2025 May Political Arithmetick (London, 1691), by Sir William Petty

Sir William Petty, Political Arithmetick … (London, 1691)

 

The Book of the Month for May 2025 is Political Arithmetick by Sir William Petty (1623-87). The Edward Worth Library boasts an impressive collection of Petty’s writing, including a 1691 edition of this book, printed posthumously for Robert Clavel and Henry Mortlock at the Phoenix in St. Paul’s Church-yard.^[1]

 

Sir William Petty, by Isaac Fuller, oil on canvas, circa 1651, NPG 2924, © National Portrait Gallery, London.

 

Early life

 

Sir William Petty was born in Romsey, Hampshire in 1623 to parents of humble means.^[2] He left England at a young age, first to pursue a short-lived career as the cabin boy of a merchant vessel, later escaping to Paris to seek refuge from the second English Civil War (1648).^[3] In Paris, he became acquainted with the likes of Samuel Hartlib (1600-62), Thomas Hobbes (1588-1679), and the ideas of Francis Bacon (1561-1626), whose influence would reverberate throughout his life.^[4] Inspired by his intellectual peers, Petty sought an education at Oxford, acquiring prestige as a physician at the university after successfully resuscitating the unconscious body of a young woman who had been hanged but had not yet died.^[5] He soon took his talents abroad, where he distinguished himself as Physician-General to the Cromwellian army in Ireland following the Irish rebellion (1641-51).^[6]

 

Time in Ireland

 

William Camden, Britannia: or a Choriographical Description of Great Britain and Ireland, together with the Adjacent Lands Written in Latin by William Camden and translated into English with additions and improvements by Edmund Gibson, 2 vols (London, 1722), ii, before Col. 1309-1310, map of Ireland.

 

From 1653 when he first arrived on Irish shores to his death in 1687, Petty ‘was to spend two-third of his time in that country’.^[7] He quickly rose in the ranks of the Cromwellian regime, and enjoyed the favour and friendship of Henry Cromwell (1628-74).^[8] Soon enough, Petty had supplanted Surveyor-General Benjamin Worsley (1618-73), and compiled a detailed analysis of the forfeited Irish lands that were to be re-distributed to English settlers.^[9] With the completion of this inventory, titled the ‘Down Survey,’ Petty succeeded in accurately mapping the country for the first time in its history.^[10] In the course of his demographic studies, Petty managed to acquire for himself a host of Irish estates, the largest in County Kerry.^[11] Despite his Cromwellian connections, Petty fared well in the Restoration of the English monarchy in 1660 – he was permitted to retain his holdings by King Charles II (1630-85), and in 1661, he was knighted by the sovereign.^[12] While in England, Petty was a founder fellow of the Royal Society of London, a learned society composed of the nation’s pre-eminent scientists and philosophers.^[13] Eager to challenge his intellect in Ireland, Petty helped to found the Dublin Philosophical Society, of which he was later the inaugural president. Petty engaged in a vast multitude of intellectual avocations throughout his life. His interests were varied: he was, at various points, a mariner, a student, a physician, a surveyor, an inventor, a scientist, a philosopher, a politician, and an economist.^[14]

 

Political Arithmetick

 

Sir William Petty, Political Arithmetick … (London, 1691), Sig. *1v.

 

As Petty became more established in his career – having connections both in governance and in intellectual circles – he became increasingly interested in economic theory, particularly as it applied to state building. Ireland occupied much of his work – he penned The Political Anatomy of Ireland in 1672, before shifting his focus back to his native England. He wrote Political Arithmetick between 1672 and 1676, though, like most of his written work, it remained unpublished until after his death in 1687. A couple of related studies appeared in that year, both of which were bought by Worth: Five essays in political arithmetick, viz. I. Objections … against two former essays, answered … II. A comparison between London and Paris … III. Proofs that at London … there live about 696 thousand people. IV. An estimate of the people in London, Paris, Amsterdam, Venice, Rome, Dublin, Bristoll and Rouen … V. Concerning Holland and the rest of the VII United Provinces (London, 1687), and his Two essays in political arithmetick, concerning the people, housing, hospitals, &c. of London and Paris (London, 1687).[15] The printing of the final version of Political Arithmetick, was, however, delayed, being first published in 1690. It owed its appearance in print to Petty’s son, Charles Petty, 1^st Baron Shelburne (1672-96), who included a foreword to the text, explaining some reasons for the delay.^[16] The actual text consisted of ten chapters, plus a preface, in which Petty considered the current state of England, especially in comparison to that of France and the Netherlands, two thriving political entities in the latter half of the seventeenth century.

