The empirical study and methodical government of populations are among the early modern period's definitive legacies to the modern. In the 1580s, Giovanni Botero described demographic knowledge as part of any effective ruler's toolkit; during the Stuart Restoration, the measurement and manipulation of problematic subpopulations became the explicit goal of William Petty's “political arithmetic.”Footnote ¹ In the eighteenth century, demographic concerns shaped projects of social engineering, empire building, and economic “improvement,” while a new demographic awareness encouraged popular agency in family limitation.Footnote ² Whether tied to the creation of scientific economics, state formation, or the rise of modern governmentality, the emergence of population as the preeminent object of political knowledge and action, and of life itself as an object of individual and collective management, was central to Enlightenment conceptualizations of society and governance, and to the experience of power.Footnote ³

As the intellectual history of population has fueled explanations of modernity, modern disciplinary models have constrained views of early modern demographic thought.Footnote ⁴ Thus the quantitative demographic discourse of political arithmetic, pioneered during the Restoration by John Graunt and William Petty, becomes a species of “political economy.” Its construction of population is assumed to resemble that of modern social science: a secular engagement, concerned with using statistics to calibrate policy in the interests of wealth or growth.Footnote ⁵ The reduction of “population” in an English discursive context to a thinly veiled concept of labor undergirds accounts of the rise of a commercial mind-set in the later seventeenth century, its domestic triumph in the Revolution of 1688–89, and its achievement of hegemonic status in the generations thereafter.Footnote ⁶ Yet placing the quantitative, empirical study of population on one side of a contest between archaism and modernity (particularly if this is seen in terms of secularization) ignores much of its content and obscures what it meant to most of those who produced, consumed, and rearticulated it.

A quantitative approach to population helped orient political and social thought to new problems of wealth and power during the long eighteenth century. At the same time, political economy came to function as a “platform” for Enlightenment.Footnote ⁷ But political economy was not the only avenue by which demographic quantification entered the Enlightenment, and its concerns did not always set the terms for the encounter. Many political economists, indeed, regarded political arithmetic as an occupation distinctly inferior to their own; Adam Smith used it as a source of data, but he expressed “no great faith” in its accuracy.Footnote ⁸ More recently, Mary Poovey has emphasized the distinction between moral philosophy, from which political economy derived, and police, the older “science of government” to which she argues political arithmetic belonged.Footnote ⁹ However, this genealogy obscures as much as it reveals. Starting in the 1660s and continuing through its “golden age” under William III and Anne, political arithmetic found a number of religious uses.Footnote ¹⁰ In particular, it played highly visible roles in “physico-theology,” the attempt to demonstrate God's providence through the empirical study of nature, and to debates about the historical and natural-philosophical plausibility of the book of Genesis.Footnote ¹¹

What one might call “sacred” political arithmetic dealt not with the management of labor or revenues but with evidence of divine government and the “oeconomy” of creation. It said less, in the first instance, about the secular present or future than about the ancient and scriptural past. It was the instrument not of bureaucrats or projectors but of natural philosophers, scholars, and clergymen—specifically, latitudinarian Anglicans and like-minded defenders of scripture and providence against the challenges of deism, preadamism, eternalism, and materialism. This is not to suggest that “religious” users of demographic quantification presented a united front. Different authors favored different texts of scripture and therefore different chronologies of sacred history. Among them were at least one High Churchman, a larger number of more or less heterodox Arians or anti-Trinitarians, and a handful of scientifically inclined New England Congregationalists. What they shared was a commitment to securing a scriptural worldview by rational means, establishing that a short chronology and a providentialist interpretation of nature and history could withstand the scientific scrutiny political arithmetic made possible—and, thereby, the skeptical assaults of deists and atheists. Alert to the epistemological promise of this new “art of reasoning,” they reaped its benefits outside the realm of modern social science.

Sacred political arithmetic was more than an archaic curiosity. In applying empirical demographic observations to the distant past in order to frame natural explanations of scriptural claims, latitudinarian and allied users of political arithmetic implied the commensurability of past and present. They thereby intimated a shift in ideas of historiographical plausibility often associated with the very “radical Enlightenment” against which their efforts were bent.Footnote ¹² Jed Buchwald and Mordechai Feingold have traced the role of population in Isaac Newton's historical research, which they argue yielded a new idea of civilization itself.Footnote ¹³ Yet even before this, and for a long time afterward, Anglican apologists probed the historical and religious implications of empirical demographic observations. More timid than Newton and less worldly than political economy, their cautious and selective engagements with demographic quantification better represent what population meant to a literate, moderate, Protestant English mainstream—a mainstream to which most “secular” political arithmeticians belonged.

Like the discourse of physico-theology and early theories of geohistory to which it sometimes contributed, sacred political arithmetic was radical more by implication than by design.Footnote ¹⁴ Nevertheless, in making empirical observation and naturalistic explanation into exegetical principles, however partially or hesitantly, it formed part of the remodeling of cognitive values identified by Stephen Gaukroger as the key to the Enlightenment and the “emergence of scientific culture.”Footnote ¹⁵ Like physico-theology, it was primarily a Protestant, and an English, endeavor—in contrast to state or economically oriented applications of demographic statistics.Footnote ¹⁶ It took shape within a distinctively English culture of demographic data gathering, centering on London's printed bills of mortality and the registration duties of the Anglican parish priest.Footnote ¹⁷ It was a specifically English fusion of theological apologetic and empirical science, effected by political arithmetic's own inventors and their Anglican readers in the decades following the Restoration and the formation of the Royal Society.Footnote ¹⁸

Sacred political arithmetic sheds light on what historians of science have described as a “latitudinarian” deployment of probabilistic reasoning, natural law, and empirical method against deism, religious “enthusiasm,” and hierocratic authoritarianism.Footnote ¹⁹ The “latitudinarian” label has been criticized, but an alternative formulation such as “Anglican rationalism”—entailing “the reasonableness of scripture and the general availability of its fundamental, saving truths to the plain sense of all readers”—captures what was at stake.Footnote ²⁰ It seems clear, however, that certain demographic arguments circulated among clerics and laymen who shared links with reputed latitudinarian figures, Low Church views, and empiricist methodological commitments; expositions of this sacred political arithmetic frequently occurred in venues, such as the Boyle Lectures, that showcased stereotypically latitudinarian ideas.Footnote ²¹ Sacred political arithmetic bears out the idea of a clerical Enlightenment shaped by the values and beliefs of seventeenth-century latitudinarian theologians and natural philosophers.Footnote ²² Conversely, political arithmetic's latitudinarian appeal helps explain its adoption by New England Puritans drawn to the theology of John Tillotson, the science of the Royal Society, and Whig ideas of Protestant empire.Footnote ²³

More than simply suggesting that religious uses of demographic quantification had political implications, however, excavating sacred political arithmetic puts secular statistics and its public profile in a different light. First, it suggests that providential interpretations and scriptural allusions should not be dismissed as extraneous bits of period dress. Second, it reminds us that while both sacred and secular works publicized new thinking about population, the former likely played the more prominent role. The “golden age” of political arithmetic was also that of the sermon, and it was through the latter that demographic claims probably reached the largest audiences.Footnote ²⁴ Far more people read William Derham's Physico-Theology than ever picked up Charles Davenant's Discourses on the Publick Revenues; as late as 1750, sacred history was still part of the intellectual mainstream.Footnote ²⁵ The religious dimension of seventeenth- and eighteenth-century demographic thought can be dismissed only at the cost of obscuring what population meant to most of the people who wrote, read, and thought about it at the time.

All this suggests, finally, that sacred political arithmetic has implications for our understanding of the “modernity” of the Enlightenment itself. Most current literature traces substantive developments in demographic thinking to operational (or, in Foucault's formulation, “biopolitical”) contexts, wherein population became an object of knowledge and management at once—for example, a labor pool, a target of disease, or an army.Footnote ²⁶ In such accounts, religion appears either as an ideological hindrance to the progress of enumeration (as with references to the biblical prohibition on census taking) or else as the archaic source of certain features of the modern state (as in Foucault's idea of “pastoral power”).Footnote ²⁷ Neither theology nor the church has been granted an active role in population's emergence as a scientific and political object. Yet until the nineteenth century, churches, and the Church of England in particular, were crucial gatherers and repositories of demographic information.Footnote ²⁸ Clergymen were prominent public interpreters of this information; they gave ideas about population polemical currency as well as practical, pastoral force.

Population attracted new political and scientific attention during the long eighteenth century, but the example of political arithmetic suggests that this could happen through, not in spite of, religious commitments. Discussions of sacred history provided space for the elaboration of “natural” ideas about population, as governed by laws and constrained by the environment; the use of these ideas in establishing the plausibility of historical claims reflected a cognitive shift fundamental for later Enlightenment reconstructions of the past. Providential interpretations of demographic data persisted longer still. Midcentury medical arithmeticians still ascribed moral significance to the course of epidemics. Indeed, as A. M. C. Waterman and Donald Winch have shown, demographic providentialism colored Malthus's Essay on the Principle of Population.Footnote ²⁹ From the Stuart Restoration to the Age of Revolutions, in short, population retained a sacred as well as a secular meaning. Almost from its inception, political arithmetic promised access to both.

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William Petty coined the phrase “political arithmetic” around 1670. He applied it to a host of works, many focused on the government of quantifiable groups: idle laborers, colonial settlers, and notoriously the Irish, whom (as the owner of extensive Irish estates) he sought to render industrious and loyal by means of an ambitious program of social engineering.Footnote ³⁰ Petty's contemporaries retrospectively affixed the same label to the work of his friend, tradesman and fellow of the Royal Society John Graunt, whose 1662 Natural and Political Observations . . . upon the Bills of Mortality came to be seen as the genre's founding text (partly for this reason, it was often misattributed to Petty).Footnote ³¹ Graunt's analysis of the London bills led him to conclusions about plague measures, social and economic policy, and the comparative salubrity of city and country. Both men aimed, in a Baconian vein, to be useful.Footnote ³² Their best-known successors after 1688 cemented political arithmetic's secular legacy. Gregory King tabulated those parts of the population increasing and those decreasing the wealth of the kingdom.Footnote ³³ Charles Davenant, using King's numbers, authored a shelf of economic and political works, becoming “probably the most influential English analyst of trade” of his time.Footnote ³⁴ He also penned the pithiest and arguably the most influential definition of political arithmetic, as “the Art of Reasoning, by Figures, upon Things relating to Government.”Footnote ³⁵ Perhaps most significantly, the polymath Edmund Halley used mortality bills from Breslau (Wrocław) to construct a “life table,” giving the probability of an individual's survival to a given age and initiating a long series of refinements in the calculation of annuities.Footnote ³⁶ These men confirmed political arithmetic's profile as a proto-statistical demography meant for concrete, secular uses.Footnote ³⁷

Yet despite Petty's influential (biblical) rhetoric of “number, weight and measure,” political arithmetic did not create the “information state.”Footnote ³⁸ On the one hand, this was because the necessary “avalanche of numbers,” such as national census data, lay far in the future.Footnote ³⁹ On the other hand, the kinds of information that Graunt and Petty used were generations old when they wrote. Bills of mortality began during sixteenth-century plague outbreaks and had been printed continuously since 1603; enshrined in popular broadsheets from the 1620s onward, they also featured in Samuel Pepys's firsthand and Daniel Defoe's fictionalized accounts of the 1665 epidemic.Footnote ⁴⁰ Registers of baptisms, marriages, and burials—the other blue chip source of population data—had been made the responsibility of parish clergy by Thomas Cromwell in 1538.Footnote ⁴¹ Both had faults: spottiness and the omission of dissenters compromised registers, while Graunt blamed inexpert “searchers” for mistaken causes of death in the mortality bills.Footnote ⁴² What was novel about political arithmetic was not the scope or accuracy of demographic information but the framework within which it had value. This framework came from natural philosophy.

The natural-philosophical roots of political arithmetic are not unknown. Baconian inductivism, Cartesian physico-mathematics, Boyle's matter theory, and Hobbes's ideas about geometrical demonstration all feature in histories of economics and studies of Petty in particular.Footnote ⁴³ However, neither the nature of such connections nor their implications for political arithmetic's reception have been fully appreciated. Natural philosophy was not simply a source of methodological inspiration or scientific rhetoric. Petty's “transmutation” of the Irish, for example, applied a corpuscularian reading of alchemical change directly to human populations, treating individuals as atoms and families as corpuscles; if new kinds of people were introduced in the right proportions, Petty suggested, the population's qualities would change with the same necessity as any other material.Footnote ⁴⁴ Similarly, when Graunt gathered the mortality bills, took “a view of the whole together,” and applied his “Shop-Arithmetique” to the resulting data, he was not proposing a “social” science analogous to “natural” science but conducting a “Natural History” in exactly the same terms as “those Noble Virtuosi of Gresham-Colledge [i.e., the Royal Society] (who reduce their subtle Disquisitions upon Nature into downright Mechanical Uses).”Footnote ⁴⁵ Political arithmetic was applied natural philosophy.

More specifically, it was a form of Baconian natural history, something Graunt and Petty both likely encountered through the Protestant “intelligencer” Samuel Hartlib and his circle in the 1640s.Footnote ⁴⁶ For Hartlibians like Gerard Boate, author of Irelands Naturall History (which Petty was invited to complete and which his 1655–56 “Down Survey” of Ireland superseded), natural history geared empirical observations to both the advancement of learning and the productive “improvement” of nature, whether by scientific, economic, or political means.Footnote ⁴⁷ Answering the Cambridge Platonist Henry More's criticism of the Hartlibians, Petty himself espoused a vision of philosophy grounded in the compilation of natural histories, which he preferred to the “Vaporous garlick & Onions” of more speculative philosophy.Footnote ⁴⁸ When they later turned their attention to population, both Graunt and Petty cited Bacon's proposed “History of Life and Death”—listed at the end of The New Organon as one of several “Histories of Man” to be pursued experimentally—as a model.Footnote ⁴⁹ It was from this model that political arithmetic's intellectual and operational power derived.

While this extension of empiricism to the social sphere foreshadowed the Enlightenment “Science of Man,” its more immediate effect was to involve demographic observation in religious disputes.Footnote ⁵⁰ Political arithmetic impinged on questions of belief by reason of its very object. Even as individual populations came to be conceived of as totalities governed by laws and susceptible to knowledge and intervention, population remained a global, historical process. The multiplication of mankind was, from an orthodox point of view, as unitary and as old as the earth itself.Footnote ⁵¹ The rules governing population were not simply tools for the sovereign but part of the structure of history, instruments of providence; the history of population was embedded in an authoritative, universal genealogy, from Adam, to Noah, to Noah's progeny.Footnote ⁵² When political arithmetic appeared, further, both providence and scripture were under attack from philosophical quarters close to those from which it had sprung. Its entanglement in these questions was inevitable and fraught.

Since the Renaissance, the authority of the book of Genesis and the short chronology its account of early history required had faced a series of challenges.Footnote ⁵³ The New World was one: why did scripture have nothing to say about its inhabitants or their origins?Footnote ⁵⁴ Encounters with other non-European cultures—Egyptian, Near Eastern, Indian, and Chinese—posed further difficulties, exacerbated by the written historical records these civilizations could boast. How could their impressive chronologies be reconciled with the biblical timeline?Footnote ⁵⁵ How could the cities and empires of the East have arisen within years of the Great Flood, which only eight people—Noah, his three sons, and their wives—had survived?Footnote ⁵⁶ Looming behind many such questions was the legacy of humanism: historical criticism in the mid-seventeenth century turned upon the Bible, and in particular the Pentateuch. At the hands of Hobbes, Spinoza, La Peyrère, and Richard Simon, scripture was historicized, its inconsistencies exposed, and its authorship and plausibility put in doubt.Footnote ⁵⁷

Biblical chronology itself was no simple matter. Interpreting texts was one thing, while accommodating the resulting data to the historical record was another. In De emendatione temporum (1583), the Huguenot scholar Joseph Scaliger used the Julian period as a framework for bringing together classical and sacred history, dating Creation to 3949 BCE; in the mid-seventeenth century, James Ussher, archbishop of Armagh, calculated that time had begun instead on the evening before 23 October 4004 BCE.Footnote ⁵⁸ By that point, over a dozen such dates had appeared, and they would multiply as attention shifted from technical details to the exigencies of religious polemic. Another challenge was the position of events within sacred history. Different versions of the Old Testament—including the Hebrew Masoretic text, the Greek Septuagint, and a recently discovered Samaritan translation—differed significantly on the time elapsed between Creation and the Flood (1656 years in the Masoretic text, 2242 in the Septuagint, 1556 in the Samaritan), as well as between the Flood and the birth of Abraham.Footnote ⁵⁹ Choosing between them meant weighing claims of divine inspiration against provenance and transmission histories. It also meant constraining to a more or less limited span of centuries the postdiluvian development of entire civilizations—and the populations they implied.

Population had featured in chronologists’ work long before political arithmetic, but it was often in the form of problem-solving exercises in speculative multiplication: how quickly could two people reproduce, adding their children's capacity to do the same, and their grandchildren's, and so on, to produce the numbers required for universal destruction in the Flood or for the construction of known civilizations afterward? Such efforts resembled and sometimes accompanied attempts to quantify other aspects of biblical history—the dimensions and layout of the Ark, for example.Footnote ⁶⁰ They could be extraordinarily complex, as scholars juggled specific demographic claims within scripture (the rapid multiplication of the Israelites in Egypt, for instance), logical presumptions about the capacity of the earth and the gradualness of increase, doctrinal requirements such as the universality of the Flood, and adherence to a particular version of scripture with its attendant chronology.Footnote ⁶¹ Such attempts made no appeal, however, to quantitative demographic data gathered in the present. Their object was not a naturalistic understanding of population that might act as a natural-historical bulwark for faith but the reconciliation of contradictory textual authorities. The biblical past was another country.

This does not detract from the inventiveness of the chronologists’ arguments. In his 1596 Chronologicarum demonstrationum libri tres, for example, Johannes Temporarius (Jean du Temps) constructed a bar graph of postdiluvian population growth in support of the Masoretic chronology. Citing Ussher's treatment of such calculations in 1662, the latitudinarian Edward Stillingfleet, future bishop of Worcester, recalled Temporarius's hypothesis “that all of the posterity of Noah when they attained twenty years of Age had every year twins,” yielding a population of 1,554,420 barely a century after the Flood.Footnote ⁶² Stillingfleet criticized these and similar suppositions (such as “that each of the sons of Noah had ten sons” or that “the multiplication of the children of Israel in Egypt,” where “from 72. men in the space of 215. years there are procreated 600000,” was typical), preferring to follow the Dutch critic Isaac Vossius in adopting the elongated chronology of the Septuagint.Footnote ⁶³ Among Anglicans, this remained a minority position, for the gradual population growth it accommodated implied limited antediluvian settlement and perhaps a less-than-universal Flood; by contrast, the latitudinarian jurist Matthew Hale (who used Graunt and whose 1677 Primitive Origination of Mankind Petty read) cited Temporarius and seventeenth-century Jesuits Petavius (Denis Petau) and Athanasius Kircher in favor of the Hebrew text.Footnote ⁶⁴

Political arithmetic did not introduce quantification to these debates; nor did it inherently favor one text over another. Rather, it changed the epistemological terms on which the quantitative defense of scripture, whether by theologians or by natural philosophers, made sense.Footnote ⁶⁵ The immediate context for this was Isaac La Peyrère's challenge to Genesis. La Peyrère's 1655 Prae-Adamitae, translated in 1656 as Men before Adam, focused on scriptural inconsistencies—some, such as the problem of where Cain's wife had come from, long familiar—and claimed in particular that a passage in Paul's epistle to the Romans established the existence of a preadamite population.Footnote ⁶⁶ But La Peyrère also alleged natural arguments in defense of his interpretation. Among these was the assertion that Noah's sons and their wives could not have multiplied quickly enough after the Flood to account for the rise of empires—attested in scriptural and pagan sources—by Abraham's time. La Peyrère concluded from this that the Bible was not the history of all humankind but only of the Jews, who had been deposited by a separate creation into a world already stocked with people. The implications of such polygenism for thinking about human diversity took a long time to unfold, but its threat to orthodoxy was immediately obvious. If Adam had not been the first man, then the world was much older than scripture allowed; if the Flood was merely a local catastrophe, the world had not been repopulated from Noah's line at all.Footnote ⁶⁷ Population—not just a number, but a dynamic entity whose growth was subject to natural laws (however unclear these were)—was now crucial.

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Into a world teeming with “Scripture Scoffers and Prae-Adamites,” as Petty called them, political arithmetic was born. Its capacity to confront these threats was clear to its creators.Footnote ⁶⁸ We have seen that Graunt embraced the secular applications of demographic observation; another use, no less important, was the elucidation of providence. This was particularly evident in the sex ratio. Finding that male births tended to exceed female births “by about a thirteenth part,” Graunt drew a religious conclusion: “That Christian Religion, prohibiting polygamy, is more agreeable to the Law of Nature, that is the Law of God, then Mahumetism, and others, that allow it.” This was not simply a pious ejaculation in the midst of an otherwise secular discourse. On the contrary, the dispensation of providence that quantitative observation revealed was both a measuring stick and an explanation of human policy. The near balance between the sexes explained why polygamous nations were compelled to make eunuchs, an artifice Graunt compared to gelding.Footnote ⁶⁹ It also established the unnaturalness of Catholic celibacy, for “if a greater number of Males oblige themselves to [be] Caelibate than the natural overplus or difference between them and Females amounts unto, then multiplication is hindered,” either because too few men circulated or because women became barren through promiscuity. The natural way to encourage growth, by contrast, was by “encouraging Marriage, and hindering Liceniousness . . . [preserving] the Laws of God from contempt, and Violation.”Footnote ⁷⁰

This was a guideline for government as well as a revelation of divine order, and in both respects it was one of Graunt's most influential insights. Gregory King and G. W. Leibniz agreed that the sex ratio made polygamy unnatural.Footnote ⁷¹ The Scriblerian wit John Arbuthnot made the sex ratio the basis of his “Argument for Divine Providence,” printed in the Philosophical Transactions in 1712. He noted the advantage a natural surplus of males represented for the conduct of trade and warfare, showing “that it is Art,” that is, “Divine Providence, working for a Good End,” and “not Chance, that governs.”Footnote ⁷² Continental Protestant statisticians such as Willem Kersseboom and Lutheran pastor Johann Peter Süssmilch repeated the point, as did later English medical arithmeticians.Footnote ⁷³ (Montesquieu—and, following him, Louis de Beausobre—challenged Arbuthnot's factual claims and providentialist interpretation, arguing that polygamy might be natural in parts of Africa or Asia where climate affected the sex ratio.)Footnote ⁷⁴ In his 1711–12 Boyle Lectures, published in 1714 as Physico-Theology, William Derham even discerned a “balance of Animals,” claiming that providence governed different species’ populations by imposing an inverse relationship between fecundity and lifespan, calibrated to the usefulness of each creature. Thus “by a curious Harmony, and just proportion between the increase of all Animals, and the length of their Lives,” he wrote, “the World is through all Ages well, but not over-stored.”Footnote ⁷⁵ War, plague, and disaster might traverse the globe, yet human population as a whole continued to flourish. “[W]hat is all this,” he asked, “but admirable and plain Management?”Footnote ⁷⁶

Such demographic providentialism had politico-religious implications. It seems probable, for instance, that discussions of the sex ratio formed part of the intellectual context for the Marriage Duty Act of 1695, associated with Gregory King.Footnote ⁷⁷ King, meanwhile, later furnished calculations used in framing Queen Anne's Bounty, designed to shore up the livings and public image of the lesser Anglican clergy.Footnote ⁷⁸ Yet as Davenant's definition implied, “Reasoning, by Figures, upon Things relating to Government” might serve either side in political debate; Julian Hoppit is surely right to describe eighteenth-century political arithmetic as a “broad church.”Footnote ⁷⁹ Political arithmetic was not the property of any political party. Some of its uses, moreover, had no obvious implications for government at all. Understanding political arithmetic's significance thus means asking not simply what sort of people embraced quantification but rather what the use of numbers might be understood to accomplish in different settings. Here the analytical distinction between secular and sacred political arithmetic becomes important. Anyone might appeal to numbers in secular matters. In sacred contexts, however, the role of empirical observation was less clear and its use more narrowly associated with latitudinarian polemic. Sacred political arithmetic was a “political” science in ways its secular counterpart was not.

This was clearest with respect to biblical history and chronology. Graunt's chapter “Of the Number of Inhabitants” predicted that London's population would double by natural increase in sixty-four years. Applying this “doubling period” to human history, Graunt concluded that Adam and Eve could, in the “5610 Years, which is the Age of the World according to the Scriptures,” produce far more offspring than now peopled the planet; “Wherefore,” he concluded, “the World is not above 100 thousand years old as some vainly imagine, nor above what Scripture makes it.”Footnote ⁸⁰ As we have seen, arguments about the rapidity of ancient population growth had long been used in defense of orthodoxy. What was distinct about Graunt was that he did not simply stipulate a set of assumptions about reproduction that would guarantee rapid doubling. Instead, he clamed to establish such doubling empirically, as a matter of fact attested not by ancient authority but by recent experience. Modern observations of London's growth here supported not only the idea of gradual increase, or even a timetable compatible with scripture in general terms, but also Scaliger's specific calculation of the date of Creation. For the first time, sacred history was justified by quantitative demographic observations made in the present.Footnote ⁸¹

For his part, Petty—when pressed by a staunch Calvinist critic, Thomas Barlow—declared “The Mysteries of the Trinity, the Incarnation, and the Resurrection” matters above reason.Footnote ⁸² In freer moments, however, he vindicated the plausibility of bodily resurrection against the jeers of “Scepticks” by showing that Ireland alone contained more than enough space for the bodies of all people ever born.Footnote ⁸³ In letters to his friend (and later president of the Royal Society) Robert Southwell and in print, Petty used observations of variable urban and rural doubling periods to construct a chronology of global demography indexed to events in sacred history, in which periods of doubling gradually lengthened, from 10 years immediately after the Flood to 290 “In Moses Time” and 750 “About the Birth of Christ.”Footnote ⁸⁴ This was not an optimally “natural” account of demographic history; in varying the doubling periods he used to fit biblical dates, Petty took a “discretionary liberty” that rendered his account merely plausible rather than precise (he took the same approach to secular calculations). Nevertheless, by restricting his discretion to the use of rates of doubling that had been observed, he made consistency with natural history the touchstone of his apologetic. Using current observations of the proportion of “Teeming [i.e., fertile] Women” in a given population, fixing an average ratio of births to deaths by comparing cities and country villages, and allowing for the effects of plagues and other disasters (judged by England's recent experience), Petty sketched a history of population designed “to solve what is written in the Holy Scriptures and other Authentick Books”—or, as he told Southwell, to “[solve] all the Phenomena of Scripture upon ground Experimentally true.”Footnote ⁸⁵

From the outset, sacred political arithmetic framed empirical observations of present-day demography as independent sources of probable, experimentally justified knowledge about the past. Shifting the epistemological burden of apologetic from biblical exegesis to empirically verifiable natural histories allowed the case for scripture's accuracy to be put to skeptics or atheists in probabilistic terms, compelling the assent of the rational reader. Like other forms of physico-theology, this involved risks as well as benefits, inviting accusations of atheism and opening the door to scientific assaults on scripture. It also involved compromises. Only a prior commitment to a Christian worldview underwrote Petty's particular arrangement of early doubling periods to suit scripture. Less orthodox reconstructions would have been equally legitimate, or equally arbitrary, in purely empirical terms. In other words, sacred political arithmetic suffered from the same ideological constraints that critics identified with natural theology in general.Footnote ⁸⁶ What is interesting is that, notwithstanding these constraints, an avowedly naturalistic, empirically grounded picture of population supplanted assertions of growth derived from the perceived requirements of a given sacred text.

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Political arithmetic's appeal for latitudinarian Anglicans and their allies is not hard to understand. Barbara Shapiro, in particular, has argued that latitudinarians embraced a probabilistic discourse of empirically discoverable “facts” as a way of confuting both radical skeptics and religious “enthusiasts” while avoiding recourse to dogmatism.Footnote ⁸⁷ Political arithmetic was such a discourse, so it is not surprising that two giants of the latitudinarian tradition, Stillingfleet and Hale, were among the first to suggest its use in a sacred context—even as they differed over the relative merits of the Hebrew and Greek texts of scripture. Writing in 1662, Stillingfleet engaged La Peyrère on this ground, asserting that if “Arithmetick” could determine the facts of ancient demography, it might reveal the extent of the Flood.Footnote ⁸⁸ Since this left the question open, however, Stillingfleet posited “a more then ordinary multiplication of the world from the sons of Noah after the Flood”—that is, a miracle: “For as God had before punished the world by destroying mankind in it by an extraordinary manner; so after the Flood, he doth in a particular manner bless Noah and his Sons, and said unto them, Be fruitfull and multiply, and replenish the earth, which may well be thought to have then had an extraordinary effect.”Footnote ⁸⁹ In the absence of firmer evidence, the same divine omnipotence that had effected the Flood could account for humankind's recovery.

Stillingfleet's was a very limited first step away from traditional apologetics. As Petty's own work suggested, answering La Peyrère depended less on exact numbers than on the probability that eight people had replenished the earth in relatively short order. As we have seen, defenders of scripture had typically posited what David Livingstone calls a “primitive hyper-fecundity” beyond the capacity of modern people, while also noting the longevity of the patriarchs.Footnote ⁹⁰ For Stillingfleet this fecundity remained miraculous; a special act of providence produced an “extraordinary” and localized effect in Noah and his family. Some thought similarly of biblical longevity, confining it to a virtuous minority.Footnote ⁹¹ One effect of political arithmetic, in comparison, was to encourage naturalistic accounts of primitive fecundity, in terms of physical (or sometimes cultural) circumstances obtaining in the wake of the Flood. Stillingfleet's dismissal of “Heathen Histories” also became less tenable.Footnote ⁹² Since the authority of scripture was at issue, political arithmetic's apologetic value lay precisely in its epistemological independence of revelation.

A more sustained attempt to exploit this was Matthew Hale's 1677 Primitive Origination of Mankind. Like many others, Hale saw in political arithmetic evidence of God's providence. Following Graunt and anticipating Arbuthnot, he noted the order and utility of the sex ratio.Footnote ⁹³ He also, like Stillingfleet, disparaged Babylonian, Egyptian, and Chinese challenges to the biblical timeline as “uncertain idle Traditions.”Footnote ⁹⁴ But he did not rest there. The propensity of populations to grow steadily over time was not only an index of providence but also a crucial piece of historical evidence against both preadamism and the Aristotelian doctrine of the eternity of the world.Footnote ⁹⁵ If population had always grown, it must have had a beginning; and if political arithmetic could establish probable rates of increase for given periods of history—whether or not precise numbers were known—then La Peyrère was vulnerable: “The Inhabitants of the World do daily increase, and their increment surmounts daily their decrease; which could not be, unless the World of Mankind had their original within some proportionate time, and could not consist with such a vast excess of duration which some would assign, much less with an eternal duration.”Footnote ⁹⁶ Hale did not think, with Stillingfleet, that a lack of ancient data hampered the application of “Arithmetick” to history. Modern observations furnished a probable account with which to work.

Yet the present could not simply be mapped onto the past without modification. Even if the Bible's authority was not assumed in its own defense, the text of scripture imposed certain restrictions on the application of political arithmetic to the past if that application was to serve any apologetic purpose. The most obvious of these was lifespan: while the few human lives now exceeded eighty years, lives ten times as long were recorded before the Flood, and lives of several centuries’ duration even in its wake. For Hale, antediluvian longevity, modestly abridged in the first postdiluvian generations, was crucial to natural explanations of the earth's repopulation: “For considering the long Life of the Ancients that lived within 300 years after the Flood, and consequently their coexistence with those that descended from them; we may without the help of a miraculous fertility find that in 104 years Mankind descended from Noah and his three Sons and their Wives, might arise to a stupendious multitude by that Arithmetical Progression that would be found in their Generations.”Footnote ⁹⁷ As a distinctly ancient condition, unknown in modern times, longevity was both an explanatory resource and an epistemological problem. Like the preternatural fecundity it here obviated, it risked turning political arithmetic from a rational proof of scripture into a fig leaf for the arbitrary demands of faith.

A third latitudinarian attempt to bridge secular present and sacred past came with William Bentley's inaugural Boyle Lectures, delivered in 1692 and printed the following year as The Folly and Unreasonableness of Atheism.Footnote ⁹⁸ Bentley was Stillingfleet's former chaplain, an avid Newtonian, and one of the preeminent exponents of physico-theology. Confronting eternalism, preadamism, and Epicureanism (which substituted chance for design), he cited Graunt, Petty, Stillingfleet, and Hale in support of his conclusion that the “Opinion of infinite Generations is repugnant . . . to matter of Fact. “Tis a Truth beyond opposition, that the universal Species of Mankind hath had a gradual increase, notwithstanding what War, and Famine, and Pestilence, and Floods, and Conflagrations, and the Religious Profession of Celibacy, and other Causes, may at certain periods of time have interrupted and retarded it. This is manifest from the History of the Jewish Nation, from the account of the Roman Census, and Registers of our own Country, where the proportion of Births to Burials is found upon observation to be yearly as Fifty to Forty.”Footnote ⁹⁹ Like Hale, Bentley assumed that knowledge of contemporary demographic patterns was applicable to the biblical past, that demographic processes were at least commensurable if not uniform across history, and that providence therefore governed populations through natural, scientifically accessible means. Only on this basis could political arithmetic defend sacred history. Yet no more than Hale or Stillingfleet had Bentley resolved the problem that in crucial respects—fertility and longevity—biblical populations had evidently not resembled modern ones. This difference was part and parcel of the orthodoxy political arithmetic was deployed to uphold; it could not be abandoned but had to be explained. Latitudinarian users of political arithmetic thus faced the dilemma that past and present must be similar enough to be subject to the same science, yet they had to be distinct enough to render natural the demographic differences upon which scripture insisted.

How could one accommodate the facts of political arithmetic to those of the Bible without betraying natural philosophy to dogmatism? Thomas Burnet—a Cartesian philosopher rather than a sacred historian, and an Arian rather than an orthodox Anglican—offered a dangerous but influential answer.Footnote ¹⁰⁰ Identifying divine providence with the regular operation of nature, the first two books of Burnet's Theory of the Earth, printed in English in 1684, defended scripture's general outline by abandoning its philosophical accuracy and treating it (as deists like Charles Blount appreciated) as an allegory tailored to the vulgar.Footnote ¹⁰¹ Burnet countered La Peyrère by noting that the “longevity of the first Inhabitants of the Earth seems to have been providentially design'd for the quicker multiplication and propagation of mankind.” Indeed, “mankind thereby would become so numerous within sixteen hundred years [roughly the Masoretic figure], that there seems . . . to be a greater difficulty from the multitude of the people that would be before the Flood, than from the want of people” before or afterward.Footnote ¹⁰² Rather than appeal to miracles, however, Burnet sought to “silence the Cavils of Atheists” by tying longevity to the antediluvian environment, wherein a springlike climate, smooth topography, and fertile soil supported greater numbers and stronger constitutions than the postdiluvian earth could.Footnote ¹⁰³ Providence worked through natural causes, so that “it is altogether as strange a thing that men should have such short lives as they have now, as that they had such long lives in the first Ages of the World.”Footnote ¹⁰⁴ Once the Flood had destroyed this primeval paradise, constitutions naturally weakened and lifespans gradually declined—“[f]or,” as Burnet wrote, “every new state of Nature doth introduce a new Civil Order, and a new face and Oeconomy of Humane affairs.”Footnote ¹⁰⁵ Nature's fundamental laws were the same in Petty's time as they had been in Noah's; its specific “Oeconomy,” however, had changed.

Burnet's physical hypothesis was scarcely more orthodox than its targets. Yet his exegetical flexibility reflected problems that none committed to the experimental proof of revelation could avoid. In this sense, the Newtonian scholar and mathematician William Whiston's reply, the 1696 New Theory of the Earth, fared no better.Footnote ¹⁰⁶ Whiston knew of political arithmetic through Sussex rector William Nicholls's antideist dialogue A Conference with a Theist, also printed in 1696. Nicholls's mouthpiece, Credentius, argued against eternalism “from the Increase of Mankind,” conjuring the skeptical Philologus to

Pressed by Philologus to explain why population might not simply oscillate around a kind of equilibrium, with years of increase followed by “Wars, Famines, and especially Plagues” and “the Eternity of the World” witnessing “successive Increases and Desolations,” Credentius delved into classical and modern histories of plague, noting Petty's comments on London's rapid recovery after 1665.Footnote ¹⁰⁸ Philologus responded by attacking Petty's variable doubling periods (“a perfect Popish Nose of Wax”) with vigor: “You make your Periods as you please, and Mankind must either double or treble . . . to serve your Hypothesis. Sir, I believe the Generation, like the Age and stature of Mankind, is governed by a steddy unalterable Law, and is not to be turn'd about to go either fast or slow like a Dukes-Place Clock. I find all of you when you have but a new Hypothesis to advance, will take Nature as well as your Bibles by the Nose, and lead them which way you please, to serve a turn.”Footnote ¹⁰⁹ Faced with the possibility that his science might not bear his argument, Nicholls, like Stillingfleet and Hale, fell back on divine intervention (the “peculiar blessing of Increase given to those first Ages after the Flood”) and the authority of “the Mosaical Books.”Footnote ¹¹⁰

Whiston agreed with Burnet that “[t]he Inhabitants of the Earth were before the Flood vastly more numerous” than since and that antediluvian longevity was environmentally conditioned.Footnote ¹¹¹ So taken was he with political arithmetic's potential and Nicholls's critique that he devoted a five-page postscript to the dispute, concluding “that, excepting what disturbance extraordinary and uncommon Wars, Famines, Plagues, and such other Merciless destroyers of Mankind of given thereto, Mankind have generally increas'd in the same determinate Proportion, and doubled themselves in three hundred and sixty years [Petty's figure for the world's then-current rate of doubling], for more than three thousand years, from the Time of Moses, till the present Age.”Footnote ¹¹²

Accepting Petty's observations but insisting on a less “discretionary” application of them to the past, Whiston sought to improve political arithmetic's methodological consistency and with it the power of the demographic argument against eternalism. But here, like Burnet, he crossed a line that had stopped earlier authors, for, as Credentius conceded, steady doubling periods were inconsistent with specific scriptural claims if not its overall chronology. While Whiston's physical explanation of the Flood was new (he attributed it to the gravitational force exerted by a passing comet), he thus followed Burnet in linking antediluvian fecundity to a distinct environment. For the postdiluvian world—essentially the same as his own—Whiston likewise abandoned scripture's literal truth to defend its chronology in terms of the uniform operation of natural demographic laws. Tainted by Arianism, and eventually driven from Cambridge, Whiston was no straightforward defender of “orthodoxy.” Yet in seeking a natural account of early demography to suit scriptural chronology, he faced the same challenges, and looked to the same resources, as his latitudinarian predecessors and successors.

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By 1700, sacred political arithmetic was an essentially apologetic, providentialist, antideist discourse, built on polemical foundations laid by latitudinarians in the 1660s, exploited to the point of heterodoxy by theorists of the earth, and incorporating a growing body of demographic observation and analysis. Despite their dubious reputations among the orthodox, even Burnet and Whiston were seldom if ever blamed for using political arithmetic, though they might be charged with failing to use it properly. Suffolk rector Erasmus Warren's 1690 Geologia faulted Burnet's attempt to tie ancient longevity to environmental conditions not only because it lacked “good authority” but also because of the implausible demographic picture that resulted from combining universal, extreme longevity with hyperfecundity and polygamy: “[T]heir Multitudes would have everlaid [sic: overlaid] the Earth, and they would have wanted room wherein to subsist.” For Warren, “either the Longaevity of the Antediluvians must not be universal, or the earth was incapable of the number of its Inhabitants.”Footnote ¹¹³ On the one hand, although the natural philosopher John Beaumont likewise insisted that such longevity had been “granted only to Patriarchs and some few others by a particular Providence” (which took effect alchemically, “through the means of a certain Panacaea”), this view was unusual in rational defenses of scripture.Footnote ¹¹⁴ On the other hand, with the exception of Newton—who was himself committed to the Masoretic text—overtly heterodox appropriations of demographic observation were seemingly few. Later theorists of the earth such as John Woodward, meanwhile, ignored human multiplication in favor of geological phenomena.Footnote ¹¹⁵

Following the lead given by their Restoration predecessors, early eighteenth-century latitudinarian and latitudinarian-influenced apologists came to stress the expression of God's design through the regular operation of physical causes, minimizing (though not altogether excluding) miraculous suspensions of the order of nature.Footnote ¹¹⁶ This tendency is striking even in Puritan New England, whence Cotton Mather—a promoter of physico-theology who read Whiston and, more comfortably, Bentley—sent Richard Waller, secretary of the Royal Society, “a Calculation of the possible Increase of the Descendants of Adam” in 1712.Footnote ¹¹⁷ In “confuting the Caviling prae-Adamites” and “Deists” for a transatlantic and ecumenical Protestant readership, Mather combined old sources, from Josephus and Pliny to Scaliger and Temporarius. He also used Graunt's findings on life expectancy, and his letter noted contemporary instances of longevity and fertility drawn from colonial experience and natural histories—observations that underscored the natural plausibility of scripture's demographic claims.Footnote ¹¹⁸ Nor was this letter a one-off. Mather's massive, unpublished biblical commentary, the Biblia Americana, cited “Sir William Petty” (really Graunt's Observations) on the sex ratio, in the context of an attempt to calculate the population of ancient Israel.Footnote ¹¹⁹ Indeed, Mather even used Graunt's life table in several funeral sermons from 1708 onward, citing high rates of infant and child mortality to keep congregants mindful of the precariousness of life.Footnote ¹²⁰ (This pastoral use of political arithmetic may elucidate Mather's promotion of smallpox inoculation in 1720–21—an instance, possibly, of sacred political arithmetic undergirding secular improvements.)Footnote ¹²¹

Thus, for latitudinarian and allied defenders of providence and scripture on either side of the Atlantic in the early eighteenth century, political arithmetic served polemical and pastoral functions in manuscript, in print, and in public. Inasmuch as it furnished an enlightened justification for various textual preferences, the antideist discourse of demographic law may sometimes have crossed confessional lines. In 1720, for example, the Irish Catholic priest and scholar Cornelius Nary defended the “Truth and Probability” of the Septuagint against “Modern Libertins, Deists, Atheists and Pre-Adamites,” by which he meant those who used the Masoretic chronology to “make the First Kings of the Assyrian, Babylonian and Egyptian Monarchies to have Reign'd some Hundreds of Years before the Deluge.”Footnote ¹²² Among his reasons was the implication “that Noah's three Sons, in the space of 367 Years, should so increase as to People all these Vast and Spacious Countries, and produce so many Millions of Men,” an idea that violated both scripture and “the very Nature of Things.” This argument, anticipated by Stillingfleet, resurfaced in Anglican controversialist John Jackson's 1752 Chronological Antiquities, which decried the Hebrew text's demographic implications as an “Absurdity against the regular and ever uniform Course of Nature.”Footnote ¹²³

Successive iterations of this discourse showed a concern with the natural peculiarities of biblical populations that reflected both refinements in secular political arithmetic and complications already noted regarding the uniformity of ancient and modern nature. The extreme longevity of biblical populations, for example, often suggested greater physical strength and stature. In his 1730 Scripture Chronology Demonstrated, the staunch High Churchman Arthur Bedford—condemning Newton's revisionist insistence on small postdiluvian populations—repeated Temporarius's suggestion that the stronger and more fecund ancients “might have had Twins every year.”Footnote ¹²⁴ But authors more mindful of the “decrements” operating on populations in their own time tried not to overstate the case for ancient population. Richard Cumberland, Tillotson's protégé and later bishop of Peterborough, supposed that ancient couples might have begun reproducing at age twenty, producing one child each year, male and female births alternating. This would rapidly produce a population in excess of biblical requirements. Yet, as he wrote in Origines Gentium Antiquissimae (printed posthumously in 1724), “[A]ll this surplusage, and all their issue in every succession we reckon not in our table, but give in liberally to compensate all later marriages, barrennesses, and casual deaths which can't be accounted for, and to the same end we reckon upon no births of twins. . . . To add to our compensation of casualties, we reckon of no births within less time than a full year.”Footnote ¹²⁵ Having demonstrated that “great numbers of men were possible,” Cumberland left it to future historians to show “great numbers actually to have been.”Footnote ¹²⁶ Petty, who had emphasized that his own numbers were probable measures of “natural possibility” rather than precise assertions of positive fact, could hardly have put it better.Footnote ¹²⁷

Norfolk rector Samuel Shuckford's three-volume Sacred and Prophane History of the World Connected (1728–37), a monument to latitudinarian exegesis and Enlightened euhemerism, imaginatively traced the natural effects of biblical demography.Footnote ¹²⁸ One result was an explanation of the “Confusion of Tongues” in terms of “The gradual Decline of Men's Lives, from longer to shorter Periods”: “for when Men's Lives were long, and several Generations lived together in the World . . . they could not but transmit their Language thro’ many Generations with but little Variation: But when the Successions of Mankind came on quicker, the Language of Ancestors was more liable to grow Obsolete, and there was an easier Opportunity for Novelty and Innovation to spread amongst Mankind. And thus the Speech of the World, confounded first at Babel, received in every Age new and many Alterations.”Footnote ¹²⁹ The Arian Robert Clayton, Church of Ireland bishop of Clogher, took an even more directly political-arithmetical approach to the question. The dispersion from Babel, he argued, was both a divine chastisement and an effect of population pressure on the land.Footnote ¹³⁰ Considering the heroic childbearing careers open to women whose lives spanned several centuries, he grounded his speculation in a proportionality between ancient and modern life cycles, “since Women, at present . . . frequently bear Children after they are fifty Years of Age, and seven hundred bears near the same Proportion to nine hundred and fifty as fifty does to seventy.”Footnote ¹³¹ He even applied to Noah's wife and her fellows the telltale political-arithmetical term for women of childbearing age: “breeders.”Footnote ¹³²

As Clayton's presumption of proportionality but not identity between ancient and modern demographic patterns suggests, attempts to establish the reasonable nature of computations prompted thinking about what assumptions were “reasonable” given what was known about the ancients on one hand and nature's economies on the other. In his Enquiry into the Truth and Certainty of the Mosaic Deluge (printed in 1750, a year after his death), Scottish Episcopalian clergyman Patrick Cockburn allowed that “as the birth of Twins is not so very rare even in our days, it might probably be more frequent at first, when human nature was vigorous and healthful, as by their long lives appears.” “For the same reason,” he thought, “we may reasonably suppose that few children died in their infancy, whereas now numbers do every year.”Footnote ¹³³ But ancient longevity made it unreasonable to assume that the patriarchs “began to propagate their kind as early” in life as at present or (since the “time allotted to the nursing of Infants” was likely longer) “that the women brought forth children every year.”Footnote ¹³⁴ On the contrary:

A later Boyle lecturer, William Worthington, went even further, pointing out that “[t]he period of gestation might not have been the same, in the old world, as in this”—yet another reasonable caution against overconfident assertions of ancient fecundity.Footnote ¹³⁶

While Cockburn's presumption of a proportionality between corresponding stages of life among ancients and moderns led him, like Stillingfleet and later Jackson, to champion the Septuagint, his emphasis on the analytical significance of such stages followed a lead given by Petty and others studying modern populations.Footnote ¹³⁷ (Even an opponent of Cockburn's based his criticism on an alternative proportionality between maturation and physical size: “Naturalists agree,” wrote Philip Howard in 1797, “that parrots, ravens, and eagles” outlive humans, “and yet we do not perceive that they attain their full vigor much later than other birds of the same size.” Thus “Man, when he lived 400 years, might be stronger . . . but we cannot reasonably suppose that the age of manhood was more than 25 in climates where it is now at 15.”)Footnote ¹³⁸ Whichever text was favored, and whether Genesis was taken literally or as a vulgarized but not false account of early history, population was the product of a network of divinely installed natural proportions whose measurement would elucidate the biblical past and providential oversight in the present.

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In a sense, such aims were increasingly marginal to the mainstream of mid- and later eighteenth-century secular political arithmetic, which was taken up with fiscal policy, public health, and the ever more refined calculation of annuities. While the Anglican clergy was still well represented among commentators on population, moreover, rational Dissenters like Richard Price and deists like Benjamin Franklin were at the forefront of new developments. Quantitative discussions of population were more likely to fuel projects for hospitals or pension schemes than defenses of Mosaic history. It is tempting to see the mid-eighteenth century as the moment that demographic quantification was definitively secularized, its sacred historical applications retreating under fire from Voltaire and Hume even as its scientific pretensions were superannuated by French and Scottish political economy. Sacred political arithmetic, having attracted some of the best minds of the Restoration and early Enlightenment, persisted after 1750 as the hobbyhorse of cranks.

There is an element of truth to this. Sacred political arithmetic never overcame the fundamental dilemma its first users had faced—namely, that their exploitation of population's natural history was compromised by their very commitment to sacred history. This was arguably a variation of the larger dilemma facing contemporaneous forms of natural theology, which Hume skewered in his Dialogues Concerning Natural Religion. It is thus fitting that Hume should also have undercut demographic defenses of sacred history in his 1752 essay “Of the Populousness of Ancient Nations,” which simply dismissed the Bible—and indeed all numbers quoted in ancient sources—as unreliable.Footnote ¹³⁹ Men like Cockburn could refine their models of biblical demography by analogy with what was known of modern populations, but while this might inform their exegesis, it brought them no closer to direct knowledge of the past outside of scripture. Meanwhile, new theories of social development anticipated by Newton and elaborated by Montesquieu, Hume, and others shifted attention from dubious numbers to the predictable effects of morals, institutions, and modes of subsistence—factors for which more reliable evidence was available.Footnote ¹⁴⁰ At the same time, new trends in English and German Protestant hermeneutics transformed the Bible itself from a definitive history of humanity into an archive of ancient beliefs—a cultural document.Footnote ¹⁴¹ In a roundabout way, La Peyrère had won.

By comparison with secular statistics, theories of civilization, or historical biblical criticism, sacred political arithmetic after 1750 was a stalled enterprise. By themselves, however, such comparisons neither explain its decline nor reduce its significance. Despite the temptation to invoke the process of secularization so long associated with the Enlightenment in accounting for sacred political arithmetic's marginalization, a couple of observations are worth making. The first is that changes in English religious life may simply have made this discourse less relevant. As the threat of radical deism receded after the early eighteenth century, Anglican apologists were confronted not so much by philosophical challenges to doctrine as by popular stirrings of inward spirituality. Against such awakenings, probabilistic natural philosophy and naturalistic exegesis ceased to be powerful weapons. A second observation is that although there was a real distinction between sacred and secular political arithmetic, the distance between them looks larger in retrospect than it did at the time. Through the 1750s, Derham's Physico-Theology was among the works most commonly cited by political arithmeticians working on secular questions, many of whom were both clergymen and amateur natural philosophers.Footnote ¹⁴² While sacred political arithmetic lost some of its applications, therefore, the broader historical and providential understanding of population that it reflected seems likely to have survived.

In this light, a fitting example with which to conclude is the Sheffield physician Thomas Short. The author of three substantial and widely cited works of medical arithmetic between 1749 and 1767, Short exemplified the tendencies now seen as central to the growth of Enlightenment human science: a concern with the health of the population and with the effects of industry and the physical environment upon it, a dogged pursuit of reliable demographic data, and a distillation of experimental and statistical research into metropolitan and colonial policy.Footnote ¹⁴³ Yet in a 1750 shortlist of major works of political arithmetic he included Derham's Physico-Theology; the only work of Petty's mentioned was the 1674 Discourse Concerning the Use of Duplicate Proportion, a mixed-mathematical tract that considered life expectancy alongside corpuscularian matter theory.Footnote ¹⁴⁴ Like Petty, Short saw political arithmetic in natural-philosophical terms, as offering an empirical basis for comparing “the Hippocratical, Galenical, Paracelsian, Willisian, Sylvisian, Helmontian, and Mechanical” systems.Footnote ¹⁴⁵ He also made much of the providential traces demographic records revealed. Analyzing London and Dublin births and burials between 1666 and 1746, Short noted as “surprizing Instances of kind Providence” the facts that years cruel to adults spared children and vice versa, that the virulence and transmission of certain “Mortalities” indicated a design to produce specific moral effects, and that “[t]hough [God's] Mercies are often general, yet his Judgments are rarely such.”Footnote ¹⁴⁶ For this enlightened practitioner, demography remained a sphere of divine trial and mercy, the punishment of vice and the reward of virtue.

It remained tied, too, to a biblical past. The very benefits of rural life, made clear in the mortality bills, underlined its “Image or Resemblances of the primeval State.”Footnote ¹⁴⁷ Moving from medical arithmetic to history, Short devoted a section of his 1750 New Observations to “the Increase and Numbering of the Israelites,” surveying disputes over chronology and concluding, on the strength of extrapolations from scriptural figures for the adult male population, that the descendants of Abraham had doubled their numbers in Egypt every fifteen years.Footnote ¹⁴⁸ Short was aware that “[t]his uncommon Increase seems surprizing to us at this Distance of Time, when human Life is much abbreviated, Constitutions weakened,” and “our Climate, Country, and Way of Life, all so different from theirs.” Yet the Israelites’ “Advantages” had included the divine promise of fertility, the natural effects of longevity, and the rarity of “Abortion or Barrenness” and “improlific deaths”; “they buried not their 33, 46, or 57 per Cent. impuberes as we do,” he concluded, “nay not one.”Footnote ¹⁴⁹ If Short differed from “religious” authors such as Cockburn, it was not only in his superior grasp of current statistics but also in his more confident invocation of providence as a driver of demographic change.

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What of Malthus? The first Essay on the Principle of Population was printed in 1798, long after the vital period of sacred political arithmetic.Footnote ¹⁵⁰ Its origins lay in French and Scottish political economy, and its targets were not deists or preadamites but adherents of Godwin and Condorcet, who hoped not only to revolutionize society but also to transcend nature itself.Footnote ¹⁵¹ To see “Parson Malthus” as the direct heir of Hale, or even of Petty, ignores context and strains credibility. But to deny any relationship between the clerical “father” of modern demography and the major native strand of demographic thought that preceded him seems hardly more plausible. In fact, anticipations of “Malthusian” language abound in latitudinarian adaptations of political arithmetic, from the notion of “Geometrical Progression” to the effects of pressure on limited resources to the inevitability of external “Prunings” or “Correctives” to growth.Footnote ¹⁵² More substantive than such isolated echoes, however, is their embedment in a providential framework of population management—a framework anchored ultimately, though by Malthus's time only obscurely, in sacred historiography.

Demographic catastrophe had been seen by Derham, as by Short, to serve natural and moral purposes simultaneously, “not only a just Punishment of the Sins of Men, but also a wise Means to keep the Balance of Mankind even.”Footnote ¹⁵³ Periodic culls of overpopulated areas by plague, war, or other means chastised human transgressions while keeping numbers within supportable bounds. What was this, Derham had asked, “but admirable and plain Management? What can the maintaining throughout all Ages and Places these Proportions of Mankind . . . this Harmony in the Generations of Men be, but the Work of one that ruleth the World!”Footnote ¹⁵⁴ Cockburn and others made a similar point about the Flood, arguing that the ensuing “abridgment” of the human lifespan represented both an inevitable adjustment to earth's physical upheaval and a much-needed check to human pride.Footnote ¹⁵⁵ In light of these discussions, the legacy of sacred political arithmetic is discernible in Malthus's own conclusion that “[t]he principle, according to which population increases, prevents the vices of mankind, or the accidents of nature, the partial evils arising from general laws, from obstructing the high purpose of creation. It keeps the inhabitants of the earth always fully up to the level of the means of subsistence; and is constantly acting upon man as a powerful stimulus, urging him to the further cultivation of the earth, and to enable it, consequently, to support a more extended population.”Footnote ¹⁵⁶ Waterman and Winch have explored Malthus's ties to the physico-theology of William Paley's day. Yet the foregoing account suggests that components of this counterrevolutionary discourse took shape over a century earlier, in the antideist polemics and philosophical sermons of the scientific revolution and the early Enlightenment.

Political arithmetic's religious career undermines any simple connection between the quantitative, naturalistic conceptualization of population and the rise of either an economistic worldview or a biopolitical state. That is not to say that the latter did not occur. It is instead to suggest that the history of demographic thought tells us more about eighteenth-century politics and culture if we recognize the limitations of approaches organized around the emergence of modern disciplines, institutions, and worldviews. Even when imagined as a quantifiable entity accessible to political and economic management, population was never a purely secular concept. Its history was seen to reflect humankind's relationship to God in an economy of nature explicitly framed to teach moral lessons; demographic patterns and events were fodder for pious broadsides and sermons to congregations large and small from London to Boston. The very process by which population became an object of scientific attention—a process tied to epidemics in London and colonial politics in Ireland, but also to the reception of Baconian natural history in the Hartlib Circle and the Royal Society—reinforced its religious significance, just as the data used ensured the involvement of the Church of England. Before political economy or the information state, the sacred history and providential meaning of human multiplication made population central to the Enlightenment in England and beyond.