mathematicians Pascal and Descartes.

After a year in Paris, Petty returned to England in 1646 to continue his medical studies at Oxford. Armed again with an introduction opening crucial doors from Professor Pell, Petty was embraced by the man who has been called "the master of ceremonies to the new learning," the enthusiastic Baconian, half-English Prussian immigrant from Poland, and exile from Catholic rule, Samuel Hartlib (1599–1670). Pell was Hartlib's earliest disciple, and his first job had been schoolmaster at a school run by the wealthy and well-connected Hartlib, whose father had been "merchant-royal" to the king of Poland. With Hartlib's backing, Petty's career at Oxford now zoomed upward with incredible speed. Petty was welcomed into a circle of mathematicians, scientists, and physicians who had gathered at Oxford to escape the Civil War and engage in multipartisan, transreligious Baconian science.

"What then was there about Sir William Petty that limited his political influence and his power at court? The problem was that Petty could not resist the impolitic dig."

This group, which called itself the "invisible college," not only received Petty warmly but they even met periodically at his lodgings, which, being at an apothecary's house, was convenient to scientific and alchemical experimentation in drugs. Hardly did Petty become a fellow of Brasenose College in Oxford than he was made vice principal, and hardly did he become a physician when he was made professor of anatomy. Finally, Hartlib got his friend and protégé Petty made professor of music in 1651 at the Gresham College in London, a new college dedicated to the experimental and mechanical arts. Petty apparently taught the applied mathematics of music. At only 28, William Petty had been vaulted to the top of the academic profession. The rapidity of Petty's climb was undoubtedly aided by the fact that the new republican regime tossed out previously openly royalist incumbents, and the "invisible college" Baconians were able to sail under the colors of value-free, Baconian science.

Hartlib also wrote voluminously inductive histories of trade, especially agriculture, helping to further the Baconian program. Hartlib himself was a friend and disciple of his fellow Baconian, the mystical millennialist Czech theologian and educationist Johann Amos Comenius (1592–1670). Comenius, a bishop in the pietist Hussite Moravian church and an exile from Catholic rule, was employed by the Swedish government to organize its school system. He went beyond Bacon to invent a new hermetic religious system, pansophism, which promised to combine all the sciences in a mystical road to all knowledge. Hartlib subscribed to these gnostic tenets, and he also followed Bacon in outlining his own new utopia, which he called Macaria (1641).

Hartlib and Comenius were the favorite philosophers and theoreticians of the Puritan country gentry, the party of the Pyms and the Cromwells. Indeed, in the summer of 1641, when the country Puritans thought that they had successfully achieved lasting rule under the king, Parliament eagerly brought Comenius to England, and it was during the autumn that Hartlib published his Macaria, a welfare-state utopia he expected to institute in England. Arrived in England, Comenius drew up his own plans for a pansophical "reform," or transformation of the English educational system, led by a "pansophical college." Comenius proclaimed "that the last age of the world is drawing near, in which Christ and his Church shall triumph, … an age of Enlightenment, in which the earth shall be filled with the knowledge of God, as the waters cover the sea."2

The renewed outbreak of the Civil War put an end to plans for quiet social and educational reconstruction, and so Comenius returned to the continent of Europe the following year, 1642. But Hartlib and the others remained, and continued under munificent Puritan patronage; during Cromwell's Protectorate, these Baconians flourished, and Pell and other Hartlib disciples were used by Cromwell as envoys to various Protestant countries in Europe.

One of Hartlib's favorite continuing projects was to try to found new colleges and institutions to promote the new science. One prospective donee was the wealthy, aristocratic, and much younger friend, the distinguished physicist Robert Boyle (1627–1691). At one point, Hartlib tried to get Boyle to finance William Petty in compiling a "history of [all] trades"; at another point Petty, in his first published work at the age of 25, urged Hartlib to finance a new college to advance "real learning," which would be a "gymnasium medicum or a college of tradesmen." This college, wrote Petty, would provide "the best and most effectual opportunities and means for writing a history of trades in perfection and exactness."3 Neither of these particular projects was to pan out.