 

Preface

 

Sir William Petty, Political Arithmetick … (London, 1691), Sig. a1r. Preface in which Petty addresses the ‘decaying condition’ of his fellow Englishmen.

 

In the opening to Political Arithmetick, Petty wrote that the general population was in a ‘decaying condition’, which was further exacerbated by issues facing the nation.^[17] However, Petty found that the same people who complained about the state of the country failed to consider how they could contribute to its betterment. He addressed the predominant misconceptions of the time: that the kingdom was becoming poor due to its endeavours in Ireland and America, scarcity of precious metals, and lack of trade opportunities; that the land was underpeopled; that the people were overtaxed; that the Netherlands could surpass England in naval power, and that France had already surpassed England in everything else; that church and state would continue to clash, and that that clash would negatively impact trade.

 

Petty argued that the cost of foreign commodities was too great, and that more focus should be placed on trade. He expressed that ‘too many Matters have been regulated by Laws, which Nature, long Custom, and general Consent, ought to only have governed’.^[18] He also lamented the loss of so many English lives in the civil wars, or by the plague, as well as the decline of England’s international reputation, which he felt had been deteriorating in the aftermath of the Great Fire of London (1666) and military defeats. He also acknowledged the increasing numbers of nonconformists, as well as the enduring difficulty England faced while colonizing Ireland.

 

Despite these real concerns, Petty’s general perception was that the country was thriving. To prove this, he listed all the areas in which England prospered: London was becoming increasingly urbanized and impressive with newly-erected public theatres and rebuilt cathedrals; American plantations were a source of revenue for the crown and provided it with an opportunity to bolster its navy; the East India Company was very profitable; despite misconceptions, English trade relations were as strong as ever; and the price of food was so cheap that there was not even a need to exploit Irish cattle.

 

Petty synthesized his findings, and prefaced the rest of the book, with the following statement: ‘And in brief, no Man needs to want that will take moderate pains. That some are poorer than others, ever was and ever will be: And that many are naturally querulous and envious, is an Evil as old as the World. These general Observations, and that Men eat, and drink, and laugh as they use to do, have encouraged me to try if I could also comfort others, being satisfied my self, that the Interest and Affairs of England are in no deplorable Condition’.^[19]

 

Chapter I: That a small Country and few People, by its Situation, Trade and Policy, may be equivalent in Wealth and Strength, to a far greater People and Territory: And particularly that conveniencies for Shipping and Water-Carriage, so most Eminently and Fundamentally conduce thereunto.

 

In this chapter, Petty compared both France and the Netherlands to Britain by assessing the strengths and weaknesses of each country. On a surface level, he found that Dutch holdings were considerably smaller than those of France, and yet the Dutch, characterized in this text as ‘Holland and Zealand’, proved to be a worthy adversary to the Kingdom of France.^[20] France, though profound in size and wealth, was ravaged by poverty more severely than any other European power. Petty then proceeded to analyze each country’s expenses and populations, considering how economic factors such as taxation, trade, and employment rates, or physical factors, such as proximity to water and quality of land, impacted each superpower’s international standing. He concluded that the Dutch, through ingenious trade, proper cultivation of land, strong infrastructure and public works, and optimal location had challenged both England and France in their dominance.

 

Chapter II: That some kind of Taxes and Publick Levies, may rather increase than diminish the Wealth of the Kingdom.

 

Sir William Petty, by and published by John Smith, after John Closterman
mezzotint, 1696, NPG D30966, © National Portrait Gallery, London.

 

Petty, a longstanding proponent of taxation as a means to reinforce domestic wealth, had first addressed the issue of English taxation in his first ever economic treatise, A Treatise of Taxes & Contributions (London, 1662), written in the aftermath of the Restoration as a contribution to the discussions over raising and spending government revenue. Ten years later, as he embarked on writing Political Arithmetick, Petty was still seeking to challenge the misconception that the depletion of one’s personal wealth would lead to the depletion of public wealth. To levy taxes, according to Petty, would be to ‘diminish the Commonwealth’.^[21] Petty acknowledged the human desire to maintain one’s wealth, while recognizing that personal wealth not spent on taxes were typically spent elsewhere, rather than being saved. He believed that tax money needed to be utilized domestically in order to support a more fortified England for all: ‘As for example, suppose that Money by Tax, be taken from one who spendeth the same in superfluous eating and drinking; and delivered to another who employeth the same, in improving of Land; in Fishing, in working of Mines, in Manufacture, &c. It is manifest, that such Tax is an advantage to the State whereof the said different Persons are Members’.^[22] Contrary to popular belief, Petty found that taxation would be a necessity to maintain the wealth and international standing of the nation, especially in the face of so many thriving adversaries: ‘Having thus in general illustrated this point, which I think needs no other proof but illustration; I come next to intimate that no part of Europe hath paid so much by way of Tax, and publick contribution, as Holland and Zealand for the last 100 Years; and yet no Country hath in the same time, increased their Wealth comparably to them’.^[23]

 

Chapter III: That France cannot by reason of natural, and perpetual Impediments, be more powerful at Sea, than the English, or Hollanders now are, or may be.

 

Here, Petty analyzed the possibility (or lack thereof) that France might surpass the English in naval excellence. In Petty’s eyes, the notion that France could strengthen its navy was an impossibility – despite having enough men to staff a formidable navy, and the money to foot the bill – the French fleet of the time was incapable of expansion, due to lack of suitable ports: ‘Wherefore, although the King of France were immensely rich, and could build what Ships he pleased, both for number, and quality; yet, if he have no Ports to receive, and shelter, that sort and size of Shipping, which is fit for his purpose; the said Riches will in this case be fruitless, and a mere expence without any return, or profit’.^[24]

 

Chapter IV: That the People and Territories of the King of England, are naturally near as considerable for Wealth and Strength, as those of France.

 

In this chapter, Petty considers the English kingdom in comparison to that of France. His ultimate position was that while France had more territories across the globe than England, the holdings of the English crown were more significant in the context of international trade.^[25] Petty determined that France had more subjects, but that England could easily catch up. He also considered the negative effects of a large population –France, with the most proverbial mouths to feed, had struggled the most out of any European nation to combat the issue of poverty.^[26] While not abundantly populated, Petty ruled that English territories had greater commodities than those of France, or at the very least, that their commodities were being better utilized for the betterment of the country.^[27] To support this claim, Petty looked to both the African slave trade and the bustling agricultural centers of America and Ireland, industries that generated tremendous profit for English interests.^[28]

 

Chapter V: That the Impediments of England’s greatness, are but contingent and removable.

 

Sir William Petty, Political Arithmetick … (London, 1691). Title page in which Petty is recognized as a late fellow of the Royal Society.

 

In this chapter, Petty considered what he felt were the greatest obstructions to the growth of the nation. The first ‘impediment’ that Petty analyzed was perhaps the greatest: that the territories were so greatly separated by water that distinct cultures were developing in each one, fit with their own societal structures and rules of governance.^[29] The physical and cultural gap between the various holdings made the territories feel less like English land, and more like a random grouping of islands. Petty felt that this separation created difficulty in taxation and trade between each territory, which in turn hindered the country’s ability to proliferate its wealth.^[30] Finally, Petty also felt that too many able-bodied Englishmen were in America, rather than closer to home where their efforts would be more appreciated.^[31]

 

Chapter VI: That the Power and Wealth of England hath increased in this last 40 years.

 

In this chapter, Petty looks to quantifiable facts about England to support his claim that despite common conception, the country continued to flourish in power and wealth. He concluded that in the last 40 years, the state had increased in territory, as well as in population despite being impacted by both civil wars and the plague.^[32] Interestingly, Petty counts enslaved Africans as part of the population of England, while also praising the cost-efficiency of their labour.^[33]

 

Chapter VII: That one tenth part of the whole Expence, of the King of England’s Subjects, is sufficient to maintain ten thousand Foot, forty thousand Horse, and forty thousand Men at Sea; and defray all other Charges of the Government both Ordinary and Extraordinary, if the same were regularly Taxed, and Raised.

 

Sir William Petty, Political Arithmetick … (London, 1691), Sig. a6r. Contents page.

 

In this chapter, Petty considered how despite the fact that the population of the poor largely eclipses that of the wealthy, the expenses of the wealthy are far greater.^[34] In Petty’s eyes, the fact that some can maintain such a lifestyle indicated that they would be able to pay heavier taxes to support the crown. He declares that ‘Where a people thrive, there the income is greater than the expence’ and notes that the only way for England to achieve this would be to tax its wealthy population more aggressively.^[35]

 

Chapter VIII: That there are spare Hands enough among the King of England’s Subjects, to earn two Millions per annum more than they now do; and there are also Employments, ready, proper, and sufficient, for that purpose.

 

Here, Petty examined what portion of the population was fit for labour. He mused that should every person in every English holding work, the nation would amass an unprecedented wealth.^[36] However, he argued that the number of viable labourers was greatly diminished when one considered the amount of children who were not fit for physical labour, and the number of wealthy Englishmen who refused to debase themselves with work.^[37] Petty felt that a truly formidable country had a high rate of its own population employed in its institutions, and utilized its own commodities, two areas in which England could improve.^[38]

 

Chapter IX: That there is Money sufficient to drive the Trade of the Nation.

 

Petty addressed the new currency of the country that was established following the Restoration of the Stuart Monarchy. While the population was wary about using the new money, Petty assured his readers that the currency would become strong so long as the population trusted it enough to use it – the country would have enough money to do well so long as its people stimulated the economy.^[39]

 

Chapter X: That the King of England’s Subjects, have Stock competent and convenient, to drive the Trade of the whole Commercial World.

 

In the final chapter of Political Arithmetick, Petty sought to assert once and for all that England was in an optimal position in the global political sphere. The trade arrangements the country engaged in were very lucrative – England was in possession of many sought-after commodities.^[40] Petty felt that such commodities would continue to generate wealth for the kingdom so long as they were not devalued in the midst of trading arrangements. The solutions Petty proposed to ensure this were to utilize exclusively English merchants and factors who would prioritize the interests of the nation.^[41] Petty suggested encouraging second and third sons who would not receive their familial inheritances to enter the trade industry to guarantee that the country had a multitude of merchants to rely on.^[42]

 

Conclusion

 

Sir William Petty, Political Arithmetick … (London, 1691), Sig. *3r. Dedication to King William III.

 

Petty’s own conclusion reaffirmed his statement that the nation was in a strong position, and would continue to thrive so long as the common man took a greater interest in its well being: ‘Having handled these Ten Principle conclusions, I might go on with others, ad infinitum; But what hath already been said, I look upon as sufficient, for to shew what I mean by Political Arithmetick; and to shew the uses of knowing the true state of the People, Land, Stock, Trade, &c. 2. That the King’s Subjects are not in so bad a condition, as discontented Men would make them. 3. To shew the great effect of Unity, Industry, Obedience in order to the common safety, and each Man’s particular Happiness’.^[43]

 

Petty’s focus on the role of the individual in the community placed greater agency in the hands of those members of the English population who were anxious about the country’s future. It is curious that Political Arithmetick was never published during Petty’s lifetime. It was an obviously thought-out piece of political scholarship, but as his son, Charles Petty, ruefully noted in his dedication of the work to William III (1650–1702), his father’s conclusions did not please everyone: ‘had not the Doctrins of this Essay offended France, they had long since seen the light, and had found Followers, as well as improvements before this time, to the advantage perhaps of Mankind’.[44] Petty’s patron James II (1633–1701), who as Duke of York had provided some support to Petty in the 1670s, had been less enamoured of Petty’s plans once he came to the throne in 1685. Charles Petty clearly hoped that James’s son-in-law, William III, a noted opponent of France, would be more willing to take on board the many arguments in Petty’s seminal political arithmetic.

 

Text: Ms Maeve Killion, Third Year Student, English Literature and History, Boston University, Boston, Massachusetts, USA.

 

Sources

 

Barnard, Toby Christopher, ‘Petty, Sir William’, Dictionary of Irish Biography.

Barnard, Toby Christopher, ‘Petty, Sir William (1623–1687)’, Oxford Dictionary of National Biography.

Fitzmaurice, Edmond, The Life of Sir William Petty (London, 1895).

Fonseca, Gonçalo L., ‘Sir William Petty, 1623-1687’, The History of Economic Thought.

Fox, Adam, ‘Sir William Petty, Ireland, and the Making of a Political Economist’, The Economic History Review, 62, no. 2 (May, 2009).

Hay, Rod, ‘Political Arithmetick By Sir WILLIAM PETTY, Late Fellow of the Royal Society’, Marxists Internet Archive.

Hoppen, K. Theodore, The Common Scientist in the Seventeenth Century: A Study of the Dublin Philosophical Society 1683-1708, (London, 1970).

Lepenies, Philipp, ‘William Petty and Political Arithmetic’, in The Power of a Single Number: A Political History of GDP (New York, 2016).

Petty, William, Sir, Political Arithmetick, or a Discourse Concerning The Extent and Value of Lands, People, Buildings; Husbandry, Manufacture, Commerce, Fishery, Artizans, Seamen, Soldiers; Publick Revenues, Interest, Taxes, Superlucration, Registries, Banks; Valuation of Men, Increasing of Seamen, of Militias, Harbours, Situation, Shipping, Power at Sea, &c. As the same relates to every Country in general, but more particularly to the Territories of His Majesty of Great Britain, and his Neighbours of Holland, Zealand, and France (London, 1691).

Petty, William, Sir, The Petty Papers; some unpublished papers of Sir William Petty (New York, 1967).

Virtual Record Treasury of Ireland, ‘Map Room’, Virtual Record Treasury of Ireland.

^[1] Hay, Rod, ‘Political Arithmetick By Sir WILLIAM PETTY, Late Fellow of the Royal Society’, Marxists Internet Archive.

^[2] Hoppen, K. Theodore, The Common Scientist in the Seventeenth Century: A Study of the Dublin Philosophical Society 1683-1708 (London, 1970), p. 5.

^[3] Lepenies, Philipp, ‘William Petty and Political Arithmetic’, in The Power of a Single Number: A Political History of GDP (New York, 2016), p. 10.

^[4] Fonseca, Gonçalo L., ‘Sir William Petty, 1623-1687’, The History of Economic Thought.

^[5] Fitzmaurice, Edmond, The Life of Sir William Petty (London, 1895), p. 18.

^[6] Lepenies, ‘William Petty and Political Arithmetic’, p. 11.

^[7] Fox, Adam, ‘Sir William Petty, Ireland, and the Making of a Political Economist’, The Economic History Review, 62, no. 2 (May, 2009), 389.

^[8] Fitzmaurice, The Life of Sir William Petty, p. 10.

^[9] Ibid., p. 72.

^[10] Virtual Record Treasury of Ireland, ‘Map Room’, Virtual Record Treasury of Ireland.

^[11] Hoppen, The Common Scientist, p. 26.

^[12] Fonseca, ‘Sir William Petty, 1623-1687’.

^[13] Petty, William, Sir, The Petty Papers; some unpublished papers of Sir William Petty (New York, 1967), p. xxx.

^[14] Barnard, Toby Christopher, ‘Petty, Sir William’, Dictionary of Irish Biography.

[15] Worth also owned a copy of Petty’s pamphlet of the previous year which focused on London: An essay concerning the multiplication of mankind: together with another essay in political arithmetick, concerning the growth of the city of London (London, 1686).

^[16] Petty, William, Sir, Political Arithmetick, or a Discourse Concerning The Extent and Value of Lands, People, Buildings; Husbandry, Manufacture, Commerce, Fishery, Artizans, Seamen, Soldiers; Publick Revenues, Interest, Taxes, Superlucration, Registries, Banks; Valuation of Men, Increasing of Seamen, of Militias, Harbours, Situation, Shipping, Power at Sea, &c. As the same relates to every Country in general, but more particularly to the Territories of His Majesty of Great Britain, and his Neighbours of Holland, Zealand, and France (London, 1691), p. ix.

^[17] Ibid., p. x.

^[18] Ibid., p. xiv.

^[19] Ibid., p. xvi.

^[20] Ibid., p. 1.

^[21] Ibid., p. 35.

^[22] Ibid., p. 36.

^[23] Ibid., pp 39-40.

^[24] Ibid., p. 54.

^[25] Ibid., pp 64-65.

^[26] Ibid., p. 73.

^[27] Ibid., p. 79.

^[28] Ibid., p. 84.

^[29] Ibid., p. 87.

^[30] Ibid., p. 90.

^[31] Ibid., pp 94-95.

^[32] Ibid., pp 96-97.

^[33] Ibid., p. 97.

^[34] Ibid., p. 102.

^[35] Ibid.

^[36] Ibid., p. 104.

^[37] Ibid., p. 105.

^[38] Ibid., p. 108.

^[39] Ibid., p. 111.

^[40] Ibid., pp 112-113.

^[41] Ibid., p. 116.

^[42] Ibid., p. 115.

^[43] Ibid., pp 116-117.

[44] Ibid., Sig. *4r.