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The conclusion draws together several of the main themes of the book, arguing that political arithmetic can only be understood properly from the manuscripts he circulated in his lifetime, and in the context of his lifelong engagement with natural philosophy and his Baconian interpretation of the methods and purposes of science. Petty's project to transform government through the systematic manipulation of populations in the interests of the state undermines any retrospective distinction between his contribution to social science and his interest in social engineering; the concept of ‘biopolitics', though equally anachronistic, is more appropriate. By the same token, however, the massive expansion (in real terms) of demographic manipulation after Petty's death suggests that political arithmetic's ambitions were not abandoned but merely concealed.

This chapter traces the transformation of political arithmetic after Petty's death from the art of government by social engineering he elaborated to the more anodyne mode of quantitative, analytical reasoning encountered in standard histories of social science. Focusing especially on the work of Gregory King and Charles Davenant — who redefined political arithmetic as ‘an art of reasoning’, acknowledging Petty's creative role but disavowing his political purposes — it argues that only after the Glorious Revolution of 1688 transformed the political landscape of the Three Kingdoms did political arithmetic come to be understood chiefly as a methodological advance rather than a policy program. Yet while these writers now based political arithmetic's value on its putative analytical objectivity, political neutrality, and statistical precision, they remained implicitly committed, as agents of a growing state bureaucracy, to managing and manipulating populations across an expanding empire.

This chapter turns from general structures and processes to consider certain ancillaries to policy making. It charts the development of the British ‘culture of fact’, as that manifested itself in studies of society and economy. It describes the increasingly public character of British debate, and the flowering of forms of enquiry linked to social-policy debates. It also details the gradual separation of two lines of enquiry that had initially been inextricably entangled: enquiries into the bases of national power, and into the nature and extent of social ‘happiness’. Nineteenth-century ‘moral statistics’ did not emerge directly out of the old political arithmetic tradition, but owed much to later 18th-century reorientations in both the mode and the focus of enquiry.

This chapter introduces William Petty and his invention, political arithmetic, setting both in historiographical perspective. It discusses the particular challenges posed by Petty's voluminous archive and his pattern of manuscript circulation to standard accounts of his life and work based on printed sources. It argues that while Petty's work in different areas (his ‘Down Survey’ of Ireland, his role in founding the Royal Society, and his political arithmetic, most famously) are usually parceled out between different historical subfields (the history of economics or social science, the history of science, and the history of seventeenth‐century Britain and Ireland, respectively), a more integrated and contextualized approach to Petty's work better fits the evidence and suggests problems with the standard interpretation of political arithmetic as an early form of quantitative economic or social analysis. Finally, it summarizes the contents of the book.

This chapter examines Petty's first articulation of political arithmetic (and the related concept of ‘political anatomy’) in the early 1670s. Examining Petty's manuscripts in light of his intellectual development and against a background of resurgent Catholic opposition to the Irish land settlement, it reveals political arithmetic's origins as a policy program for settling and improving Ireland. Combining Hartlibian improvement proposals, elements of earlier English writing on Irish plantation, a demographic vision of politics, and a conceptual framework derived from corpuscularian models of alchemy, political arithmetic promised to ‘transmute the Irish into English’ through a series of forced population exchanges, intermarriage, and procreation. Installing English women in Irish households, Petty's Baconian program of social engineering would harness the natural affections of men for women and mothers for children to fuse the two populations, channeling nature to produce desirable qualities — industry and loyalty — in human populations.

The history of the search for a science of society is traced back to the political arithmeticians of the seventeenth century. Social survey is defined. What is right and what is wrong with sociology is discussed in the context of historical development. Claims for statistical originality are considered in respect of Graunt, Pascal, Quetelet, Florence Nightingale, Galton, Fisher, Lazersfeld, and Yule. Booth's biography is retailed. Social surveys and sampling multivariate analysis and log linear modelling, and the new English statistics are put historically into the context of a developing society and its concern with social policy.

This chapter develops the concept of the “data state”—a condition of being governed by number. It notes that government by number emerges from “political anatomy” and “political arithmetic.” It focuses on the emergence of these political forms as engines for counting and calculating natural and political objects. It examines Samuel Hartlib and William Petty's designs and concludes with the great innovations in censuses and cartography developed in Ireland in the first half of the nineteenth century. It argues that the modern census is a political technology engineered by bringing metering and graphing into a simultaneously practiced and representational relationship.

Eighteenth‐century French writers became convinced that France was depopulating; this public concern was the context in which the French royal government would revive its pronatalist policy to reward fathers of large families between 1760 and 1789. This chapter begins by surveying the evolution of thinking about population and of reproductive behavior since the seventeenth century. By the mid‐eighteenth century, French writers increasingly noted that large families were rare. They wrote nostalgically about the natural, rustic family values that contraceptive practices had corrupted. The second part of the chapter examines the royal government's renewed interest in rewarding large families during the last four decades of the Old Regime. During this period, royal administrators distributed tax reductions and payments to hundreds and perhaps thousands of fathers with many children every year, to households that ranged from the very poor to comfortable noblemen.