No sooner had William Petty reached the apex of academia in 1651, however, and before giving his first lecture, than he left the university world for good. He was out to make a fortune, and he saw his opportunity in the midst of Cromwell's devastating conquest and decimation of Ireland. A fellow Oxford "invisible," Jonathan Goddard, had gone off to become physician-in-chief of Cromwell's army in Ireland, and had returned two years later to the prestigious post of warden of Merton College; taking a two-year leave from Oxford, Petty went to Ireland as Goddard's replacement. When Petty got to Ireland, he found a golden opportunity to make his fortune.

Cromwell had despoiled Irish lands, and decided to pay his soldiers and the financial supporters of his military campaign by handing out conquered and confiscated Irish land. But to parcel out the land, it first had to be surveyed, and this task was being conducted by a surveyor-general, a friend of Petty and Hartlib, Dr. Benjamin Worsley, a fellow physician, who had published influential pamphlets that led to the Navigation Act of 1652, a mercantilist measure for the subsidizing and privileging of English shipping. Petty, however, did not let friendship stand in his way. Reaching Ireland in the autumn of 1652 and sizing up the situation, Petty launched a propaganda campaign denouncing the alleged slowness of Worsley's survey, and promising to perform the task himself in a mere 13 months. Getting the job in February 1653, despite the ferocious opposition of Worsley, Petty indeed completed the task on time.

With the huge sum of cash earned from this job, Petty set about accumulating ownership of the confiscated Irish lands — some lands he acquired in lieu of cash payment; others he got by buying land claims from needy English soldiers. By 1660, William Petty had accumulated Irish landed estates totaling 100,000 acres, making him one of the largest landowners in Ireland. In fact, his eventual accumulation of Irish land was still greater, for by the time of his death in 1687 Petty owned 270,000 acres in south Kerry alone. By the late 1650s, Petty was back in London, serving for a time in Parliament and renewing his friendships in scientific circles.

Back in England, Petty joined a Baconian-Hartlibian circle headed by another German émigré, Theodore Haak, the organizing secretary of Comenius's English disciples. Other members included Dr. Jonathan Goddard, now Protector Cromwell's personal physician; and the famed architect Christopher Wren, whose first architectural work was a transparent three-story beehive-like structure built for Hartlib. The group met largely in the Oxford home of Cromwell's brother-in-law, John Wilkins, whom the protector had made ruler of Oxford University.

The Baconians, it must be understood, though flourishing under Cromwell, were never truly committed to any particular form of government. Like Bacon himself, they could flourish under an absolute monarchy. Monarchy, republic, parliament, crown, church — all these forms of government made no particular difference to these "scientific," "value-free" would-be rulers of the nation. So long as the regime was sufficiently statist, and at least nominally Protestant, the polity could afford ample scope for the dreams of power and "science" held by these Baconian philosophers and men of affairs.

Hence Petty and his colleagues, always seekers of the main chance whatever the government, were well-placed when the Stuart monarchy was restored in 1660.4 Petty himself was well received at the court of Charles II, who granted him a knighthood, and in 1662 Petty and his colleagues' Baconian dreams culminated when Petty became a founding member of the newly chartered Royal Society of London for the Improving of Natural Knowledge. The Royal Society was specifically dedicated to the Baconian project of empirical observation and experiment, first to the study of the natural world and technology, and then to the study of society.5 Throughout his life, Petty remained an active member of the Royal Society, especially contributing to its studies of the history of trades and technology. Petty's own contribution, "political arithmetic," or statistics, he saw as the application of the empiricist Baconian program to the social world.

True to Petty's goal of "empirical" science, each of his studies was designed to promote his own economic or political advancement. His major publication, a Treatise of Taxes and Contributions, was published in 1662, and went into three further editions in his lifetime. Petty, however, was disappointed, since the tract did not lead to his hoped-for public office or political influence. Petty's later tracts were written, but not published, in his lifetime, the others being published in 1690 or later, after his death. This was because, in the words of a generally admiring historian, they were written "not for publication but for circulation in the corridors of power or with a view to acquiring influence and jobs — which he never managed to obtain."6 And even though Petty's daughter, from a marriage a few years later, was to give rise to the aristocratic Shelburne and Lansdowne families, Petty derived little enjoyment from his vast ill-gotten lands in Ireland, since he had to spend half his days in that country defending his claims from lawsuits from royalist claimants and his lands from "bandits" who believed that he had despoiled their land.

