The Mathematical Minister: John Wallis (1616-1703) at the Intersection of Science, Mathematics, and Religion

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Adam Richter

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Institute for the History and Philosophy of Science and Technology University of Toronto

Adam Richter Doctor of Philosophy Institute for the History and Philosophy of Science and Technology University of Toronto

2018

Abstract

John Wallis, Savilian Professor of Geometry at Oxford, is primarily known for his contributions to seventeenth-century mathematics. However, as a founder member of the Royal Society and an

Anglican minister, Wallis also had a productive career in both natural philosophy and theology.

This thesis considers Wallis as a “clerical practitioner” of science—a member of the clergy who studied natural philosophy as well as divinity—and seeks to articulate his unique perspective on the relationship between God and nature. This account of Wallis serves as a case study in the history of science and religion, establishing several novel connections between secular and sacred studies in seventeenth-century England. In particular, Wallis blends elements of experimental philosophy, Calvinist theology, and Scholastic philosophy in creative ways to make connections between the natural and the divine. This thesis has three main goals. First, it traces Wallis’s unique and idiosyncratic role in the history of science and religion. Second, it complicates two common narratives about Wallis: first, that he is historically significant mostly because his mathematics served as a precursor to Isaac Newton’s development of calculus, and second, that his successful career is the result of his ambition and political savvy rather than his original contributions to mathematics, natural philosophy, theology, and other fields. Third, it emphasizes how Wallis interacted with the ideas of the major intellectual figures of his time, including Galileo, Descartes,

Hobbes, Boyle, Newton, and Leibniz, in order to suggest how the interaction between the natural and the divine in his works might impact our understanding of the broader history of science and

ii religion in the seventeenth century. Each of the five chapters in this thesis contributes to these goals by identifying and analyzing connections—methodological, epistemological, and rhetorical—between Wallis’s natural philosophy and theology.

iii For Morry. We’re so glad that you’re here.

“Words are, in my not-so-humble opinion, our most inexhaustible source of magic.” -Professor Albus Percival Wulfric Brian Dumbledore

Acknowledgments

First, for his many contributions to the completion of this thesis—and for so many other academic opportunities—I thank my singularly supportive supervisor, Yiftach Fehige. No one has done more to help me figure out what I want to say about John Wallis, science and religion, and the seventeenth century. Todah rabah.

Along the way, many people have kindly offered their time and attention to read drafts and to discuss my research. Thanks especially to Steve Snobelen, Philip Beeley, Elizabeth Harvey, Craig Fraser, Doug Jesseph, Jason Rampelt, Peter Harrison, and Jacqueline Stedall for their contributions. Thanks also to the other faculty and my fellow grad students at the IHPST. Together you’ve broadened my horizons, challenged my ideas, and taught me how to think about the world from the perspective of a crotchety seventeenth-century mathematician with a penchant for picking fights.

The staff at the IHPST has been supportive day in and day out for over six years. Thanks for everything, Muna Salloum and Denise Horsley.

Thanks to my family for keeping my spirits up and listening to me drone on about Galileo or whatever every time I see you. Thanks especially to my parents for their generous and unwavering support. Thanks to Tonks for distracting me and for sleeping on my exams while I’m trying to get my grading done.

I owe the greatest debt of all to one person in particular: my wonderful wife, Jess. You give me the courage to get through all of life’s challenges, not least of which has been my seven-year journey through grad school. I love you, and I couldn’t have done this without you.

This is a time in my life where some things are coming to an end, but many other things are just beginning. I hope the next chapter has just as many moments of joy, challenge, excitement, and sudden clarity.

“I have no idea where this will lead us, but I have a definite feeling it will be a place both wonderful and strange.” -Special Agent Dale Cooper

Table of Contents

Acknowledgments ...... v

Table of Contents ...... vi

List of Figures ...... viii

Abbreviations ...... ix

Chapter 1: Introduction ...... 1

Who Was John Wallis? ...... 9

Chapter 2: “Deep Things of God”: Nescience in Wallis’s Natural Philosophy and Theology ...... 21

Theology and the rise of science: Harrison’s Fall of Man and Grant’s response ...... 24 Wallis’s rhetorical strategies ...... 28 The Trinity and the cube: nescience in Wallis’s defence of the Trinity ...... 31 Nescience of nature: Wallis’s theory of the tides ...... 45 Conclusion ...... 52

Chapter 3: “Nature Doth Not Work by Election”: Wallis on Natural and Divine Action ..... 58

Physically performed, mathematically measured: Wallis’s comprehensive laws of motion ...... 63 Gifts freely given: divine action and its relation to the laws of nature ...... 71 “Nature doth not work by Election”: Wallis’s appropriation of Grosseteste’s principle .. 76 Conclusion ...... 81

Chapter 4: On Food and Fossils: Biblical History in Wallis’s Works ...... 84

Wallis versus Hobbes on biblical mathematics ...... 92 Hooke’s fossil theory and Wallis’s biblical geography ...... 102 Wallis, Tyson, and Gassendi on the history and anatomy of the human diet ...... 114 Conclusion ...... 122

Chapter 5: John Wallis and the Catholics: Confessional and Theological Antagonism in Wallis’s Mathematics and Philosophy ...... 126

Dissenters, Heathens, Catholics, Turks: Wallis and the rivals to the Church of England ...... 130 The metaphysics of the Eucharist in Truth Tried ...... 135 Anti-Catholic calculations: Wallis and the Interpretation of the Number 666 ...... 139 Plagiarized algebra and speculative theology: Wallis and Descartes revisited ...... 149 Conclusion ...... 164

Chapter 6: Wallis’s Hammer: Language, Rhetoric, and Their Applications ...... 168

Language studies and experimental philosophy in Grammatica and De loquela ...... 174 The rhetoric and grammar of mathematics and theology: Wallis versus Hobbes ...... 184 Language and authority in the Trinitarian controversy ...... 200 Conclusion ...... 214

Chapter 7: Conclusion ...... 219

Bibliography ...... 225

Manuscript Sources ...... 225 Primary Sources ...... 226 Secondary Sources ...... 236

vii

List of Figures

Figure 1: Wallis’s cube diagram ...... 33

Figure 2: Diagrams of the Earth and moon orbiting a common centre of gravity, as described by Wallis’s theory of the tides...... 47

Figure 3: Wallis’s depiction of the Torricellian Experiment ...... 67

Figure 4: Wallis’s depiction of liquid coming to rest ...... 78

Figure 5: Map of the Garden of Eden from the Geneva Bible (1560) ...... 89

Figure 6: Christoph Helvig’s historical tables ...... 96

Figure 7: Wallis’s calculation of the age of the Earth ...... 97

Figure 8: Wallis’s marginal note in Broccard’s Alarm to All Protestant Princes (1679) ..... Error! Bookmark not defined.

viii

Abbreviations

ESO Gunther, R. T., ed. Early Science in Oxford. 15 vols. Oxford: Printed for the Author, 1923-1967.

OM Wallis, John. Opera mathematica. 3 vols. Oxford, 1693-1699.

Phil Trans Philosophical Transactions of the Royal Society of London.

WC Beeley, Philip and Christoph Scriba, eds. The Correspondence of John Wallis. 4 vols. Oxford: Oxford University Press, 2003-2014.

Chapter 1: Introduction

When John Wallis, Savilian Professor of Geometry at the University of Oxford, died in 1703 at age 87, he was the subject of an unusual elegy written by the bookseller and author John Dunton.

The poem makes numerous references to Wallis’s mathematical and scientific achievements, including his most famous algebraic work, Arithmetica infinitorum (1655), as well as his theory of the tides, his astronomical observations, his career as a codebreaker, and even his work giving language lessons to the deaf. Dunton leaves no doubt, however, that while each of these achievements is noteworthy, it is in the realm of mathematics that Wallis truly left his mark. The elegy describes a “Matron” named Rhedycina and her sister Granta—archaic names for Oxford and Cambridge—planning a “Mathematical Funeral” for the late Wallis. At the funeral, a

“Geometrical Progression” will be led by “Sage Algebra,” who will be followed by various geometrical and algebraic objects: cubes, cones, cylinders, and even “A gentle band of Fluxions,” which refers to Isaac Newton’s infinitesimal calculus, the development of which was a recent and massively important mathematical innovation. The elegy concludes with Granta telling

Rhedycina not to dwell on Wallis’s death since he has been succeeded by the mathematical luminaries of the next generation, namely Newton and David Gregory.1

As Dunton’s elegy would suggest, it is chiefly for his mathematics that Wallis has been remembered. Indeed, the poem shows that the process of establishing his reputation as a historically significant mathematician had already begun by the time of his death. What is unusual,

1 John Dunton, The Life and Errors of John Dunton, Citizen of London: with the Lives and Characters of More Than a Thousand Contemporary Divines, and Other Persons of Literary Eminence: to Which are Added, Dunton’s Conversation in Ireland: Selections from His Other Genuine Works: and a Faithful Portrait of the Author vol. II (London, 1818), 658-661.

1 2 however, is that, in terms of emphasis, Dunton’s elegy differs considerably from Wallis’s account of his own life. In an autobiographical letter to his friend Thomas Smith in 1697, Wallis offers little detail about his work in mathematics, focusing instead on two other subjects that he studied throughout his long career: divinity and natural philosophy. It is occasions such as the proceedings of the Westminster Assembly of Divines, which Wallis attended as a secretary, and the founding of the Royal Society of London, of which Wallis was one of the original members, that form the bulk of his apologia pro sua vita. Such episodes, it seems, are the ones that Wallis considered to have shaped his life and his legacy.2

In his autobiographical letter and elsewhere, Wallis himself emphasized the importance of his work in both natural philosophy and divinity. Accordingly, this thesis seeks to flesh out these two aspects of his intellectual career, and the relationship between them. Each of the chapters below explores an aspect of Wallis’s role in the history of science and religion. For the modern- day scholar seeking to understand Wallis and his times, this emphasis on science and religion offers two advantages. The first is that it reflects how Wallis spent a considerable amount of his time when he was not engaged in strictly mathematical studies. While working as a cleric in

London during the 1640s, Wallis participated in the meetings of experimentalists that would evolve into the Royal Society. His two accounts of how the Society began are among the most detailed to have survived.3 By the time the Society had been officially recognized by Royal

Charters in 1660 and 1662, Wallis had been installed as Savilian Professor of Geometry in Oxford, but for decades he continued to exchange letters with several successive secretaries of the Society and other Fellows. He contributed regularly to its journal, the Philosophical Transactions, with

2 See Christoph Scriba, “The Autobiography of John Wallis, F.R.S.,” Notes and Records of the Royal Society of London 25 (1970): 17-46. 3 See Jason M. Rampelt, “The Last Word: John Wallis on the Origin of the Royal Society,” History of Science 46 (2008): 177-201.

3 reports of his own experiments and observations, and those of his correspondents abroad. During the 1680s, he served as president of the Oxford Philosophical Society, a group modelled on the

Royal Society, and according to the minutes he dominated many meetings with reports of interesting natural phenomena.4

The attention that Wallis devoted to mathematics and natural philosophy did not detract from his productive career as a preacher and theologian. The son of a minister (also named John),

Wallis attended grammar schools in Kent and Essex before matriculating in 1632 at Emmanuel

College, Cambridge, which was known for training Puritan ministers. He received his BA and

MA from Emmanuel and was ordained as a minister in 1640. During the Civil War period, Wallis was on a trajectory for a clerical career before Parliament installed him as Savilian Professor in

1649 to replace Peter Turner, a Royalist. After the Restoration of the monarchy, despite his personal inclination toward Presbyterianism, Wallis conformed to the Anglican Church and also became a royal chaplain. For the rest of his life, he continued to publish sermons and polemical theological treatises. Although he never advanced through the hierarchy of the Church, Wallis consistently expended much of his energy on matters of divinity, publishing on topics ranging from the observance of the Sabbath to the doctrine of the Trinity. Beginning in 1654, when he received a doctorate of divinity, he was known to his contemporaries as Dr. Wallis, and this remained an important part of his identity for the rest of his life.5

The second advantage of this emphasis on natural philosophy and theology is that it allows

Wallis to serve as an instructive case study in the history of science and religion. Since the study

4 See ESO IV. 5 Wallis’s biographical details are described in Amir Alexander, Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World (New York: Scientific American / Farrar 2014), 230-257; Jason Michael Rampelt, “Distinctions of Reason and Reasonable Distinctions: The Academic Life of John Wallis (1616-1703)” (PhD diss., Cambridge, 2005), passim; Scriba, “Autobiography of Wallis,” 17-46.

4 of science and religion was reinvigorated by the publication of John Hedley Brooke’s Science and

Religion: Some Historical Perspectives in 1991, leading scholars in the field have called for more case studies of individual lives, as a means to contend with the daunting complexity of the science- religion relationship.6 Today most historians working in this field adhere to what Ronald Numbers has called the “complexity thesis,” which is the historiographical claim that no overarching

“master-narrative” about science and religion through the centuries works as an accurate description of the relationship.7 According to the complexity thesis, the only constant in the interaction between science and religion is complexity.8 Many historians have responded to this complexity by engaging in case studies, focusing on the particular ways that individuals relate the natural and the divine, rather than attempting to develop a more general thesis. So far this strategy has produced much sophisticated and informative scholarship.9

But for an additional case study to be worthwhile, the subject has to be distinctive in ways that promise to offer some novel lessons about the science-religion relationship. What is distinctive about John Wallis? Many idiosyncrasies in how he relates the natural and the divine

6 For examples of appeals for additional case studies, see, for example, John Brooke and Geoffrey Cantor, Reconstructing Nature: The Engagement of Science and Religion (Edinburgh: T&T Clark, 1998), 15-37, 247-277; Geoffrey Cantor and Chris Kenny, “Barbour’s Fourfold Way: Problems with His Taxonomy of Science-Religion Relationships,” Zygon 36 (2001): 779; Peter Harrison, “‘Science’ and ‘Religion’: Constructing the Boundaries,” in Science and Religion: New Historical Perspectives, eds. Thomas Dixon, Geoffrey Cantor, and Stephen Pumfrey (Cambridge: Cambridge University Press, 2010), 42. 7 See Ronald Numbers, “Simplifying Complexity: Patterns in the History of Science and Religion,” in Dixon, Cantor, and Pumfrey, Science and Religion, 263. 8 On the development of the complexity thesis as a response to essentialist master-narratives about science and religion, see Noah Efron, “Sciences and Religions: What It Means to Take Historical Perspectives Seriously,” in Dixon, Cantor, and Pumfrey, Science and Religion: New Historical Perspectives, 247-262; Stephen P. Weldon, “Science and Religion,” in Science and Religion: A Historical Introduction, 2nd ed., ed. Gary B. Ferngren (Baltimore: Johns Hopkins University Press, 2017), 3-19. 9 This is not the place for an exhaustive list of excellent case studies in the history of science and religion, if such a list is even possible, but the following is a small sample: Peter Barker and Bernard Goldstein, “Theological Foundations of Kepler’s Astronomy,” Osiris 16 (2001): 88-113; Rivka Feldhay, Galileo and the Church: Political Inquisition or Critical Dialogue? (Cambridge: Cambridge University Press, 1995); Andrew Janiak, Newton as Philosopher (Cambridge: Cambridge University Press, 2008); Matthew Stanley, Huxley’s Church and Maxwell’s Demon: From Theistic Science to Naturalistic Science (Chicago: University of Chicago Press, 2015); Jan A. Wojcik, Robert Boyle and the Limits of Reason (Cambridge: Cambridge University Press, 1997).

5 will emerge from the chapters that follow. A crucial factor, though, is that Wallis approached these two bodies of knowledge from the perspective of an ordained Anglican minister trained in

Calvinist theology. This background, I argue, shaped his work in natural philosophy and mathematics, as he considered how to relate natural knowledge to central theological doctrines, to biblical evidence, and to his contests with religious opponents ranging from Roman Catholics to anti-Trinitarians to suspected atheists like Thomas Hobbes. In such cases, each of which will be discussed in the chapters to come, elements of Wallis’s Calvinist theology and his identity as a minister affected how he reacted to ideas about nature and mathematics, and how he related such ideas to matters of theology, ecclesiology, and biblical hermeneutics.

Clerics such as Wallis are underrepresented in the historiography of science and religion, as most studies of the early modern period focus on “lay” or “secular” theologians, those who studied and wrote extensively on theology but never joined the clergy. In the English context, historians have mainly addressed such lay theologians as Francis Bacon, Robert Boyle, John

Locke, and Isaac Newton. As for continental Europe, those whose ideas about science and religion have attracted the most attention are Galileo Galilei, René Descartes, and Gottfried Leibniz.10 One reason for this emphasis seems to be an underlying assumption that lay theologians are less constrained in their thinking about science and religion, lacking the cleric’s responsibility to adhere to a prescribed theological orthodoxy. Amos Funkenstein, for instance, insists on the importance of “secular theology” in the early modern period, a theology that for the first time in

10 There are, of course, some exceptions: certain clerical figures who were productive in natural philosophy or mathematics have attracted historiographical attention. For example, there have been important studies on the Catholic priest Pierre Gassendi (Margaret J. Osler, “Early Modern Uses of Hellenistic Philosophy: Gassendi’s Epicurean Project,” in Hellenistic and Early Modern Philosophy, ed. Jon Miller and Brad Inwood [Cambridge: Cambridge University Press, 2003], 30-44) and the Anglican minister Isaac Barrow (Ian Stewart, “‘Fleshy Books’: Isaac Barrow and the Oratorical Critique of Cartesian Natural Philosophy,” History of Universities 16 [2000]: 35- 102; Mordechai Feingold, “Isaac Barrow: Divine, Scholar, Mathematician” in Before Newton: The Life and Times of Isaac Barrow, ed. Mordechai Feingold [Cambridge: Cambridge University Press, 1990], 1-104).

Western history “was conceived by laymen and for laymen.” It was the secular theologians—the likes of Galileo and Leibniz—who transcended traditional Aristotelian disciplinary boundaries to an unprecedented extent, and were the first to integrate natural and divine knowledge in more than a superficial way.11 Brooke, too, hints at this distinction between clerical and secular theologians when he notes that, among the prominent figures in the history of science who were also theists, the majority are those who “might experience discomfort with contentious elements in a classical creed” and are not “typical representatives of the religious traditions in which they were nurtured.”12

The idea that only secular theologians, not clerics, could flourish in early modern science is given a fuller treatment in Mordechai Feingold’s article on clerical practitioners of science.

Feingold rightly points out that clerical science is “a rather neglected point of view” in studies of early modern science, but he attributes this neglect not to the preoccupations of historians but the nature of the early modern clergy itself. According to Feingold, clerics faced intellectual constraints that stunted their productivity in science, and it was this that made them negligible.

Social pressure compelled members of the clergy to devote their lives to preaching and to tending their flock—to subordinate the secular to the divine—and this generated “inner tensions” and

“insurmountable challenges” for clerics interested in science. Since “the essence of this [clerical] vocation was such as to impinge fundamentally on their ability to dedicate themselves to science”—since, in other words, conflict between clerical and scientific commitments was essential, fundamental, and therefore unavoidable—scientifically-minded clerics had to choose to pursue one kind of knowledge or the other, secular or divine. This dilemma, Feingold argues,

11 Amos Funkenstein, Theology and the Scientific Imagination from the Middle Ages to the Seventeenth Century (Princeton: Princeton University Press, 1986), 1-9. The quotations are from 1. 12 John Hedley Brooke, Science and Religion: Some Historical Perspectives (Cambridge: Cambridge University Press, 1991), 45.

7 explains why there were so few noteworthy clerics in early modern science and why clerics were gradually marginalized as modern science developed.13

In addition to some problems with how Feingold approaches his sources,14 his argument does not easily accommodate someone like John Wallis, a clerical practitioner whose writings leave no trace of an inner tension between secular and divine interests—and one who is conspicuously absent from the article, except for a passing reference.15 Wallis remained productive as a preacher and theologian while actively engaged in mathematical and natural philosophical studies. Although his preaching was perhaps secondary to mathematics and natural philosophy after his appointment as Savilian Professor, he evidently never felt compelled to choose between secular and theological pursuits. Feingold does discuss Wallis in a later article comparing his career to that of John Pell, a contemporary who, Feingold claims, settled his inner dilemma by choosing a mathematical career over a clerical one.16 As for Wallis, Feingold

13 Mordechai Feingold, “Science as a Calling? The Early Modern Dilemma,” Science in Context 15 (2002): 79-119. The quotations are from 79 and 80. 14 For two main reasons, I contend that Feingold overstates the tension between science and divinity that he detects in the writings of early modern clerics. First, some of his own examples show that clerical practitioners were praised by certain contemporaries, even if they were criticized by others, for devoting their time to the study of nature; see his discussion of Francis Potter, an experimentalist and divine who will feature prominently in Chapter 5 below (Feingold, “Science as a Calling,” 98). Second, Feingold’s argument relies on evidence from biographies, autobiographies, and the front matter of publications. The authors of such texts frequently describe the triumph of a practitioner’s divine interests over their secular ones, projecting an image of the practitioner in question as pious and aloof from worldly concerns. However, such references to the cleric’s piety, decorum, and detachment from mundane matters are examples of the rhetorical tropes that pervade these kinds of texts. One common trope is the author’s reluctance to publish until overwhelmed by the importunity of his friends. Feingold takes clerical authors’ apparent reluctance to publish on secular matters as evidence for their inner dilemma (see Feingold, “Science as a Calling,” 101, 111-112), but this is a fairly standard trope in early modern publications and such statements should be treated with skepticism. On the prominence of such tropes and self-fashioning in early modern biographical and autobiographical writing, see Katharine Hodgkin, Madness in Seventeenth-Century Autobiography (New York: Palgrave MacMillan, 2007), 19-20; Michael Mascuch, Origins of the Individualist Self: Autobiography and Self- Identity in England, 1591-1791 (Stanford: Stanford University Press, 1996), 8-9, 67-69, 76-83, 91. See also John Morgan’s argument that the reputation of English Puritans as resistant to secular learning was invented in part by their opponents for rhetorical purposes (John Morgan, Godly Learning: Puritan Attitudes toward Reason, Learning, and Education, 1560-1640 [Cambridge: Cambridge University Press, 1986], 67-68, 77-78). 15 Feingold, “Science as a Calling,” 105. 16 Mordechai Feingold, “Parallel Lives: The Mathematical Careers of John Pell and John Wallis,” The Huntington Library Quarterly 69 (2006): 457.

8 attributes his success as both a minister and a mathematician not to his intellectual abilities, but rather to his ruthless ambition. According to Feingold, “What distinguishes Wallis, even in an era of strong personalities, is an ironclad ego and unbounded sense of entitlement,” which gave him the ill-founded confidence to accept the position of Savilian Professor of Geometry despite his rather limited exposure to mathematics.17 At Oxford, Feingold explains, “Wallis’s covetousness and ambition continued unabated” as he schemed his way to a position of power, pressuring colleagues to grant him additional privileges at Oxford and to promote his reputation as a mathematician in their works.18 This dubious account of Wallis’s rise to prominence takes his enemies, such as Anthony à Wood and Henry Stubbe, at their word. It also overlooks contemporary sources like Dunton’s elegy—among many others—that celebrate Wallis’s scholarly achievements, with no signs of the Savilian Professor’s machinations behind the scenes.

Feingold’s depiction of Wallis reads like an effort to explain him away: since he exhibits no signs of the usual inner conflict, his success must be the result of luck and ambition, rather than a genuinely productive career in both science and divinity.

In truth, Wallis was a sincere and dedicated scholar who left a lasting impression on natural philosophy, mathematics, theology, and other fields including grammar and cryptography.

His rise to prominence has more to do with his considerable intellectual output, his cultivation of a vast network of correspondence, and his engagement with the ideas of the leading intellectuals of his time—the likes of Galileo, Descartes, Boyle, Newton, and Leibniz—than with guile or ambition. Wallis, though a cleric, was a prominent member of the intellectual community in which

17 In his autobiographical letter, Wallis claims to be self-taught in mathematics. He recalls that, during a Christmas vacation when he was home from Cambridge, he learned some basic arithmetic from his brother who was studying for a trade. As Wallis explains, he quickly absorbed the material from his brother’s textbook, and this experience was the closest he came to receiving formal mathematical education: “This was my first insight into Mathematicks; and all the Teaching I had” (Scriba, “Autobiography of Wallis,” 26-27). 18 Feingold, “Parallel Lives,” 462.

9 these secular theologians flourished. Furthermore, just like these more famous contemporaries,

Wallis sometimes perceived tension between natural and theological knowledge, but this tension was by no means an insurmountable obstacle. On the contrary, as I will demonstrate in the chapters below, it is precisely at the points of intersection between science and religion that Wallis is at his most creative as a thinker.19 The strategies that Wallis develops to relate his preferred methodologies in natural philosophy and theology, to compare natural action with divine action, to integrate biblical evidence into questions of natural philosophy—these, I argue, constitute some of Wallis’s most profound insights and demonstrate his important place in the history of science and religion. Wallis’s innovations in algebra and English grammar have rightly been identified as having an enduring impact on their respective fields. Yet, in less immediately apparent ways that

I will highlight in the chapters that follow, Wallis’s work at the intersection of science and religion contains some of his most historically significant ideas, ones that both reflected and helped to shape his intellectual world. At least in Wallis’s case, clerical science was not a contradiction in terms, but rather a source of considerable insight into the natural and the divine.

Who Was John Wallis?

Dunton and Feingold are two of many writers who, since the early eighteenth century, have sought to answer the question posed in the title of this section. Probably the most common answer, and certainly the most Whiggish, is that Wallis was a mathematician whose algebraic techniques— particularly his use of infinite series to “square” or find the area bound by certain types of curves—

19 My approach here is informed by Geoffrey Cantor’s argument that an inner tension between scientific and religion ideas is not necessarily an impediment to development within either field, but instead can lead to creative thinking as a means to resolve that tension. As Cantor puts it, “In the context of science and religion, conflict has been the engine of change, even perhaps of what we might call progress” (Geoffrey Cantor, “What Shall We Do with the ‘Conflict Thesis’?,” in Dixon, Cantor, and Pumfrey, Science and Religion: New Historical Perspectives, 291.

10 helped to inspire Newton’s development of the “method of fluxions,” or calculus. This is the answer given by most historians who discussed Wallis’s work in the middle decades of the twentieth century. Such accounts focus on Wallis’s Arithmetica infinitorum, “the Arithmetic of

Infinites,” a work that culminates in his famous discovery that the value of π can be expressed as an infinite product, known today as the Wallis product:

×××××××××××… = ×××××××××××…

Thus Margaret E. Baron’s The Origins of Infinitesimal Calculus (1969) notes that “Newton on first reading the Arithmetica was inspired to begin an investigation on his own behalf” into the

“squaring” or “quadrature” of the circle—that is, determining the area bound by a circle, which requires the precise value of π.20 Likewise, in D. J. Struik’s A Source Book in Mathematics, also published in 1969, Wallis’s work in Arithmetica infinitorum is described in a chapter entitled

“Analysis before Newton and Leibniz” and his work is said to have “influenced Newton, Gregory, and other mathematicians.”21 Each of these authors echoes J. F. Scott’s The Mathematical Work of John Wallis (1938), which remains the only monograph specifically on Wallis written in

English, whose preface describes him as “a precursor of the mighty Newton” and emphasizes

“Newton’s indebtedness to Wallis,” particularly the Arithmetica infinitorum.22 Scott repeatedly returns to his thesis that Newton arrived at his great mathematical achievements by synthesizing and generalizing techniques he learned from Wallis. He asks with rhetorical flourish, “Did not

Newton erect his mighty superstructure upon foundations laid by Wallis?”23 Although Scott’s

20 Margaret E. Baron, The Origins of Infinitesimal Calculus (Oxford: Pergamon Press, 1969), 211. 21 D. J. Struik, ed., A Source Book in Mathematics, 1200-1800 (Cambridge, MA: Harvard University Press, 1969), 244. 22 J. F. Scott, The Mathematical Work of John Wallis, D.D., F.R.S. (1616-1703), 2nd ed. (New York: Chelsea Publishing Company, 1981; orig. pub. 1938), vii. 23 Scott, Mathematical Work of Wallis, 150.

11 account no longer represents the historiographical standard on Wallis’s mathematics, for most of the time that the history of science and mathematics have been professional fields of study,

Wallis’s legacy has been identified as the trail that he blazed for Newton to follow.

Certainly, Newton was attracted to the powerful method for summing infinite series that

Wallis’s demonstrates in Arithmetica infinitorum. Here Wallis relies on a process that he calls

“induction,” by which he means not the modern technique of mathematical induction, but a method of discovery that makes a general conclusion based on a finite number of cases, comparable to Baconian induction in natural philosophy. Wallis begins by considering the following arithmetic series:

0 + 1 1 = 1 + 1 2

Next, Wallis sums several more series of this kind, each time increasing the number of terms, and making the recurring number in the denominator equal to the highest number in the numerator.

0 + 1 + 2 1 = 2 + 2 + 2 2

0 + 1 + 2 + 3 1 = 3 + 3 + 3 + 3 2

And so on. Noting that this rule seems to apply in every case, Wallis proceeds by “induction” to the general rule that would apply, he claims, even with an infinite number of terms:

0 + 1 + 2 + 3+ . . . + � 1 = � + � + � + �+ . . . +� 2

A similar pattern emerges when all the terms in the series are squared.

0 + 1 0 + 1 1 1 = = + 1 + 1 1 + 1 3 6

0 + 1 + 2 0 + 1 + 4 5 1 1 = = = + 2 + 2 + 2 4 + 4 + 4 12 3 12

0 + 1 + 2 + 3 0 + 1 + 4 + 9 14 1 1 = = = + 3 + 3 + 3 + 3 9 + 9 + 9 + 9 36 3 18

As the number of terms increases, the sum of the series gets closer and closer to 1/3. Wallis reasons by induction that such a series with an infinite number of terms would have a sum of 1/3. In modern notation, the rule is:

0 + 1 + 2 + 3 + ⋯ + � 1 lim = → � + � + � + � + ⋯ + � 3

Wallis goes on to show that this pattern still applies when the terms are raised to any exponent, whether it be a whole number, a fraction, zero, or a negative number. Hence the general rule:

0 + 1 + 2 + 3 + ⋯ + � 1 lim = → � + � + � + � + ⋯ + � � + 1

After several more steps, he extends his method of induction to find an infinite series equal to 4/π, and so he arrives at the famous Wallis product, which is as close as anyone in his generation would come to determining the value of π.24

However, Wallis’s attempt to find the value of π was not what ensured that the Arithmetica infinitorum would have a lasting impact on the history of mathematics. Rather, it was the

“inductive” method that he developed for his infinite series, and how that method was extended and applied by Newton. The value of Wallis’s rules was that they could be applied to the quadrature of curves, which was a preoccupation of many seventeenth-century mathematicians.

The terms in Wallis’s series can be plotted to generate a curve, and his rules for summing the series show how to find the area bound by that curve. Newton’s close reading of Arithmetica infinitorum led him to apply Wallis’s “inductive” method to different kinds of series, a process

24 See OM I, 355-478. For a modern translation of the Arithmetica infinitorum, see Jacqueline A. Stedall, trans., The Arithmetic of Infinitesimals (New York: Springer, 2004). A useful overview of Wallis’s methods in Arithmetica infinitorum can be found in Alexander, Infinitesimal, 266-274.

13 that was decisive in Newton’s development of a general methodology for analyzing curves, which he called the method of fluxions, and which today we refer to as calculus.25 It is Newton’s reception of Wallis’s work—along with Wallis’s introduction of the symbol ∞ for infinity in his treatise De sectionibus conicis (1655)—that has ensured Wallis’s place in the canon of mathematics and has had the greatest effect on how he has been remembered. In addition, Wallis’s role in supporting Newton in his priority dispute over calculus with Leibniz—he included

Newton’s letters on the subject in later mathematical publications—has only reinforced the perception of Wallis as a precursor to Newton in mathematics.26

To be sure, Wallis devoted a great deal of time to developing and applying novel algebraic methods. He authored numerous mathematical publications, exchanged letters with prominent mathematicians in England and abroad, and lectured at Oxford on both ancient and modern mathematics. In addition, he investigated the history of mathematics, particularly in England, publishing the results of his research in his lengthy Treatise of Algebra (1685).27 Yet mathematics was far from Wallis’s only passion. For instance, he also collected a wealth of information on all sorts of natural phenomena, from the temperature and atmospheric pressure in Oxford, which he measured using his own “thermoscope” and “baroscope,” 28 to extreme weather events and other

25 Richard Westfall details how Newton’s reading of Wallis, along with other early algebraists such as Descartes and Viète, was crucial to his development of calculus. See Richard S. Westfall, Never at Rest: A Biography of Isaac Newton (Cambridge: Cambridge University Press, 1980), 105-139. For a list of the works by Wallis in Newton’s library, see John Harrison, The Library of Isaac Newton (Cambridge: Cambridge University Press, 1978), 259. 26 On Wallis’s efforts to establish Newton’s priority in his Treatise of Algebra (1685) and Opera mathematica (1693- 1699), see Niccolò Guicciardini, “John Wallis as Editor of Newton’s Mathematical Work,” Notes and Records of the Royal Society of London 66 (2012): 3-17; A. Rupert Hall, Philosophers at War: The Quarrel between Newton and Leibniz (Cambridge: Cambridge University Press, 1980), esp. 92-97. 27 For an overview of Wallis’s research into the history of mathematics, see Jacqueline A. Stedall, “Of Our Own Nation: John Wallis’s Account of Mathematical Learning in Medieval England,” Historia Mathematica 28 (2001): 73-122. 28 See Wallis, “A Relation Concerning the Late Earthquake Neer Oxford: Together with Some Observations of the Sealed Weatherglass, and the Barometer Both upon That Phænomenon, and in General,” Phil Trans 1 (1665-1666): 166-171; Wallis, “A Discourse concerning the Air’s Gravity, Observd in the Baroscope, Occasioned by That of Dr. Garden: Presented to the Phil. Soc. of Oxford, by the Reverend Dr. Wallis, President of That Society. April, 14, 1685,” Phil Trans 15 (1685): 1002-1014; WC II, 282; WC III, 281-287.