English thought about the political economy of population witnessed three distinct phases in the early modern period. In the first, stretching from the early sixteenth century through the early seventeenth, population as an abstract quantity took a back seat to specific, localized and qualitatively defined “multitudes” whose existence was bound up with particular legislative interventions. In the second, specific multitudes came to be seen as products of regional or national environment or “situation,” tied to “nature” but subject also to scientific interventions therein. The Restoration witnessed the birth of the third phase, when concepts of “political arithmetic” combined with other features of Hartlibian political economy to conceptualize population as an autonomous, natural, and historical process of “multiplication” and a quantifiable totality, which could be the foundation of economic and social analysis. The transformation in demographic thought, so closely associated with the history of mercantilism, was as much an episode in the history of economic thought as it was in the history of social and natural science.

Describes how in the 17th century, the Englishman William Petty proposed the idea of "political arithmetic" - i.e. the notion that rulers should base their political decisions on numbers and statistics; highlights how the idea of political arithmetic and national income was received and underlines, that for many centuries no government was convinced that numbers and statistic mattered.

This chapter describes the great expectations raised by civil war and political revolution and their impact on ways of thinking about economic and social change. It stresses the role of the Hartlib circle in fashioning an ideology of improvement which extended from husbandry and education to banking and trade, and promised infinite progress towards universal prosperity and happiness. Improvement was exported to Ireland, inherited by the Royal Society, and given even greater publicity after the Restoration. In the 1660s William Petty used his political arithmetic to construct a new kind of political economy which measured the national income for the first time, and made comparisons with France and Holland. Expectations of immediate and total reformation were replaced by expectations of intellectual and material progress far into the future.

This chapter explores the origin of John Sinclair's political arithmetic of land use to determine the precise measure of marginal soil still available for improvement in the Highlands. The changing scene of conservative reaction among Sinclair's Scottish allies is surveyed, including the activities of the Highland Society of Scotland and the chemical project of Archibald Cochrane, the Earl of Dundonald. This is followed by an examination of Sinclair's agitation in Parliament and the Board of Agriculture. These threads converge into a broader thesis about island consciousness. Sinclair's ambition with his political arithmetic to quantify the environmental limits of the nation preceded the better-known pessimistic political economy of Malthus by several years. Ecological strains multiplied because of the rapid British population growth in the second half of the eighteenth century, but in the nineteenth century, these limits were overcome thanks to the “ghost acres” of the colonies and the transition into a new industrial society based on mineral energy and steam power.

This chapter discusses statistics as social science. The systematic study of social numbers in the spirit of natural philosophy was pioneered during the 1660s, and was known for about a century and a half as political arithmetic. Its purpose, when not confined to the calculation of insurance or annuity rates, was the promotion of sound, well-informed state policy. Political arithmetic was, according to William Petty, the application of Baconian principles to the art of government. Implicit in the use by political arithmeticians of social numbers was the belief that the wealth and strength of the state depended strongly on the number and character of its subjects. Political arithmetic was supplanted by statistics in France and Great Britain around the beginning of the nineteenth century. The shift in terminology was accompanied by a subtle mutation of concepts that can be seen as one of the most important in the history of statistical thinking.

This chapter is divided into two parts. The first deals with the pre-history of Victorian statistics, examining the development of political arithmetic in Britain and ‘statistik’ in German states from the seventeenth century. Both disciplines described state and society numerically, through the collection of leading numeral indicators. Both sought to calculate population, wealth, and overall national strength. The pioneering demographic work of John Graunt and William Petty is explained and the subsequent development of political arithmetic is sketched across the eighteenth century. Similarities rather than differences between the two socio-intellectual traditions are emphasized, and political arithmetic is related to an earlier British antiquarian tradition of social and natural description and compilation. In the second part, the origins of the British statistical movement in the 1820s and 1830s are explained in relation to a varied set of social and political reforms in this era, and the intensification of the role of the state. Reforms of parliament and the franchise, of local government and the poor laws, of education and factory regulation, as well as the abolition of slavery and the financial compensation of former slaveholders, required calculations. The state needed accurate data and this stimulated the institutionalization of statistical collection and analysis both inside government, in new organizations like the General Register Office that collected demographic data, and in statistical societies formed in 1833–4 in Cambridge, London, and Manchester, which studied the profusion of numbers caused by the data revolution of the 1830s.

By the final decade of the eighteenth century, the political economy of conquest had crystalized into a distinctively recognizable modern form. Expanded scale of war-making created a need to surveil the financial operations of the colonial state. The changing valence of ‘corruption’ came to include a growing insistence on eliminating leakages from the financial flows that enabled conquest. Corruption was not merely a moral scourge but a structural flaw, which if left unresolved would drain the war-making capability of the early colonial regime. Financial accounts of the East India Company therefore had to be rendered legible to public scrutiny and parliamentary debate in the form of an annual India Budget. Colonial conquest captured the cultural imagination of metropolitan Britain – from painting and the Georgian stage to a new graphic scheme of statistical visualization – all sought to comprehend Britain’s territorial empire in South Asia. The growing appetite for war was fed by territorial conquest on an ever-expanding scale and transformed colonial warfare into the most fiscally impactful activity. An entire infrastructure of financial surveillance had to be created to organize warfare and conquest more efficiently. This edifice of control and scrutiny rested upon a growing appetite for reliable information about the financial health of the Indian empire and forecasting the dividends of territorial conquest.