As befitted a presumed experimental scientist, Petty claimed several important inventions, only one of which, however — the double-hulled ship — ever came to fruition. He spent a great deal of money building several versions of this ship, but they all suffered from the same problem — even though very fast, they all "had an embarrassing tendency to break up in a storm," a defect, we are told, "in which Charles II took a certain amount of malicious glee."7

What then was there about Sir William Petty that, despite his gifts, his seizure of the main chance, and his powerful friends, brought him up sharply against a "glass ceiling," that limited his political influence and his power at court, and that led even the king of England to treat his discomfiture with "malicious glee"? Apart from his sabotage of Benjamin Worsley, the problem was that Petty could not resist the impolitic dig, whether he was wickedly mimicking the aristocracy at a party, or was reproving His Majesty's policies in the very pamphlet he was writing to court the king's favor. Not being a gentleman by birth, Sir William could ill afford to act less than a gentleman to his betters.

While publishing his Treatise of Taxes, Petty delivered several papers to the Royal Society on the histories of the dyeing of cloth, and shipping, advancing the Baconian history-of-trades program. His major work, the Political Arithmetic, was written in the 1670s and published posthumously in 1690. The goal was to show that England, far from suffering from a decline as commonly believed, was actually wealthier than ever before. In the Political Arithmetic, Petty claimed to eschew mere "words" and "intellectual arguments," and state only "arguments of sense" — that is, derived from sensate facts of nature, which could all be boiled down to "number, weight, and measure" — a slogan which he enjoyed repeating on many occasions. Thus, at the end of an essay on algebra, Petty grandiloquently maintained that he had at last applied algebra "to other than purely mathematical matters, viz: to policy, by the name of Political Arithmetic, by reducing many terms of matter to terms of number, weight, and measure, in order to be handled mathematically."8

In fact, there is virtually no mathematics in Petty; what there is are statistics, loosely gathered, and arbitrarily asserted, employing many hidden assumptions, to arrive at preordained ideological conclusions.

As William Letwin writes, in his rewarding study of Petty,

Petty's way with numbers, here as always, was utterly cavalier. The facts, whatever they were, always had a congenial way of upholding Petty's conclusions. Or rather, Petty's factual assertions did; for he was not averse to citing authorities mysterious, unknown, and even non-existent, when he needed their help.

Letwin then cites the conclusion of Major Greenwood, a modern historian of statistics: "It is not I believe too cynical to say that any calculation Petty made would have produced war losses around 600,000."9 At one point, Petty actually submits the justification for his arbitrary figures and assumptions that they make no difference anyway since the figures are not totally false, and therefore can illustrate the method of arriving at knowledge. But fake illustrations, of course, are scarcely an advertisement for the method of political arithmetic. Thus Petty tried to come to conclusions pleasing to the king — that England was gaining not declining in wealth — by borrowing the spurious precision of numbers and the prestige of science. Sometimes his conclusions were so wildly optimistic as to abandon all sense, as when he claimed that it was "a very feasible matter, for the King of England's subjects, to gain the universal trade of the whole commercial world."10

In the course of his discussions, Petty delivered himself of some economic theories — qualitative not quantitative theories we might add — in violation of his stated program. They were either not very remarkable — urging the king not to levy taxes that are so high that they will lead to severe declines in output or employment — or incorrect, such as attributing the value of goods not to the demand for them but to their costs of production.

Indeed, the quality of Petty's economic reasoning was generally that of a jejune mercantilist. Like all early-modern writers, with the exception of Botero, Petty was a naive expansionist on population — the more people, the more "income" and output will increase. Like mercantilists generally, Petty counseled and identified with the aristocratic power elite rather than with the laborers. His yen for increased or "full" employment stemmed from a wish to increase the national output at the command of the state and employed by the elite.