14 natural wonders.29 Wallis also wrote extensively on mathematical physics, most notably in his

Mechanica, published in three parts between 1669 and 1671, which spans nearly five hundred pages.

Apart from his work in mathematics and natural philosophy, Wallis found time for an impressive range of other intellectual pursuits. In 1653 he published the first edition of his Latin text on English grammar, the Grammatica linguae Anglicanae. Although it was never his primary focus, Wallis returned to matters of grammar and language throughout his career, publishing several revised editions of the Grammatica and giving language lessons to the deaf. He also frequently turned his attention to the study of logic. Early in his career, Wallis composed an unpublished “Treatise of Logick” that became the basis for his Institutio logicae (1687).30 The latter was one of few texts by Wallis that rivalled the Grammatica in popularity and number of editions. Finally, as he published prolifically on these and other subjects, Wallis had a more secretive career as a codebreaker, working first for the Parliamentary forces during the Civil War, and continuing to decode intercepted letters for the Interregnum government and several successive regimes after the Restoration. For nearly his entire career, Wallis performed this

29 Like many of his colleagues, Wallis took an interest in both the regularity of nature—in the mathematical laws that affect the motions of bodies—and in its irregularity, that is to say, in natural wonders or marvels. In their magisterial treatment of wonders and marvels in the history of natural philosophy, Lorraine Daston and Katherine Park argue that members of the Royal Society and other early scientific academies were obsessed with recording all of nature’s unusual and preternatural particularities. In both observing nature and conducting experiments, the Fellows of the Royal Society sought “a new kind of scientific experience: the strange fact.” Hence the Society’s publications and correspondence abound with reports of monstrous births, surprising overseas discoveries, and catastrophic weather (Lorraine Daston and Katharine Park, Wonders and the Order of Nature, 1150-1750 [New York: Zone Books, 1998], 215-253; the quotation is from 231). Wallis frequently discussed natural wonders in correspondence, at meetings of the Oxford Philosophical Society, and in items published in the Philosophical Transactions. For example, his account of a massive and deadly thunderstorm clearly conveys his feelings of wonder and terror: “. . . the Lightening [came] with flashes very bright . . . once or twice, I observ’d [the thunder] to follow (in a manner) immediately upon it, as it were in the same moment; and the lightening extream red and fiery. I do not use to be much apprehensive of Thunder and Lightning, but I was at this time (I know not well, why?) very apprehensive, more than ordinary, of mischief to be done by it” (Wallis, “A Relation of an Accident by Thunder and Lightning, at Oxford,” Phil Trans 1 [1665-1666]: 222). 30 For the “Treatise of Logick” see Royal Society MS 21.

15 cryptanalytical work in an unofficial capacity, until he was finally made an official decipherer for the Crown in 1701.31 The more one considers the breadth of Wallis’s intellectual output, the more difficult it becomes to give a simple answer the question with which we began: Who was John

Wallis?

No satisfactory answer to that question would leave out Wallis’s career as a minister and his many texts on theology. My thesis aims to emphasize this aspect of Wallis’s work and to show how it interacts with his secular interests. Wallis never developed a comprehensive system of the world that incorporated both theology and natural philosophy, unlike such prominent contemporaries as Descartes, Newton, and Leibniz. In general, Wallis was content to write either as a mathematician, or an experimental philosopher, or a theologian, or a contributor to a different field. Yet connections between the natural and the divine can be found in Wallis’s corpus, even if the compartmentalization of his work makes this more difficult than in the cases of his more famous contemporaries. The connections are no less significant because Wallis rarely makes them explicit. Accordingly, in five chapters below, I will address various points of contact between

Wallis’s theology and his work on other subjects, chiefly natural philosophy and mathematics.

Each of the five chapters below addresses a different connection between Wallis’s secular and divine studies. Chapter 2 focuses on two episodes in Wallis’s intellectual career—his theory of the tides and his defence of the doctrine of the Trinity—in order to highlight the methodological, epistemological, and rhetorical similarities in the ways that he approaches these two fields. I argue that, in both cases, Wallis depends on the Scholastic principle of similitudes to support his interpretation of the evidence at hand. This, along with other similarities, shows that

31 That position was created for Wallis and his grandson, William Blencowe, who thereby became the first official codebreakers for the English government. For an overview of Wallis’s career in cryptanalysis, see Philip Beeley, “Breaking the Code: John Wallis and the Politics of Concealment,” in G. W. Leibniz und der Gelehrtenhabitus. Anonymitaet, Pseudonymitaet, Camouflage, eds. Wenchao Li and Simona Noreik (Cologne: Böhlau, 2016), 49-81.

Wallis employs many of the same techniques in his work on the natural and the divine. Next,

Chapter 3 outlines Wallis’s understanding of natural action, as it emerges from his works on mathematical physics, and divine action, as described primarily in his published sermons. Again, this chapter highlights a principle that Wallis draws from Scholastic philosophy—Robert

Grosseteste’s principle that “Nature doth not work by Election”—which indicates how Wallis conceived of God’s relation to the natural world. On Wallis’s understanding, I argue, natural action is bound by the mathematical laws of nature, unlike divine action which always includes an element of choice. These two chapters reveal areas of overlap between Wallis’s thoughts on

God and nature, and how both are informed by Scholastic philosophy.

While the two chapters described above demonstrate that Wallis was consistently in touch with his medieval forebears, the next three chapters highlight the features of his own time and place that were crucial to his overall philosophy. Chapters 4 and 5 discuss the distinctive features of Protestant theology and biblical hermeneutics that pervaded the intellectual world of seventeenth-century England and shaped Wallis’s thought. Chapter 4 investigates what it meant for Wallis, like many English Protestants of his time, to regard the Bible as a storehouse of knowledge about the natural world, and also about the mathematical knowledge of ancient societies. This chapter shows that the Bible was a crucial resource in Wallis’s assessment of ideas about nature and mathematics, particularly when those ideas involve events in the distant past.

The Bible, I argue, was one of the tools that Wallis used to mediate between tradition and innovation, to decide which novel ideas were plausible and which were far-fetched. In Chapter 5,

I discuss Wallis’s antipathy toward the Roman Catholic Church, particularly the pope and the

Jesuits, and how this antipathy affected his reception of ideas about nature and mathematics. I argue here that Wallis was more or less amenable to certain ideas depending on whether he considered them to hinder or to help Catholic interests.

Finally, Chapter 6 discusses Wallis’s language studies, and also returns to his rhetorical strategies, to show the central importance of words in his work as a mathematician, natural philosopher, and divine. This chapter situates Wallis within a historiographical discussion of the relative importance res and verba—words and things—in early modern natural philosophy. I argue that Wallis’s engagement with experimental philosophy did not entail a preference for the study of things rather than words. On the contrary, Wallis viewed his linguistic studies—his work on English grammar and his education of deaf students—as some of his most important contributions to natural philosophy. In addition, I argue that the study of words in other senses, namely rhetoric and etymology, was crucial to Wallis’s work on both secular and divine subjects.

This chapter shows that Wallis’s polemical treatises in both mathematics and theology rely on particular rhetorical techniques, and also on his wealth of knowledge about grammar and etymology.

Methodologically speaking, my research on Wallis follows the lead of those scholars who, especially since the publication of Brooke’s Science and Religion, have explicitly sought to understand the modern science-religion relationship by studying their interaction in the past. Like those scholars, I intend to contribute to the refinement of the “complexity thesis” by resolving that complexity into particular types of interactions between natural and divine knowledge, in a particular time and place, and especially in the writings of a particular, instructive individual. My research is especially indebted to historians who have investigated how various consequences of the Protestant Reformation contributed to the rise of modern science, most notably Peter Harrison,

Charles Webster, and James J. Bono.32 How and whether the Reformation contributed to the

32 See Peter Harrison, The Bible, Protestantism and the Rise of Natural Science (Cambridge: Cambridge University Press, 1998); idem, The Fall of Man and the Foundations of Science. Cambridge: Cambridge University Press, 2007; Charles Webster, The Great Instauration: Science, Medicine and Reform 1626-1660, 2nd ed. (Oxford: Peter Land, 2002; orig. pub. 1975); James J. Bono, The Word of God and the Languages of Men: Interpreting Nature in Early

“Scientific Revolution” is among the oldest questions asked by professional historians of science.

By now, many historians doubt whether the concept of the Scientific Revolution, as the supposed starting point of modern science, remains useful, since the idea of a decisive break between medieval and modern science has been effectively questioned from several angles. Nevertheless, the relationship between the Reformation and the rise of modern science remains a challenging historiographical problem and a fruitful source of inspiration for historical research. My work on

Wallis is intended to contribute to this strain of research by exploring what a very particular type of Protestant—an Anglican minister with a Presbyterian inclination, who passionately engaged with the secular knowledge of his own time and that of previous generations—can teach us about the complex relationship between “science” and “religion.”

In addition to the historiography of science and religion, my work on Wallis has been guided by Michel Foucault’s description of genealogy as a historical methodology. In his 1971 essay, “Nietzsche, Genealogy, History,” Foucault laments what he views as the traditional way of writing history, which is to consider concepts and traditions that exist today and then to look backward in time to discover their origins. This approach implies that these concepts and traditions have inevitably progressed toward their current forms, as if guided by a teleological impulse. But this, Foucault argues, is not how history unfolds. On the contrary, the features of modern society have emerged through a historically contingent recombination of existing elements, a process that is arbitrary, disorderly, and unpredictable. Accordingly, genealogy does not start with what exists today and look backward to find its origin; rather, it starts with what existed in the past and looks forward. As Foucault puts it, genealogy does not assume that the past

Modern Science and Medicine, vol. 1. (Madison: University of Wisconsin Press, 1995), esp. 48-84.

“continues secretly to animate the present, having imposed a predetermined form on all its vicissitudes.” Instead, genealogy traces the chaotic and contingent path from past to present:

. . . to follow the complex course of descent is to maintain passing events in their proper dispersion; it is to identify the accidents, the minute deviations—or conversely, the complete reversals—the errors, the false appraisals, and the faulty calculations that gave birth to those things that continue to exist and have value for us; it is to discover that truth or being does not lie at the root of what we know and what we are, but the exteriority of accidents.33

One of the goals of my analysis of Wallis’s works is to reveal some of the religious elements in the genealogy of modern science. I suspect that much of the recent historiography of science and religion has been motivated by the same goal, although it is rarely made explicit. The religious factors that shaped science in its infancy are often surprising, given the popular association of science with secularism, naturalism, and unbelief. Science might appear secular— if not downright irreligious—when viewed from the present, but it does not appear that way from the perspective of the highly religious societies of early modern Europe in which modern science began to emerge. The job of historians of science and religion is, in part, to explain how theologically-infused thinking about nature eventually produced secular, naturalistic science, and the answers will elude anyone whose starting point is the way science looks today. Accordingly, scholarship that operates under the complexity thesis tends to contain many references to the contingencies and historical accidents that helped to shape modern science.34 Complexity is exactly what we would expect from the disorderly process that Foucault describes, and perhaps the most accurate account of the protean relationship between science and religion is a

33 Michel Foucault, “Nietzsche, Genealogy, History,” in The Foucault Reader, ed. Paul Rabinow (New York: Pantheon Books, 1984), 76-100. The quotations are from 81. 34 The language of anti-essentialism, anti-teleology, and genealogy is especially apparent in the works of Peter Harrison, (see Harrison, “Constructing the Boundaries,” 23-49; idem, The Territories of Science and Religion [Chicago: University of Chicago Press, 2015], esp. 1-19, 142-144), but see also the anti-essentialist remarks in Brooke, Science and Religion, 8, 40; Andrew Cunningham, “Getting the Game Right: Some Plain Words on the Identity and Invention of Science,” Studies in the History and Philosophy of Science 19 (1988): 365-389.

20 genealogical one. It is important, therefore, not to focus only on those figures whose impact on the modern world is obvious—the likes of Galileo, Descartes, and Newton—but also on those who, like John Wallis, made contributions to the genealogy of science and religion that are less apparent and quite surprising from a twenty-first-century perspective.

Chapter 2: “Deep Things of God”: Nescience in Wallis’s Natural Philosophy and Theology

How is the Holy Trinity like a cube? According to John Wallis, it is easier to understand the relationship between the Father, Son, and Holy Spirit if one compares them to the length, width, and height of a cube. Just as the three dimensions are equal and equally necessary to make up a cube, so the three persons are equal and equally necessary parts of the Godhead. As Philip Beeley and Siegmund Probst have discussed, Wallis’s anti-Trinitarian critics considered this comparison the height of sophistry; it struck them as “almost the return of the worst side of scholasticism.”1

But Wallis insisted that the three dimensions bear a significant resemblance to the three persons of the Trinity.

Wallis defended the doctrine of the Trinity in eight letters written in the early 1690s and published together under the title Theological Discourses (1692).2 At that point, the septuagenarian Wallis could support his theological views with knowledge of nature that he had acquired over a long career. When he thrust himself into the Trinitarian controversy of the 1690s,

Wallis benefited from decades’ worth of knowledge from his studies of mathematics, natural philosophy, anatomy, and even botany––all of which served as resources to complement his extensive knowledge of Christian theology and Scripture. This chapter highlights similarities–– rhetorical, methodological and epistemological––between Wallis’s works in natural philosophy and theology. After a brief historiographical discussion, my analysis begins with the rhetorical strategies that characterize Wallis’s work in both fields. These point to deeper epistemological and

1 Philip Beeley and Siegmund Probst, “John Wallis (1616-1703): Mathematician and Divine,” in Mathematics and the Divine: A Historical Study, eds. T. Koestier and L. Bergmans, (Amsterdam: Elsevier, 2005), 451. 2 For a useful overview of the contents of these letters, see Philip Dixon, “Nice and Hot Disputes”: The Doctrine of the Trinity in the Seventeenth Century (London: T & T Clark, 2003), 116-122.

21 22 methodological connections, which I will explore in two case studies: Wallis’s defence of the

Trinity, which demonstrates his approach to divine mysteries, and his theory of the tides, which shows that he approaches natural phenomena in a remarkably similar way. According to Wallis, divine mysteries necessarily involve a degree of nescience: beyond a certain point, they cannot be grasped by the human mind. I argue that, for Wallis, the fact that God created the natural world ensures that nescience is also inevitable in natural philosophy. This makes him reluctant to speculate on the physical causes of natural phenomena. I have chosen the word “nescience” to emphasize that these are not things about which he is skeptical or happens not to know. They are things he cannot know on account of the limitations of the human mind.

Wallis’s conception of the unknowability of God is clearest in his eight letters on the

Trinity. Here he attempts to refute the arguments of those whom he labels “Socinians.” This was a protean term in seventeenth-century theology, but toward the end of the century it had become primarily an epithet that mainstream Protestants hurled at anyone who challenged central doctrines. The Socinian movement, named for the Sienese theologian Faustus Socinus, began in

Poland in the sixteenth century. The original Socinians expanded on the Protestant principle of rejecting religious doctrines that they considered contrary to reason. While Protestants in general considered it unreasonable to believe that the bread and wine of the Eucharist become the body and blood of Christ, Socinians considered it just as unreasonable to believe, for example, that

Christ was the incarnate Son of God, or that three persons could exist in one God. From Poland the movement spread west, attracting a vocal minority of supporters in England by the mid- seventeenth century.3 By the time that Wallis wrote his letters on the Trinity, however, the anti-

3 On the origins of Socinianism, see Christopher J. Walker, Reason and Religion in Late Seventeenth-Century England (London: I.B. Tauris, 2013), 97-110; Jan A. Wojcik, Robert Boyle and the Limits of Reason (Cambridge: Cambridge University Press, 1997), 42-55. On the Trinitarian controversy in England during the 1690s, see Maria Rosa Antognazza, Leibniz on the Trinity and the Incarnation: Reason and Revelation in the Seventeenth Century, trans.

Trinitarians had begun to call themselves “Unitarians,” distancing themselves from the increasingly negative connotations of the term “Socinian.”4 Wallis declined to recognize this distinction in his letters, disparaging all those who rejected the Trinity as Socinians.

These challenges to the doctrine of the Trinity came in a period when the very notions of

“reason” and “reasonableness” were in a state of flux. As Christopher Hill explains, many seventeenth-century philosophers sought to shift the criteria for reasonableness away from the medieval Scholastic standards of logic and authority, and toward “[c]ommon sense, the senses, evidence, experience, [and] experiment.”5 Wallis’s approach to reason cannot be fitted neatly into either of these two camps. As we shall see, he was too appreciative of both Scholastic and experimental methods of inquiry to dismiss one or the other. Wallis’s letters on the Trinity reflect his effort to fit a slippery concept of reason into a theological debate. His defence of the doctrine of the Trinity rests on the notion that such divine mysteries are beyond reason but not contrary to it; they represent truths about God that a human mind cannot fully grasp.

The explicit epistemological considerations in Wallis’s theology elucidate those that are implicit in his natural philosophy. This will become clear from my analysis of Wallis’s theory of the tides, which he described in letters, some of which he had published in the Philosophical

Transactions of the Royal Society. In this case, too, Wallis identifies limits to human reason, and suggests at certain moments that, just as God’s ineffability constrains what one can learn by reading Scripture, so it constrains what one can learn by observing nature. In both fields, once

Wallis has identified the appropriate boundaries, he works confidently within them. First he gathers data from one of Gods Two Books. Then he subjects these data to reason, and on that basis

Gerald Parks (New Haven: Yale University Press, 2007), 91-102; Walker, Reason and Religion, 147-237. 4 See Antognazza, Leibniz on the Trinity, 92; Walker, Reason and Religion, 157. 5 Christopher Hill, “‘Reason’ and ‘Reasonableness’ in Seventeenth-Century England,” British Journal of Sociology, 20 (1969): 240.

24 he makes conclusions. In important ways, then, his approach to Scripture resembles his contributions to the emerging experimental philosophy. However, as much as Wallis embraced the innovations of the new philosophy, he always remained receptive to the lessons of the

Scholastic tradition.

This places Wallis at the nexus of two competing views of the role of theology in the rise of modern science. On one hand, Peter Harrison argues in The Fall of Man and the Foundations of Knowledge that the methodology and epistemology that characterized experimental philosophy were products of scholars’ reflection on theological questions highlighted by the Protestant

Reformation.6 On the other hand, Edward Grant responds to Harrison’s argument by downplaying theology in favour of the maturation of Scholastic natural philosophy.7 I argue that both of these elements––the medieval Scholastic tradition and Protestant theology––are crucial to Wallis’s philosophical perspective. In typical Protestant fashion, Wallis bases his theology primarily on a close reading of Scripture, and his collection of biblical evidence bears a strong resemblance to his empirical approach to natural philosophy. However, at a time when the sands were shifting under the concept of “reason,” Wallis appeals to the Scholastic tradition in an effort to determine which ideas could reasonably be believed.

Theology and the rise of science: Harrison’s Fall of Man and Grant’s response

I will argue below that the case of Wallis shows how Harrison’s and Grant’s views on science and theology might be brought closer together. In Harrison’s account, the key to the development of modern science is theological anthropology, that is, accounts of human nature informed by a close

6 Peter Harrison, The Fall of Man and the Foundations of Science (Cambridge: Cambridge University Press, 2007). 7 Edward Grant, “The Fall and Foundations,” Metascience 18 (2009): 43-51.

25 reading of the Bible. He explains that early modern natural philosophers (mainly the Protestants and especially the Calvinists) believed that Adam had been able to give names to all animals that corresponded to their natures, but had lost this ability when he sinned and was expelled from

Eden. Depending on how they interpreted the effects of Adam’s Fall, early modern natural philosophers adopted particular methodologies that would allow them to recover some of the lost

Adamic knowledge.8 As the seventeenth century advanced, Harrison explains, the philosophers who discussed the limitations of reason and the senses focused less on the Fall and more on the relationship between an infinite God and his finite creations. For the likes of Robert Boyle, John

Locke, and Isaac Newton, the decisive factor was not how God had punished humanity for Adam’s

Fall, but rather where he had placed humanity in the grand scheme of the universe.9 It is within this group of natural philosophers that we can place Wallis, whose time at Oxford overlapped with those of Boyle and Locke in the 1650s. Wallis does acknowledge that the Fall weakened humanity’s cognitive abilities. But he does not dwell on this point, and he notes that, even before the Fall, the human mind still depended on God to acquire knowledge.10

Although Harrison’s account can help us to understand Wallis’s views on the human- divine relationship, his argument does not fit well with Wallis’s attitude toward Scholastic philosophy. Harrison claims that theological anthropology took a central role at the expense of

8 For instance, the experimental philosophy conceived by Francis Bacon and further developed by the Royal Society reflected a view that the Fall had impaired mankind’s senses. The only remedies for this were patient observation and experimental trials, as well as instruments like telescopes and microscopes that allowed the senses to recover some of their prelapsarian power. See Harrison, Fall of Man, 248-50. 9 See Harrison, Fall of Man, 218-44. 10 Responding to what he perceives as Thomas Hobbes’s arrogant belief that one does not need God’s help to gain geometrical knowledge after the Fall, Wallis claims that “no sober person will doubt” (nemo sobrius dubitabit) that the Fall weakened the human intellect. Yet he insists that the Fall did not create humanity’s reliance on God for knowledge, but rather increased it, “for God did not first take care of our matters after the Fall” (non enim post lapsum primò suscepit Deus rerum nostrarum curam; John Wallis, Elenchus geometriæ Hobbianæ. Sive, geometricorum, quæ in ipsius elementis philosophiæ, à Thoma Hobbes Malmesburiensi proferuntur, refutatio [Oxford, 1655], 89). My translation.

“the Aristotelian-scholastic dominance of human learning.”11 Late-medieval Scholastics had embraced Aristotle’s optimism about achieving certain knowledge through reason and the senses, and accordingly they downplayed the effects of the Fall. As early modern natural philosophers challenged the authority of Aristotle, Harrison explains, they replaced his epistemology with the skepticism that lent itself so well to the development of experimental philosophy.12 This aspect of

Harrison’s argument is perhaps the most vulnerable to criticism, since he seems to neglect the ongoing importance of Aristotle and the Scholastics in early modern science. Indeed, in his compelling critique of Harrison’s book, Grant argues that the epistemological and methodological developments that laid the foundation for modern science had very little to do with the Fall or the human-divine relationship. Rather, these changes grew organically out of a tradition of “natural philosophy . . . based on reason” that had emerged in late-medieval universities. Grant contends that the rise of modern science would have happened without the help of theological anthropology, which at most “stimulated scientific activity that was already an integral part of European intellectual life.”13

The case of Wallis seems to support Grant’s position that the Scholastic tradition remained crucial to early modern natural philosophy. As Jason Rampelt has shown, Wallis did not perceive

11 Harrison, Fall of Man, 248. 12 See Harrison, Fall of Man, 43-5. 13 Grant, “Fall and Foundations,” 45-6. Elsewhere Grant has argued that, despite some fruitful interaction between theology and natural philosophy in the late Middle Ages, modern science could not have developed in the West if not for the fact that “Christians were largely convinced that the Bible was not a book about science.” On Grant’s account, apart from the Church’s toothless condemnations of Aristotle in the thirteenth century and the ugly Galileo affair in the seventeenth, natural philosophers generally succeeded in avoiding religious interference, and this is what allowed natural philosophy gradually to mature into modern science. Edward Grant, Science and Religion, 400 B.C. To A.D. 1550: From Aristotle to Copernicus (Baltimore: Johns Hopkins University Press, 2006), 223-4. On the other hand, Grant argues that while the effects of theology on natural philosophy in the Middle Ages were minimal, the effects of natural philosophy on theology were profound. Theologians applied novel ideas about matter and motion to subjects as diverse as angels, transubstantiation, and God’s infinitude. Everything apart from revealed truths that were beyond reason––such as the Trinity and the Incarnation––was reinterpreted in light of natural philosophy, logic, and mathematics (Grant, Science and Religion, 205-22).

27 any conflict between the Aristotelian tradition and the new philosophy, and he taught his students to draw on whichever methodology was appropriate for a particular intellectual pursuit.14

However, while I agree that Scholastic reasoning is crucial for Wallis, I intend to clarify precisely how he uses Scholastic principles in theology and natural philosophy. On Rampeltʼs reading of

Wallis, it is Scholastic reasoning that shapes Wallis’s theology and natural philosophy alike.15 In contrast, this chapter aims to shift the focus to the theological commitments embedded in Wallis’s intellectual pursuits. However, I do not follow Harrison in treating early modern theology as the source of an outright rejection of the Scholastic tradition.16 Wallis’s work in mathematics and physics was at the heart of the Royal Society’s activities, but he spent most of his time at a significant remove from London, steeped in the university culture of Oxford. His presence in both

14 See Jason Rampelt, “Distinctions of Reason and Reasonable Distinctions: The Academic Life of John Wallis (1616- 1703)” (unpublished Ph.D. thesis, Cambridge University, 2005), 224-8. 15 Rampelt identifies a Scholastic principle, Francisco Suárez’s principle of inadequate concepts, as the foundation of Wallis’s epistemology. Suárez identifies distinctions between things within one’s own mind as distinctiones rationis ratiocinantis, which yield “adequate” or complete conceptions of those things. Conversely, one makes distinctiones rationis ratiocinatae based on objects in the world, and these yield only “inadequate” or incomplete conceptions of those things. For Rampelt, a Suarezian notion of inadequate concepts is the linchpin of Wallis’s philosophical outlook. Any knowledge based, in Wallis’s view, on real things in the world, including geometrical figures, human language, experimental results, and truths about God learned from Scripture, will yield inadequate concepts of those things (Rampelt, “Distinctions of Reason,” 33-6, 76-7). 16 That is to say, I agree with Grant about that Scholastic philosophy continued to shape the development of science in the early modern period. On the other hand, I disagree with Grant’s claim that theology had a negligible impact on natural philosophy. In his review of Harrison’s book, Grant insists that early modern scholars followed their medieval forebears in keeping their theological commitments separate from their natural philosophy, and he takes as his chief example Isaac Newton as he is described in Richard Westfall’s biography, Never at Rest, which was published in 1980. Grant adopts Westfall’s position that Newton left considerations of God out of the Principia mathematica and only added the highly theological “General Scholium” to the second edition in order to avoid suspicion of atheism (Grant, “Fall and Foundations,” 47-48). Westfall, however, no longer represents the prevailing attitude among historians toward Newton or early modern science and religion in general. Already by 1980 Westfall’s biography ran counter to the growing trend among historians of identifying the interdependence of science and religion in the work of Newton and his contemporaries (see Margaret J. Osler, “Religion and the Changing Historiography of the Scientific Revolution” in Science and Religion: New Historical Perspectives, eds. Thomas Dixon, Geoffrey Cantor and Stephen Pumfrey [Cambridge: Cambridge University Press, 2010], 79-82). More recently, Stephen Snobelen has argued that theology was built into the Principia from the first edition (Stephen D. Snobelen, “The Theology of Isaac Newton’s Principia Mathematica: A Preliminary Survey,” Neue Zeitschrift für Systematische Theologie und Religionsphilosophie 52 [2010]: 377–412). Likewise, Andrew Janiak has shown that Newton’s beliefs about God’s qualities are so intimately tied to his metaphysics that any separation of Newton’s thought into the categories “science” and “theology” introduces serious distortions (Andrew Janiak, Newton as Philosopher [Cambridge: Cambridge University Press, 2008], 173-174).

28 of these intellectual settings––one known for challenging the Scholastic tradition and one known for maintaining it––provides an important opportunity to consider where Scholastic reasoning fits into the dynamic landscape of early modern science and religion. Accordingly, in addition to identifying rhetorical, methodological, and epistemological similarities in Wallis’s natural philosophy and theology, I will discuss below how the Savilian Professor follows Scholastics such as Thomas Aquinas when he supports his arguments by identifying similitudes.

Wallis’s rhetorical strategies

We can begin to appreciate how similarly Wallis approaches theology and natural philosophy by considering his rhetorical strategies. The stubborn and quickly offended Wallis rarely shied away from a chance to display his rhetorical gifts. Jacqueline Stedall has described the rhetorical techniques that Wallis brought to his mathematical disputes with several French rivals. These include distorting the truth without lying outright, ad hominem argumentation, and drowning out his opponents’ arguments “with a deluge of words.”17 To these we can add Wallis’s practice of shifting the blame for perpetuating conflicts onto his opponents despite his obvious enthusiasm for controversy.18

Wallis employs the same strategies in his dispute with fellow English cleric William

Holder concerning the education of the deaf. In 1670 Wallis had a letter published in the

Philosophical Transactions describing his remarkable success teaching two deaf men to speak, which he treats as an important experimental achievement.19 The problem was that Wallis failed

17 Jacqueline Stedall, “John Wallis and the French: His Quarrels with Fermat, Pascal, Dulaurens and Descartes,” Historia Mathematica 39 (2012): 277. 18 See Adam Richter, “Priority and Nationalism: The Royal Society’s International Priority Disputes, 1660-1700” (unpublished MA thesis, Dalhousie University, 2011), 117-118, 167-168. 19 John Wallis, “A Letter of Dr. John Wallis to Robert Boyle Esq, Concerning the Said Doctor’s Essay of Teaching a

29 to mention Holder’s earlier work in this field, including his treatment of one of Wallis’s patients.

After Holder complained about this in a polemical attack on Wallis, the Savilian Professor had to account for this omission. He responded with his rambling and misleadingly titled Defence of the

Royal Society (1678), in which his main tactic was to attack Holder’s abilities and character.20 He had not mentioned Holder, Wallis claims, because he wanted to spare him the embarrassment of pointing out that his efforts had been unsuccessful. Wallis suggests that now the jealous Holder had dreamed up a conspiracy intended to deprive him of credit. Thus it is Holder’s paranoia that has dragged Wallis into this conflict, and he is only responding because he feels compelled to defend himself and the others whom Holder has involved in this imagined conspiracy.21

Another case that reflects Wallis’s rhetorical strategies––distorting the truth, shifting the blame, ad hominem attacks––is his defence of the Trinity. In four of the letters included in the

Theological Discourses he claims that the cause of the conflict is the “cavils” of his anti-

Trinitarian opponents (a descriptor that he also applied to Holder’s complaints).22 In his fourth letter, responding to the latest volley from his anti-Trinitarian opponent Stephen Nye, Wallis claims that “it is He that is the Aggressor, not I: and I only upon the Defence.” But his supposed

Person Dumb and Deaf to Speak, and to Understand a Language; together with the Success Thereof: Which Letter Though Written Many Years Since, Was but Lately Obtainʼd to be Inserted Here, It Being Esteemed Very Well Worth to be Preserv’d and Communicated for Publick Use,” Phil Trans 5 (1670): 1087-99. 20 John Wallis, A Defence of the Royal Society and the Philosophical Transactions, Particularly those of July, 1670. In Answer to the Cavils of Dr. William Holder (London, 1678). 21 See Wallis, Defence of the Royal Society, especially 9-11, 22-4. For a brief overview of Wallis’s and Holder’s efforts to educate the deaf and their dispute, see Mordechai Feingold, “The Origins of the Royal Society Revisited” in The Practice of Reform in Health, Medicine, and Science, 1500-2000: Essays for Charles Webster, eds. Margaret Pelling and Scott Mandelbrote [Aldershot: Ashgate, 2005] 168-175; Jonathan Rée, I See a Voice: Deafness, Language and the Senses––A Philosophical History (London: HarperCollins, 1999), 106-19. Wallis’s work with the deaf, and his dispute with Holder, will be described in more detail in Chapter 6 below. 22 John Wallis, “An Explication and Vindication of the Athanasian Creed. In a Third Letter, Pursuant of Two Former, concerning the Sacred Trinity. Together with a Postscript, in Answer to Another Letter,” 54-6; “A Sixth Letter, concerning the Sacred Trinity; in Answer to a Book Entituled, Observations on the Four Letters, &c.” 7, 18; “A Seventh Letter, concerning the Sacred Trinity; Occasioned by a Second Letter from W. J.,” 18; “An Eighth Letter concerning the Sacred Trinity; Occasioned by Some Letters to Him on That Subject,” 10, in Theological Discourses; Containing VIII Letters and III Sermons concerning the Blessed Trinity (London, 1692). Wallis labels Holder’s objections “cavils” in the full title of his Defence of the Royal Society; see n. 20 above.

30 aversion to conflict does not stop him from answering Nye’s objections and provoking another response: “Yet, because he is so desirous of it, I am content to go somewhat out of my way, to wait on him; and to hear what he hath to say.” 23 In this and subsequent letters Wallis continues to suggest that he is the only participant in the conflict who has behaved decorously. He writes, for instance, that he has made his case “Calmly,” without “scurrillous Language” and “Reproachful terms,” the implication being that his opponent has not shown him the same courtesy.24

As in his mathematical disputes, Wallis was accused of distorting the truth during the

Trinitarian controversy. Nye suggests that Wallis has willfully mischaracterized the position of the anti-Trinitarians in order to dismiss their objections. According to Wallis’s account, Socinians consider it impossible for an entity to be three things when considered from one perspective, and one thing when considered from another perspective; but Nye claims that no reasonable person would doubt this. What is inconceivable, Nye argues, is that three things together could be considered the same as what each on its own is considered to be: how can the three persons of the

Trinity make up God if each of them is called God on its own? Wallis has suggested that the three persons make up the Trinity much like three groats make up a shilling. But surely he would concede that one groat on its own could not be called a shilling, as each of the three persons is called God.25 Nye is arguing here, and not without reason, that Wallis has intentionally distorted his opponents’ position to make it seem ridiculous and to smooth over their serious objections to the doctrine of the Trinity.

23 John Wallis, “A Fourth Letter, concerning the Sacred Trinity; in Reply to What is Entituled, an Answer to Dr Wallisʼs Three Letters” in Theological Discourses, 23. 24 Wallis, “Fourth Letter,” 36. See also Wallis, “A Fifth Letter, concerning the Sacred Trinity; in Answer to What is Entituled, The Arians Vindication of Himself against Dr Wallisʼs Fourth Letter on the Trinity” in Theological Discourses, 13-14; “Eighth Letter,” 19-20. 25 [Stephen Nye], Observations on the Four Letters of Dr. John Wallis, concerning the Trinity and the Creed of Athanasius (London, 1691), 4.

Indeed, Nye argues that Wallis’s analogy of the Trinity and the cube is just a typical

Trinitarian ploy. He suggests that proponents of the Trinity routinely cloud the issue with misleading metaphysical language to prevent people from realizing the absurdity of the doctrine, and this is all that Wallis’s analogy achieves.26 But here Nye exaggerates Wallis’s willful manipulation of the truth. Wallis evidently thought that his cube analogy was a legitimate approach to understanding the Trinity, founded on the established Scholastic practice of identifying similitudes in nature in order to clarify the doctrine. My intention in discussing

Wallis’s rhetorical techniques is not to argue, as Nye does, that his defence of the Trinity is merely a smokescreen behind which no viable philosophical content lies. The fact that Wallis’s writing is highly partisan does not render it mere propaganda. Rather, I suggest that the rhetorical similarities across multiple fields are an outward manifestation of the deeper methodological and epistemological similarities that will be discussed in two case studies below: firstly, Wallis’s defence of the Trinity, and secondly, his theory of the tides. Having considered the philosophical attitude that Wallis explicitly adopts in his theology, which emphasizes nescience on account of the unknowable nature of God, we can better appreciate the similar attitude he adopts when he admits to the nescience involved in his natural philosophy.

The Trinity and the cube: nescience in Wallis’s defence of the Trinity

In their analysis of the relationship between Wallis’s work as a mathematician and a divine, Beeley and Probst find that he sometimes resists comparisons between mathematical and theological

26 Nye, Observations on the Four Letters, 5. This accusation resonates with one that Thomas Hobbes directed at Wallis and his fellow English clerics decades earlier. According to Hobbes, Wallis exemplified the clergy’s practice of using abstruse metaphysical language to obscure the absurdities in their doctrines. See Chapter 6 below.

32 concepts, such as that between mathematical infinity and the infinitude of God.27 In this example, though, Wallis opposes an analogy between God and a concept in arithmetic, whereas the cube analogy draws on an example from geometry. For Wallis, as Katherine Hill has shown, arithmetic deals with purely abstract quantities whereas geometry describes extended bodies in the real world.28 Accordingly, he considers the cube in his analogy to be among the “Corporeals” or

“Material Bodies” found in nature.29 When Beeley and Probst suggest that Wallis links geometry and theology “only in the employment of analogy,” they understate the importance of this aspect of his defence of the Trinity.30 Here Wallis explains a theological concept with reference to a similitude in nature, a practice which, as I discuss below, is grounded in the Scholastic tradition.

Notwithstanding his reservations about introducing arithmetic into theological discussions, Wallis depends on his knowledge of nature to support his theological beliefs.

In comparing the Trinity to a cube (and illustrating it with a diagram; see Figure 1) in his published letters, Wallis may have hoped to make a complex theological concept more intelligible to a mathematically literate readership. Wallis employs a similar strategy in other cases. In a letter to Boyle, for example, he likens his experiments on teaching a deaf man to speak to the solution of a mathematical problem, in which one works toward a demonstration from a few known

27 See Beeley and Probst, “Mathematician and Divine,” 449. 28 Katherine Hill, “Neither Ancient nor Modern: Wallis and Barrow on the Composition of Continua. Part One: Mathematical Styles and the Composition of Continua,” Notes and Records of the Royal Society of London 50 (1996), 170-171. Since arithmetic deals only with abstract quantities and not physical bodies, Wallis evidently believes that it can generate certain knowledge. For instance, when he uses the method of “induction,” for which his Arithmetica infinitorum is well-known, Wallis reasons on the basis of a finite number of cases that a particular rule applies in all such cases. As I will discuss below, Wallis is not so confident about the knowledge he generates in other fields. On Wallis’s methodology in Arithmetica infinitorum see David Dennis and Jere Confrey, “The Creation of Continuous Exponents: A Study of the Methods and Epistemology of John Wallis,” CBMS Issues in Mathematics Education 6 (1996), 33-60. Thanks to Doug Jesseph for pointing out the differences in Wallis’s treatment of arithmetic. 29 John Wallis, “The Doctrine of the Blessed Trinity Briefly Explained, in a Letter to a Friend” in Theological Discourses, 11-12. 30 Beeley and Probst, “Mathematician and Divine,” 450.

33 elements.31 But Wallis considers his cube analogy to accomplish more than rendering a challenging concept more approachable: it demonstrates that the doctrine of the Trinity is reasonable.

Wallis claims that the only point of contention between orthodox Trinitarians and

Socinians is whether the three-in-one relationship of the Trinity is “inconsistent with natural

Reason.”32 The Scholastics used the term “natural reason” to

distinguish knowledge generated by the human mind from

knowledge conveyed by divine revelation. Aquinas writes of

theology, “What is peculiar to this science’s knowledge is that it is

about truth which comes through revelation, not through natural

reasoning [naturalem rationem].”33 This terminology was still Figure 1: Wallis’s current in Wallis’s time. For instance, Boyle distinguishes between cube diagram knowledge of God gained from “meer Natural Reason” and that (Theological gained from “Revelation-Discovery” in his Excellency of Theology Discourses, 1692) (1674).34

Wallis, too, distinguishes natural reason from revelation, arguing that they both play an important part in the evaluation of theological doctrines: natural reason demonstrates whether a doctrine is “possible” while revelation confirms that the doctrine is true. In his letters on the

Trinity, Wallis insists that Scripture is unambiguous on this matter, so all that he needs to do is show that the Trinity is possible by demonstrating its compatibility with reason.35 Implicit in these

31 Wallis, “Letter to Boyle,” 1096. 32 Wallis, “Trinity Briefly Explained,” 5. 33 Thomas Aquinas, Summa theologiæ, ed. Thomas Gilby, vol. 1 (Cambridge: Blackfriars, 1964), 22-3. 34 Robert Boyle, The Excellency of Theology, Compar’d with Natural Philosophy, (as Both are Objects of Men’s Study) (London, 1674), 19-20. 35 See Wallis, “Third Letter,” 22-3.

34 remarks is another distinction, commonly employed by Wallis’s contemporaries, between what is inconsistent with reason and what is simply above reason.36 Wallis seeks to demonstrate that even if divine mysteries like the Trinity are above reason and can never be fully understood by the human mind, they are nevertheless consistent with reason. To that end he constructs an analogy between the persons of the Trinity and the dimensions of a cube.

As Wallis identifies what he calls “similitudes” for theological concepts in nature, he follows a Scholastic precedent. Aquinas, for example, argues that God intends for humans to conceive of spiritual things in terms of similitudes with corporeal things; this is one of the reasons why God endowed humans with the ability to learn about nature through their senses.37 Closer to

Wallis’s time, the Reformed Scholastic theologian Lucas Treclatius, Jr., wrote that God’s attributes should be understood “Metaphorically . . . eyther after humane affection (or passion) as man, angrie, sleeping, or else by a congruency and similitude, as a Lyon, a Stone, a River, &c.”38

In his first letter on the Trinity, Wallis follows precedents like these when he explains that the length, width, and height of a cube are distinct but equal, and equally necessary to make a cube. For Wallis, this relationship between the dimensions resembles the doctrine of the Trinity, which holds that there is one God in three persons: the Father, Son, and Holy Spirit. Each of these persons instantiates full divinity, but God is properly understood to be all three of the persons together. A cube, Wallis claims, exemplifies how something treated as one entity can be treated as

36 See Wojcik, Robert Boyle, especially 6-7. 37 Aquinas makes this argument in Part 1, Question 1, Article 9 (Aquinas, Summa theologiæ, vol. 1, 33-7). On the roots of Aquinas’s use of similitudes see Max Herrera, “Understanding Similitudes in Aquinas with the Help of Avicenna and Averroes” in Gyula Klima and Alexander W. Hall, eds., Universal Representation, and the Ontology of Individuation (Newcastle upon Tyne: Cambridge Scholars, 2011), 19-22. 38 Lucas Treclatius, A Briefe Institution of the Commonplaces of Sacred Divinitie, trans. John Gawen (London, 1610), 52. See Richard A. Muller, “Unity and Distinction: The Nature of God in the Theology of Lucas Treclatius, Jr,” Renaissance and Reformation Review 10 (2008): 325-326. Gottfried Leibniz also took this approach to the Trinity, claiming that the distinction between the persons of the Trinity is like a mind thinking of itself; the thinking mind is distinct from the mind being thought of, and yet they are the same mind. See Antognazza, Leibniz on the Trinity, 108- 9.

35 three entities from a different perspective: it is a cube, but it is also the combination of length, width, and height.39 Wallis sees no problem in taking the epistemic step from this geometrical concept to a theological one. He writes, “if it may be so in Corporeals, [it may be] much more in

Spirituals.” Suppose, Wallis continues, that the cube were infinite. In that case, infinite height, length, and width would together (but not separately) make an infinite cube. And if one supposes that this infinite cube exists eternally, “its Dimensions also must be infinite and Co-eternal.”

Taking the analogy further, Wallis suggests that if one were to determine the length, derive the width from it, and derive the height from both of them, this would be comparable to the Father begetting the Son, and the Holy Spirit proceeding from both.40

In his Trinity letters, Wallis also provides similitudes to demonstrate the possibility of the

Incarnation of Christ. He claims that the two things required for Christ to become human, namely a virgin birth and hypostatic union of a human and a divine being, are both consistent with reason.

Wallis notes that there are well-documented cases of hermaphroditism, and it is possible that a hermaphrodite could self-impregnate; likewise, certain plants can “propagate without a fellow.”

So there is nothing contrary to reason in the notion that offspring can be produced without intercourse between a man and a woman.41 As for the hypostatic union, everyone accepts examples in nature of corporeal things interacting with incorporeal things, despite the popularity of mechanical philosophy, which seeks to attribute all phenomena to matter in motion. For instance, everyone knows that people’s souls control their bodies. The Socinians have no reason,

39 Wallis, “Trinity Briefly Explained,” 11-12. 40 Wallis, “Trinity Briefly Explained,” 12-13. 41 Wallis, “Third Letter,” 25-6. Wallis studied hermaphroditic animals himself early in his career. In a letter to the naturalist Martin Lister written in 1694, he explains that he is surprised to see Lister and others treat “Androgynous” snails “as a late discovery,” since Wallis had observed them as early as 1651 or 1652 (British Library MS Add 4276, f. 179r). Wallis also discussed hermaphroditism at a meeting of the Oxford Philosophical Society in 1687, relaying a report sent to him by Edmond Halley of a French person who appears to be female but has male genitalia (ESO IV, 204; Eugene Fairfield MacPike, ed., Correspondence and Papers of Edmond Halley [Oxford: Clarendon Press, 1932], 81-82).

36 then, to doubt that God could effect an interaction between Himself and a human body such as the Incarnation.42 On the basis of such similitudes, Wallis considers his demonstration complete: natural reason has demonstrated the possibility of these doctrines, and Scripture has demonstrated their truth. Even if his critics considered such reasoning by similitude to be mere Scholastic sophistry, to Wallis’s mind it demonstrates the reasonableness of these doctrines.

Wallis admits that how the hypostatic union might work is less clear than how the virgin birth might work, but he does not consider this a blow to his argument. He argues that there are many things found in nature or described in Scripture whose workings we do not understand, but are nevertheless not ruled out by reason. Wallis attributes this nescience of both nature and

Scripture to the ineffability of God. He cites the example of King Solomon, who was not only wise but also greatly “skilled in Natural Philosophy.” Quoting what were thought to be Solomon’s words in the Book of Ecclesiastes, Wallis suggests that the wise king knew that God’s actions were beyond the scope of natural philosophy, just as the true nature of the Trinity is beyond the scope of Wallis’s analysis:

When (says he) I applied my heart, to know wisdom, and to see the business that is done upon the earth: Then I beheld all the work of God; that a man cannot find out the work of God that is done under the sun: Because though a man labour to seek it out, yet he shall not find it. Yea further, though a wise man seek to know it, yet shall he not be able to find it, Eccles. 8. 16, 17. And shall we then say, of the deep things of God, [1 Cor. 2:10], The thing is impossible, because we cannot find it out?43

If even Solomon admitted his ignorance of “the deep things of God” then what can Wallis––skilled

42 Wallis, “Third Letter,” 28-9. Of course, Wallis is ignoring the objections of materialists like Hobbes who deny the existence of immaterial souls. He also ignores the subtleties of the Socinians’ position concerning how God the Father actually relates to the Son. Faustus Socinus, for instance, argued that Christ was fully human, but he maintained that God acted through Christ to show humanity the path to salvation. See Sarah Mortimer, Reason and Religion in the English Revolution: The Challenge of Socinianism (Cambridge: Cambridge University Press, 2010), 18. 43 Wallis, “Third Letter,” 26 Italics in original.. Here Wallis takes part in a tradition that developed among early modern English scholars of treating Solomon as a brilliant natural philosopher “second only to Adam and Moses” (Harrison, Fall of Man, 122).

37 though he is in studying both Scripture and nature––hope to learn by comparing the Trinity to a cube? Certainly he does not aspire to full knowledge of God, so he does not mind that his cube analogy does not withstand scrutiny in all respects.

He does, however, respond to some objections in order to support his claim that the Trinity resembles a cube. When a correspondent points out that a dimension cannot be called a cube, but each person of the Trinity can be called God, Wallis responds,

. . . though we cannot say (in the Abstract) that length is a Cube, (and so with the rest;) yet (in the Concrete) this Long thing (or this which is Long) is a Cube; and so, this which is Broad, or this which is High, is a Cube: Just so; we do not say (in the Abstract) that Paternity is God; but (in the Concrete) the Father is God; (and so of the Other Persons.)

So, Wallis explains, a dimension of a particular cube––its being a long thing, for instance––is comparable to a person of God, whereas an abstract dimension like length is comparable to abstract “Personality.”44 Thus Wallis maintains that, in many significant ways, the dimensions of a cube really do resemble the persons that make up the Trinity.

In general, though, Wallis does not take the time to respond to all the ways that a Trinity is not like a cube. He acknowledges in the first letter that his analogy is inexact because it is a case of “parvis componere magna”––bringing great things together with small things.45 However,

Wallis argues, one does not need to understand something fully in order to believe it. He writes,

. . . because we do not know How the bones grow in the womb of her that is with child [Ecc. 11:5], shall we therefore say they do not grow there? Or, because We cannot by searching find out God, because we cannot find out the Almighty to perfection [John 11:7], shall we therefore say, things cannot be, when God says they are, only because we know not How?46

All reason must do is demonstrate that a doctrine is possible; if so, one can accept it because

44 John Wallis, “A Second Letter concerning the Holy Trinity. Pursuant to the Former from the Same Hand; Occasioned by a Letter (There Inserted) from One Unknown” in Theological Discourses, 9. 45 Wallis, “Trinity Briefly Explained,” 14. 46 Wallis, “Trinity Briefly Explained,” 19.

Scripture has revealed it. Jason Vickers situates Wallis near the beginning of a long tradition of

English Protestant theologians who view the Trinity “first and foremost as a puzzle to be solved; it only requires the correct analogy. The Trinity is like cherry pie. It is like a triangle. It is like ice, water, and steam.”47 But Wallis does not really treat the Trinity as a puzzle nor his similitudes as solutions; he does not expect them to generate full knowledge of God. Although he knows that such analogies will eventually dissolve under scrutiny, they have done their job if they establish something like the Trinity as possible.

Here Wallis seems to model his epistemology on that of Solomon, whose knowledge of both God and nature is apparently framed by his recognition of the limits of reason. It is perhaps not surprising, then, that the methodology Wallis brings to the study of Scripture resembles his empirical approach to natural philosophy. Although Wallis grants an important role to reason in the consideration of theological issues, he relies on what is known a posteriori in consideration of what we might call biblical data. But since the limited human mind must be involved in the interpretation of what is revealed, Wallis remains cautious about the conclusions he draws from

Scripture.

In fact, the caution that Wallis shows here closely resembles the epistemological attitude that he and his fellow experimental philosophers adopted in the study of nature. As Steven Shapin and Simon Schaffer have argued, the credibility of the early Royal Society depended on the

Fellows showing modesty by treating their conclusions about physical causes as probable rather than certain.48 Likewise, the account of Wallis’s tidal theory in the Philosophical Transactions, which will be discussed below, is preceded by a note from the editor, Henry Oldenburg, praising

47 Jason E. Vickers, Invocation and Assent: The Making and Remaking of Trinitarian Theology (Grand Rapids: Eerdmans, 2008), 104. 48 Steven Shapin and Simon Schaffer, Leviathan and the Air-Pump, 2nd ed. (Princeton: Princeton University Press, 2011 [orig. pub. 1985]), 67.

39 the author for the “Modesty” he has shown in treating his theory as a “Conjecture” rather than a matter of certainty.49 In fact, in a letter to Oldenburg, Wallis admits that his theory is provisional and that he would give it up if anyone should come up with a better explanation for the tides.50

The same attitude of “modesty,” or its cognate “moderation,” is repeatedly invoked in

Wallis’s defence of the Trinity. The Theological Discourses include two letters written to Wallis from a sympathetic correspondent identifying himself only as “W. J.” who recommends strict adherence to scriptural evidence on the matter of the Trinity.51 Wallis replies that he approves of the “Moderation” W. J. shows regarding “the Mysterious Truths [of] the Sacred Trinity.”52 Indeed,

Wallis’s last letter on the Trinity claims that his goal has been to provide a “modest defence of what Scripture teacheth us.” This, he explains, is an important “middle way” between describing the Trinity with obscure Scholastic language and giving up the project entirely.53 Here Wallis suggests that an empirical approach to divine mysteries is preferable to the alternatives of speculative, over-confident Aristotelian logic on the one hand, and outright skepticism on the other, even though it means that the theologian can reach only probable conclusions about God.

Again, this parallels the epistemology of the experimental philosophers: as Harrison suggests, a middle-ground between skepticism and unwarranted certainty is precisely what the they were

49 John Wallis, “An Essay of Dr. John Wallis, Exhibiting His Hypothesis about the Flux and Reflux of the Sea, Taken from the Consideration of the Common Center of Gravity of the Earth and Moon; Together with an Appendix of the Same, Containing an Answer to Some Objections, Made by Severall Persons against That Hypothesis,” Phil Trans 1 (1665-1666), 264. 50 WC III, 321. Wallis indeed accepted Newton’s explanation that the tides are caused by the moon’s gravitational pull. In typical Wallis fashion, however, he tried to take some credit for suggesting a connection between the Earth and the moon before Newton (J. F. Scott, ed., The Correspondence of Isaac Newton, vol. 4 [Cambridge: Cambridge University Press 1967], 100-1). 51 See Wallis, “Seventh Letter,” 12. For W. J.’s other letter see Wallis, “Second Letter,” 2-7. 52 Wallis, “Seventh Letter,” 13. Likewise, W. J. praises Wallis for the “Modest, Peaceable and Christian Stile” with which he approaches the Trinity question. These qualities call to mind Boyle’s reputation for gentlemanly, Christian behaviour (see Steven Shapin, A Social History of Truth: Civility and Science in Seventeenth-Century England [Chicago: University of Chicago Press, 1994], xxviii, 160-168). 53 Wallis, “Eighth Letter,” 20.

40 trying to achieve.54

Some of Wallis’s most clearly empiricist remarks appear, fittingly, in his letters on the

Trinity. Accounting for humanity’s difficulty in understanding theological concepts, Wallis explains in the seventh letter that humans “have no Notions in our Mind, other than what we derive, Mediately or Immediately, from Sensible Impressions of Finite Corporeal Beings.”55

These sense perceptions hold clues about the nature of God. One learns about God, Wallis explains, by identifying what is excellent in nature and likening it to God, which is called

“Eminency,” and by identifying what is imperfect in nature and distinguishing it from God, which is called “Negation.” Again, however, the limited ability of humanity to understand God necessitates a degree of nescience. Wallis argues that the best way to understand God is to adopt his approach of identifying similitudes that clarify certain aspects of divine mysteries, even though they are ultimately impenetrable. He writes, “we know no better way to express these

Conceptions, than by Metaphors taken from such Objects, from whence these Notions take their

Rise, or some such Figurative Expressions.” Indeed, God uses the same method of similitudes to convey information about his nature when Scripture describes him using human language.56

In fact, Wallis insists that any description of God in human language is necessarily metaphorical. The human mind will always remain nescient to some degree about God’s nature because it is beyond human reason. What Wallis aims at with his cube analogy is simply a better approximation of the nature of God than that conveyed by the existing metaphorical alternatives.

In his first letter, Wallis explains that all language used to describe the Trinity––from “persons”

54 For instance, as Harrison explains, Joseph Glanvill found the Scholastic tradition too optimistic about the power of human reason, and viewed experimental philosophy as a “narrow path between scepticism and dogmatism” (Harrison, Fall of Man, 204-5). 55 Wallis, “Seventh Letter,” 15. 56 Wallis, “Eighth Letter,” 16.

41 to “begetting” and “proceeding”––is “but Metaphorical.”57 Wallis prefers to describe the parts of the Trinity as three “somewhats,” a term that reflects how little humanity can actually understand them.58 But he deems it acceptable to continue referring to “begetting” and “proceeding” despite the shortcomings of these terms, as long as one maintains the sense of the metaphor that Scripture intends to communicate.59 Wallis argues that while metaphorical descriptions of the Trinity–– including his own, those of Scripture, and those of the Church Fathers––are necessarily inexact, they are still the best tools available to describe the Trinity, so it is reasonable to keep using them.60

Indeed, Wallis notes in his seventh letter that it is in the nature of metaphors (or similitudes) to be inexact. When two things are compared by analogy, he argues, “it is seldom that the Similitude is so Absolute between them, but that there is some Dissimilitude likewise.” This dissimilitude will be more pronounced when one compares “Finite Corporeal beings, and what is Infinite and

Incorporeal. So that we cannot always argue cogently from one to the other.”61

Likewise, in a sermon called “The Life of Faith,” first published in 1684 and later appended to the Theological Discourses, Wallis explains that most language used to describe a person’s relation to God is metaphorical because we only possess language appropriate for describing a person’s relation to other things in the world. Yet Wallis does not see this as a reason

57 Wallis, “Trinity Briefly Explained,” 3. Wallis lists several other terms “borrowed” from human language which can only describe God metaphorically (see Wallis, “Seventh Letter,” 15), but he focuses on the metaphorical meaning of “person” since the Sociniansʼ main argument against the Trinity is that one God having three persons is contrary to reason. Wallis argues that the Socinians have confused the modern word “person” with the Latin word persona. Whereas “person” is roughly interchangeable with “man,” persona originally referred to offices (like “king,” “father,” or “judge”) of which a man can hold more than one. If the Church Fathers had meant to suggest the seventeenth- century meaning of “person,” Wallis argues, they would have used the word homo instead of persona (Wallis, “Fifth Letter,” 15; “Sixth Letter,” 6). As Vickers notes, Wallis is responding here to what he feels has been a distortion of the word “person” since Boethius used it to describe the two natures of Christ in the early Middle Ages (Vickers, Invocation and Assent, 122). 58 See Wallis, “Second Letter,” 3; “Third Letter,” 38-9; “Seventh Letter,” 16-17; “Eighth Letter,” 19. 59 See Wallis, “Third Letter,” 12. In this letter Wallis also adds “Father,” “Son” and “Generation” to the list of imperfect metaphorical descriptors of the nature of the Trinity (Wallis, “Third Letter,” 31). 60 Wallis, “Third Letter,” 31. 61 Wallis, “Seventh Letter,” 15. Wallis does not distinguish sharply between similitudes, metaphors, and analogies; he uses these terms almost interchangeably.

42 to abandon the conventional language used to describe God. Firstly, he argues, such language still conveys what a person means, and secondly, without metaphorical language there is very little that we can say at all. Wallis suggests that, if the writer of the Psalms found metaphorical descriptions of God acceptable, so should his successors. He writes, “When the Psalmist says,

The Lord is my Rock, my Fortress, my Strength in whom I will Trust; my Bucler, my Horn of

Salvation, and my High Tower [18:2]: These are all Metaphors; But their Meaning is easily understood.”62

Wallis benefits from the Scholastic precedents of using similitudes to understand God, but he acknowledges that there is a limit to their power. Accordingly, he restricts similitudes––and

Scholastic reasoning in general––to a particular role. This is clear in his second letter on the Trinity as Wallis defends the Athanasian Creed, a statement of Christian belief dating from the fifth or sixth century that emphasizes the triune nature of God. Here he suggests that Scholastic language is merely one of many tools in theological debates, and it does not guarantee an improved understanding of theological concepts. He emphasizes that the writer of the Creed, though insistent that a Christian ought to believe in the Trinity, did not mean “that Children, and Idiots, and all who do not understand the School-terms, or perhaps have never heard them, should be therefore denied Salvation.”63 If, Wallis claims, they grasp that the Father, Son, and Holy Spirit together make up the one true God, that is sufficient. Likewise, in the eighth letter Wallis denies an accusation from a commentator on the debate, Bishop Edward Wetenhall, that he has made the discussion needlessly complicated with “Scholastick cramping Terms.”64 Wallis insists that his

62 John Wallis, The Life of Faith. In Two Sermons to the University of Oxford, at St. Mary’s Church There; on the 6th. of January, 1683/4. and June the 29th. following (London, 1684), 38-9. 63 Wallis, “Second Letter,” 9. See also “Third Letter,” 15. 64 [Edward Wetenhall], An Earnest and Compassionate Suit for Forbearance: to the Learned Writers of Some Controversies at Present (London, 1691), 2.

43 intention has never been to muddle the debate with esoteric Scholastic language. He explains, “I know not how I could speak more tenderly than to say these Three are three Somewhats.”65

Elsewhere, Wallis marks the particular places where he has found Scholastic terminology useful with phrases like “to use the School-language”66 and “as the Schools speak.”67 These phrases do not reflect the ironic tone of an experimental philosopher disparaging the Scholastic tradition. As

Rampelt has shown, Wallis prefers to remain receptive to as many legitimate sources of knowledge as possible, including Aristotle and the Scholastics.68 But it would also be a mistake to see Wallis’s efforts to defend the Trinity as chiefly an exercise in Scholastic reasoning; he identifies a particular role for similitudes in the evaluation of theological arguments, and otherwise relies on scriptural evidence.

Accordingly, Wallis feels compelled to rein in his correspondent W. J.’s increasingly metaphysical discussion of the Trinity. W. J. engages, for instance, with William Sherlock’s notion that the three persons of the Trinity share a mutual consciousness, and therefore are not three Gods but one. Wallis declines to comment on Sherlock’s argument, setting such questions aside as not directly relevant.69 In his next letter, W. J. considers what degree of distinction properly characterizes the relationship between the Father, Son and Holy Spirit: is it a real distinction or just a modal one? In response, Wallis briefly engages with some of W. J.’s arguments before reining in the metaphysics once again. In fact, he distances himself from anti-Trinitarians’ tendency to raise metaphysical objections, dismissing these as “the Cavils of those who study to pick Quarrels with the Doctrine of the Trinity as delivered in Scripture.”70 His tone here suggests

65 Wallis, “Eighth Letter,” 19. 66 Wallis, “Second Letter,” 10. Italics in original. 67 Wallis, “Fourth Letter,” 33. 68 See Rampelt, “Distinctions of Reason,” 199, 204-5, 209, 224-9. 69 Wallis, “Second Letter,” 4-5, 9-10. 70 Wallis, “Seventh Letter,” 16. W. J.’s letter is quoted at 3-13.

44 that W. J.’s focus on the metaphysics of the Trinity has distracted him from the main issue: the theological content of the relevant scriptural passages.

As he concludes his response to W. J., Wallis returns to the question of the degree of distinction between the parts of the Trinity, introducing the terms distinctio realis (real distinction) and distinctio modalis (modal distinction). While he suggests that the relationship between the three persons is best described as a modal distinction, he adds that he would not be prescriptive about this designation because, in the first place, different writers have different ideas about what exactly the various distinctions mean. Furthermore, these distinctions are meant to describe

“Created Beings [a]nd are not intended as applicable to God, otherwise than by Analogy.”71 This suggests that Wallis considers Scholastic distinctions to be only as useful as his other analogous ways of representing the nature of the Trinity such as the cube, which he readily admits does not correspond to the Trinity exactly.72

Indeed, it seems that Wallis finds metaphysics less useful than geometry for this purpose.

While he is able to find a reasonably apt geometrical analogy, Wallis suggests “that (in strictness of speech) our Metaphysicks have not yet given a Name to [the] Distinctions” that actually apply in the case of the Trinity.73 Here Wallis seems to find Scholastic terminology only useful for communicating his thoughts to a correspondent who happens to be Scholastically inclined.

Otherwise his defence of the Trinity rarely employs this language. Ultimately, these terms merely allow Wallis to reiterate his point that similitudes can demonstrate the possibility of a three-in-

71 Wallis, “Seventh Letter,” 20. 72 Rampelt treats this as one many instances when Wallis adopts Suárez’s notion of inadequate concepts (see n. 15 above). (Rampelt, “Distinctions of Reason,” 116-118). What is clear here, however, is Wallis’s reluctance to employ any such Scholastic language since he finds it minimally useful for improving humanity’s knowledge of a divine mystery. Wallis explains that this discussion about which kind of distinction characterizes the persons of the Trinity “is only ex abundanti, as what doth not much concern the main question at hand,” namely, whether the doctrine of the Trinity is reasonable (Wallis, “Seventh Letter,” 20). 73 Wallis, “Seventh Letter,” 20-1.

45 one relationship, but they cannot yield any deeper knowledge than that.

Elsewhere, Wallis recommends adapting a theological discussion to a particular audience.

In a published sermon entitled The Resurrection Asserted, he cites examples of the Apostle Paul doing exactly that. When preaching that God would raise the dead at the end of time, Paul changed his approach according to the amount of common ground he had with his audience. Among heathens who did not respect Scripture, he merely argued that resurrection was possible; among

Jews he argued that resurrection had been promised in the Old Testament; and among Christians he based his argument on truths they already accepted, such as the fact that Christ had been resurrected. Wallis finds that Paul’s strategy “may be a good Direction for Us in like cases. When we are preaching to Christian Auditories . . . it is not prudence [sic] to quit the Principles of

Christianity, and divert those of Reason and Natural Light onely: As if we were Preaching to

Heathens, not to Christians.”74 Wallis indeed seems to be accommodating a particular audience when he occasionally brings Scholastic terminology into the Trinity debate. And when he does have occasion to use Scholastic language, he circumscribes it, treating it as merely one of many imperfect tools for understandings God’s nature, actions and intentions.

Nescience of nature: Wallis’s theory of the tides

The foregoing section argued that Wallis’s approach to theology involves a combination of empiricism and Scholastic reasoning. The same combination can be found in Wallis’s natural philosophy. In his theory of the tides, for instance, Wallis employs a sort of similitude to defend his position that the Earth and moon rotate around a common centre of gravity. At the same time,

74 John Wallis, The Resurrection Asserted: in a Sermon Preached to the University of Oxford, on Easter-Day, 1679 (Oxford, 1679), 2-8, 25-6.

46 he acknowledges that some nescience is inevitable in natural philosophy, just as in theology, and he leaves clues that the reason is the same. As we shall see below, Wallis suggests that the deepest truths about nature are in fact God’s actions and are therefore inaccessible, just like the divine mysteries recorded in Scripture.

Wallis’s tidal theory sparked the interest of the Royal Society, to whom he communicated it through a letter to Oldenburg. Fellows such as Christopher Wren and Robert Moray had dabbled in tidal theories in the early 1660s but, perhaps on account of the difficulty, had not given it sustained attention.75 The Society was therefore curious about Wallis’s effort to account for the complicated phenomenon of the changing tides. First published in the Philosophical Transactions in 1666, Wallis’s theory is essentially a modification of Galileo’s, according to which the tides have a daily cycle due to the diurnal rotation of the earth and a yearly cycle due to the annual orbit of the earth around the sun. Wallis adopts Galileo’s technique of explaining the tides through the motions of the earth, focusing on a third tidal cycle that Galileo’s theory did not adequately explain: the “menstrual” (i.e., monthly) cycle in which the tides change in accordance with the position of the moon. Wallis argues that the earth and moon revolve once a month around a common centre of gravity, and it is this point that revolves around the sun. The earth is therefore on a small epicycle with a period of one month, and this additional motion affects the timing and level of the tides (Figure 2).76

By the time Wallis’s theory was published in the Philosophical Transactions, the other

Fellows of the Royal Society had heard about it and had sent Wallis some questions; his response

75 See Margaret Deacon, Scientists and the Sea 1650-1900: A Study of Marine Science, 2nd ed. (Aldershot: Ashgate, 1997 [orig. pub. 1971]), 72-3, 93. 76 Wallis, “Hypothesis about the Flux and Reflux of the Sea,” 263-81. Wallis explicitly likens his theory to Galileo’s on pp. 265-66, 273-74. For accounts of Wallis’s tidal theory and comparisons to Galileo’s theory, see David Edgar Cartwright, Tides: A Scientific History (Cambridge: Cambridge University Press, 1999), 28-30; Deacon, Scientists and the Sea, 94-6.

Figure 2: Diagrams of the Earth and moon orbiting a common centre of gravity, as described by Wallis’s theory of the tides.

(Phil Trans 1, No. 16 [1665-1666]) appears as the subsequent item. As this exchange occurred long before universal gravitation was widely accepted, the Fellows wondered how Wallis could account for the apparent action at a distance on which his theory depends: if the Earth and moon have a common centre of gravity, then what mechanism connects them? Wallis replies that this is beyond his concern. In general, his goal as a natural philosopher is to recognize phenomena and describe them mathematically, rather than to explain their underlying physical causes. For example, his theory of motion, first described in letters to Oldenburg and later published in his Mechanica (1669-71), uses gravity to account for many observed phenomena. But whenever he is pushed to explain what causes gravity, or why the laws of motion operate as they do, Wallis refuses to speculate on these matters because

48 they are beyond the scope of his investigation.77

In his response to the Fellows’ questions about his tidal theory, Wallis points out that natural philosophers routinely accept the existence of certain forces without knowing their cause.

Here Wallis compares the connection between the Earth and moon to magnetism:

That the Load-stone and Iron have somewhat equivalent to a Tye; though we see it not, yet by the effects we know. And it would be easy to shew, that two Load-stones, at once applyed, in different positions, to the same Needle, at some convenient distance; will draw it, not to point directly to either of them, but to some point between both; which point is, as to those two, the common Center of Attraction; and it is the same, as if some one Load-stone were in that point. Yet have these two Load stones no connexion or tye, though a Common Center of Virtue according to which they joyntly act.78

If it is possible to discuss magnetism without knowing how a loadstone is connected to iron, then the Fellows should have no problem with Wallis discussing the Earth and moon in the same way.

Indeed, Wallis explicitly declines to speculate on how the earth and the moon affect each other at a distance; it is enough for him to know that “there is somewhat, that doth connect them.”79 That

Wallis would later choose the same term, “somewhats,” as a label for the Father, Son, and Holy

Spirit reflects his adoption of a similar epistemological position in these two cases. He is satisfied with knowing the facts that the Trinity and the connection between the Earth and moon exist, even though he does not know how or why they exist. As he does when he points out that all descriptions of the Trinity are metaphorical, Wallis notes here that natural philosophers routinely function with a degree of nescience, not only in the case of magnetism but also in cosmology. If they believe that earth and Jupiter have “Satellites that attend their Lords” during their orbits around the sun,

77 See WC III, 73, 81, 94; OM I, 576; Wallis, A Discourse of Gravity and Gravitation, Grounded on Experimental Observations: Presented to the Royal Society, November 12. 1674 (London, 1675), 2. Newton, of course, also refused to “feign hypotheses” about the cause of gravity in the General Scholium. See Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy, trans. I. Bernard Cohen and Anne Whitman (Berkeley: University of California Press, 1999), 943. 78 John Wallis, “An Appendix, Written by Way of Letter to the Publisher; Being an Answer to Some Objections, Made by Several Persons, to the Precedent Discourse,” Phil Trans 1 (1665-1666): 282. Italics in original. 79 Wallis, “An Answer to Some Objections,” 282.

49 then they have already accepted a natural phenomenon for which they apparently cannot provide a physical explanation. The theological overtones of this point are clear: Wallis notes that everyone accepts this relationship between planets and their satellites “though we do not See [the]

Tye, nor Hear the Words of Command.”80

Although it was not uncommon to compare celestial motion to magnetism in the seventeenth century,81 Wallis seems to use this analogy to hint at God’s involvement in the natural world. This is more apparent when we consider that, elsewhere, Wallis also employs a magnetical metaphor in a theological context. In a sermon on the Song of Songs, published in his posthumous collection of sermons, Wallis likens magnetism to the force by which God draws believers to him.

God’s connection to believers, Wallis explains, is like the “secret sympathy” between a loadstone and steel. Extending the metaphor, Wallis explains that these two kinds of attractive force are both affected by distance:

This magnetical attraction, that I spoke of just now, this motus sympathiæ, must be at a convenient distance: lay the iron and the loadstone close together; and you will see no motion, because they are already conjoined, and need it not. Again, lay it at too great a distance, and then it moves not neither, because not within reach of the magnet’s virtue. And so here, some there are at so great a distance from God, that for their parts they scarcely know whether there is a God or no, only as others, and things around them, tell them so; and then they take it upon trust; so that there is in these a distance too great to be drawn by this magnetic attractive virtue. On the other hand, the time will come, when those that now run after him shall attain to him; and instead of desiring him, shall embrace him (in fruition) and then the motion will be ended.82

At that time, Wallis adds, believers who have not yet reached God will continue to be drawn to him as steel is drawn to a loadstone. Here, as in the tidal theory, Wallis suggests that God acts through unseen connections similar to that between magnetic objects.

80 Wallis, “An Answer to Some Objections,” 282. 81 See J. A. Bennett, “Cosmology and the Magnetical Philosophy, 1640-1680,” Journal for the History of Astronomy 12 (1981): 165-177. 82 John Wallis, Sermons: Now First Printed from the Original Manuscripts of John Wallis, D. D., ed. W. Wallis (London, 1791), 94-95. Italics in original.

Wallis’s use of magnetical metaphors in these two cases points to a deeper connection between his work in natural philosophy and theology. The methodology that Wallis uses in his tidal theory closely resembles that which he later uses to defend the doctrine of the Trinity. First, he gathers evidence from Scripture or nature. Next, he makes a conclusion in accordance with what the evidence seems to indicate. Finally, leaving aside the precise mechanisms involved,

Wallis uses reason to determine whether such a thing is possible. This last step takes the form of identifying similitudes. In the case of the tides, the Earth and the moon appear to share a common centre of gravity, and the examples of magnetism and the orbits of satellites show that such a relationship between two distant bodies is possible. Therefore, Wallis sees no reason not to believe what the evidence indicates, even though he does not know how it works.

In his letters on the Trinity, Wallis justifies this approach by insisting that God only reveals traces of his nature, actions, and intentions through Scripture. Evidently, Wallis’s belief in the ineffability of God also supports his empirical approach to natural philosophy, since, as the words of Solomon suggest, nature, too, only offers such traces to the observer. In natural philosophy, as in theology, one can collect data to learn matters of fact, but deeper truths lay beyond human reason. Rampelt notices this area of overlap but, I think, does not make a strong enough conclusion thereon. He writes,

For Wallis, theology and natural philosophy are engaged in the same linguistic and epistemological challenge. In the former case, the mind meets the natural world in human experience; in the latter, the mind, by faith, meets the revelation of God in the biblical texts. The God of the Bible is infinite in his being and the natural world is likewise, for all practical purposes, infinite as well to the minuscule human observer.83

Yet the similarities in Wallis’s epistemological and methodological outlook in these fields do not merely result from a superficial likeness between a God who is infinite and a world that is

83 Rampelt, “Distinctions of Reason,” 118.

51 practically infinite. It is the infinite God who created that world, who is as deliberate in what he reveals in that world as in what he reveals in Scripture, whose inaccessibility is key in both cases.

For Wallis there may well be divine mysteries in nature, too, perhaps including the mechanisms responsible for apparent cases of action at a distance.

On the other hand, Rampeltʼs comments reflect another source of nescience that Wallis acknowledges in his tidal theory: nescience on account of complexity. Sometimes a matter exceeds the grasp of human reason not because it concerns an inaccessible truth about God, but because the human mind simply cannot consider the multitude of factors all at once. This form of nescience enters Wallis’s tidal theory when he responds to a letter written by an astronomer and cleric named Joshua Childrey, which appeared in the Philosophical Transactions in 1670.

Childrey identifies several factors affecting the tides that Wallis does not mention, including the wind and the proximity of the moon to the earth (rather than only its position in the sky).84 In his reply, Wallis admits that these factors do affect the tides, but he argues that his theory can accommodate them because it seeks to explain how the tides function in general, not in particular cases:

. . . the Complication of such Accelerations and Retardations [of the earth’s motions], concurring or interfering one with another, doth occasion the perplex Varieties in them: Of which therefore there is no clear account to be given, without considering severally the proper Effects of each, from whence doth result the Compound Effect of all together.85

In other words, the motions of the Earth generate an overwhelming number of interrelated factors

84 Joshua Childrey, “A Letter of Mr. Joseph [sic] Childrey to the Right Reverend Seth Lord Bishop of Sarum, Containing Some Animaversions [sic] upon the Reverend Dr. John Wallis’s Hypothesis about the Flux and Reflux of the Sea, Publishʼt No. 16 of These Tracts,” Phil Trans, 5 (1670): 2061-68; Deacon, Scientists and the Sea, 102-5. The letter was written to Wallis’s friend, Seth Ward, the former Savilian Professor of Astronomy. Ward sent it to Oldenburg, who published it in the Philosophical Transactions (referring to the writer as Joseph rather than Joshua). See WC III, 305-313. 85 John Wallis, “Dr. Wallis’s Answer to the Foregoing Animadversions, Directed in a Letter to the Publisher, March 19. 1669/70,” Phil Trans 5 (1670): 2069. Wallis responded similarly to Henry Hyrne, another critic who pointed out several ways in which Wallis’s theory did not match observations. (WC III, 321). Deacon notes that Wallis’s work on the tides was unusual for having a theoretical rather than practical focus (Deacon, Scientists and the Sea, 94).

52 that affect the tides, and unless one could consider all of these factors, one could never predict the tides accurately.

What Wallis acknowledges here, however, is a practical limitation, rather than a necessary one resulting from the human-divine relationship. The distinction is made clear by Wallis’s theory of motion, wherein he suggests that, in principle, an observer equipped with a complete set of the laws of motion would be able to account for all interactions between bodies. He writes, “these are

(as far as I judge) the general laws of motion, which, I reckon, can be accommodated to particular cases.”86 For Wallis the precise applications of the laws of motion are only practically unknowable, unlike the physical causes that explain those laws, about which he rarely speculates: matters like gravitation, magnetism, and the connection between the Earth and the moon seem to be “deep things of God” which even Solomon knew he could never understand.

Conclusion

I have argued in this chapter that Wallis applies many of the same rhetorical, methodological, and epistemological strategies in his natural philosophy and theology. These similarities, I contend, reflect a theological commitment that guides his work in both of these fields: Wallis believes that some nescience is inevitable in both theology and natural philosophy because one eventually runs up against divine truths that are inaccessible to the human mind. Scholastic reasoning plays a key role in his assessment of these divine mysteries. In particular, by employing the Scholastic technique of identifying similitudes, Wallis shows that what is above reason may still be consistent with reason. This allows him to accept facts that are demonstrated by either scriptural evidence or

86 “. . . hae sunt (quantum ego judico) Generales Motuum leges; quae, ad casus particulares, Calculo sunt accommodandae” (WC III, 52).

53 natural phenomena but whose precise causes are unknown. The use of such similitudes, however, seems to be the limit of Wallis’s dependence on Scholastic reasoning in the consideration of divine mysteries. For Wallis, neither Scholastic reasoning, nor biblical hermeneutics, nor the empirical study of nature can overcome the nescience that necessarily results from a limited human mind’s attempt to understand God and his creation. Despite their limitations, however, each of those tools remains an important source of knowledge for Wallis. Thus the case of Wallis complicates two competing accounts of the rise of science in early modern Europe. His perspective is fully explained neither by Harrison’s argument that theological anthropology encouraged the decline of Scholastic philosophy and the rise of modern science, nor by Grant’s argument that Scholastic philosophy would have matured into modern science without any impetus from theology.

To place Wallis’s thoughts on the limits of reason in context, it is helpful to compare him to Newton. In the General Scholium to the Principia mathematica, Newton, too, suggests that personifications of God are necessarily inaccurate. He writes that God “is all eye, all ear, all brain, all arm, all force of sensing, of understanding, and of acting, but in a way not at all human, in a way not at all corporeal, in a way utterly unknown to us.” For Newton, like Wallis, the ineffability of God is inescapable. It is as though a person who tries to acquire full knowledge of God lacks a sense needed to do so: “As a blind man has no idea of colors, so we have no idea of the ways in which the most wise God senses and understands all things.”87 Although Wallis could scarcely have disagreed more with the anti-Trinitarian Newton on certain key doctrinal matters, he depicts the human-divine relationship in a remarkably similar way. In his third letter on the Trinity Wallis writes that a man cannot hope to understand the means by which the Father begets the Son, “For

I think it is much the same as if a man born Blind, and who had never seen, should employ his

87 Newton, Principia, 942.

Fancy to think, What kind of thing is Light or Colour.”88

Furthermore, like Wallis and Newton, Boyle classifies divine mysteries as things above reason but not inconsistent with reason. However, he prefers to convey this distinction with different analogies. For instance, Boyle asks readers to imagine looking down into the sea from the surface, where one cannot see all the way to the bottom. If a diver were to bring oysters and mussels up to the surface, the reader would believe that these creatures lived on the floor of the sea. On the other hand, one would be skeptical if the diver said that the pearls they contained were cube-shaped, or the size of tennis balls. Like theological matters that are only conveyed to humanity through revelation, the existence of the oysters and mussels on the ocean floor is unobservable, but obviously consistent with reason. This is unlike something that is clearly contrary to reason, like the odd shape and size of the pearls.89

This resonance with prominent contemporaries in English natural philosophy makes

Wallis’s thoughts on the limits of reason seem rather typical. Each of these philosophers treats

God as fundamentally unknowable and identifies boundaries to human knowledge accordingly.

What, then, makes Wallis’s epistemology distinctive? In the first place, Wallis appears to be unusual in the sense that he values the Scholastic tradition despite his enthusiasm for experimental philosophy. I suggest that, in addition, what might make Wallis distinctive is that he finds the identification of the limits of reason quite useful in several ways.

88 Wallis, “Third Letter,” 49. Wallis expands on this metaphor in the seventh letter (Wallis, “Seventh Letter,” 14-15). Newton also alludes to the blind-man metaphor earlier in his unpublished “Treatise on Revelation” written in the mid- to late 1680s. Referring to the New Jerusalem described in prophecies in the Books of Ezekiel and Revelation, Newton writes, “If you ask where this heavenly city is, I answer, I do not know. It becomes not a blind Man to talk of colours” (Isaac Newton, “Treatise on Revelation [Section 2],” Yahuda MS. 9.2, f. 139r; available from http://www. newtonproject.ox.ac.uk/view/texts/normalized/THEM00270). Many thanks to Stephen Snobelen for directing me to this source. 89 Robert Boyle, “Reflections upon a Theological Discourse. According to Which, ʼtis Said, that Some Articles of Faith Are Above Reason, but Not Against Reason. In a Letter to a Friend” in The Christian Virtuoso: Shewing, that By Being Addicted to Experimental Philosophy, a Man is Rather Assisted, than Indisposed, to Be a Good Christian, vol. 1 (London, 1690), 3-5.

Firstly, by acknowledging his nescience, Wallis delineates the intellectual space within which he can work confidently. Wallis often emphasizes the significance and utility of his intellectual contributions; recall that he treats his laws of motion as applicable to all cases.

Rampelt finds Wallis’s confidence difficult to reconcile with his reflections on the limits of reason.

In an autobiographical letter written in 1697, Wallis claims that, throughout his career, “I made it my business to examine things to the bottom; and reduce effects to their first principles and original causes.”90 According to Rampelt, there is an “irony” in the fact that Wallis makes himself out to be an “epistemological foundationalist” in his autobiographical letter, while elsewhere he acknowledges that complete knowledge of anything in the world is impossible.91 Yet if one considers that Wallis had repeatedly identified appropriate boundaries for human intellectual pursuits when he wrote his autobiography, and had done so most clearly just a few years earlier in his letters on the Trinity, then these boundaries seem to be an implicit qualification on Wallis’s

“epistemological foundationalism.” Especially since likeminded scholars shared his appreciation for the theological source of the limits of reason, Wallis may not have felt compelled to make them explicit once again in his autobiography.

Secondly, partly because he identifies epistemological limits at similar levels in the study of both nature and Scripture, Wallis is comfortable drawing on examples from one field to support another. We have seen this in the similitudes he identifies in his defence of orthodox doctrines: the Trinity is like a cube, the virgin birth is like the self-impregnation of a hermaphrodite, and the hypostatic union is like the soul’s interaction with the body. These are matters about which a person can learn, but the more fundamental truths in both fields are “deep things of God” that the

90 See Christoph J. Scriba, “The Autobiography of John Wallis, F.R.S.,” Notes and Records of the Royal Society of London 25 (1970): 40-1. 91 Rampelt, “Distinctions of Reason,” 79-80.

56 human mind cannot hope to penetrate.

Thirdly, on account of these epistemological limits, Wallis can tolerate the arbitrariness of conventions. Rampelt identifies many cases in which Wallis recommends maintaining conventional practices and terminology since there is no way to replace them with something more accurate. Along with the use of words like “persons” to describe the members of the Trinity, this includes algebraic symbols, philosophical methods, and human language in general. As

Rampelt explains, Wallis doubts that words can ever be made to correspond exactly to the essences of the things they represent. But it makes little difference whether we know exactly what time, space, and atoms are when we talk about them. Even if the meanings we assign to these words are arbitrary and ultimately inaccurate, they can still be useful.92 Similarly, Beeley and Probst note that Wallis treats the dating of holidays in a similar way. There is no reason, Wallis argues, to adopt the Gregorian calendar to correct the dating of Easter since we can never actually be sure of the right date; the important thing is that Easter is celebrated properly.93 For Wallis, conventions may be arbitrary but they still have practical value. I argue that this liberating consideration follows from Wallis’s belief that God only allows people to learn truths that are below a certain threshold.

Finally, Wallis’s thoughts about the theological basis of the limits of reason make it at least possible to find common ground with thinkers who subscribe to vastly different theologies. This includes even those anti-Trinitarians whom he is so anxious to refute. Perhaps, in publishing his letters on the Trinity, Wallis sincerely hoped that he could convince the anti-Trinitarians that the

92 See Rampelt, “Distinctions of Reason,” 115-17, 221. 93 Beeley and Probst, “Mathematician and Divine,” 455-56. Similarly, while some of his contemporaries sought to move the Christian day of rest to Saturday because this would supposedly realign the Sabbath with God’s original day of rest, Wallis favoured maintaining the convention of celebrating the Sabbath on Sunday (Wallis, A Defense of the Christian Sabbath. In Answer to a Treatise of Mr. Tho. Bampfield Pleading for Saturday-Sabbath [Oxford, 1692], 9-13).

57 doctrine is reasonable by appealing to theological ideas that they might accept, such as the ineffability of God. Indeed, an ardent Trinitarian like Wallis and a vehement opponent of the

Trinity like Newton could at least agree that the truth lying beyond what is recorded in the

Scripture and observed in nature is an ineffable God, which means that the knowledge generated in either field must be limited.

What remains to be considered is whether Wallis’s contemporaries shared his appreciation for the help that Scholastic philosophy could offer in these matters. Historians of science and religion would benefit from further research into such uses of Scholastic reasoning in the work of experimental philosophers. This may help to refine both Harrison’s position, which denies the continued importance of Scholastic philosophy, and Grant’s position, which pushes theology to the margins. It is possible that Wallis was more receptive to these Scholastic techniques than the likes of Boyle and Newton because he remained embedded in a university culture throughout most of his career. On the other hand, perhaps he simply made more explicit the Scholastic reasoning that continued to mediate between God and humanity in the minds of seventeenth- century English scholars.

Chapter 3: “Nature Doth Not Work by Election”: Wallis on Natural and Divine Action

Among his contemporaries, one of John Wallis’s most popular works was a textbook on logic.

His Institutio logicae was first published in 1687, and five more editions were published during the rest of Wallis’s lifetime and beyond, the last appearing in 1763.1 In the text Wallis makes numerous digressions, including one on the ambiguities built into certain expressions that allow for multiple interpretations. For example, he discusses the expression that “it is possible for a seated person to stand.” This is only possible, Wallis explains, if one considers the sitting and the standing “in a divided sense” (in sensu diviso) rather than “in a composite sense” (in sensu composito). In other words, it makes sense to say that a person can sit at one time and stand at another, but not that he can do both at once.2

Wallis’s next example is not so straightforward. He notes that many writers have grappled with the seemingly self-evident expression, “God can make whatever he can make.” Does this mean that God can create only finite things, or that he can make something infinite in number, magnitude, power, or some other measure? Wallis argues that the expression is not so confusing if one bears in mind how it is meant to be understood: it refers to things separately, not collectively, and means that God can make anything that could conceivably exist. The idea is not that God could create something of such great number, size, or power that even he could not add to it. The latter interpretation would limit God’s infinite power, which would be a contradictio in adjecto.3

1 On the Institutio logicae and its legacy, see Wilbur Samuel Howell, Eighteenth-Century British Logic and Rhetoric (Princeton: Princeton University Press, 1971), 29-41. See also Steffen Ducheyne, “Newton’s Training in the Aristotelian Textbook Tradition: From Effects to Causes and Back,” History of Science 43 (2005): 217-237. 2 “Possible est sedentem stare” (John Wallis, Institutio logicae. Ad communes usus accommodata, 1st ed. [Oxford, 1687], 109). 3 “Potest Deus facere quicquid potest facere” (Wallis, Institutio logicae, 109).

In general, Wallis concludes, one should interpret an ambiguous expression in a way that accords with experience and common sense. To explore every alternative interpretation would be fruitless and infinitely laborious.4

This passage from the Institutio logicae reflects an important element of how, in Wallis’s conception, God interacts with the created world. So long as it does not create a logical contradiction, he is careful not to restrict God’s freedom to act as he chooses. And as I will discuss below, Wallis holds that God is not bound by the laws of nature and can suspend them at any time.

However, in his works of experimental philosophy, his goal is to determine what the laws of nature are, rather than to emphasize their dependence on God’s will. For Wallis, nature acts in a regular and predictable manner according to mathematical rules. On the other hand, in his religious works, Wallis is primarily interested in how God interacts with immaterial things, namely, people’s souls and minds. It is clear from his sermons that Wallis regards the salvation and damnation of souls as anything but predictable, since God is free to act as he chooses. I will argue in this chapter the element of choice distinguishes divine action from natural action in

Wallis’s thought: whereas God acts freely, the actions of natural bodies are bound by mathematical laws. In addition, I will argue that this attitude is partly informed by Wallis’s adoption of the principle that “nature doth not work by Election,” which he encountered in an optical treatise written by Robert Grosseteste, a Scholastic philosopher who lived and taught in Oxford in the thirteenth century.

Wallis is one of numerous natural philosophers who participated in the search for the mathematical laws of nature in the seventeenth century. This preoccupation with laws of nature was more pronounced than in earlier centuries, but not unprecedented. The Scholastic

4 Wallis, Institutio logicae, 109.

60 philosophers certainly did not pursue a systematic experimental program, but several historians have argued that certain theoretical developments in the Middle Ages legitimated the mathematical and experimental approach to natural philosophy in later centuries. For instance, A.

C. Crombie has argued that natural philosophers began the process of mathematizing nature after the reintroduction of Aristotelian philosophy in the twelfth century. Particularly important in this context is Grosseteste who, as Crombie explains, applied geometry to the study of optics and began to think of nature in terms of mathematical rules. According to Crombie, it was Grosseteste–

–as well as other Scholastic philosophers including Roger Bacon, Duns Scotus, and William of

Ockham––who provided the theoretical arguments for a mathematical and experimental study of nature. Thus the famous experimentalists of the seventeenth century were simply realizing the programme conceived by their medieval predecessors.5

Crombie and others have discussed at length the theological ideas built into both medieval and early modern concepts of laws of nature. For Crombie, the important steps were taken by medieval scholars, including Albertus Magnus and Thomas Aquinas, who were keen to adopt the useful parts of Aristotelian philosophy while insisting that its rules were not constraints on God’s power. The world was orderly, they argued, because God had ordained it to be so, and he voluntarily restricted his absolute power in order to maintain nature’s regular course. The idea that God’s ordained power restricted his absolute power, combined with the mathematization of natural phenomena, eventually developed into the concept of laws of nature.6 Keith Hutchison proposes a similar explanation, connecting the mechanical philosophies of the seventeenth

5 A. C. Crombie, “The Significance of Medieval Discussions of Scientific Method for the Scientific Revolution,” in Critical Problems in the History of Science, ed. Marshall Clagett (Madison: University of Wisconsin Press, 1969), 79-101. 6 A. C. Crombie, Styles of Thinking in the European Tradition: The History of Argument and Explanation Especially in the Mathematical and Biomedical Sciences and Arts, vol. 1 (London: Duckworth, 1994), 400-408.

61 century to medieval reflections on God’s power. He argues that the mechanical philosophers adopted a “mitigated supernaturalism,” that is, a way of providing natural explanations for phenomena while recognizing their dependence on God’s will. This crucial distinction elaborated on earlier arguments made by Aquinas; it was he who took the crucial step of distinguishing between natural and supernatural action, arguing that the difference is whether God acts mediately through natural forces or immediately through miraculous intervention.7 Finally, John Henry, placing a greater emphasis on how early modern writers transformed the medieval notion of a law of nature, argues that the crucial step was taken by Descartes who, seeking to establish the conservation of motion as a law, claimed that God’s omnipotence ensures that bodies remain in motion. Descartes, Henry argues, did not just passively receive medieval ideas about God and nature; as he theorized about the conservation of motion, he adapted medieval ideas to suit the particular concerns of a seventeenth-century philosopher.8

Each of these accounts identifies an important element in the genealogy of the concept of

“laws of nature.” In particular, I appreciate Henry’s notion that the mechanical philosophers refashioned medieval ideas to solve seventeenth-century problems, and in this chapter I will make a similar case about Wallis’s reading of Grosseteste. However, none of these writers focuses on the specific implications of Calvinist theology on mechanical philosophy. Yet Calvinism

7 Keith Hutchsion, “Supernaturalism and the Mechanical Philosophy,” History of Science 21 (1983): 297-333. 8 John Henry, “Metaphysics and the Origins of Modern Science: Descartes and the Importance of Laws of Nature,” Early Science and Medicine 9 (2004): 73-114. Not all historians who discuss the emergence of laws of nature grant an important role to theology. Jane E. Ruby argues that, while most historians assume the concept of natural laws developed from a metaphorical comparison to God’s moral laws, natural philosophers had described laws of nature since the thirteenth with virtually no references to God as the lawmaker. According to Ruby, the earliest medieval reference to a natural law appears in Roger Bacon’s work on optics, where “law” (lex) is used almost interchangeably with “rule” (regula), a term that carried no connotations of divine legislation. On Ruby’s reading, it is Bacon’s understanding of a law as an especially well-established rule that was adopted by writers in the sixteenth and seventeenth centuries. She suggests that it was only when Descartes received and “re-invented” the concept of natural laws that it was imbued with a theological meaning. (Jane E. Ruby, “The Origins of Scientific ‘Law’,” Journal of the History of Ideas 47 [1986]: 341-359).

62 flourished in England during much of the seventeenth century, and so forms a major part of the context in which some of the most important mechanical philosophers—including Boyle, Hooke, and Newton—developed their theories of nature. The case of Wallis, particularly his adoption of the principle that “nature doth not work by Election,” helps us to relate mechanical philosophy to

Calvinist theology, according to which God is actively involved in every step leading a person to either salvation or damnation. As we will see below, this view of divine action stands in stark contrast to Wallis’s view of natural bodies bound by mathematical laws.9

My analysis begins with Wallis’s experimentalist texts written in the 1660s and 1670s, including his works on hydrostatics and the collision of bodies. These texts demonstrate his understanding of the laws of motion that constrain natural phenomena. Notwithstanding his belief that God’s will underpins the laws of nature, Wallis sought to describe phenomena in terms of mathematical laws without reference to divine action. Indeed, he seems to have believed that a natural philosopher with perfect knowledge of those laws could predict the motions of all natural bodies accurately. In the next section, I turn to the sermons that Wallis published throughout his career, which reflect his conception of divine action. According to Wallis, I argue, God primarily interacted with the world by acting on people’s souls––predestining and electing certain people for salvation according to Calvinist doctrine––which reflects his freedom to choose to how to act.

This freedom ensures that God’s actions in the spiritual realm are entirely unpredictable. Finally, in the last part of my argument, I discuss an oblique reference in Wallis’s Discourse of Gravity to

9 My approach in this chapter is also informed by the work of Margaret Osler, who argues that it is useful to consider a seventeenth-century figure’s attitude toward earlier traditions in terms of “appropriation.” Pierre Gassendi, she argues, did not passively receive the Epicurean atomic philosophy that he was known for promoting. Rather, he transformed the ideas of the ancient atomists to conform to a Christian cosmological and moral framework. Likewise, I argue in this chapter that Wallis did not merely adopt Grosseteste’s principle; he appropriated the principle so that it could contribute to his work as an experimental philosopher in the seventeenth century (Margaret J. Osler, “Early Modern Uses of Hellenistic Philosophy: Gassendi’s Epicurean Project,” in Hellenistic and Early Modern Philosophy, eds. Jon Miller and Brad Inwood [Cambridge: Cambridge University Press, 2003], 30-44).

Grosseteste’s thirteenth-century optical treatise De lineis, angulis et figuris which, I contend, shows how the element of choice distinguishes natural and divine action in Wallis’s thought.

Physically performed, mathematically measured: Wallis’s comprehensive laws of motion

In the 1660s and 1670s, Wallis was an active contributor to the experimental program of the newly-founded Royal Society of London. As such, along with Christopher Wren and Christiaan

Huygens, Wallis was one of three Fellows who wrote treatises on the laws of motion in 1668 upon request from the Society.10 Wallis’s elaborated on his laws of motion in his lengthy treatise

Mechanica, which he published over the course of the three subsequent years (1669-71).11

However, his initial treatise, sent as a letter to the Society’s secretary, Henry Oldenburg, was intended to include all the laws needed to describe the interactions between solid bodies.

In his letter to Oldenburg, Wallis begins with the most basic principles, proposing simple mathematical relationships between momentum, mass, speed, and distance. Then he describes what happens each time a layer of complexity is added: how much momentum is transferred when two bodies collide, what happens if they collide at an oblique angle, how much do they bounce back if they are elastic, what happens if one or both of them is accelerating or decelerating, and so on.12 Although elsewhere Wallis insists that the human mind cannot predict physical

10 For Wren’s account see A. Rupert Hall and Marie Boas Hall, eds., The Correspondence of Henry Oldenburg vol. 5 (Madison: University of Wisconsin Press, 1968), 320-321. For Huygens’ account see J. Bosscha, ed., Oeuvres complètes de Christiaan Huygens vol. 6 (The Hague: Martinus Nijhoff, 1895), 336-343. 11 WC III, 49-52. The editors of Wallis’s Correspondence have cross-referenced the laws in Wallis’s letter with those in the Mechanica (WC III 49, n. 197; cf. OM I 580-594, 1002-1012). 12 Scott notes some differences in terminology between Wallis’s physics and modern physics: he generally uses “force” where today we would use “momentum,” and “momentum” where we would use “impulse.” His use of pondus sometimes corresponds to what we call “weight,” and sometimes to what we call “mass” (Scott, Mathematical Work of Wallis, 108-110).

64 phenomena in the real world on account of their complexity,13 he suggests here that if one could consider all of the relevant factors, one could, in principle, use these laws to predict the outcome of any interaction between solid bodies. Viewed another way, Wallis’s laws allow him to treat a collision between bodies like an algebraic problem: given all the elements (momentum, mass, speed, acceleration, distance, elasticity, and so on) except one, he could work out the missing value. The result of these few pages is a set of mathematical formulas that, Wallis claims, constitute “(as far as I judge) the general laws [leges] of motion, which, I reckon, can be accommodated to particular cases.”14 In Mechanica, too, Wallis suggests that his laws can be applied to all cases. Before describing how particular machines work, he explains that his predecessors have failed to articulate the fundamental principles that apply to all machines, so it is appropriate for him to do that here. Indeed, at the conclusion of the treatise, Wallis encourages his readers to apply his principles to other cases.15

Presumably, the fact that these regularities are intended to apply in every case is what warrants his calling them laws (leges). Wren and Huygens also apply this label to their findings, and Wren records his under the heading “The Law of Nature” (lex naturae).16 In fact, in his letter to Oldenburg, Wallis notes that he hopes his laws can be reconciled with those of Huygens and

Wren because he suspects that each of them has presented the same laws in a slightly different way.17 In Wallis’s view, any diligent experimentalist will arrive at the same laws of motion which

13 See Chapter 2 above. 14 “. . . hae sunt (quantum ego judico) Generales Motuum leges; quae, ad casus particulares, Calculo sunt accommodandae” (WC III, 50, 52). 15 OM I, 579, 1063. 16 Oldenburg Correspondence vol. 5, 319-320; Huygens, Oeuvres Complètes vol. 6, 337. However, perhaps considering that nature is more complex than contrived experiments, Wallis builds ceteris paribus clauses into his laws that protect him from criticism, in case his laws do not conform to observed phenomena exactly (See Wallis, “Mechanica,” 587). He also admits that his laws are subject to revision. In a letter to Oldenburg he notes that he remains open to alternatives, since he is both “sparing to determine positively” and “sparing and wary in assessing Universall Negatives” (WC III, 90). 17 See WC III, 55, 101, 157. Wallis’s and Wren’s laws were eventually published together in Phil Trans 43 (1668/9):

65 can, in principle, account for all interactions between solid bodies.

On the other hand, a protracted debate with the mathematician William Neile in the spring of 1669, carried out through letters to Oldenburg, shows that Wallis would reject a theory of motion when he was convinced that it could not save the phenomena. Neile proposed a system in which a moving body that collides with a slower one (or one at rest) would transfer its precise velocity to that body. In several letters Wallis tries to convince Neile that this would quickly cause all bodies to travel in the same direction and at the same speed, which is clearly not what is observed in nature or experiments. Failing to grasp Wallis’s objection, Neile claims that the scenario Wallis described in which all motion was reduced to one velocity would require either divine intervention or “myryiads of years.”18 But Wallis maintains that no divine action would be needed to bring about this uniformity of motion in Neile’s system: if all moving bodies were subject to Neile’s laws of motion, it would not require “either Miracles, nor Myriads of years, to reduce them to a much smaller number [of velocities].”19 This exchange reflects Wallis’s view that one can describe natural action comprehensively –– at least at a mathematical level –– by employing a combination of reason and experimental results, without considering God’s involvement.20

In treating mathematical rules as the appropriate subject for natural philosophy, Wallis adopts an attitude reminiscent of Newton in the Principia. In fact, J. F. Scott and E. B. Davies

864-868. Huygens doubted that Wallis’s work could be reconciled with his and Wren’s, but Wallis did not see why (Oldenburg Correspondence vol. 5, 556-557; WC III, 191). 18 WC III, 183. For Niele’s theory see 172-178. 19 WC III, 186. 20 This disagreement does not seem to have created any ill will between Wallis and Neile. Wallis had already defended Neile’s priority for squaring the semi-cubical parabola in his treatise De cycloide (1659), challenging the claim that he had been preceded by the Dutch mathematician Hendrick van Heuraet, and Wallis did so again when the priority dispute was revived in 1673 (which was three years after Neile’s death). See OM I, 550-554; WC IV, 269-274; Margaret E. Baron, The Origins of Infinitesimal Calculus (Oxford: Pergamon Press, 1969), 223-224; Jan A. van Maanen, “Hendrick van Heuraet (1634-1660?): His Life and Mathematical Work,” Centaurus 27 (1984): 244-250.

66 have both argued that Wallis at least partly anticipates Newton’s famous three laws of motion.21

Wallis sometimes refers to his findings as laws, but more frequently he calls them principles,22 and he may well have considered Philosophae naturalis principia mathematica an appropriate label for his own work. Accordingly, he refuses to speculate on the physical causes underlying his mathematical principles of motion. Responding to a request for such causes from the Royal

Society, Wallis claims that mathematical principles themselves are the sort of physical causes that natural philosophers should investigate. He writes,

. . . the Hypothesis I sent, is indeed of the Physical Laws of Motion, but Mathematically demonstrated. For I do not take the Physical and Mathematical Hypothesis to contradict one another at all. But what is Physically performed, is Mathematically measured. And there is no other way to determine the Physical Laws of Motion exactly, but by applying the Mathematical measures & proportions to them.23

The Fellows in London replied that this was not what they had in mind: they wanted to know why the laws of motion operate as they do. Again Wallis demurs, insisting that “the Mathematick hypothesis satisfyes.”24 Likewise, he repeatedly declines to speculate on the nature of gravity. In the Mechanica he defines it as simply “the motive force downward, or toward the centre of the

Earth” and adds, “What then, in consideration of physics, is the origin of gravity; this we do not seek.”25 In his Discourse of Gravity, Wallis is similarly reticent about gravity’s cause: “I will not dispute the Nature of Gravity or Gravitation, what or whence it is.” He explains that he is content

21 E. B. Davies, “Some Reflections on Newton’s Principia,” British Journal for the History of Science 42 (2009): 211-215; Scott, Mathematical Work of Wallis, 104-108, 111, 119-126. Davies claims that Newton benefitted from the work of Wallis, Wren, and Huygens alike. Indeed, Newton himself acknowledges the similarities of his laws on motion to theirs in the Principia, claiming that each of them had employed the Third Law of Motion and “entirely agree[d] with one another” in the principles they had sent to the Royal Society (Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy, trans. I. Bernard Cohen and Anne Whitman [Berkeley: University of California Press, 1999], 424). 22 See for example WC III, 49, 70, 91, 178; OM I, 579, 1063. 23 WC III, 73. 24 WC III, 81. 25 “Gravitas, est vis motrix, deorsum; sive, ad Centrum Terræ . . . Quodnam sit, in consideratione Physica, Gravitatis principium; non hic inquirimus” (OM I, 576). Italics in original. See also WC III, 94, 96.

67 to define gravity as “a natural Propension to move downward

(toward the Earth, or its Center).”26

On the other hand, Wallis does introduce physical mechanisms into his theory of motion when he sees them as

“matters of fact” established by experimental results.27 For example, in a letter to Oldenburg written in December 1668 Figure 3: Wallis’s depiction of he introduces the concept “[t]hat all rebounding comes from the Torricellian Experiment Springynesse.” By this he means that, since no body is (Discourse of Gravitation, 1675) absolutely hard, everything changes shape to some degree upon impact. An elastic body springs back to its original shape which causes it to bounce away from the other body.28 Having thought more on the matter,

Wallis adds in his next letter that some rebounding is caused by “repercussion” such as when a racket hits a ball. But, Wallis insists, given these two mechanisms, “I think all Phaenomena may

. . . be salved.”29 This is typical of Wallis: he includes as few mechanisms as possible and claims that they accommodate all relevant phenomena.

Similarly, Wallis uses the weight of air as a mechanism to save the phenomena observed

26 Wallis, A Discourse of Gravity and Gravitation, Grounded on Experimental Observations: Presented to the Royal Society, November 12. 1674 (London, 1675), 2. 27 Wallis’s references to matters of fact are typical of the early Royal Society. Steven Shapin and Simon Schaffer note that Boyle, as a spokesman for the Royal Society, insisted that his natural philosophy was built on a solid foundation of “matters of fact” produced by careful and repeatable experiments. See Steven Shapin and Simon Schaffer, Leviathan and the Air-Pump: Hobbes, Boyle, and the Experimental Life, 2nd ed. (Princeton: Princeton University Press, 2011; orig. pub. 1985), 20-79. Likewise, Wallis’s arguments about the natural world are based on matters of fact generated by experiment and observation. See, for instance, Wallis, Hobbius Heauton-timorumenos. Or a Consideration of Mr Hobbes His Dialogues. In an Epistolary Discourse, Addressed, to the Honourable Robert Boyle, Esq. (Oxford, 1662), 152; Wallis, “A Second Letter of Dr Wallis to Dr Tyson, on the Same Subject,” Phil Trans 22 (1700-1701): 783; J. F. Scott, ed., The Correspondence of Isaac Newton, vol. 4 (Cambridge: Cambridge University Press, 1967), 301. 28 WC III, 69. 29 WC III, 71.

68 in pneumatical experiments, and he dismisses additional mechanisms, such as nature’s abhorrence of a vacuum, as superfluous. Wallis raises the issue of vacuism in the Mechanica when he describes the Torricellian experiment (see Figure 3). Here Wallis supplies the weight of the air as the mechanism by which a vacuum is created: when a tube containing mercury is turned upside- down in a vessel also containing mercury, the weight of the air pressing down on the mercury in the vessel is insufficient to raise the mercury in the tube all the way up, so a vacuum forms at the top of the tube. Wallis does not propose any metaphysical reason why a vacuum must exist. He simply claims that if anyone were to suggest that the space at the top of the tube is filled with some invisible substance, he would merely be making an unhelpful speculation.30

Later in the chapter Wallis moves on to siphons and pumps, noting that for centuries philosophers tried to explain their effects using the ancient concept of fuga vacui: nature abhors a vacuum, so when air is sucked out of the top of a siphon, any substance at the bottom is drawn through the tube in order to fill the vacuum that would otherwise form at the other end. As a rule,

Wallis prefers to explain phenomena with mechanical explanations, which describe them strictly in terms of matter in motion, rather than Aristotelian accounts such as fuga vacui, according to which bodies simply act according to their natures. The real problem with fuga vacui in particular, though, is that it simply cannot save all the phenomena in pneumatical experiments. As Wallis explains, some philosophers have argued that water could be raised to any height to fill a potential vacuum, but experiments have shown a siphon cannot raise water beyond a certain height. Wallis’s explanation, however, saves the phenomena: air presses down on the water and forces it through the tube, but since the weight of air is finite it can only raise the water to a certain height. Thus the weight of air accounts for the results of all pneumatical experiments of this nature. In fact,

30 OM I, 1036.

Wallis argues, “static laws” (leges Staticas) can determine the height to which any liquid can be raised by air pressure.31 Likewise, he claims in the Discourse of Gravity that the phenomena observed in the Torricellian experiment and its derivatives “are easily solved from Static

Principles, without having recourse to a Fuga vacui.”32 Wallis concedes here that fuga vacui could explain some of these experiments, but not all of them. Since the weight of air covers all of the relevant phenomena, any ad hoc proposal of fuga vacui to explain some of them would be “gratis dictum, without any cogent proof.”33

Wallis uses a similar argument to dismiss a mechanism called “simple circular motion.”

His perennial rival, Thomas Hobbes, proposed this mechanism as a way to account for the motions of all bodies. Hobbes insisted that all phenomena should be explained in terms of motion, and felt that Wallis and his colleague Seth Ward had neglected this rule when they attributed phenomena to the rarefaction and condensation of substances. These terms were so meaningless, Hobbes claimed, that they might as well be called “Wallifaction” and “Wardensation.”34 But Wallis claims that rarefaction and condensation are legitimate descriptions of the motion of particles, and these

31 OM I, 1053-1054. The quotation is from 1054. 32 Wallis, Discourse of Gravity, 29. 33 Wallis, Discourse of Gravity, 31. Italics in original. Although Wallis felt compelled to argue against fuga vacui during the 1660s and 1670s, in later works he considered the matter to be settled in favour of the weight of air. In an article printed in the Philosophical Transactions in 1685, Wallis claims that “[t]he notion of the Air’s weight and spring, hath been so well settled, by innumerable Experiments of this present Age; that hardly any considering Person doth now doubt of it. And it hath chased away from before it, the notion of Fuga vacui, formerly received” (John Wallis, “A Discourse concerning the Air’s Gravity, Observd in the Baroscope, Occasioned by That of Dr. Garden: Presented to the Phil. Soc. of Oxford, by the Reverend Dr. Wallis, President of That Society. April, 14, 1685,” Phil Trans 15 [1685]: 1002; italics in original). Likewise, in a letter to Hans Sloane written in 1699, he scoffs at a paper arguing for fuga vacui and notes that, if anyone still believes in it, “I am content that he injoy his own fansy; & do not think it worth the while to disabuse him” (Royal Society Early Letters MS W 2 f. 84). 34 See Simon Schaffer, “Wallifaction: Thomas Hobbes on School Divinity and Experimental Pneumatics,” Studies in the History and Philosophy of Science 19 (1988): 279-281, 287, 293. The Fellows of the Royal Society, as well as the experimentalist group in Oxford that preceded it, regarded Hobbes’s absolutist politics and materialist philosophy as dangerous. This motivated Wallis and his colleagues in Oxford to attack all aspects of Hobbes’s thought in order to weaken his credibility, with Wallis focusing on Hobbes’s problematic mathematical works. Wallis and Hobbes continued to attack each other in polemical treatises for over two decades; the conflict finally ended when Hobbes’s died in 1679. See Douglas M. Jesseph, Squaring the Circle: The War between Hobbes and Wallis (Chicago: University of Chicago Press, 1999) 69-72, 293-339. The Wallis-Hobbes dispute will be discussed in detail in Chapters 4 and 6 below.

70 mechanisms are necessary to account for certain phenomena.35 Furthermore, Hobbes’s physics relies on a mechanism that Wallis dismisses as redundant. Wallis’s account of simple circular motion in Hobbius Heauton-timorumenos (1662) suggests that this mechanism is anything but simple and circular. It does not refer to a simple revolution around a centre; rather, each point in a body revolves around a different centre. The motion of the whole body is the sum of all these small circles, but the body itself does not necessarily move in a circle. So, Wallis explains, being neither simple nor circular, this motion might as well be called “Hobbiana.”36

Yet the real problem with Hobbes’s simple circular motion, according to Wallis, is that it is not necessary for saving the phenomena. Wallis complains that it is typical for Hobbes to introduce such a superfluous concept: just as he draws many unnecessary lines in his mathematical demonstrations, so in his natural philosophy he introduces a type of motion that “is to no purpose, as to the Effects of Nature.” Unlike the few physical mechanisms that Wallis views as required by reason and experimental results, he describes Hobbes’s use of simple circular motion as

“Arbitrary.”37 In a telling remark, Wallis explains in a letter to Oldenburg that he accepts

“springyness” as a mechanism because he has been “forced to it by the necessity of a consequence from those principles which I layd down” in Mechanica.38 Wallis assigns physical mechanisms to his mathematical laws of motion only when forced, and nothing forces him to accept fuga vacui or simple circular motion. To introduce more mechanisms than necessary would be to make nature choose between them, so to speak, and this is not how Wallis considers nature to operate.

35 He defends this view, for example, in John Wallis, Due Correction for Mr Hobbes, or Schoole Discipline, for Not Saying His Lessons Right (Oxford, 1656), 56-57. 36 Wallis, Hobbius Heauton-timorumenos, 154-156. The quotations are from 155 and 156. 37 Wallis, Hobbius Heauton-timorumenos 156-157. Schaffer notes that Hobbes used a similar argument against mechanisms like condensation, claiming that they were unnecessary to save the phenomena. See Schaffer, “Wallifaction,” 282-283. 38 WC III, 91.

Gifts freely given: divine action and its relation to the laws of nature

For Wallis, natural action is regular, mathematical, and predictable. This understanding of nature motivates his search for mathematical laws that apply to all bodies. It also motivates his resistance to laws and mechanisms––such as those proposed by Neile and Hobbes––that seem to render natural action less consistent and predictable. Conversely, Wallis’s published sermons suggest that

God is free to suspend the laws of nature at any moment. In general, however, Wallis suggests that God’s interventions affect spiritual rather than material things, and he leaves the laws of nature intact. In any case, divine action as Wallis sees it is anything but regular, mathematical, and predictable.

As a Presbyterian minister, Wallis occupied a potentially awkward position in Restoration

England. The Presbyterians became unpopular under Charles II’s regime on account of their desire to restructure the Church hierarchy, as well as their Calvinist theology, both of which were reminiscent of Interregnum ideals. Under Charles’s rule, Presbyterian ministers had either to commit to an Anglican ecclesiology and liturgy or give up their livings. Wallis was among those who capitulated and kept their positions.39 He participated in the Royal Society’s effort to support the Anglican Church and the monarchy after the Restoration, and he evidently felt that there were greater threats than Episcopalianism, such as Hobbes’s materialist natural philosophy.40

However, Wallis’s Presbyterian roots often show in his theological writings, chiefly when

39 On the precarity of English Presbyterians after the restoration see Philip Benedict, Christ’s Churches Purely Reformed: A Social History of Calvinism (New Haven: Yale University Press, 2002), 405-411; C. G. Bolam and Jeremy Goring, “Presbyterianism in Separation: The Cataclysm,” in The English Presbyterians: From Elizabethan Puritanism to Modern Unitarianism by C. G. Bolam, Jeremy Goring, H. L. Short and Roger Thomas (London: George Allen & Unwin, 1968), 73-92; Michael Mullett, “Radical Sects and Dissenting Churches, 1600-1750,” in A History of Religion in Britain: Practice and Belief from Pre-Roman Times to the Present eds. Sheridan Gilley and W. J. Sheils (Oxford: Blackwell, 1994), 204-206. On Wallis’s Presbyterianism and its role in his conflict with Hobbes, see Jesseph, Squaring the Circle, 295-308; Jason Michael Rampelt, “Distinctions of Reason and Reasonable Distinctions: The Academic Life of John Wallis (1616-1703)” (PhD diss., Cambridge, 2005), 118-123. 40 See Shapin and Schaffer, Leviathan and the Air-Pump, esp. 132, 136, 287, 295, 311-313.

72 he emphasizes Calvinistic doctrines of election and predestination.41 These doctrines play a key role in his conception of divine action. For Wallis, the election of certain members of Christian society is a prime example of how God freely chooses how to interact with the created world. In an age when miracles no longer seem to happen, Wallis believes that God primarily intervenes by bringing about the salvation of certain people. In addition, as I will argue below, Wallis’s emphasis on election provides an important context for his work on the mathematical laws of motion.

According to Wallis, nature cannot choose which bodies to act on, so it affects them all indiscriminately. For one who knows the laws of motion, natural phenomena are predictable.

Conversely, God is free to choose precisely how to intervene in the world, so his actions cannot be generalized and predicted like natural phenomena.

Among all Wallis’s theological works, it is his sermons that most clearly articulate his views on God’s nature and actions. Wallis published sermons throughout his career, and many others were included in a collection that was published posthumously in 1791.42 Many of his core theological beliefs are articulated, for instance, in a sermon on the doctrine of the Trinity, published in 1691. Here Wallis provides biblical evidence to show that Christ exhibits the same qualities as God the Father. Enumerating the “Characters of the True God,” Wallis explains that

God is an eternal, infinite, and omnipotent being, and the creator of everything in the universe.43

To these qualities we can add God’s absolute freedom. In a sermon entitled “Salvation the Free

Gift of God,” Wallis adopts the typical Protestant position that grace is a gift freely given. So, he adds, is everything else that God gives to people, “for God in his will being absolutely independent

41 See, for instance, WC I, 43; John Wallis, Sermons: Now First Printed from the Original Manuscripts of John Wallis, D. D., ed. W. Wallis (London, 1791), 197. 42 Wallis, Sermons. Cited in full in n. 41 above. 43 John Wallis, Three Sermons concerning the Sacred Trinity (London, 1691), 87.

73 cannot, in any of his decrees, act otherwise than freely.”44

The details of divine action, as Wallis understands it, are outlined in sermon called The

Life of Faith (1684). Here he argues that God is responsible for every step that leads a person to salvation. These include “Election, Regeneration, Justification, Adoption, Sanctification, and (as fruits thereof) a Holy Life, with Perseverance therein to the end.” Wallis identifies Election,

Justification, and Adoption as “Relative Acts, (of God towards us . . .)”; it is obvious that these actions are performed by God. But he claims that God deserves credit even for the steps which seem to reflect a person’s own actions: “Regeneration and Sanctification, are Works of God, wrought in us, by his Spirit.” Of all these steps, though, Wallis singles out Election as a process that is inscrutable to humanity. He writes, “Election, is the Act of God; which we are not curiously to pry into: nor can we know it otherwise, than as the Effect discovers it in time.”45

These sorts of changes in people’s minds and souls are not the only divine actions that

Wallis recognizes. He also has no doubt that biblical miracles happened as described in Scripture.

However, Wallis believes that the Age of Miracles is over: God’s interventions in the world no longer resemble the spectacular miracles recorded in the Bible. Nevertheless, he recognizes miracles as a kind of divine action, and in The Life of Faith he explicitly likens them to God’s actions on people’s souls. As Wallis explains, it was faith that saved Daniel from the lions, allowed

Sarah to bear a child, and spared Moses from the plagues in Egypt; it was lack of faith that caused the people of Sodom to be destroyed. In the New Testament, it was the faithful who were healed by Jesus and the Apostles. Likewise, Wallis adds, even if God no longer punishes or rewards people in the form of miracles, he still acts to reward or punish people in accordance with their

44 Wallis, Sermons, 200-202, 220. The quotation is from 202. 45 John Wallis, The Life of Faith. In Two Sermons to the University of Oxford, at St. Mary’s Church There; on the 6th. of January, 1683/4. and June the 29th. following (London, 1684), 18-19.

74 faith by saving them or damning them: “though Miracles be now ceased; yet the Effects of Faith are not.”46

Elsewhere Wallis indicates why God may have changed the way that He intervenes in the world. In a sermon entitled The Resurrection Asserted (1679), Wallis suggests that anyone who would be convinced of God’s power by miracles would already have been convinced by the examples recorded in Scripture. Unbelievers would find ways to doubt new miracles just as they doubt biblical ones. Furthermore, God has no obligation to perform miracles when someone demands them.47 Wallis echoes this latter point in his Defense of Infant-Baptism (1697) where he suggests that those who want a clear sign from God that it is right to baptize their children will be disappointed. This is because God is more concerned to teach his doctrines to those who are willing to learn patiently rather than “Captious” people who challenge those doctrines at every opportunity.48 Since God is absolutely free, He does not need to perform miracles to make people believe in him. Nevertheless, Wallis insists that a faithful person must believe in the biblical miracles, even if they conflict with the teachings of natural philosophy. For instance, he argues in

The Life of Faith that believers must accept that God created the universe ex nihilo despite the ancient dictum that nothing can be created from nothing.49 Likewise, in a sermon on Matthew

11:28, Wallis notes that “God can countermand the course of Nature” as he did, for instance, when he parted the Red Sea.50 No matter what natural philosophers believe or know, it is a matter of faith that God can act however he wants, even in contradiction of the laws of nature.

46 Wallis, Life of Faith, 33-41. The quotation is from 41. 47 John Wallis, The Resurrection Asserted: In a Sermon Preached to the University of Oxford, on Easter-Day, 1679 (Oxford, 1679), 28. 48 John Wallis, A Defense of Infant-Baptism: In Answer to a Letter (here Recited) from an Anti-Pædo-Baptist (Oxford, 1697), 10. 49 Wallis, Life of Faith, 21, 29. 50 Wallis, Sermons, 43-44.

As he describes God’s nature and actions in his sermons, his intention is to lay out the basic principles on which more complex arguments can be built. In The Resurrection Asserted, he explicitly compares this approach to the one he takes in mathematics, arguing that, in either field,

“till there be some Data, some Concessions agreed upon; there can be no Demonstration.”51 In theology these principles are to be gleaned from reading Scripture, and Wallis supports each of them with scriptural citations. In addition, his attitude toward these divine qualities is similar to his attitude toward matters of fact in his natural philosophy, which are founded on reliable and carefully collected evidence.52 In both natural philosophy and theology, Wallis restricts his analysis to matters of fact because, as discussed in Chapter 2, deeper truths––whether metaphysical or theological––are beyond the scope of human reason. In a sermon on the Trinity, he likens things such as time, space, motion, heat, colour, and taste to divine mysteries: we can discuss them, but it is impossible for us to know precisely what they mean.53

However, Wallis evidently felt that the theologian cannot use matters of fact in quite the same way that the natural philosopher does. Whereas facts about nature allow for generalization, mathematization, and prediction, the facts recorded in Scripture demonstrate only how God has acted in the past, and offer no guarantees about how he will act in the future. In The Resurrection

Asserted, Wallis notes that God punishes people in a variety of ways, not because he is constrained by various factors, but because he freely chooses one punishment over others.54 And as early as

1652, in a letter to the theologian Richard Baxter, Wallis argues that God was not constrained to punish Adam exactly as He did for eating the forbidden fruit in the Garden of Eden. He writes, “I

51 Wallis, Resurrection Asserted, 2. See also 26-27. 52 In his Defense of Infant-Baptism, Wallis suggests that the details of events described in Scripture are much like matters of fact in natural philosophy, except that they lack support from mathematical demonstration (Wallis, Defense of Infant-Baptism, 10). 53 Wallis, Three Sermons, 65-66. The quotation is from 66. 54 Wallis, Resurrection Asserted, 35.

76 see not why the creatures miscarriage should divest God of that absolute soveraignty over it, to dispose of it as he pleaseth.” In fact, Wallis adds, “God might, by his absolute soveraignty, dispense with the whole punishment.”55 In Wallis’s view, we may know the matters of fact about how God has acted in the past, but we cannot use these facts to understand his decisions or to predict how he will act in the future.

“Nature doth not work by Election”: Wallis’s appropriation of Grosseteste’s principle

For Wallis, God’s action pervades the created world, occasionally in the form of miracles but usually in terms of how he affects people’s minds and souls. But how does Wallis relate divine action to the mathematical laws of nature revealed by experiments? In one of the earliest texts in his corpus, his inaugural address as Savilian Professor of Geometry in 1649, Wallis suggests that

God created the laws of nature so that they could serve as a basis for the generation and transmission of knowledge. After extolling mathematical education, Wallis anticipates his listeners’ question: what use is mathematics to those who will never pursue a profession that requires it? He responds by suggesting that God wants people to learn as much as they can, not simply what is useful to them. Referencing Ovid’s Metamorphoses, he asks rhetorically, “Did God therefore give man an uplifted face, and order him to look at heaven so that he would contemplate only these things which he himself could produce?” Wallis insists that the philosopher’s purpose is to learn about everything “which God himself constructed, and which either art or nature could accomplish.”56 More importantly, though, mathematics is crucial to the transmission of

55 WC I, 46, 48. 56 “Ideone Deus Os homini sublime dedit, cælemque videre, Jussit––ut ea tantum comtempletur, quæ possit ipse conficere?”; “ea scire quæ Deus ipse condidit, quæque vel Ars vel Natura possit efficere” (OM I, 8). The italics are

77 knowledge. Wallis notes that communication has improved since the printing press had been introduced in Europe, but he insists that scholars will never communicate anything worthwhile unless they share a foundation in mathematics.57

Elsewhere, Wallis likens knowledge of mathematics to grace: they are both gifts freely given by God. This is one of many points that Hobbes, according to Wallis, fails to grasp. In his

Elenchus geometriæ Hobbianæ (1655), Wallis rebukes Hobbes for mocking those who believe that one needs divine help to understand geometry, especially after Adam’s Fall from Eden. Wallis maintains that even before the Fall, but especially after it, humans need God’s help to learn, just as they need His help to be saved. This includes the geometrical knowledge that Hobbes takes for granted. Wallis writes, “For if the merchant is taught by God how to grow rich (Deuteronomy

8:18) or even the farmer how to till the Earth (Isaiah 28:24, 25, 26) why not also the geometer to do geometry?”58 For Wallis, everything that people learn reflects God’s choice to grant them that knowledge.

Evidently, then, Wallis identifies God as the source of both the laws of nature themselves and humanity’s knowledge of them. Nevertheless, I argue that Wallis conceives of natural action as different in kind from the divine actions he describes in his sermons, and the key to that difference is the element of choice. A particularly telling part of Wallis’s Discourse of Gravity, where he describes how a wavy liquid returns to equilibrium, helps to illustrate this point. Here

Wallis’s, and are a direct quotation of Ovid (Ovid, Metamorphoses, 2nd ed., vol. 1, trans. Frank Justus Miller [London: Heinemann, 1921; orig. pub. 1916], 8). Here Wallis attributes to philosophers a view expressed by Chremes, a character in Terence’s play, Heauton Timorumenos: “I am a man, I consider nothing human alien to me” (“Quem melius deceat Chremetis illud Terentiani, quam Cheremetum ipsum, Homo sum, nihil humanum a me alienum puto”; OM I, 8). Significantly, Wallis assigns to philosophers the duty to learn all human things, and not simply all things. The philosopher learns what God wants him to learn, and this apparently does not include most facts about God’s own nature, actions, and intentions. But it does include whatever other humans know about the created world. 57 OM I, 8-9. 58 “Si enim à Deo edoctus sit Negotiator ditescere, Deut. 8. 18. aut etiam Colonus terram colere, Isai. 28. 24, 25, 26. quid ni & Geometra γεωµετρειν?” (John Wallis, Elenchus geometriæ Hobbianæ. Sive, geometricorum, quæ in ipsius elementis philosophia, à Thoma Hobbes Malmesburiensi proferuntur, refutatio [Oxford, 1655], 89).

Wallis explains that gravity affects the liquid in two ways at once. On one hand, the raised parts of the liquid spread out sideways because the space around them is empty; on the other hand, the raised parts press down on the parts below them, which causes the empty spaces to be filled from below (see Figure 4). Wallis argues that both mechanisms must be involved in returning the liquid to equilibrium, since any factors that affect a body do so Figure 4: Wallis’s simultaneously. This concept is straightforward, but the way depiction of liquid coming

Wallis expresses it adds some complexity. He writes, “For nature to rest doth not work by Election, but ad ultimum virium, and at all the (OM II) ways it can, where one doth not oppose the other.”59 The illustration highlights under “A” the part of the liquid affected by gravity in two ways I suggest that this principle should be understood in two at once. ways. Firstly, it reveals the distinction in Wallis’s thought between God’s unpredictable and freely chosen actions on one hand, and the predictable and mathematical actions of nature on the other.

Secondly, it is a subtle reference to a treatise written by Grosseteste in the 1230s called De lineis, angulis et figuris.60 Grosseteste explains that optical phenomena are always subject to geometrical rules, “for [a natural agent] does not act through deliberation and election” (Non enim agit per deliberationem et electionem).61 The reference is clearer in the Latin translation of the Discourse of Gravity, included in Wallis’s Opera mathematica, which closely follows Grosseteste’s wording:

59 Wallis, Discourse of Gravity, 5. 60 On the dating of De lineis, angulis et figuris and other treatises by Grosseteste, see James McEvoy, “The Chronology of Robert Grosseteste’s Writings on Nature and Natural Philosophy,” Speculum 58 (1983): 614-655. 61 Robert Grosseteste, “De Lineis angulis et figuris seu de fractionibus et reflexionibus radiorum” in Die philosophischen Werke des Robert Grosseteste, Bischofs von Lincoln, ed. Ludwig Baur (Münster: Aschendorff, 1912), 60. For useful expositions and translations of the relevant parts of Grosseteste’s treatise, see George Molland, “Roger Bacon’s Corpuscular Tendencies (& Some of Grosseteste’s Too),” in Late Medieval and Early Modern Corpuscular Theories, eds. Christoph Lüthy, John E. Murdoch, and William R. Newman (Leiden: Brill, 2001), 68; Amelia Carolina Sparavigna, “Reflection and Refraction in Robert Grosseteste’s De Lineis, Angulis et Figuris,” arXiv e-prints, History and Philosophy of Physics (2013); available from http://arxiv.org/pdf/1302.1885v1.

“Non enim agit Natura per Electionem.”62

In turn, Grosseteste may have adapted this principle from the Metaphysics of Healing by

Avicenna, the eleventh-century Persian philosopher, whose work was translated into Latin in the twelfth century as Avicenna latinus. Avicenna argues that the circular motion of celestial bodies is not natural, but is rather impressed on them by an external intellect. He explains that the bodies themselves could not be responsible for such an unnatural motion: “For a natural thing does not act by election, but rather in the way of serving, and in the way of that which follows from its essence” (Naturalis enim non agit per electionem, sed ad modum servientis et ad modum eius quod comitatur per essentiam).63 Here Avicenna intends to emphasize that God is the source of the circular celestial motion. Where the Latin text reads servientis, the original Arabic text uses the word Tashkir. In his English translation of the Arabic text, Michael E. Marmura renders

Tashkir as “enforcement” and notes that the Qur’an uses this word to refer to God compelling the celestial bodies to move.64 Evidently, the principle that nature does not act by election had carried theological implications since at least the eleventh century.

It is more likely, though, that Wallis adapted this principle from Grosseteste than directly from Avicenna. Firstly, Grosseteste’s De lineis, angulis et figuris would have been available to

Wallis in Oxford, having been donated to the Bodleian Library by Archbishop Laud in the 1630s.65

Secondly, Wallis’s and Grosseteste’s respective uses of this principle are similar in tone. Rather than emphasizing God’s active role in the natural world like Avicenna, Wallis and Grosseteste use

62 OM II, 711. 63 S. van Reit, ed., Avicenna latinus liber de philosophia prima sive scientia divina V-X (Louvain: E. Peeters, 1980), 448. 64 Michael E. Marmura, trans., Avicenna: The Metaphysics of Healing (Provo, UT: Brigham Young University Press, 2005), 308, 418 n. 4. 65 This manuscript is found in Bodleian MS Laud Misc 644, ff. 207-208. On the history of the Laudian collection, see Falconer Madan and H. H. E. Craster, A Summary Catalogue of Western Manuscripts in the Bodleian Library at Oxford, vol. 2.1 (Oxford: Clarendon Press, 1922), 12-19.

80 this principle to suggest that natural phenomena should be regarded as operating under mathematical rules. Finally, we know that Wallis was familiar with other manuscripts written by

Grosseteste because he refers to them in his Treatise of Algebra (1685).66

There is much in Grosseteste’s treatment of the relationship between mathematics, nature, and God that Wallis may have found useful. As Steven J. Livesey has discussed, Grosseteste argued that Aristotle, despite his insistence on the autonomy of the disciplines, did in fact allow philosophers to import mathematical demonstrations into their work in other disciplines.67 This would have been no trivial matter for Wallis, who was steeped in the intellectual culture of Oxford where Aristotle still cast a long shadow in the seventeenth century.68 In addition, as Simon Oliver explains, Grosseteste believed that motion was necessary for all knowledge of nature: we learn about the heavens by observing the motion of celestial objects; we learn that the terrestrial realm is different from the celestial realm because we observe different kinds of motion in each; we sense things via the motion of light and the elements; and we even commit things to memory through motion within the sensitive soul. Grosseteste contrasts this system to God’s actions which require no mediation and thus lack motion and temporality, the hallmarks of natural phenomena.69

Wallis may have found in Grosseteste a useful precedent for describing natural phenomena with mathematical regularity, in contrast to the elective actions of God. For both Grosseteste and

Wallis, divine action differs in kind from natural phenomena, and is therefore not subject to

66 See Jacqueline A. Stedall, “Of Our Own Nation: John Wallis’s Account of Mathematical Learning in Medieval England,” Historia Mathematica 28 (2001): 84, 98. 67 Steven J. Livesey, “Science and Theology in the Fourteenth Century: The Subalternate Sciences in Oxford Commentaries on the ’Sentences’,” Synthese 83 (1990): 274-278. 68 Wallis shows respect for Aristotle in many texts, including a letter where he describes the Oxford Philosophical Society, of which he was the president, to a colleague at the University of St Andrews. Wallis assures his colleague that, even though the Society is committed to experimental philosophy, “we would by no means be thought . . . to slight or undervalue the Philosophy of Aristotle; which hath (for so many ages) obtained in the schools. But have (as we ought) a great esteem of him; & judge him to have been a very great man: I think those who do most slight him, to be such as are lest [sic] acquainted with him” (Bodleian Library MS Ashmole 1813, f. 314). 69 Simon Oliver, “Robert Grosseteste on Light, Truth and Experimentum,” Vivarium 42 (2004): 162-168.

81 mathematical demonstration: God, unlike nature, works by election. Wallis’s innovation was to appropriate Grosseteste’s principle and apply it to the mechanical philosophy that emerged in the seventeenth century.

Conclusion

I have argued in this chapter that Wallis’s conceptions of divine action and natural action pivot around the idea of free choice. For Wallis, natural phenomena are entirely constrained by the laws of nature, including the laws of motion that he discovered in his experiments. The laws of nature are in effect at all times and bodies cannot choose whether to follow them. The only exceptions are miracles, and these no longer seem to happen. As a result, in Wallis’s view, natural phenomena are generalizable, predictable, and subject to mathematization. On the other hand, divine action–

–meaning here the actions that God takes to damn or save people’s souls––contains an irreducible element of choice. A theologian can learn the facts about how God acted in the past, but he cannot generalize, mathematize, and predict God’s actions the way a natural philosopher can learn to do through experimentation. I have also argued here that this distinction is reflected in Wallis’s appropriation of a principle he encountered in the work of Robert Grosseteste: the principle that

“nature doth not work by Election.” Wallis adapted this principle to contribute to his mechanical and experimental philosophy, and, I suggest, perhaps he also consciously intended to relate it to

Calvinist theology.

Once again, it is useful to compare Wallis to Newton, the intellectual giant of the subsequent generation who seems to have grasped the importance of Wallis’s work more than anyone else did. Newton’s position on divine action was famously represented by Samuel Clarke in his correspondence with Gottfried Leibniz in 1715-1716. Clarke and Leibniz engage in a stimulating debate on many subjects, but they seem to talk past each other on the issue of the

“Mathematical Principles of Philosophy.” Clarke introduces this phrase in his first letter to

Leibniz, echoing the title of Newton’s Principia mathematica. Apparently he confuses Leibniz when he claims that materialism contradicts the mathematical principles of philosophy which,

Clarke argues, clearly indicate that the world has an “Intelligent and Free” creator. Leibniz objects that he does not see what mathematical principles have to do with refuting materialism: if these principles reflect the existence of an immaterial God, are they not metaphysical rather than mathematical? In subsequent letters, Clarke continues to argue that mathematical principles in themselves constitute evidence of design, and Leibniz continues to insist that once they are used in that way they cease to be strictly mathematical principles.70

In these exchanges there seems to be some implicit point preventing Clarke and Leibniz from understanding each other. Since Wallis, too, described mathematical principles of philosophy, and since Newton paid such close attention to his work, perhaps Wallis’s perspective can help to understand the source of the divergence between the positions of Newton/Clarke and

Leibniz. Wallis believed that God works by election but his creation does not; since God wants nature to be intelligible to people, he causes it to act according to fixed mathematical laws. The mathematical principles of natural philosophy, then, represent the extent of what people can learn about how God freely choose to design the world. God’s reasons for creating the world as he did are ultimately beyond human comprehension, but whatever few insights we can gain about God’s actions by observing nature take the form of mathematical principles. Evidently Leibniz does not consider it legitimate to interpret mathematical principles as evidence of divine action. But Wallis follows Grosseteste in pushing the boundaries of mathematical investigation, and perhaps Newton

70 Samuel Clarke, ed., A Collection of Papers, Which Passed between the Late Learned Mr. Leibnitz, and Dr. Clarke, in the Years 1715 and 1716. Relating to the Principles of Natural Philosophy and Religion (London, 1717), 9, 19-21, 37, 55, 73. The quotations are from 9 and 37.

83 and Clarke follow Wallis in turn.

Chapter 4: On Food and Fossils: Biblical History in Wallis’s Works

In the spring of 1671, Henry Oldenburg wrote to John Wallis in Oxford to ask his opinion of a bright, young scholar named Gottfried Leibniz. The Royal Society wanted Wallis to evaluate the

German philosopher’s Hypothesis physica nova, a text that attempts to explain all natural phenomena within a comprehensive mechanical system. Wallis wrote back to Oldenburg with a favourable review of the Hypothesis, but he anticipated that not everyone would immediately appreciate its value. In his letter, he explains that reactions to a new theory are like a pendulum that swings back and forth many times before coming to rest in the middle. When Copernicus proposed a heliocentric cosmology, for example, his hypothesis was “supported by the best reason,” but it encountered stubborn resistance for decades. Now, however, “reason finally having prevailed over authority,” nearly every educated person accepts the heliocentric model of the cosmos as a physical reality. Wallis goes on to describe how the pendulum swung back and forth for many other theories that are now widely accepted: whether it was William Harvey’s theory of the circulation of blood, Galileo’s refutation of the Aristotelian principle that nature abhors a vacuum, or the discovery of the lymphatic vessels, every highly original theory has provoked fierce opposition. Yet, in each case, reason prevailed when the pendulum stopped swinging.1

Once such new ideas have overcome the inevitable resistance, Wallis explains, their erstwhile critics typically engage in a sort of historical revisionism. According to Wallis, when his colleague Richard Lower conducted the earliest experiments in blood transfusion, French writers

1 “. . . optima ratione suffulta”; “tandem rationibus authoritati praevelentibus” (WC III, 445-446). On the Hypothesis physica nova, Wallis’s response, and the importance of Wallis’s support to the trajectory of Leibniz’s career, see Philip Beeley, “A Philosophical Apprenticeship: Leibniz’s Correspondence with the Secretary of the Royal Society, Henry Oldenburg,” in Leibniz and His Correspondents, ed. Paul Lodge (Cambridge: Cambridge University Press, 2004), 47-73.

85 in particular scoffed at his attempt to perform a procedure that they considered impossible. Once

Lower had succeeded, however, the French changed their attitude toward blood transfusion and in fact tried to claim priority for the procedure.2 Wallis goes on to list other English discoveries for which foreign writers had tried to take credit once they had been widely accepted: George

Joyliffe discovered the lymphatic vessels and Thomas Wharton discovered the salivary ducts, but in each case rivals from the Continent claimed to have made the discovery first.3 It was typical of

Wallis to make dubious claims for English priority in every noteworthy discovery and invention,4 but he also makes an important point here about disputed historical facts. History, no less than the theories of natural philosophy, is rife with uncertainly and competing explanations.

Wallis’s letter to Oldenburg gives us a sense of his historical philosophy. According to

Wallis, an adequate understanding of natural philosophy––or any other subject for that matter–– required an appreciation of its history. Indeed, he himself included a historical component in his writings on mathematics, music, English grammar, and other subjects.5 At the same time, Wallis

2 Blood transfusion was the subject of a particularly fierce and nationalistic priority dispute between English and French writers. See A. Rupert Hall and Marie Boas Hall, “The First Human Blood Transfusion: Priority Disputes,” Medical History 24 (1980): 461-465; Holly Tucker, Blood Work: A Tale of Medicine and Murder in the Scientific Revolution (New York: W.W. Norton, 2011). 3 WC III, 446-447. 4 See Adam Richter, “Priority and Nationalism: The Royal Society’s International Priority Disputes, 1660-1700” (unpublished MA thesis, Dalhousie University, 2011), 103-158. 5 Wallis’s historical research in mathematics in his Treatise of Algebra, Both Historical and Practical (1685) was so original and insightful that Jacqueline Stedall has called him “perhaps . . . the first modern historian of mathematics.” Based on a careful study of manuscripts and artefacts, Wallis concluded that Europeans had been using Hindu-Arabic numerals at least as early as the twelfth century, significantly revising the estimate of Gerard Vossius who claimed that the numerals were adopted in Europe no earlier than 1250 (Jacqueline A. Stedall, “Of Our Own Nation: John Wallis’s Account of Mathematical Learning in Medieval England,” Historia Mathematica 28 [2001]: 73-122; the quotation is from 73). Wallis demonstrated his knowledge of the history of music when he edited the first printed version of Ptolemy’s Harmonics in 1682 and appended his own study comparing ancient and modern theories of harmonics (John Wallis, “Letters to Andrew Fletcher, August 1698,” in John Wallis: Writings on Music, eds. David Cram and Benjamin Wardhaugh [Ashgate: Surrey, 2014], 75-204). In Grammatica linguae Anglicanae (1653), his textbook on English grammar, Wallis included a chapter on etymology, providing a historical overview of the words that the English language had adopted Latin, French, German and Greek. He expanded this historical account in later editions of the Grammatica, and in the fourth edition of 1674, he describes the etymological history of specific English words. For example, the Latin “presbyter” became the English “priest,” and “paralysis” became “palsy”; the names “Augustinus,” “Hieronymus” and “Radulphus” became “Austin,” “Jerom” and “Ralf.” (John Wallis, Grammatica linguæ Anglicanæ, 1st ed. [Oxford, 1653], 123-127; idem, Grammatica linguæ Anglicanæ, 4th ed.

86 was reluctant to trust the authors of historical sources. Throughout history, writers had done what

Wallis saw them doing in his own time: they obscured the truth, they exaggerated, and they made conclusions based on incomplete information. For instance, in a letter concerning ancient Greek music, Wallis discusses certain anecdotes about musicians who could apparently elicit strong emotional reactions in their listeners, the likes of which had never been observed in the modern era. Wallis is skeptical about the supposed intensity of these reactions and argues that these accounts are “highly Hyperbolical, & next door to Fabulous.” The Greeks, he argued, exaggerated about their music as they did about most subjects.6 Wallis was always attentive to the lessons of history, but he appreciated that not all sources were reliable.

Fortunately, there was one historical source that Wallis regarded as beyond doubt: the

Bible. In particular, Wallis turned to Scripture, especially the Book of Genesis, for evidence about what the world was like shortly after Creation. Like most Protestant theologians in his time, Wallis insisted that Scripture generally had a plain and accessible meaning. We see this, for instance, in his defense of the doctrine of the Trinity, which he considered to be clearly established by a straightforward reading of the Bible.7 In this chapter, I will discuss moments throughout Wallis’s career when he turned to the Bible as a uniquely reliable historical source. Specifically, I will explain how Wallis draws on biblical evidence to support his positions in natural philosophy and mathematics. Yet Wallis was no strict biblical literalist. The letter to Oldenburg discussed above implies Wallis’s acceptance of the Copernican hypothesis, and elsewhere he confirms that he accepts the motion of the Earth.8 Nevertheless, Wallis was one of the many scholars of the

[Oxford, 1674], 125-129). 6 Cram and Wardhaugh, Wallis on Music, 223-230. The quotation is from 225. 7 See Chapter 2 above. 8 Wallis briefly defends the Copernican hypothesis in his earliest publication, Truth Tried (John Wallis, Truth Tried: or, Animadversions on a Treatise Published by the Right Honorable Robert Lord Brook, Entituled, The Nature of Truth, Its Union and Unity with the Soule. Which (Saith he) is One in its Essence, Faculties, Acts; One with Truth

87 seventeenth century who treated the Bible as an accurate historical record (apart from those passages that were accommodated to the understanding of common people, such as those that describe a geocentric cosmos).9 Firstly, in the 1650s and early 1660s, while defending the historical veracity of the Bible against his perennial opponent Thomas Hobbes, Wallis gleaned from Scripture such facts as the precise age of the Earth and the extent of mathematical learning before Noah’s Flood. Secondly, while presiding over the Oxford Philosophical Society in the mid-

1680s, Wallis appealed to biblical history for evidence against Robert Hooke’s theory of fossils.

Hooke’s theory entailed dramatic geographical changes throughout history. Wallis’s argument against Hooke’s theory depended on biblical passages indicating that the geography of the Earth had not significantly changed since the Flood. Finally, around the turn of the eighteenth century,

Wallis turned to the Bible to determine whether humans had always eaten meat. This evidence informed his response to Pierre Gassendi’s argument, based on the anatomy of human teeth, that the natural human diet is a herbivorous one.

Like many of his contemporaries, Wallis treated the Old Testament of the Bible, especially the Books of Moses, as a repository of historical information about the Earth and its inhabitants in the earliest generations after Creation. As Peter Harrison has argued, the Protestant Reformation encouraged people to treat the Book of Genesis as a factual historical record––the most accurate

[London, 1643], 73-74). See also WC II, 174-177; John Wallis, “An Essay of Dr. John Wallis, Exhibiting His Hypothesis about the Flux and Reflux of the Sea, Taken from the Consideration of the Common Center of Gravity of the Earth and Moon; Together with an Appendix of the Same, Containing an Answer to Some Objections, Made by Severall Persons against That Hypothesis,ʼ Phil Trans 1 (1665-1666): 263-281; idem, “An Extract of Two Letters . . . Concerning a Considerable Meteor Seen in Many Distant Places of England at the Same Time,” Phil Trans 12 (1677- 1678): 863-866. Wallis also refers to discussions of the Copernican hypothesis during the meetings of the experimentalist groups that preceded the founding of the Royal Society. See Christoph J. Scriba, “The Autobiography of John Wallis, F.R.S.,” Notes and Records of the Royal Society of London 25 (1970): 40. 9 Many astronomers and natural philosophers resolved the apparent contradiction between Scripture and the Copernican hypothesis by employing this “accommodationist” argument. See Stephen D. Snobelen, “‘In the Language of Men’: The Hermeneutics of Accommodation in the Scientific Revolution,” in Nature and Scripture in the Abrahamic Religions vol. 2, ed. J. M. van der Meer and S. Mandelbrote (Leiden: Brill, 2008), 691–732.

88 record ever written––including what it says about the natural world. Numerous early modern figures (including Wallis) considered the Pentateuch to have been written by Moses himself, whom they viewed as a historian and natural philosopher. Treating Scripture as a historical record, scholars could employ their knowledge of nature to interpret the text, and they could also extract knowledge of nature from it. Whether their preferred natural philosophy was Cartesian,

Newtonian, or Paracelsian, these early modern scholars sought to interpret the Genesis account of

Creation in terms of natural processes.10 Furthermore, Jim Bennett and Scott Mandelbrote, discussing the same historical attitude toward Scripture in this period, note that the Book of

Genesis was used to determine what the Garden of Eden was like and where precisely it was located. These geographical descriptions of Eden were so precise that they were sometimes accompanied by maps depicting the location of the Garden relative to familiar places, such as the map in Figure 5 that locates it in Mesopotamia. These maps were even included in some Bibles.11

Wallis’s engagement with biblical history allows us to consider Harrison’s broader argument about the relationship between the Bible and early modern natural philosophy.

According to Harrison, the literalist approach to Scripture promoted by the Protestant Reformers removed the need for the allegorical interpretations that were typical of medieval biblical scholarship. This new approach to texts inspired many writers to adopt a similar style in their

10 Peter Harrison, The Bible, Protestantism and the Rise of Natural Science (Cambridge: Cambridge University Press, 1998), 121-160. 11 See Jim Bennett and Scott Mandelbrote, The Garden, the Ark, the Tower, the Temple: Biblical Metaphors for Knowledge in Early Modern Europe (Oxford: Museum of the History of Science, 1998), 24-25. Harrison notes various other early modern determinations of the location of Eden, including Ethiopia, Palestine, America, and the South Pole (Harrison, The Bible, 127). In addition to those who read the Bible as a source of historical data, many seventeenth-century scholars, particularly those of a puritanical bent, used the prophecies in the Books of Daniel and Revelation to structure all of history. These millenarians argued that the world had reached some point in the “last days” described by the prophetic books, although they disagreed about which moments described by the prophets should be identified with historical events in the past, and which were yet to come (see Richard W. Cogley, “Survey Article: Seventeenth-Century English Millenarianism,” Religion 17 [1987]: 379-396). Despite his connections to the Puritans, though, Wallis did not adopt the millenarian approach to history.

89 accounts of the natural world. Whereas natural historians had formerly included the allegorical, moral, and mystical significance of the objects they described, in the seventeenth century they typically eschewed this extraneous material and provided only empirical facts about nature.12 In addition, Harrison argues, one consequence of the literalist approach to texts was that exegetes no longer treated the Bible as though it “contained eternal truths which transcended time and place” as they had done in the Middle Figure 5: Map of the Garden of Eden from the Geneva

Ages. Rather, the Bible came to be Bible (1560) seen as a historical record that This map locating Eden in Mesopotamia was adapted from Jean Calvin’s Commentary on Genesis (1553). Calvin claimed that the reflected the time when it was Garden was located near the conjunction of the Tigris and written. The historical approach to Euphrates, in the middle-right of the map. (Calvin, Commentaries on the First Book of Moses Called Genesis, vol. 1, trans. John King, biblical hermeneutics allowed 1847) natural philosophers to treat the Bible as “a kind of scientific text-book” in which the authors of

Scripture had deposited their knowledge of nature, so that perceptive readers in later centuries could recover it.13

While Harrison’s account helps to place Wallis’s attitude toward biblical history in context,

12 See Harrison, The Bible, 4-5, 8. 13 See Harrison, The Bible, 121-160; the quotations are from 122 and 140.

90 this alone does not explain when Wallis chose to invoke biblical authority in matters of natural philosophy and when he relied only on data gleaned from experimentation and observation.

Certainly, Wallis valued the Bible as a unique source of natural knowledge. In each of the cases discussed below, he claims that his opponents are inattentive to the natural and mathematical knowledge contained in Scripture. He accuses Hobbes of denying the truth of Scripture outright, and implies that Hooke and Gassendi have developed theories that neglect this important source.

On the other hand, these uses of biblical history in natural philosophy and mathematics represent a minority of cases throughout Wallis’s career. Most of the time, he is content to wear different hats: he writes either as a natural philosopher, a mathematician, a linguist, a minister, or a practitioner of whatever other subject has attracted his attention. The following analysis helps to clarify when such an English polymath felt that he needed support from biblical authority. I will argue below that it is only when a matter requires knowledge of conditions shortly after Creation that Wallis turns to the Bible as a historical source.

Nevertheless, in each of the cases discussed below, Wallis treats the Bible as an indispensable source of knowledge in either mathematics or natural philosophy. However, the case of Wallis creates an additional problem for Harrison’s argument. For Harrison, natural philosophers’ use of the Bible as a historical source is one aspect of a broader narrative about how the Bible indirectly promoted the methodological hallmarks of modern science: experimentation and observation. He argues that “[t]he literal approach to texts precipitated [a] change of attitude towards the world, while the literal content of key passages of the Bible further motivated natural philosophers in their quest to master nature.” Harrison suggests that his argument challenges “the contemporary association of biblical literalism with religious bigotry and hostility toward the

91 sciences.”14 Rather than assume that biblical literalism entails (and has always entailed) a rejection of empirical science, Harrison proposes that historians consider how it has promoted science among Christians who study the natural world.

Harrison’s historical evidence successfully challenges any simplistic notion of an essential conflict between biblical literalism and scientific evidence. What I would like to emphasize, however, is that the same individuals who used the Bible to support new ideas about nature could also use it to protect old ideas and to cast doubt on theories that they did not find convincing. This will become clear from the following analysis of Wallis, an English Protestant with connections to the Puritans––that is to say, exactly the sort of person most often cited in support of historiographical theses that link Protestantism to the emergence of science.15 For Wallis, as we will see, the Bible provided a useful way of negotiating between tradition and innovation in natural philosophy and mathematics.16 In his letter on Leibniz’s Hypothesis physica nova, Wallis suggests that it is difficult to determine which new ideas represented important advances in natural philosophy and which were unsubstantiated follies. Fortunately, the Bible provided a reliable way to determine which innovative ideas about the natural world had the support of historical

14 Harrison, The Bible, 267-269. 15 As Harrison notes, historians developed arguments linking Puritanism and the rise of science beginning in the 1930s. More recently, however, historians (including Harrison himself) “have retreated to a more general thesis: not puritanism and science, but Protestantism and science.” Such theses might emphasize intellectual developments, such as the Calvinist doctrine of Election, or social factors, such as the decline of clerical authority, that resulted from the Reformation and may have facilitated the empirical study of nature. Still, English Puritans invariably feature prominently in these accounts (Harrison, The Bible, 7-8). 16 My approach here is informed by Maurice Finocchiaro’s argument that apparent cases of conflict between science and religion in early modern Europe reflect a more fundamental conflict between “cultural conservation and innovation.” According to Finocchiaro, the Galileo affair, for instance, was not a contest between Scripture and scientific evidence. Rather, it was an instance of a broader cultural conflict between conservation and innovation, “one that operates in such other domains of human society as politics, art, economy, and technology.” Finocchiaro does not provide a precise definition of conservation and innovation, but this general framework is a useful heuristic tool for understanding a figure like Wallis who vacillates in his attitude toward novel ideas (Maurice A. Finocchiaro, “The Copernican Revolution and the Galileo Affair,” in The Blackwell Companion to Science and Christianity, eds. J.B. Stump and Alan G. Pagett [Chichester: Wiley-Blackwell, 2011], 23-24; see also idem, Defending Copernicus and Galileo: Critical Reasoning in the Two Affairs [Dordrecht: Springer, 2010], xxx, 233, 294-295, 305-306).

92 evidence.17

Wallis versus Hobbes on biblical mathematics

Wallis made some of his earliest comments on the relationship between biblical history and natural knowledge during his protracted conflict with Thomas Hobbes. From 1655 to 1678, Wallis and

Hobbes attacked each other’s ideas in printed treatises. On the surface, their conflict was about mathematics––particularly Hobbes’s dubious claims to have solved the ancient mathematical problems of squaring the circle and doubling the cube––but the polemics expanded to include a range of other subjects. In the most comprehensive account of the conflict, Douglas Jesseph explains that Wallis sought to weaken Hobbes’s credibility in general by criticizing his mathematics. He and his colleagues at Oxford hoped that this strategy would make readers skeptical of other, more dangerous ideas espoused by Hobbes. These ideas included his absolutist political philosophy, his denouncement of the clergy, his ridicule of the Scholastic tradition, and his materialist natural philosophy which Wallis and his colleagues considered tantamount to atheism. It is no surprise, then, that the exchanges between Wallis and Hobbes addressed matters beyond mathematics, including politics, natural philosophy, ecclesiology, and theology.18

From the beginning of the conflict, Wallis objected to what he perceived as Hobbes’s skeptical and dismissive attitude toward Scripture. In Elenchus geometriae Hobbianae (1655), his

17 Of course, Wallis realized that certain passages of Scripture, even when read literally, could be interpreted in different ways. We will see this below, for example, in Wallis’s biblical chronology, when he grapples with ambiguous references to the births and deaths of biblical figures. Nevertheless, for Wallis the Bible was a uniquely accurate historical record whose evidence could be used to arbitrate between new and old ideas about the natural world. 18 Douglas M. Jesseph, Squaring the Circle: The War between Hobbes and Wallis (Chicago: University of Chicago Press, 1999), 69-72, 293-339. See also Ted H. Miller, Mortal Gods: Science, Politics, and the Humanist Ambitions of Thomas Hobbes (University Park: Pennsylvania State University Press, 2011), 156-158. Wallis’s negative reaction to Hobbes’s ideas was far from unique. For an overview of the numerous contemporary English criticisms to Hobbes’s philosophy, see Samuel I. Mintz, The Hunting of Leviathan: Seventeenth-Century Reactions to the Materialism and Moral Philosophy of Thomas Hobbes (Cambridge: Cambridge University Press, 1962).

93 first text attacking Hobbes, he accuses his opponent of holding ideas clearly contrary to “Sacred

History” (Historiae Sacrae).19 Hobbes provoked Wallis’s umbrage when he discussed the rectification of curves in his first major mathematical publication, De corpore (1655). Here

Hobbes claims that he has succeeded in rectifying a curve––which means to find a straight line equal in length to a given curved line––and he ridicules those mathematicians who, since antiquity, have considered this impossible. Among those whom he mocks is an unnamed contemporary who admitted that rectification is possible but lamented that “since the fall of Adam” it cannot be accomplished “without the special assistance of Divine Grace.”20

In the Elenchus, Wallis denounces Hobbes for this apparent dismissal of divine grace. In a moment that reflects his Calvinist convictions, Wallis insists that divine grace, a gift freely given by God, is responsible for everything that a person achieves, including solutions to “mysteries of nature” (Naturae mysteria). He explains,

. . . I do not deny that there are many people, and I indeed am one of them, who—not only in those things that immediately concern eternal salvation, but truly also in matters of daily life and especially in either philosophical or mathematical studies—consider an accomplishment to be by divine help, which is freely given.21

19 John Wallis, Elenchus geometriæ Hobbianæ. Sive, geometricorum, quæ in ipsius elementis philosophiæ, à Thoma Hobbes Malmesburiensi proferentur, refutatio (Oxford, 1655), 135. 20 Thomas Hobbes, Elements of Philosophy, the First Section, concerning Body (London, 1656). This work was originally published in Latin in 1655 as Elementorum philosophiae sectio prima de corpore. In his edition of De corpore, Karl Schuhmann identifies that target of Hobbes’s quip as Quadratura circuli et hyperbolae segmentum demonstrata (1651) by Antoine de la Loubère (Karl Schuhmann, ed., De corpore: elementorum philosophiae sectio prima by Thomas Hobbes [Paris: Librarie Philosophique J. Vrin, 1999], 376 n. 3). 21 “. . . ego non diffiteor complures esse; & me quidem ex eo numero unum, qui non tantum, in iis quæ ad æternam salutem immediatè spectant, verùm & in rebus quotidianæ vitæ, & speciatim in studiis sive Philosophicis sive Mathematicis, Divino putant opus esse auxilio, eoque gratuito” (Wallis, Elenchus, 89). Wallis was not alone in his insistence that God was the source of insights about the natural world. Boyle, for instance, suggests that God leads natural philosophers to “happy and pregnant Hints” in nature so that they can make discoveries that they “would scarce have imagin’d to be possible” (Robert Boyle, Some Considerations Touching the Usefulnesse of Experimental Natural Philosophy: Propos’d in a Familiar Discourse to a Friend, by Way of Invitation to the Study of It [Oxford, 1664], 110-111). Likewise, Méric Casaubon claims that God determined when humanity made such inventions as the compass, gunpowder, and the printing press. The latter invention, he suggests, was made at precisely the right time to “promote learning” and ultimately to provoke the Protestant Reformation “which God intended in his Church” (Méric Casaubon, A Letter of Meric Casaubon D. D. &c. to Peter du Moulin D.D. and Prebendarie of the Same Church concerning Natural Experimental Philosophie, and Some Books Lately Set Out about It [Cambridge, 1669], 26). Many thanks to Peter Harrison for drawing my attention to these sources.

Wallis supports this view of God’s role in the acquisition of knowledge by referring to two passages of Scripture: “For if the merchant is taught by God how to grow rich (Deuteronomy

8:18) or even the farmer how to till the Earth (Isaiah 28:24, 25, 26) why not also the geometer to do geometry?”22 Deuteronomy 8:18 states that it is God “who gives you power to get wealth,” and Isaiah 28: 24-26 explains that farmers know how to sow seeds and harvest crops because

“they are well instructed; their God teaches them” (NSRV). Here Wallis provides specific examples showing that God has given humanity its knowledge of mathematics and nature. Unlike

Hobbes, Wallis trusts the Bible as a historical source on this matter.

In the Elenchus, Wallis establishes that God is the source of natural and mathematical knowledge, and that the Bible is a trusted source of history, but he stops short of actually extracting knowledge of those subjects from the Bible itself. However, he does precisely that in a text that inspired one of Hobbes’s most thoroughgoing critiques. In 1657, Wallis published a mathematics textbook called Mathesis universalis that consists of a series of lectures that he delivered in

Oxford. The topics of these lectures range from basic arithmetic to the latest developments in algebra. In Chapter 17, as an exercise in adding large numbers, Wallis leads his students through a calculation of the age of the world based on figures recorded in the Bible.23

The starting point for Wallis’s calculation is Theatrum historicum et chronologium by the

German theologian and historian Christoph Helvig (1581-1617). This work, essentially a timeline of historical events since creation, was first published in Giessen in 1609. Certain later editions

22 “Si enim à Deo edoctus sit Negotiator ditescere, Deut. 8. 18. aut etiam Colonus terram colere, Isai. 28. 24, 25, 26. quid ni & Geometra γεωµετρειν?” (Wallis, Elenchus, 89). 23 OM I, 79-84. For an overview of the contents of Mathesis universalis, see Jason Rampelt, “Distinctions of Reason and Reasonable Distinctions: The Academic Life of John Wallis (1616-1703)” (unpublished Ph.D. thesis, Cambridge University, 2005), 88-91. Many early modern scholars took a serious interest in calculating the precise age of the world based on biblical evidence. Newton was especially active in the field of biblical chronology and expended much effort to determine how quickly the human population expanded after the Flood. See Jed Z. Buchwald and Mordecai Feingold, Newton and the Origin of Civilization (Princeton: Princeton University Press, 2013).

95 were printed at Oxford, including the fifth edition of 1651, which was presumably Wallis’s source.

Each page contains a table with each row corresponding to a decade, and each column representing a different part of the world.24 Helvig’s table allows readers to keep track of the number of years that had elapsed since Creation at the time of a given historical event. The early pages cite passages of Scripture to establish the ages of biblical figures or that a specific number of years has passed (see Figure 6).

In his addition exercise, Wallis follows Helvig’s approach but diverges from his chronology in several places. His corrections are based on his own reading of the Bible as well as a trusted secondary source, Sir Walter Raleigh’s Historie of the World (1614), to which he refers readers who are curious about chronology.25 Raleigh also begins his history at Creation, but he records events in a long and meandering prose account rather than a table.26 Wallis notes that the current year at the time of writing (1655) would be year 5604 since Creation according to Helvig’s chronology but, following Raleigh’s chronology rather than Helvig’s, he determines that the current year is actually 5661.27

Wallis begins his calculation by noting the milestones that structure Helvig’s chronology and the corresponding biblical passages: the genealogy of the first generations of humanity as

24 Christoph Helvig, Helvig, Christoph. Theatrvm historicvm et chronologicvm, æqualibus denariorum, quinquagenariorum & centariorum intervalis: cum assignatione imperiorvm, regnorvm, dynastiarvm, regvm, aliorvmque virorvm celebrivm, prophetarvm, theologiorum, iureconsultorum, medicorum, philosophorum, oratorum, historicorum, poetarum hæreticorum, rabbinorum, conciliorum, synodorum, academiarum, &c. itemque usitatarum epocharum, ita digestum, ut vniversa temporvm et historiarvm series, 5th ed (Oxford, 1651). 25 OM I, 80. 26 Sir Walter Raleigh, The Historie of the World in Five Bookes (London, 1652 [orig. pub. 1614]). Bennett and Mandelbrote describe Raleigh’s Historie as typical of the genre of biblical history, including its preoccupation with the geographical location of Eden which Raleigh illustrates with a map (Bennett and Mandelbrote, The Garden, the Ark, the Tower, the Temple, 173). 27 OM I, 79-81. In a sermon published in the posthumous collection from 1791, Wallis notes that he divides human history into three periods: the time from Adam’s fall to Abraham, from Abraham to Christ, and from Christ to the end of the world. See John Wallis, Sermons: Now First Printed from the Original Manuscripts of John Wallis, D. D., ed. W. Wallis (London, 1791), 238-239.

recorded in Genesis, the references to the Israelites’ 430 years of slavery in Egypt, the construction

of Solomon’s Temple, the birth of Christ, and so on. But Wallis claims that “this calculation of

Helvig is to be amended in a few

places, so that it will better agree

with the historical truth.”28 In

particular, he doubts Helvig’s

dating of the birth of Abraham.

The Book of Genesis is

ambiguous on this point,

establishing only that Abraham’s

father, Terah, had the first of his

three sons at age 70. Helvig

assumed that Abraham is the

oldest son because his name is

listed first, but Wallis cites

certain passages suggesting that

Figure 6: Christoph Helvig’s historical tables Abraham was 75 years old when

(Theatrum historicum, 5th ed., 1651) Terah died at age 205, so

This page from Helvig's Theatrum depicts the Israelites’ Exodus Abraham must have been born from Egypt in comparison to the age of the world and other historical when his father was 130.29 Here events. Wallis follows Raleigh closely,30

28 “. . . calculus ille Helvici est aliquot in locis emendadus, ut cum veritate historica melius consentiat” (OM I, 79). 29 OM I, 80. 30 See Raleigh, Historie of the World, 186-190.

97 but his thoughts on the birth of Arphaxad––Noah’s grandson and a distant ancestor of Abraham––seem to be original. Genesis 11:10 records Arphaxad’s birth as two years after the Flood. Wallis argues that, although Helvig and others have assumed that these two years are to be counted from the beginning of the Flood, they should in fact be counted from the end of the Flood, which was an Figure 7: Wallis’s calculation of entire year later.31 Finally, Wallis makes similar the age of the Earth observations to show that Helvig overestimated (Mathesis universalis, 1657) Abraham’s age at the time of God’s promise (Genesis 17) by four years. This means that Helvig’s chronology is off by a total of 57 years, a calculation that

Wallis depicts in a convenient table for the reader (see Figure 7).32 For Wallis, then, the figures recoded in Scripture reveal an important piece of natural knowledge: the precise age of the world.

The observant reader can also calculate precisely how many Israelites lived in Egypt, which Wallis includes as another example of how to add large sums.33

In addition to these facts, Wallis uses biblical numbers to learn about another subject that always attracted his attention: the history of mathematics. As an introduction to the Mathesis universalis, Wallis included the inaugural address he had delivered in Oxford after his appointment as Savilian Professor of Geometry in 1649. Here he discusses the antiquity of mathematical learning, and finds evidence that Moses and his ancestors had extensive mathematical knowledge. This claim echoes a tradition extending back to at least the first century

31 OM I, 79-80. 32 OM I,” 80-81. 33 OM I, 81-84.

CE when Josephus wrote that Seth, the third son of Adam and Eve, had erected two pillars to preserve the great knowledge of humanity’s first generation, including the “mathematical arts”

(Mathematicas artes).34

Wallis realizes that no one alive has seen Seth’s pillars and he anticipates skepticism about

Josephus’ account. However, he explains, this is no reason to doubt that mathematics thrived before the Flood: the best evidence for this comes from Scripture itself. Wallis notes that the Bible counts years “in ones, tens, and hundreds, aptly arranged” beginning at Creation. Humanity’s first generations could have chosen any number system, but they chose a decimal system because they recognized that it was “absolutely necessary” for arithmetic; this is why the same number system has been retained until the present. Adam, or “whoever first divided the infinite multitude of numbers into an order,” appreciated as mathematicians still do that a base-ten number system is well-suited to calculation. And perhaps, Wallis adds, God himself taught arithmetic to Adam so that he could count the animals in the Garden of Eden as he named them.35

Wallis argues that the first humans would also have developed geometry when they needed to measure objects. Likewise, they would have begun to study astronomy once they realized that

“God had placed the sun, and the moon, and the remaining stars for the division of days, years, and months.”36 Nor, according to Wallis, were these various mathematical practices lost when

34 OM I, 4. Presumably Wallis read about Seth’s pillars in Antiquities of the Jews by Josephus, which is the apparent source of the myth of Seth’s pillars and was available in Oxford in manuscript form (see Tommaso Leoni, “The Text of Josephus’s Works: An Overview,” Journal for the Study of Judaism 40 [2009]: 159). He may also have read about it in Raleigh’s Historie of the World which discusses Josephus’ account (Raleigh, Historie of the World, 35). 35 “. . . per Monadas, Decadas, Centuriasque apte dispositos”; “absolute necessariam”; “qui primus infinitam numerorum multitudinem in ordinem digessit” (OM I, 4-5). Privately, Wallis expressed a preference for a base-twelve system. While his colleague John Wilkins argued that a base-eight system would be best in his Essay towards a Real Character (1668), Wallis wrote in his copy of the Essay that a base-twelve system is ideal because twelve has more factors than either eight or ten. The base-ten system had become the accepted convention, Wallis suggests, simply because people have ten fingers (John Wilkins, An Essay towards a Real Character, and a Philosophical Language [London, 1668], 190; Wallis’s copy is owned by the Bodleian Libraries [Savile A 4, i]). 36 “Qui Solem enim, & Lunam, reliquaque Sydera, ad dierum, annorum, mensumque discrimina constituit Deus, noluit hæc temporum indicia diu ignorari” (OM I, 5).

99 most of humanity perished during Noah’s Flood. The Bible mentions that the Chaldeans––the

Babylonian nation into which Abraham was born––practised astronomy (and astrology) shortly after the Flood. Wallis concludes that mathematics was “either preserved on Noah’s ark or awakened thereafter,” presumably by the Chaldeans. Later, either Abraham or “some other master of Chaldea” brought mathematics to the Egyptians, who came to excel particularly in geometry.

Later, after the conquests of Alexander the Great, the mathematical knowledge of the Chaldeans and Egyptians was absorbed by the Hellenistic world.37 This means that classical mathematics, which constituted much of the content of Wallis’s lectures, was based (at least in part) on a mathematical tradition extending back before the Flood, and probably to Adam who may have been educated by God Himself. One way or another––whether through grace, the study of biblical chronology, or historical tradition––Wallis considered humanity’s mathematical knowledge to flow from God.38

Hobbes found much to object to in Wallis’s Mathesis universalis, including his biblical history of mathematics. In his Examiatio et emendatio mathematicae hodiernae (1660), Hobbes criticizes the Mathesis universalis point by point, beginning with Wallis’s inaugural address.

Wallis assumed that Bible’s account of the time before the Flood reflected the mathematical knowledge of that age. On the contrary, Hobbes argues, “everyone agrees that it [the Book of

Genesis] was written either by Moses or long after Moses’ time by Ezra,” meaning it may have been written only a few centuries before the common era. So when Wallis points out that Genesis counts the years before the Flood using a decimal system, he only proves that such a system was

37 “. . . sive Noachi arca conservata, sive deinceps postea exsuscitata” (OM I, 5). 38 Raleigh’s Historie may have given Wallis a sense of the mathematical abilities of biblical figures––for instance, he notes the mathematical elegance of the calendar used by the ancient Hebrews––but Raleigh does not address the importance of the decimal number system as Wallis does. See Raleigh, Historie of the World, 214-216.

100 available in the time when Genesis was written, rather than the time that Genesis describes.39

Hobbes also objects to Wallis’s assumption that the Chaldeans taught mathematics to the

Egyptians. He notes that this contradicts the account of the Greek historian Diodorus Siculus, who claims that it was the Egyptians who taught the Chaldeans. Hobbes demands that, if Wallis has more evidence to support his version of events than a few biblical references to the Chaldeans’ knowledge of astronomy, he should name his source.40

Wallis responded to Hobbes’s Examinatio in 1662 with Hobbius Heauton-timorumenos.

The title of this work, adapted from a play by Terence, means “Hobbes, Self-Tormentor”; so weak is Hobbes’s reasoning, Wallis suggests, that his works only succeed in tormenting their author.

Here Wallis defends his argument that the antediluvian generations used a decimal number system. He does not deny that Genesis may have been written by Moses or Ezra, but he challenges

Hobbes to “produce more Authentick evidences, or more Ancient, than what we produce for the

Antiquity of Computation.” It is Hobbes’s burden to prove that the number system changed between the time that Genesis describes and the time when it was written. In the meantime, “there is no . . . reason to think that Moses did otherwise Record, than they did Reckon.”41

As for naming the Chaldeans the first to practice mathematics after the Flood, Wallis cites several ancient sources to support this claim, including Cicero, Pliny, Vitruvius, and Josephus. In fact, Wallis continues, Diodorus Siculus also held that the Egyptians learned mathematics from the Chaldeans; Hobbes has simply read him wrong.42 More importantly, Wallis’s interpretation of

39 Thomas Hobbes, Examinatio & emendatio mathematicæ hodiernæ. Qualis explicatur in libris Johannis Wallisii Geometriæ Professoris Saviliani in Academia Oxoniensi. Distributa in sex Dialogos (London, 1660), 2. This work is written in dialogue format, so it is the interlocutors created by Hobbes who voice these arguments, rather than Hobbes himself. 40 Hobbes, Examinatio, 2-3. 41 John Wallis, Hobbius Heauton-timorumenos. Or a Consideration of Mr Hobbes His Dialogues. In an Epistolary Discourse, Addressed, to the Honourable Robert Boyle, Esq. (London, 1662), 18. 42 Wallis, Hobbius Heauton-timorumenos, 19-22.

101 history has biblical support. Hobbes’s reading of Diodorus suggests that the Egyptians brought mathematics to Chaldea when they colonized it, about a century after the Flood. Wallis objects by pointing out that Noah’s Ark came to rest on Mount Ararat, which he (like many others) believes to be located in Armenia. After that, Noah and his family must have lived close by, perhaps in

Chaldea itself. From there humanity spread outward, eventually reaching distant lands such as

Egypt. Wallis argues that this sequence of events does not give the Egyptians enough time to have colonized Chaldea within a century after the Flood, so Hobbes’s interpretation of Diodorus is impossible:

. . . that Ægypt, a place so far off from Armenia where the Ark rested, should, before the birth of Peleg, be so well [p]eopled as to send out Colonies to inhabit Chaldea, (as Mr Hobs from what is said by Diodorus Siculus, would have us believe) is so incredible, and so unagreeing with Holy Story, with those aforecited, and with what Diodorus himself (lib. 2.) delivers, that it needs no other Refutation.43

His knowledge of other historical sources helps Wallis to make his point, but the bottom line seems to be that Hobbes’s interpretation of history is “unagreeing with Holy Story”; Hobbes has not recognized the historical primacy of the Bible.

Hobbes does not specifically address Wallis’s calculation of the age of the Earth in

Examinatio, but Wallis evidently read in the text a challenge to the practice of biblical chronology.

As Wallis explains, Hobbes tried to question the “Universality” of numbers and implied that “the

Præ-Adamites might reckon at another Rate” than those who lived when the Book of Genesis was written.44 Here Wallis suggests that Hobbes believes in Pre-Adamite humans and therefore doubts

43 Wallis, Hobbius Heauton-timorumenos, 21. 44 Wallis, Hobbius Heauton-timorumenos, 18. Decades earlier, Raleigh had already encountered the view that the Bible counts years at a different rate, which would explain why certain biblical figures are said to have lived for nearly a thousand years. Raleigh rejects this view and seeks to explain why people lived so much longer in biblical times. As I will discuss below, he attributes their longer lives in large part to their diet (Raleigh, Historie of the World, 65-67).

102 the entire Genesis account of Creation.45 In addition, though, he takes Hobbes to be claiming that the numbers recorded in Scripture are not reliable, since they may have been counted differently in the distant past. This would mean that any effort to determine the age of the world based on these numbers is futile. In short, Wallis perceives in Hobbes’s text a challenge to the continuity between past and present on which the project of biblical history depended. For Wallis, it was not only a matter of historical importance that people practised mathematics before the Flood. If the earliest generations of humanity did know mathematics, this fact served as a foundation for the efforts of Wallis and others to extract certain facts about nature from the Bible.

Hooke’s fossil theory and Wallis’s biblical geography

The next significant episode in Wallis’s use of biblical history occurred in a very different context.

Over thirty years after his initial exchange with Hobbes, Wallis turned to biblical history for support in a matter of natural philosophy, namely, a theory about the origin of fossils. In this case his opponent was not a dangerous enemy, but rather a colleague, albeit one with whom he had a tense relationship: the Royal Society’s curator of experiments, Robert Hooke.46 By now Wallis’s career at Oxford was firmly established. He responded to Hooke’s theory as the president of the

45 Most early modern interpreters of Scripture assumed that Adam was the first human being ever created, but a minority of writers at this time argued that certain human societies predated Adam. These writers took into account histories from non-Christian cultures, such as Egypt, China, Persia, and Babylonia, whose historical records extend back further than conventional biblical chronology would allow. The “Pre-Adamite” thesis was made more credible by the existence of native Americans, who were geographically cut off from the other continents and are not mentioned in the Bible. Furthermore, writers such as Giordano Bruno and Tommaso Campanella argued that the stars might be orbited by other planets populated by people who could not be descendants of Adam. Some writers drew evidence from the Bible itself, interpreting certain ambiguous passages in a way that implies the existence of Pre- Adamite peoples; they argued, for instance, that Cain could only have founded a city, as reported in Genesis, if people lived in the world before his father, Adam. The most notorious advocate of such heretical views was the French historian and theologian Isaac La Peyère, whose Prae-Adamitae (1655) scandalized seventeenth-century readers no less than the works of Hobbes and Spinoza. See David N. Livingstone, Adam’s Ancestors: Race, Religion, and the Politics of Human Origins (Baltimore: Johns Hopkins University Press, 2008), 1-51. 46 On the animosity that developed between Wallis and Hooke, see Lisa Jardine, The Curious Life of Robert Hooke: The Man Who Measured London (New York: Harper Perennial, 2004), 266-268.

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Oxford Philosophical Society, an experimentalist group founded in 1683 and modelled on its counterpart in London.47 As president, Wallis attended weekly meetings, often bringing in the results of his own experiments and observations, and those reported by colleagues abroad. Among his regular correspondents in this period was Edmond Halley, secretary of the Royal Society, and it was he who wrote to Wallis to describe a theory, presented to the Society by Hooke, that sought to explain the seemingly erratic distribution of fossils around the world. In particular, Hooke sought to account for the fossils discovered on mountaintops that resembled sea creatures, and those discovered in England that resembled species normally found in a tropical climate.

Hooke’s solution was to posit a mechanism that would cause the oceans to rise and fall over long stretches of time. Noting that sea levels are higher at the equator than at the Earth’s poles, Hooke suggested that the Earth is a slightly flattened sphere, or an oblate spheroid, with a shorter axis from pole to pole than from two opposite points on the equator. Furthermore, Hooke argued, if the poles of the Earth were to shift gradually, then the dimensions of the Earth’s spheroid shape would change with it: the oceans would drop at the new location of the poles, and rise at the new equator running perpendicular to the poles. With these repeated dramatic changes in ocean levels across the world throughout history, Hooke’s theory of “polar wandering” could explain why the remains of sea creatures had been found on the peaks of the Alps and, in general, why fossils resembling other species were frequently unearthed in places where they did not seem to belong. Hooke lacked the evidence to demonstrate that the poles move, but he did have experimental support for his theory about the shape of the Earth. In one experiment, he showed that bubble of melted glass becomes flattened when spun. In another, he showed that water in a

47 On the Oxford Philosophical Society and its relationship with the Royal Society, see ESO IV and XII, passim; Anna Marie Roos, “The Chymistry of ‘The Learned Dr Plot’ (1640-96),” Osiris 29 (2014): 81-95.

104 spinning round dish moves away from centre toward the sides, forming half of a flattened sphere.

Why, then, would the water surrounding a spinning Earth not act the same way, with the water moving toward the equator and to give the Earth the shape of an oblate spheroid?48

Halley wrote to Wallis about Hooke’s theory in February 1686/7, explaining that it could account for the strange distribution of fossils “if the change of the Earths Axis may be allowed.”

The shifting sea levels across the globe would explain why fossilized sea shells had turned up in the Alps and nautili and ammonites had been found in England, findings that were difficult to reconcile with the current distribution of animal species. Anticipating the objection that familiar locations had apparently not changed their latitude since antiquity, Hooke explained that the ancients had made only “very crude” measurements of latitude. He suggested that the Royal

Society take greater care in this matter than their predecessors: if a long telescope were fixed on the pole star for an extended period, a change in latitude “might be discovered in the life time of a single Observer.”49

Wallis wrote back to Halley in March and expressed the collective skepticism of the

Oxford Philosophical Society toward Hooke’s theory. As Wallis explains, they found that Hooke had not provided enough evidence to support so radical a hypothesis. He writes, “They seemed not forward, to turn the world upside down (for so ‘twas phrased) to serve an hypothesis, without cogent reason for it; not onely, that possibly it might be so; but that indeed it hath been so.” Nor did the Oxford group accept Hooke’s interpretation of the experiments on spinning fluids: his

48 See Ellen Tan Drake, Restless Genius: Robert Hooke and His Earthly Thoughts (Oxford: Oxford University Press, 1996), 87-91; David R. Oldroyd, “Geological Controversy in the Seventeenth Century: ‘Hooke vs Wallis’ and Its Aftermath,” in Robert Hooke: New Studies, eds. Michael Hunter and Simon Schaffer [Woodbridge: Boydell, 1989], 207-233. In other texts, spanning from 1667 to 1700, Hooke emphasizes earthquakes, rather than polar wandering, as the source of the geological changes that explain the distribution of fossils. See Rhoda Rappaport, “Hooke on Earthquakes: Lectures, Strategy and Audience,” British Journal for the History of Science 19 (1986): 129-146. 49 ESO XII, 124-126. Halley had referred to Hooke’s discussions of fossils in a letter written in January, but without a detailed account. See ESO XII, 121-124.

105 claim that a spinning Earth would become an oblate spheroid rather than a sphere was “but a conjecture, of what may be; without any evidence from Observations that so it is.”50

The problem was not only had Hooke failed to provide sufficient evidence: according to

Wallis and his colleagues in Oxford, the theory was clearly contradicted by experiments and astronomical observations. Astronomers had observed the shadow of the Earth to be a circle, or very nearly a circle, during lunar eclipses. Experiments had shown that bodies fall perpendicular to the Earth’s surface, no matter their geographical location. According to Wallis, each of these points provides compelling evidence that the Earth is a perfect sphere rather than an oblate spheroid.51 In fact, Wallis suggests that the entire history of astronomical observation is against

Hooke. For instance, he claims that the ancient Greek geographer Pytheas made accurate observations of the Earth’s axis in relation to the ecliptic. These observations, Wallis explains, differ little from their modern counterparts, such as the observations made by the Jesuit astronomer Giovanni Riccioli. Certainly, astronomers have disagreed slightly on the angle of the

Earth’s axis, but according to Wallis,

. . . so vast a change as is now suggested [by Hooke], could not possibly have been (within the reach of Histories now extant) but that some foot-steps thereof would certainly have been found in History: since it is so many Hundred years (not to say thousands) since Astronomers have been curiously inquiring into such matters.52

While it is not always clear which member of the Philosophical Society was responsible for each particular point raised against Hooke’s theory, these historical objections seem to have come from

Wallis himself. The minutes recorded during the Society’s meeting of 1 March note that he referred his colleagues to “the Alphonsine Tables & some MSts. in Oxford,” texts which Wallis

50 Bodleian MS Ashmole 1813, f. 327v. The relevant parts of this and the next letter from Wallis to Halley on Hooke’s theory are printed in A. J. Turner, “Hooke’s Theory of the Earth’s Axial Displacement: Some Contemporary Opinion,” British Journal for the History of Science 7 (1974): 166-170. 51 Bodleian MS Ashmole 1813, f. 328r. 52 Bodleian MS Ashmole 1813, f. 328r.

106 knew well from the research he conducted for his recently-published Treatise of Algebra.53 Hooke may have downplayed the lessons of history in an effort to promote his theory, but Wallis would not make the same mistake.54

According to Wallis, historical evidence indicates even more clearly that the Earth had experienced no dramatic change in sea levels since Noah’s Flood. It is this point that prompts

Wallis to turn to the Bible as a reliable historical source. We can be sure from the Society’s minutes that Wallis was the one who introduced the biblical evidence against Hooke’s theory:

Upon mentioning of Mr. Hooks Discourse about the changes which he supposes to have been made upon the Surface of the Earth, Mr. President observd that if any soe great changes had happen’d it is probable Tygris & Euphrates would not have continued to be the same rivers ever since the Creation.55

Wallis elaborated on this point in his letter to Halley, explaining that the Bible mentions geographical locations that do not seem to have moved since Creation. He writes, “If we give credit to the Story of Genesis (the most ancient certainly of any extant;) we shal find the world

(soon after Noah’s floud) so divided amongst its Inhabitants & so planted (Gen. 20) as agrees very well with the present Geography.”56 Genesis describes humanity’s spread around the world after the Flood with references to familiar regions, cities, and bodies of water. Wallis provides a list of places whose present locations apparently match those referred to in the Bible, including Egypt,

53 ESO IV, 201. The Alphonsine tables, which recording the positions of celestial bodies, were compiled by astronomers in thirteenth-century Spain. Wallis studied them during his research on the adoption of Hindu-Arabic numerals in Europe. See Stedall, “Of Our Own Nation,” 93-97. 54 Of course, as Drake notes, Hooke was right that the Earth was an oblate spheroid, and England’s natural philosophical community came to accept this position when it was advocated by Newton. Furthermore, Drake claims that Wallis and his fellows in the Oxford Philosophical Society misunderstood what Hooke meant when he suggested that the Earth’s poles could move. Hooke’s theory held that the poles changed their positions relative to the Earth’s surface; this does not mean that the axis on which the Earth rotates would change its position in relation to the cosmos, as Wallis and his colleagues believed (Drake, Restless Genius, 90-92). 55 ESO IV, 201. 56 Bodleian MS Ashmole 1813, f. 328r. Note that Wallis uses “story” as a synonym for “history” rather than a potentially fictional account. See, for instance, his reference to “Holy Story” in Hobbius Heauton-timorumenos, as quoted above.

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Chaldea, Arabia, and Mesopotamia, and the rivers Tigris, Euphrates, Nile, and Jordan. Even cities mentioned in the Bible but long since destroyed, such as Babylon and Nineveh, have locations that can be determined in relation to places that still exist.57 Popular works of biblical history of the seventeenth century provided ample support for Wallis on this point. The so-called “Dutch

Annotations,” a work of biblical commentary authorized by the Synod of Dort, supplies useful geographical information, identifying Nineveh, for example, as the ancient capital of Assyria.58

Similarly, George Hughes’ Analytical Exposition of Genesis and Exodus (1672) argues that the river where God inflicts the plague of blood on the Egyptians in Exodus 7:17 must be the Nile.59

In his critique of Hooke’s theory, Wallis implies that the shifting oceans caused by Hooke’s wandering poles would eliminate the continuity of geographical locations that such works on biblical history takes for granted.

The Bible even refers to familiar locations in the time before the Flood: various early modern sources, including Raleigh, Hughes, and the Dutch Annotations, identify two of the rivers running through Eden as the Tigris and Euphrates.60 If the Earth’s geography was essentially the same in Adam’s lifetime as it is in the present, then when, Wallis asks, could the ocean levels have risen and fallen to the extent that Hooke’s theory requires? As he explains to Halley,

57 Bodleian MS Ashmole 1813, f. 328r. 58 Theodore Haak, trans., The Dutch Annotations upon the Whole Bible or, All the Holy Canonical Scriptures of the Old and New Testament: Together with, and According to Their Own Translation of All the Text, as Both the One and the Other were Ordered and Appointed by the Synod of Dort, 1618 and Published by Authority, 1618 and Published by Authority, 1637, Now Faithfully Communicated to the Use of Great Britain, in English: Whereunto is Prefixed an Exact Narrative Touching the Whole Work, and This Translation (London, 1657; orig. pub. 1637]), sig. 7G4v. Haak, who translated the Dutch Annotations into English, knew Wallis personally; evidently Haak had hosted the meetings of experimentalists in London during the 1640s that eventually evolved into the Royal Society. See Jason M. Rampelt, “The Last Word: John Wallis on the Origin of the Royal Society,” History of Science 46 (2008): 179. In addition, the Dutch Annotations were an important source for the Westminster Assembly, the clerical body that met to reform the Church of England during the 1640s, for which Wallis served as secretary. See Bennett and Mandelbrote, The Garden, the Ark, the Tower, the Temple, 175. 59 George Hughes, An Analytical Exposition of the Whole First Book of Moses, Called Genesis, and of XXIII Chap. of His Second Book, Called Exodus (1672), 730-731. 60 Haak, Dutch Annotations, sig. B2v; Hughes, Analytical Exposition, 17-19; Raleigh, Historie of the World, 49-51, 56.

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. . . (unless it were before the Creation of Adam) we cannot find a time wherein the Earth should (so often) have been tossed & turned upside down, for the Equator & Poles to change places, & the tops of the Alps become a sea; onely to enable us to give an account of some Fish-shels found there.61

Wallis suggests here that Hooke’s theory could only conform to historical evidence if great deal of extra time were added at some point. This would invalidate the sort of biblical chronology that

Wallis had conducted in Mathesis universalis. Hooke’s theory, then, represented a challenge to the credibility of biblical history, and its utility in mathematics and natural philosophy, which

Wallis had defended decades earlier in his conflict with Hobbes.

In his reply written the following month, Halley tells Wallis that he accepts that the Earth is a flattened sphere, adding that Newton is convinced of this too, but he joins Wallis in his skepticism towards Hooke’s theory of polar wandering. Like Wallis, Halley expects that measurements of latitude would have changed dramatically if Hooke’s theory were true. But recent measurements matched those recorded in ancient sources almost exactly. Nevertheless,

Halley notes, Hooke remains convinced that he can refute each of the objections raised by Wallis and his fellows in the Philosophical Society.62 Responding to Halley later that month, Wallis restates his reasons for believing that Earth is a sphere, but he admits that it might only be spherical

“as to sense” and not “Mathematically so.” As for the motion of the poles, Wallis writes that he will judge Hooke’s latest arguments when he has heard them, but in the meantime, he sees no reason to assent to a theory so contrary to “all History, sound & profane.”63 This appears to be the last communication between Wallis and Halley about Hooke’s fossil theory. Wallis read his second letter on the subject at a meeting of the Philosophical Society, and the minutes report no objections

61 Bodleian MS Ashmole 1813, f. 328v. 62 Eugene Fairfield MacPike, ed., Correspondence and Papers of Edmond Halley (Oxford: Clarendon Press, 1932), 80-81. 63 Bodleian MS Ashmole 1813, f. 329r.

109 from the other members.64 Evidently his colleagues were sympathetic to the position that he had built upon a combination of biblical, geographical, and astronomical evidence.

Wallis did not provide an alternative explanation for how fossilized sea creatures came to be located on mountaintops, but he did not really need one. In the late seventeenth century, not every natural philosopher accepted that fossils were the remains of living things. Several writers advanced a chymical explanation for fossils, arguing that they were unusual formations of rock or mineral that had never been alive.65 In fact, two of the most vocal advocates of this position were Martin Lister, a prominent contributor to the Royal Society, and Robert Plot, Oxford’s first professor of chymistry. Plot has been credited with founding the Oxford Philosophical Society and was an active contributor to its experimental programme.66 As Anna Marie Roos has discussed, Lister and Plot were heavily influenced by the teachings of the Flemish chymist Jan van Helmont (1580-1644) who argued that minerals contained seeds or “seminal principles” that caused them to grow and to propagate like organisms. Although they disagreed on some details

64 ESO IV, 205. Hooke rebutted each of Wallis’s letters in papers he read before the Royal Society. They are transcribed in Oldroyd, “Geological Controversy,” 213-218, 220-224. Hooke’s replies suggest that he took the criticisms raised in Wallis’s letter as personal attack, but he nevertheless responded to each of the points raised by Wallis and the Oxford Philosophical Society. For instance, regarding the round shadow cast by the Earth during an eclipse, Hooke claims that this is a crude method to determine the shape of the Earth that would not be sensitive enough to distinguish between a perfect circle and a slightly flattened one. Hooke also introduces his own evidence from the Book of Genesis, citing Genesis 7:19-20, which state that the entire Earth, including mountains, were underwater during the Flood. Biblical evidence, then, confirms that even the Alps had once been covered by sea. Although Hooke pushed back against Wallis’s objections, the exchange evidently inspired him to consider historical evidence more seriously in this matter. Less than a year after he made these replies to Wallis, Hooke delivered geological lectures that sought historical support for his theory, drawing on ancient and modern sources that suggested that the Earth had experienced major geological changes over time. However, he also gave a physico-theological account of creation in a 1688 lecture that essentially followed a biblical chronology, a fact that is not easily reconciled with the views expressed in his fossil theory (Oldroyd, “Geological Controversy,” 225-230). 65 Here I follow William Newman and Lawrence Principe who use the term “chymistry” to encompass activities that modern readers would associate with both chemistry and alchemy. Chymists in the sixteenth and seventeenth centuries did not distinguish between these two fields; the same individual might investigate the transmutation of lead into gold and conduct seemingly modern experiments on chemical reactions. See William R. Newman and Lawrence M. Principe, “Alchemy vs. Chemistry: The Etymological Origins of a Historiographic Mistake,” Early Science and Medicine 3 (1998): 32-65. 66 See K. Theodore Hoppen, “The Nature of the Early Royal Society. Part II,” British Journal for the History of Science 9 (1976): 257; Roos, “The Chymistry of Dr Plot,” 82.

110 of the process, Lister and Plot each argued that fossils were expressions of the seminal principles contained in the “exhalations” of minerals such as pyrite, which was known to emit sulphur. In addition, Lister experimented on the chemical properties of fossils and found them to be composed of precisely the same substance as the surrounding rocks. Based on his findings, he explicitly opposed Hooke’s fossil theory at a Royal Society meeting. Plot, meanwhile, was the main source of chymical ideas in the Oxford group, and like Lister he combined Helmontian chymistry and microscopic observations to argue that fossils were non-organic in nature. Each of them also emphasized that, although fossils superficially resemble living things, on closer inspection they often do not correspond to any known living species––a powerful argument against their organic origin at a time when the fixity of species was generally taken for granted.67

Although Lister and Plot’s chymical theories are mentioned in the minutes of the Oxford

Philosophical Society,68 I have not found any source in which Wallis himself addresses them.

However, we can assume that Wallis would have found a chymical explanation of fossils credible based on his adoption of similar ideas to explain other phenomena. In particular, Wallis adhered to the “gunpowder” explanation of lightning, which attributes thunderstorms to the ignition of atmospheric nitre and sulphur, the same substances that react during an explosion of gunpowder.

The gunpowder explanation, which seems to be Paracelsian in origin, was a popular way to account for thunder and lightning in the early modern period before it was supplanted by Benjamin

Franklin’s electrical explanation.69 Lister, in fact, explicitly linked thunder and lightning to the

67 See Anna Marie Roos, “Salient Theories in the Fossil Debate in the Early Royal Society: The Influence of Johann Van Helmont,” in Controversies within the Scientific Revolution, eds. Marcelo Dascal and Victor D. Boantza (Amsterdam: John Benjamins, 2011), 157-170. Several other works by Roos provide a broader account of the chymistry in the works of Lister and Plot, and how it relates to fossils, including idem, “All That Glitters: Fool’s Gold in the Early-Modern Era,” Endeavour 32 (2008): 147-151; idem, “The Chymistry of Dr Plot,” 81-95; idem, The Salt of the Earth: Natural Philosophy, Medicine, and Chymistry in England, 1650-1750 (Leiden: Brill, 2007), 47-107; idem, Web of Nature: Martin Lister (1639-1712), the First Arachnologist (Leiden: Brill, 2011), 167-184. 68 See, for instance, references to Plot, Lister, and pyrites in ESO IV, 59, 104. 69 See Allen G. Debus, “The Paracelsian Aerial Nitre,” Isis 55 (1964): 43-61; Henry Guerlac, “The Poets’ Nitre,” Isis

111 sulphurous exhalations of pyrites, the same substance he believed to be responsible for fossils.70

When Wallis submitted an article on thunder and lightning to the Philosophical

Transactions in 1697, he provided a typical chymical explanation:

Thunder and Lightning are so very like the Effects of fired Gun-powder, that we may reasonably judge them to proceed from like Causes. The violent Explosion of Gun- Powder, attended with the Noise and Flash, is so like that of Thunder and Lightning, as if they differed only as natural and Artificial; as if Thunder and Lightning were a kind of Natural Gun-powder, and this is a kind of Artificial Thunder and Lightning.71

He goes on to suggest that thunderstorms are caused by the ignition of “Nitrous and Sulphurous

Vapours,” which is why they often produce a “Sulphurous Smell.” He even refers to “Chymists” who have told him that sulphur combusts when in contact with steel and water, and suggests that the “Aqueous Matter in the Clouds” might catalyze the combustion that causes thunderstorms.72

Wallis’s milieu included several passionate students of chymistry––including Lister, Plot,

Boyle, and Newton––but there is no evidence that he conducted original chymical research. Still, he valued the subject highly and considered it to be one of Oxford’s strengths at the turn of the eighteenth century. In 1700, he wrote a letter defending the education that Oxford students receive, and recalled that Peter Stahl, “a skilfull Chymist” from Strasbourg, had visited Oxford nearly fifty years earlier:

. . . [he] made it his business here, to instruct such as desire it, in the practise of chymistry (a piece of knowledge not mis-becoming a gentleman:) that is, when 6, 8, or more (of the better rank amongst us) agreed together for that purpose; he did, with them (in a convenient place for that affaire) go through a whole course of chymistry. And so,

45 (1954): 243-255; Vladimir Jankovic, Reading the Skies: A Cultural History of English Weather, 1650-1820 (Manchester: Manchester University Press, 2000), 26-30. 70 Roos, “All That Glitters,” 149. 71 John Wallis, “A Letter of Dr. Wallis to Dr. Sloane, concerning the Generation of Hail, and of Thunder and Lightning, and the Effects Thereof,” Phil Trans 19 (1695-1697): 655. 72 Wallis, “Letter to Dr. Sloane,” 655-657. Wallis submitted another letter on thunderstorms to the Philosophical Transactions the following year, and again argued that lightning results from the same chemical reaction as an explosion of gunpowder (John Wallis, “A Letter from D. Wallis of Jan. 11. 1697/8. To Dr. Sloane, concerning the Effects of a Great Storm of Thunder and Lightning at Everdon in Northamptonshire, [Wherein Divers Persons Were Killed] on July 27. 1691.,” Phil Trans 20 [1698]: 10).

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with one company after another from time to time.73

Wallis goes on to explain that Boyle, Plot, and others have continued to study chymistry at Oxford since then, and he notes that they even have a laboratory “well furnished with furnaces and utensils for that purpose.” For Wallis, chymistry is a worthy subject for industrious students interested in the natural world, just like experimental philosophy, anatomy, and botany.74

Although Wallis does not mention chymical explanations of fossils in his letters to Halley, it seems likely that he would have taken such explanations seriously, and they appear to be implicit in his critique of Hooke’s theory. In his first letter, Wallis mentions an anecdote about a woman whose kidney stone resembled a “Fish-shel.” He and his colleagues find that the stone is “more likely to have been formed there, than that the Kidney had once been sea.”75 Wallis is suggesting here that the same principle should be applied to fossils: an explanation based on the materials surrounding them is more reasonable than one that requires an entirely different environment.

This anecdote directly follows Wallis’s point that the oceans could not have risen and fallen as

Hooke suggests “unless it were before the Creation of Adam.” Evidently Wallis sees no reason why, in the absence of compelling evidence, he should adopt a theory that requires a violation of biblical history when a more credible theory is available.

It should be noted that Wallis did not consider gradual geological changes caused by natural forces to be impossible. In 1701, Wallis wrote several letters to Hans Sloane, secretary of the Royal Society, one of which was printed in the Philosophical Transactions, about a hypothesis

73 John Wallis, “Dr. Wallis’ Letter against Mr. Maidwell. 1700,” in Collectanea, First Series, ed. C.R.L. Fletcher (Oxford: Oxford Historical Society, 1885), 315-316. Italics in original. On Stahl’s visit to Oxford, see Charles Webster, The Great Instauration: Science, Medicine and Reform 1626-1660, 2nd ed. (Oxford: Peter Land, 2002 [orig. pub. 1975]), 165; G.H. Turnbull, “Peter Stahl, the First Public Teacher of Chemistry at Oxford,” Annals of Science 9 (1953): 265-270. 74 Wallis, “Letter against Maidwell,” 316. 75 Bodleian MS Ashmole 1813, f. 328v.

113 that England and France had formerly been joined by an isthmus between Dover and Calais.

Wallis accepts this hypothesis and contributes additional evidence to support it. In the printed letter, he agrees that the shores of Dover and Calais seem to fit together “as if, that [land] between them, had been violently torn away.”76 Furthermore, he notes that the languages of ancient Gaul and Britain are similar enough to suggest “an easie Communication between the one and the other.”77 Wallis goes on to explain how geological changes involving land becoming sea (or sea becoming land) can result from either gradual or sudden natural events: an isthmus might be eroded by tidal activity, or an island might be destroyed by an earthquake and a flood. Such changes can even explain the distribution of animal remains. The remains of a marine animal buried in a valley near Canterbury, for instance, might indicate that a river used to run through the valley. Indeed, Wallis notes here that the “Fish Shells, and even the Bodies of Fish Petrified” found buried near Oxford might be remains left by a river that has since disappeared.78

According to Wallis, it was likely that many significant geological changes had not been recorded in any written history. Of course, he had not referred to these naturally-occurring changes in his debate with Hooke. Whether his views on the distribution of fossils changed by the turn of the eighteenth century is unclear. What certainly did not change, however, was his commitment to the biblical history. In his letter to Sloane he explains that we might lack direct historical evidence for geological changes because “the World was of a great Age, before the Writing of any

76 John Wallis, “A Letter of Dr John Wallis, D. D. Professor of Geometry in the University of Oxford, and Fellow of the Royal Society of London; To Dr Hans Sloane, Secretary to the Said Royal Society; Relating to That Isthmus, or Neck of Land, Which is Supposed to Have Joyned England and France in Former Times, Where Now is the Passage between Dover and Calais,” Phil Trans 22 (1700-1701): 973. Wallis’s other letters to Sloane on this subject are located in British Library MS Sloane 4025, ff. 304-305, 326-330. 77 Wallis, “Passage between Dover and Calais,” 968. 78 Wallis, “Passage between Dover and Calais,” 969, 977. In another letter to Sloane, Wallis notes that bones recently found underground in Kent and Essex might not be from hippopotami or other marine animals as has been suggested, but rather elephants that the Roman Emperor Claudius brought to Britain in the first century CE (British Library MS Sloane 4025, ff. 326-329).

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Histories (except the Bible) now extant.”79 Wallis could accept that historians were ignorant or mistaken about changes in the Earth’s geology––he notes here that Plato’s account of the sinking of Atlantis might be inaccurate80––but the Bible remains unchallenged as the most ancient and reliable historical record. We can only speculate whether, in the last years of his life, Wallis still believed that the “great Age” of the world meant fewer than 6000 years but, as the next section of this chapter will show, he remained confident that an accurate theory in natural philosophy would conform to the biblical record. Around the same time that he discussed the possibility of an isthmus between Dover and Calais, Wallis was engaged in an investigation of the natural human diet, a subject that, for the last time in his long career, would bring together his research into biblical history and the natural world.

Wallis, Tyson, and Gassendi on the history and anatomy of the human diet

In the last years of his life, Wallis again used the Bible as a historical source in a matter of natural philosophy. In early 1700 he wrote to Edward Tyson, a physician famous for his work in comparative anatomy, to discuss the controversial subject of the natural human diet. In the seventeenth and eighteenth centuries, the question of proper diet was at once medical, moral, religious, and natural philosophical. Each of these aspects is apparent, for instance, in the work of

George Cheyne, a dietician famous for prescribing a highly restricted vegetarian diet to his patients. As Steven Shapin has discussed, Cheyne founded his reputation on his training in

Newtonian physics and his experience as a physician. But to persuade his patients to follow his advice, he also acted as a moral authority, linking a moderate diet to the classical virtues of

79 Wallis, “Passage between Dover and Calais,” 979. 80 Wallis, “Passage between Dover and Calais,” 974-975.

115 temperance, courage, and fidelity, and reminding them that moderation was a reflection of a godly life.81 Newton, too, considered moral and religious factors when reflecting on the matter of proper diet. In an unpublished manuscript, Newton recorded his qualms about consuming blood, since the Bible identifies blood with the soul and prohibits its consumption.82 Furthermore, according to Raleigh, the main reason why people no longer live as long as they did in biblical times is “the exceeding luxuriousness of this gluttonous age”; now people disregard the “temperate use of dyet, pleasure, and rest” that kept the earliest generations healthy.83

Like these writers, Wallis applied both natural and biblical evidence to the question of the natural human diet. As Justin E.H. Smith has shown, when early modern writers discussed the

“natural” human diet––whether humans were naturally herbivorous or carnivorous––evidence from anatomy and mechanical philosophy was at the fore, but moral and religious concerns were always in the background. This is true of Wallis’s and Tyson’s exchange on the subject. The immediate context for their discussion of diet was the work of Pierre Gassendi, who considered evidence from anatomy, natural philosophy, and anthropology to conclude that the human body is not designed to consume meat, and therefore a herbivorous diet is natural and proper. Indeed,

Gassendi argued (as did Boyle) that cannibalism is merely a particularly horrific form of the carnivorous diet, which is morally dubious in the first place. On the other hand, Tyson expresses no moral reservations about humans eating meat, and he draws on his extensive knowledge of anatomy and anthropology to argue that it is perfectly natural.84 The various early modern writers

81 Steven Shapin, “Trusting George Cheyne: Scientific Expertise, Common Sense, and Moral Authority in Early Eighteenth-Century Dietetic Medicine,” Bulletin of the History of Medicine 77 (2003): 263-297. 82 Isaac Newton, “The Question Stated about Absteining from Blood,” MS SL232; available from http://www. newtonproject.ox.ac.uk/view/texts/normalized/THEM00124. 83 Raleigh, Historie of the World, 66-67. 84 See Justin E.H. Smith, “Diet, Embodiment, and Virtue in the Mechanical Philosophy,” Studies in the History and Philosophy of Biological and Biomedical Sciences 43 (2012): 338-348. A note of clarification about terminology is needed here: according to the Oxford English Dictionary, while the nouns “herbivore” and “carnivore” have only been in use since the nineteenth century, their adjectival counterparts “herbivorous” and “carnivorous” are of a mid-

116 who discussed diet agreed that what was morally proper aligned with what was physically and anatomically natural, but they reached no consensus on how to interpret the available evidence.

While reflecting on Gassendi’s argument that humans are naturally herbivorous, Wallis sought the opinion of Tyson, whom he would have known from his contributions to the Oxford

Philosophical Society in the 1680s.85 In a letter to Tyson published in the Philosophical

Transactions, Wallis describes himself as an outsider in anatomy and medicine, but not a novice.

Although he might seem like an “interloper,” Wallis explains, he eagerly studied medicine and anatomy “as a piece of Natural Philosophy” as a student at Cambridge in the 1630s, and he was among the first students to defend Harvey’s theory of circulation “when it was but a New

Doctrine.”86 Wallis, then, was conversant in anatomy and felt qualified to take part in this debate, but he wrote to Tyson to ensure that he was not out of his depth.

According to Wallis’s recollection, Gassendi argued that it was “not (originally) Natural for Man to feed on Flesh,” but people had gradually become accustomed to meat by eating it since the time of Noah’s Flood.87 Wallis begins his assessment of this argument where he is most comfortable, that is, with biblical history. According to Wallis, Gassendi echoes the opinion of

“many Divines” who believe that humans only began to eat meat after the Flood, since God told

Noah he could eat animals (Gen. 9:3) but only told Adam about that fruits and seeds that he could eat (Gen. 1:29). Wallis diverges from Gassendi’s interpretation of Genesis, citing biblical evidence

seventeenth-century coinage. 85 See ESO IV, 22-23, 97-98, 178. Wallis communicated with Tyson through Sloane, with whom Wallis also discussed the natural human diet, advancing essentially the same arguments. Tyson was evidently not as enthusiastic about the correspondence as Wallis was, since Wallis had to remind Sloane repeatedly that he had not received a reply to his initial letter. See British Library MS Sloane 4025, f. 318; Royal Society MS Early Letters W.2, ff. 70, 72; Royal Society MS LBC 12, ff. 422-423; Royal Society MS LBC 13, f. 59; Wellcome Institute MS 7633/1, f. 1. 86 John Wallis, “A Letter of Dr Wallis to Dr Tyson, concerning Mens Feeding of Flesh,” Phil Trans 22 (1700-1701): 769. Wallis also mentions his adoption of Harvey’s theory in his autobiographical letter, which was written a few years before his exchange with Tyson. See Scriba, “The Autobiography of John Wallis,” 29. 87 Wallis, “Letter to Tyson,” 770.

117 that humans ate meat before the Flood. Firstly, Cain and Abel are described (Gen. 4:2) as, respectively, “a Tiller of the Ground” and “a Keeper of Sheep.” If, as Wallis suspects, each of these is a reference to how they produced food, then Abel must have raised sheep for meat. Wallis anticipates the objection that Adam’s sons might only have raised animals so they could be sacrificed to God, but he argues that “even their Sacrifices seem to have been offered but as a

Portion (or First-fruits) of things appointed for Food.”88 In addition, Wallis doubts that God would have granted Noah greater dominion over living things than he gave Adam, and he suggests that

God mentioned meat to Noah only because in the next verse, God adds the condition that Noah and his offspring may only eat food once the blood has been drained from it.89 For Wallis, there is no indication in the Bible that it is immoral or unnatural for humans to consume meat.

Wallis recognizes, though, that biblical history can only supplement natural evidence on this issue. Setting aside the biblical record, he declares that, “without disputing it as a point of

Divinity,” he will now “consider it (with Gassendus) as a Question of Natural Philosophy, whether

[meat] be a proper Food for Man.” Next Wallis relates what he remembers from Gassendi’s evidence, beginning with the anatomy of human teeth: while carnivorous animals have teeth designed to cut through flesh, humans have mainly incisors and molars, “[a]s if Nature had rather furnished our Teeth, for Cutting Herbs, Roots, &c. and for bruising Grain, Nuts, and other hard

Fruits, than for Tearing Flesh.” In addition, Gassendi cites medical and anthropological evidence suggesting that humans are not naturally carnivorous. Unlike carnivores, humans have to cook meat before they can eat it, and even then “we forbid it to persons in a Fever, or other like distempers as of too hard digestion.” Finally, children prefer to eat “Fruits” until they become

88 Wallis, “Letter to Tyson,” 770. 89 Wallis, “Letter to Tyson,” 770-771.

118 accustomed to meat, and when they develop worms, the cause is said to be that meat was introduced into their diet too early.90

Wallis finds Gassendi’s argument “ingenious,”91 but he feels that it needs support from additional anatomical evidence. To this end he supplies his own novel observations about the human digestive system which, he argues, more closely resembles that of a herbivorous animal than a carnivorous one. According to Wallis’s research, herbivores such as pigs, sheep, and oxen have longer colons than carnivores such as dogs, foxes, and wolves. Furthermore, the herbivores have a pouch called a caecum at the “upper end” of the colon from which food is gradually passed into the intestines, whereas the caecum is absent in carnivores. Wallis explains that he is writing to Tyson, the famous comparative anatomist, to find out whether his findings can be generalized to other animal species. If so, Wallis suggests, this could hold the key to resolving the question of natural diet: the digestive system might be how Nature “inform[s] us, to what Animals Flesh is proper aliment, and to what it is not.”92

Wallis goes on to suggest that, according to his theory, the human digestive system looks exactly as one would expect in an animal that eats more meat as it grows older. He notes that the caecum in the human body is small and almost useless, but in a fetus the caecum is larger compared to the rest of the body. Wallis speculates that, as people grow and introduce meat into their diet, diverging from “what originally would be more natural,” the caecum grows more slowly than other body parts.93 Despite these observations, however, Wallis hesitates to conclude that humans are naturally herbivorous: humanity is an exceptional species, and comparative anatomy might not tell the whole story. The key difference is “Man’s being indu’d with Reason, [which]

90 Wallis, “Letter to Tyson,” 771. Italics in original. 91 Wallis, “Letter to Tyson,” 771. 92 Wallis, “Letter to Tyson,” 772. 93 Wallis, “Letter to Tyson,” 772.

119 doth supply the want of many things, which to other animals may be needful.” Unlike animals, humans do not need fur or feathers because reason allows them to make clothes; they do not need claws or horns because reason allows them to build weapons; and they do not need a digestive system or a set of teeth conducive to consuming raw meat because reason allows them to cook it.94 The exceptionalism of rational human beings allows Wallis to accommodate what he knows from biblical history, that humans have always eaten meat, with what he believes based on anatomical evidence, that humans are not natural meat-eaters.

Tyson’s reply to Wallis, written nearly a year later, appears as the next item in the

Philosophical Transactions. He appears to take Wallis’s theory seriously, admitting that he considers it more credible than Gassendi’s account based on the anatomy of teeth. However, Tyson doubts that Wallis’s findings regarding the colon can be generalized. On the matter of biblical history, he defers to the expertise of Wallis as a doctor of divinity: he accepts that people ate meat before the Flood. But for Tyson, unlike Wallis, this fact is consistent with the anatomical and anthropological evidence. Tyson notes that there have been practically no vegetarian civilizations in history. The only exception is the Pythagoreans, who believed that eating meat prevented the transmigration of souls, but this was only “a mistake in their Philosophy, and not a Law of

Nature.” Furthermore, Tyson joins Wallis and Gassendi in viewing the question of diet chiefly as a matter of natural philosophy, and he insists that human anatomy provides the strongest evidence.

He grants that Wallis took the right approach by focusing on the digestive system, which, being absent in plants, is the sine qua non of animal species. And, indeed, the human digestive system seems to resemble those of most herbivorous animals, so “it may seem reasonable to conclude, that Nature never designed him to live on Flesh; But that the Wantonness of his Appetite, and a

94 Wallis, “Letter to Tyson,” 772-773.

120 depraved custome, had inured him to it.”95

However, Tyson argues that additional anatomical evidence must be considered apart from the correlation between long colons and herbivorous diets. Considering the stomach in particular, he explains that, even among animal species that eat the same foods, there can be major anatomical differences in the anatomy of the digestive system. Indeed, the digestive systems of two species with different diets can be more similar to each other than two species with the same diet. Tyson points out that in digestion, as in other anatomical matters, Nature “shews her great Wisdom, in attaining the same end, different ways.”96 He also provides examples of animals that contradict

Wallis’s findings: the opossum has a colon and a caecum but eats birds, and the hedgehog has neither a colon nor a caecum but eats only plants. In addition, Tyson reaches a conclusion different from Gassendi’s about teeth, arguing that humans have teeth suited to eating both meat and vegetation. In fact, Tyson adds, his position is even supported by a biblical passage that Wallis referred to in his letter, Genesis 9:3, in which God permits Noah and his family to eat “[e]very moving thing” on the Earth (NSRV).97 In short, Wallis may have identified a rule that applies in most cases, but this, “as all other rules, may have some Exception.”98

In light of their respective arguments, it would be wrong to assume that Wallis the divine only took biblical evidence seriously, while Tyson the anatomist only took natural evidence seriously. Each of them is more comfortable writing in his own area of expertise, but each appreciates the evidence offered by the other. In fact, Tyson draws a connection between proper anatomy and proper theology when discussing Gassendi, who was well-known for trying to

95 Edward Tyson, “The Answer of Dr Tyson to the Foregoing Letter of Dr Wallis, concerning Man’s Feeding on Flesh,” Phil Trans 22 (1700-1701): 775-777. Italics in original. 96 Tyson, “Answer to Wallis,” 781. 97 Tyson, “Answer to Wallis,” 782. 98 Tyson, “Answer to Wallis,” 783.

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Christianize the atomic natural philosophy developed by Epicurus. Throughout the early modern period, Epicurean philosophy scandalized Christian readers with its account of an eternal and uncreated world in which bodies are formed by random collisions between atoms. In an effort to make atomism palatable to a Christian world, Gassendi reformulated Epicureanism to include the existence of God, incorporeal souls, and creation ex nihilo.99 In his letter to Wallis, Tyson expresses his approval of Gassendi’s opinion that body parts are designed to perform particular functions, in contrast to the Greek atomists who believed that the structures of bodies resulted from random chance. Indeed, for Tyson, the notion of design is what makes it possible to debate whether Nature intends for humans to eat meat. Thus, simply to discuss the natural human diet is to refute the dangerous views of “Unphilosophical Atheists” such as Epicurus.100

Evidently, Wallis carefully considered how to respond to Tyson’s letter. He wrote two unfinished drafts before settling on the version that was printed in the Philosophical

Transactions.101 Wallis accepts the anatomist’s conclusion that his observations about the digestive system cannot be generalized, and he agrees “[t]hat all Nations (as well before as since the Deluge) have used to feed on Flesh.”102 However, he still insists that the natural human diet is distinct from that of carnivorous animals. Unlike carnivores, humans can only digest cooked meat.

While it is natural for many animals to consume “Raw Flesh,” only meat that is “duly prepared” by cooking is “proper Food for Man.” And even cooked meat is not always healthy: it often satisfies “the Wantonness of the Palate, rather than the Health of the Body.”103 Furthermore,

99 See Margaret J. Osler, “Early Modern Uses of Hellenistic Philosophy: Gassendi’s Epicurean Project,” in Hellenistic and Early Modern Philosophy, ed. John Miller (Cambridge: Cambridge University Press, 2003), 30-44; Catherine Wilson, Epicureanism at the Origins of Modernity (Oxford: Clarendon Press, 2008), 24-27. 100 Tyson, “Answer to Wallis,” 776. 101 See Bodleian MS Add. D. 105, f. 121r. 102 John Wallis, “A Second Letter of Dr Wallis to Dr Tyson, on the Same Subject,” Phil Trans 22 (1700-1701): 784. 103 Wallis, “Second Letter to Tyson,” 784-785. Italics in original.

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Wallis notes, there remain outstanding anatomical questions: why does meat pass more slowly through the digestive system than vegetation, and why does a fetus have a larger caecum than an adult?104

By emphasizing the distinction between raw and cooked meat, Wallis ingeniously reconciles the facts of biblical history with the more ambiguous evidence provided by anatomy.

Rather than fit humanity into the conventional categories of “herbivorous” and “carnivorous,”

Wallis redefines these terms so that humans can be considered herbivorous even though they eat meat. In his first letter to Tyson, Wallis argues that humanity’s ability to cook and eat meat is a product of reason. But when reason exceeds what Nature intends, the results can be dangerous: immoderate consumption of meat is detrimental to one’s health. Throughout his career, Wallis treated the Bible as a repository of historical facts. However––as is evident from this case in particular––Wallis recognized that these facts require interpretation, and that the best interpretations are those that consider biblical history in conjunction with natural evidence.

Conclusion

From the above discussion, we can make two conclusions about Wallis’s use of the Bible as a historical source. Firstly, except in his explicitly theological works, Wallis only relies on biblical history when making an argument about nature or mathematical practice in the time shortly after creation. In his major works of mathematics and physics, including Arithmetica infinitorum

(1656) and Mechanica (1669-71), he does not feel compelled to support his arguments with biblical references. Even in his Treatise of Algebra, both Historical and Practical (1685), a work expressly intended to describe the historical development of mathematics, Wallis makes no

104 Wallis, “Second Letter to Tyson,” 785.

123 reference to biblical history. After all, his main concern in that text is to demonstrate how noteworthy Englishmen had advanced algebra in recent decades.105 It was only when he made an argument about nature or mathematics in the very remote past that Wallis needed to invoke biblical authority.

The second conclusion is that the integration of biblical history into natural philosophy and mathematics does not always commit Wallis to an intellectually conservative position. The

Bible may sometimes constrain Wallis’s thought, but at other it times inspires novel ideas. On the one hand, in Mathesis universalis, Wallis estimates the age of the Earth based solely on the Bible, and he promptly rejects theories that challenge such conventional biblical chronology. On the other hand, his reading of Scripture leads him to make original observations about the mathematical knowledge of humanity’s first generations. When writing on fossils as president of the Oxford Philosophical Society, Wallis objects to Hooke’s theory––which at least superficially resembles the theories of modern geology––largely because of biblical evidence. In doing so, however, he implicitly aligns himself with the proponents of chymistry, which was one of the fastest-growing areas of natural philosophy. Finally, in one of the last episodes of his intellectual career, Wallis struggles to reconcile biblical history with what he believes is compelling evidence that humans are naturally herbivorous. His solution is to question the conventional dietary classifications of “herbivorous” and “carnivorous” and to suggest that only a more nuanced classification can accommodate an exceptional and rational species like humanity.

A tension between tradition and innovation is typical of Wallis, as well as many other prominent figures in the intellectual world of the seventeenth century.106 This tension is an

105 On the English bias in the Treatise of Algebra, see Stedall, “Of Our Own Nation,” 73-122. 106 For example, Katherine Hill has identified the traditional elements in Wallis’s philosophy of mathematics that balance out his innovative algebraic methods. See Katherine Hill, “Neither Ancient or Modern: Wallis and Barrow on the Composition of Continua. Part One: Mathematical Styles and the Composition of Continua,” Notes and

124 important feature of the moments in Wallis’s career when “science” and “religion” meet. Against

Hobbes, Wallis defends experimental philosophy and the novel algebraic techniques that he applies to the quadrature of curves in Arithmetica infinitorum.107 Yet he chastises Hobbes for breaking with tradition, not only in biblical history, but also in mathematics. Hobbes developed a materialist philosophy of mathematics that allowed no difference between abstract and physical bodies. This was a challenge to the traditional distinction between pure and applied mathematics that Wallis could not tolerate.108 Only certain deviations from tradition were appropriate, and we see Wallis trying to articulate the appropriate boundaries for innovation in the above cases. He also disagreed with colleagues such as Hooke, Halley, and Tyson about where to draw the line, but less dramatically than he did with Hobbes.

In his use of biblical history, as elsewhere, Wallis is totally committed neither to tradition nor to innovation. From our perspective in the twenty-first century, we might assume that the

Bible is a strictly conservative influence, but we have seen that this was not the case in Wallis’s time. On the contrary, Harrison describes biblical history chiefly as a stimulus for new ideas, an aspect of the literalist biblical hermeneutics that contributed to the development of modern science. But the case of Wallis suggests that this, too, is an incomplete account of how biblical history interacts with natural evidence in the seventeenth century. For the Savilian Professor, biblical history is a means of mediating between the traditional and the novel. Part of the process by which he evaluates new ideas is to consider whether they are “unagreeing with Holy Story.”

By no means should we conclude that early modern figures can be classified as either “pro-

Records of the Royal Society of London 50 (1996): 165-178; idem, “Neither Ancient nor Modern: Wallis and Barrow on the Composition of Continua. Part Two: The Seventeenth-Century Context: The Struggle between Ancient and Modern,” Notes and Records of the Royal Society of London 51 (1997): 13-22. For further discussion of the relationship between tradition and innovation in the early modern period, see n. 16 above. 107 This will discussed further in Chapter 6 below. 108 On this aspect of the Hobbes-Wallis conflict see Jesseph, Squaring the Circle, 131-188.

125 science” or “pro-religion” on the basis of their attitude toward the scientific content of Scripture.

Rather, Wallis shows us that an individual can adopt an attitude of ambivalence toward novel ideas about the natural world, and can introduce biblical evidence either to support or to oppose such innovations.

Of course, biblical history is not the only criterion by which Wallis judges a novel theory in natural philosophy. Regarding Hooke’s theory, for instance, he argues not only that it requires a major revision of biblical history, but also that it diverges from centuries’ worth of observations collected by astronomers and geographers. Yet Wallis is also concerned about specious objections that could hold back useful innovations. In his letter on Leibniz’s Hypothesis physica nova, Wallis notes that many people opposed the Copernican hypothesis until “reason finally . . . prevailed over authority,” and he reminds Oldenburg that commentators are rarely objective about new ideas in natural philosophy. It is no wonder, then, that, in the historical investigations described above,

Wallis relies on the Bible, which he considers more trustworthy and impartial than any other source. When he defends the truth of Scripture against Hobbes, what is at stake is (among other things) a uniquely valuable source of historical, natural, and mathematical knowledge. For Wallis, the great advantage of the Bible as a historical source is that, as long as everyone accepts its authority, its facts are immune to the quibbles and historical revisionism that inevitably accompany the works of human authors.

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Chapter 5: John Wallis and the Catholics: Confessional and Theological Antagonism in Wallis’s Mathematics and Philosophy

As a minister whose career spanned most of the seventeenth century, John Wallis faced the difficult task of remaining in favour with a Church of England whose theology and ecclesiology changed with every new political regime. Fortunately, when writing on religious matters, Wallis could rely on one uncomplicated fact: Protestantism in England was under constant threat from the Catholic Church, especially the pope and the Jesuits. Regardless of the rising and falling fortunes of Puritans, High Anglicans, Presbyterians, and Episcopalians throughout Wallis’s lifetime, English Protestants of all stripes shared a hostility toward the pope, the Jesuits, and

Catholic doctrines such as transubstantiation. This chapter considers how Wallis’s participation in the anti-Catholic culture of early modern England affected his thought, not only in theology, but also in mathematics and philosophy. I will argue that, in many cases, Wallis’s judgement of mathematical and philosophical ideas was swayed by whether they might help or hinder Catholic interests. These episodes from Wallis’s career will help to explain what it meant for Wallis and his fellow experimental philosophers to study nature and mathematics from within an anti-Catholic society, including how it affected their attitude toward such prominent continental thinkers as

René Descartes.

It is almost trivial to state that early modern England was predominantly anti-Catholic.

Recent studies, however, have added depth and nuance to this claim by describing particular kinds of anti-Catholic discourse that changed according to political and intellectual developments in the period, and varied according to genre.1 Yet few scholars have addressed the role of anti-Catholic

1 On the various forms and uses of anti-Catholic rhetoric in early modern England, see Peter Hinds, “The Horrid Popish Plot”: Roger L’Estrange and the Circulation of Political Discourse in Late Seventeenth-Century London (Oxford: Oxford University Press for the British Academy, 2010); Ema Vyroubalová, “Catholic and Puritan

127 sentiment in the history of science in early modern England.2 As John Hedley Brooke has observed, religious commitments sometimes play a “selective role” when a natural philosopher or scientist chooses one theory over another.3 Brooke notes several cases when historical figures have adopted physical and astronomical theories that cohere with their theology. This chapter focuses on an aspect of religion’s selective role that Brooke does not emphasize. For Wallis, scientific ideas are appealing not only when they resonate with his own theological commitments, but also when they somehow thwart Catholic interests or give the Church of England an advantage over its rivals, especially the Church of Rome. The case of Wallis suggests that the selective role of religion in the history of science––at least in early modern England––should be considered within the context of the mutual antipathy of Catholics and Protestants, as well as the many political and nationalistic aspects of that relationship.

This chapter identifies two ways in which Wallis’s anti-Catholic attitude affects his reception of ideas about nature and mathematics. First, he is inclined to reject ideas that he considers to support Catholic interests. For instance, Wallis rejects a theory about the metaphysics

Conspiracies in Samuel Ward’s The Double Deliverance (1621),” in Puritans and Catholics in the Trans-Atlantic World 1600-1800, eds. Crawford Gribben and Scott Spurlock (New York: Palgrave Macmillan, 2016), 47-65; and the contributions to Arthur F. Marotti, ed., Catholicism and Anti-Catholicism in Early Modern English Texts (New York: St. Martin’s Press, 1999). 2 As an exception, several historians have discussed the anti-Catholic element in English writers’ responses to the Galileo affair. As Mordechai Feingold puts it, “the very fact that the Catholic church chose to publicly censure Galileo and the new astronomy made the English more amenable toward it” (Mordechai Feingold, “Galileo in England: The First Phase,” in Novità celesti e crisi del sapere: atti del Convegno internazionale di studi galileiani, ed. P. Galluzzi [Florence: Giunti Barbèra, 1984], 419). Lawrence Principe claims that the response to the Galileo affair marks the beginning of the long-standing assumption in the English-speaking world that the Catholic Church has historically obstructed the development of science (Lawrence M. Principe, “Myth 11: That Catholics Did Not Contribute to the Scientific Revolution,” in Galileo Goes to Jail and Other Myths about Science and Religion [Cambridge, MA: Harvard University Press, 2009], 100; see also Maurice A. Finocchiaro, Defending Copernicus and Galileo: Critical Reasoning in the Two Affairs [Dordrecht: Springer, 2010], 167-168, 307-309). For a study of scientific cooperation that crossed international and confessional lines in a slightly later period, and the difficulties it faced, see Lorraine Daston, “The Ideal and Reality of the Republic of Letters in the Enlightenment,” Science in Context 4 (1991), 367- 386. 3 John Hedley Brooke, Science and Religion: Some Historical Perspectives (Cambridge: Cambridge University Press, 1991), 28. Italics in original.

128 of time and place that seems to support to the Catholic doctrine of transubstantiation (as well as the Lutheran doctrine of consubstantiation). Secondly, Wallis is evidently more receptive to subjects that normally do not interest him––namely, numerology and biblical prophecy––when they are used to support the claim that the pope is the Antichrist.

On the other hand, despite the prominence of anti-Catholicism in Wallis’s thought, he values the work of certain Catholic scholars highly. Jason Rampelt has shown that Wallis incorporated the metaphysical distinctions described by Francisco Suárez, a Spanish Jesuit, into his epistemology.4 Furthermore, in mathematics and physics, Wallis praised the contributions of

Galileo, Cavalieri, Torricelli, and Viviani, all Italian Catholics.5 In fact, each of these scholars was either a member of a religious order or was educated by one at some point in his life. As Anthony

Milton argues in his essay on the limits of English anti-Catholicism in this period, English thinkers could not help but absorb some elements of Catholic thought despite the ubiquity of anti-Catholic rhetoric. Milton’s claim that “English people did not suffer from a simple allergic reaction to all things popish” applies to Wallis perhaps more than he would have liked to admit.6 Nevertheless,

I contend that the Catholic figures noted here represent the relatively few cases when, in Wallis’s assessment, the benefits of a Catholic writer’s ideas outweigh the risk of papist intrusions into

English intellectual culture. Most of the time, Wallis’s receptivity to ideas correlates with their

4 Jason Michael Rampelt, “Distinctions of Reason and Reasonable Distinctions: The Academic Life of John Wallis (1616-1703)” (unpublished Ph.D. thesis, Cambridge University, 2005), passim. 5 For instance, Wallis praises each of these Italian scholars as “great men” (magni viri) in a letter to Viviani written in 1693/4 (Bodleian MS Savile J 2, f. 2). In his algebraic work, Wallis was particularly indebted to Cavalieri and Torricelli, who developed the method of indivisibles, and he acknowledged their influence. See Amir Alexander, Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World (New York: Scientific American / Farrar, Straus and Giroux, 2014), 258-288; Philip Beeley, “Infinity, Infinitesimals, and the Reform of Cavalieri: John Wallis and His Critics,” in Infinitesimal Difference: Controversies between Leibniz and his Contemporaries, eds. