In Britain

William Petty was held in high esteem in circles populated by the likes of Robert Boyle, John Wallis, Samuel Hartlib, and Thomas Hobbes. Considered by Samuel Pepys "the most rational man that I ever heard speak with a tongue,"^[14] Petty fit in well with the successful men of science who met in the Invisible College and the Royal Society. He dreamed of a perfectly rational society, a social edifice as stable and unassailable as a mathematical theorem. Each element had to be weighed, measured, and evaluated before it could be incorporated into this rational system. Petty made the point explicitly: "The Method I take. . .is not very usual; for instead of using only comparative and superlative Words, and intellectual Arguments, I have taken the course. . .to express myself in Terms of Number, Weight or Measure ; to use only Arguments of Sense, and to consider only such Causes, as have visible Foundations in Nature; leaving those that depend upon the mutable Minds, Opinions, Appetites, and Passions of particular Men."^[15]

Petty aimed at a science that used quantitative methods (counting and measuring) to isolate, describe, and analyze the elements that created a society's prosperity. Available observations of population, land, and resources—all in numerical form—were used in the calculation of values of other, as yet unknown, resources.^[16]

[14] Quoted in C.H. Hull, ed., The economic writings of Sir William Petty (Cambridge: The University Press, 1899), 1 , xxxiii.

[15] Ibid., 1, 244, Cf. E. Fitzmaurice, The life of Sir William Petty (London: J. Murray, 1895); E. Strauss, Sir William Petty (London: Bodley Head, 1954); W. Letwin, The origins of scientific economics: English economic thought 1660–1776 (London: Methuen, 1963), chap. 5; The Petty papers: Some unpublished writings of Sir William Petty , ed. the Marquess of Lansdowne, 2 vols. (London: Constable & Co., 1927). On political arithmetic, see Lazarsfeld, "Notes of the history of quantification"; Peter Buck, "Seventeenth-century political arithmetic: Civil strife and vital statistics," Isis, 68 (1977), and "People who counted: Political arithmetic in the eighteenth century," ibid., 73 (1982); Robert Kargon, "John Graunt, Francis Bacon and the Royal Society: The reception of statistics," Journal of the history of medicine and allied sciences, 18 (1963).

[16] Cf. Petty, "Verbum sapienti" (1664), "The political anatomy of Ireland" (1672), "Political arithmetick" (1671–6), "Two essays in political arithmetick" (1687), and "Five essays in political arithmetick" (1687), all in his Economic writings .

To reduce Petty himself to arithmetic, or rather geometry, his program lay at the intersection of inspiration of Baconian empiricism and Newtonian natural philosophy.^[17] He called for the assembly of individual measurements (of, for example, birth and mortality rates, work capacity, output, consumption, and fertility) to form a valid picture of a general reality. In practice, however, he often relied on estimates and averages; and his columns of numbers necessarily remained isolated from one another since correcting principles analogous to the law of gravity eluded him. Petty and his successors Gregory King and Charles D'Avenant framed a general program of social analysis based on computations and systematic collection of facts: "He who will pretend to Compute, must draw his Conclusions from many Premises; he must not argue from single Instances, but from a thorough view of many Particulars; and that Body of Political Arithmetick, which is to frame Schemes reduceable to Practise, must be compos'd of a great variety of Members."^[18]

The strong political context of political arithmetic may be discovered in a fight in Parliament over a proposal to provide it with one of its basic instruments. In 1753 advocates of a coherent program of social statistics, among them the mathematician James Dodson, called for a general census. But the census bill fell victim to strong opposition fed by fears of an expanding government. Five years later Parliament rejected a similar proposal for mandatory registration of births, marriages, and deaths.^[19] Prosperity appeared better served by capital, industry, and steam power than by the calculations of a power-hungry central government. Parliament thereby denied to proponents of political arithmetic both the means of collecting

[17] Cf. Robert Schware, Quantification in the history of political thought: Towards a qualitative approach (Westport, Conn.: Greenwood Press, 1981), 55–82; J.H. Cassedy, "Medicine and the rise of statistics," in A.G. Debus, ed., Medicine in seventeenth-century England (Berkeley: University of California Press, 1974), 283–312.

[18] C. D'Avenant, "Of the use of political arithmetick," Discourses on the public revenues and on the trades of England (London: Printed for J. Knapton, 1698), 1, on 29.

[19] See Martin Shaw and Ian Miles, "The social roots of statistical knowledge," in Irvine et al., eds., Demystifying social statistics , 27–38, on 32 and Buck, "People who counted."

data—the census and the registration of vital statistics—and the function intended by Petty and his contemporaries—that of a political instrument of scientific legitimacy.

That, of course, did not prevent private groups from compiling vital statistics for their political purposes. Republicans and religious dissenters picked up political arithmetic and wielded it to combat the "faithful guardians of the state" and reduce their authority.^[20] These advocates of local power counted local conditions as more significant than national aggregations of class, rank, and occupation. A good example is Richard Price's statistical studies of national debt and local prosperity based on data privately collected. Another is development of the work of John Graunt and Edmund Halley on the mathematical analysis of life expectancy. Graunt had demonstrated the utility of vital statistics for establishing the laws of demography; Halley's studies (published in 1693) of mortality lists from the city of Breslau had shown that generally valid calculations of life expectancy could be based on mathematical analysis of available, incomplete data on births and deaths.^[21] As a basis for calculating insurance premiums and annuities, quantitative data thus offered real practical value. By the second half of the 18th century, both governments and private investors recognized insurance ventures as a promising prospect. Price saw annuity societies, if guided by mathematicians, as a solution to England's economic ills.^[22]