So little was Petty, like most mercantilists, concerned for the laboring classes that he denounced them for becoming more idle and drunken whenever their real wages rose. Petty, in fact, was more imaginative than his mercantilist confreres in proposing a governmental price-support scheme for keeping up the price of corn — specifically in order to prevent real wage rates from ever rising and thereby keeping the workers' noses to the grindstone and preventing them from enjoying more idleness (or leisure). Petty, indeed, denounced these laborers as "the vile and brutish part of mankind." Sometimes Petty's imagination ran away with him, his zeal for increasing the laboring population of England leading him to recommend, in the Political Arithmetic, forcibly moving the bulk of the population of Scotland and Ireland to England, allegedly in "their own interests," so as to increase English productivity and to raise rents in England.11

The 17th-century enthusiasm for the sciences, building upon the quasiunderground age-old numerological mysticism of the hermetic and Kabbalah tradition, led to an arrogant frenzy of enthusiasm for quantitative and mathematical study of social life as well among the scientists and especially their cheering sections. The eminent Harvard sociologist Pitirim Sorokin has perceptively referred to this frenzy, from that day to the present, as "quantophrenia" and "metromania." Thus, writes Sorokin,

The mathematical study of psychosocial phenomena was especially cultivated in the seventeenth and the eighteenth centuries. Spinoza, Descartes, Leibnitz, Newton … and others, began to build a universal quantitative science, Pantometrika or Mathesis universae, with its branches of Psychometrika, Ethicometrika, and Sociometrika designed for investigating psychosocial phenomena along the lines of geometry and physical mechanics. "All truths are discovered only through measurement," and "without mathematics human beings would live as animals and beasts," were the mottoes of the Social Physicists of these centuries.12

William Letwin writes perceptively of this metrophrenic phenomenon among the Baconians of England during the Stuart Restoration period. The "scientific revolution" of this period, writes Letwin, "owed much of its vigor to faith … the simple belief that many things in nature, as yet mysterious, could and should be measured precisely." Unfortunately, "Hand in hand with this revolutionary ideal went a devout but misplaced notion that to measure and to understand were one and the same. Restoration scientists believed that to cast a mathematical mantle over a problem was tantamount to solving it." As a result, Letwin goes on,

The scientists united themselves in the Royal Society and set off on an absolute orgy of measurement … the virtuosi continued, endlessly and pointlessly, to record, catalogue and count. The best minds of England squandered their talents in minutely recording temperature, wind, and the look of the skies hour by hour, in various corners of the land. Their efforts produced nothing more than the unusable records.

popularly chosen

This impassioned energy was turned also to the measurement of economic and social dimensions of various sorts. The search for number, weight and measure was conducted in the happy belief that good numbers would inevitably make for good policy.13

Unfortunately, this quantophrenia and metrophrenia seems to have taken over the modern economics profession. Fortunately for the development of economic thought, however, the quantophrenic enthusiasm in the social sciences dribbled away after the effusion of some Baconian writers in the 1690s. It would be nice to think that this decline was speeded up by the brilliant and devastating satires directed against the Baconians in the 1720s by the great Anglo-Irish Tory-libertarian satirist Jonathan Swift (1667–1745). In his classic Gulliver's Travels, Swift effectively lampooned the crazed scientists of Laputa and elsewhere who were putting into effect what would now be called the Baconian "research programme." Finally, in 1729, Swift followed up this satire with his famous Modest Proposal, what Letwin justly calls "the last word on political arithmetic as an instrument of social policy."

For Swift went after Petty, taking as his text Petty's claim that the more people the better, and in particular Petty's serious proposal, in his Treatise of Taxes, to cure Ireland's alleged cause of poverty, underpopulation, by urging government subsidies for births among unmarried Irish women. The subsidies were to be financed by a tax on all Irish, especially on Irish men. The subsidies were only to be allowed if the woman kept records registering each father's time of cohabitation, and signed agreements by the father on the disposal of the children.

Swift's Modest Proposal satirized every aspect of Petty's style, from the solemnly avowed absurd policy proposals, to the fake precision of the numerological style. Thus, the Modest Proposal doggedly stated,

The number of souls in this Kingdom being usually reckoned one million and a half, of these I calculate there may be about two hundred thousand couples whose wives are breeders; from which number I subtract thirty thousand couples who are able to maintain their own children … this being granted, there will remain a hundred and seventy thousand breeders.

After making due deductions for miscarriage, or for children who die each year, Swift is left with "a hundred and twenty thousand children of poor parents annually born." After demonstrating that there is no way by which these poor children can be reared or employed, Swift concludes with his famous "modest" proposal, not "liable to the least objection."

Being assured by a knowledgeable American in London that a young healthy well-nursed child of one year old is "a most delicious, nourishing and wholesome food, whether stewed, roasted, baked or boiled," Swift then goes on to demonstrate, in the best value-free, numerological, empiricist Pettyite manner, the economic advantages of selling 100,000 children per annum to be eaten.

Most of the special pleading economic writers of the day ended their tracts professing no personal gain and their devotion to the public weal. And so Swift ends his Modest Proposal accordingly!

I profess, in the sincerity of my heart, that I have not the least personal interest in endeavouring to promote this necessary work, having no other motive than the public good of my country, by advancing our trade, providing for infants, relieving the poor, and giving some pleasure to the rich. I have no children by which I can propose to get a single penny, the youngest being nine years old, and my wife past child-bearing.14

  • 1. On Hobbes and the Tew circle, see the illuminating work by Richard Tuck, Natural Rights Theories (Cambridge: Cambridge University Press, 1979).
  • 2. See the fascinating article by H.R. Trevor-Roper, "Three Foreigners and the Philosophy of the English Revolution," Encounter, 14 (Feb. 1960), pp. 3–20, esp. p. 15, and on Comenius and his neo-Rosicrucian group, see Frances Yates, "Francis Bacon, 'Under the Shadow of Jehova's Wings.'" in The Rosicrucian Enlightenment (London, Routledge and Kegan Paul, 1972), note 1, pp. 156–92. Also see the illuminating discussion in William Letwin, The Origins of Scientific Economics (Garden City, NY: Doubleday, 1965), pp. 125–6, 134–5.
  • 3. In Petty's The Advice of W.P. to Mr. Samuel Hartlib, for the advancement of some particular parts of learning…. See Letwin, The Origins of Scientific Economics, note 12, pp. 136–7.
  • 4. The exception was poor Hartlib, who lost his Cromwellian pension and died in 1670 after fleeing his creditors to Holland.
  • 5. The Royal Society was headed by Dr. John Wilkins, head of Oxford University and later bishop of Chester. In addition to being Cromwell's brother-in-law, Wilkins, author of the book Mathematical Magick (1648), was a leading adept of the hermetic and magic-steeped Rosicrucian movement as well as of the leading Elizabethan magus, Dr. John Dee and his hermetic alchemist disciple, Robert Fludd. See Yates, "Under the Shadow," note 10, pp. 182ff.
  • 6. Terence W. Hutchison, Before Adam Smith: The Emergence of Political Economy, 1662–1776 (Oxford: Basil Blackwell, 1988), p. 386, note 9, p. 29.
  • 7. Letwin, The Origins of Scientific Economics, note 12, p. 131.
  • 8. Ibid., note 12, p. 140.
  • 9. Ibid., note 12, pp. 144–45.
  • 10. Hutchison, Before Adam Smith, note 9, p. 39.
  • 11. Hutchison, Before Adam Smith, note 9, pp. 38–9. Also see in particular Edgar S. Furniss, The Position of the Laborer in a System of Nationalism: A Study of the Labor Theories of the Later English Mercantilists (1920, N.Y.: Kelley & Millman, 1957), pp. 128, 134.
  • 12. Pitirim A. Sorokin, Fads and Foibles in Modern Sociology (Chicago: Henry Regnery, 1956), pp. 103, 110, and passim.
  • 13. Letwin, The Origins of Scientific Economics, note 12, pp. 106–7.
  • 14. Letwin, The Origins of Scientific Economics, note 12, pp. 149–51. On the libertarian impact of Swift's writings, see Caroline Robbins, The Eighteenth-Century Commonwealthman (Cambridge, Mass.: Harvard University Press, 1959), pp. 152–3; and James A. Preu, The Dean and the Anarchist (Tallahassee, Fl: Florida State University Press, 1959). On the Modest Proposal, see Louis A. Landa, "A Modest Proposal and Populousness," in Essays in Eighteenth-Century English Literature (1942, Princeton, NJ: Princeton University Press, 1980), pp. 39–48.


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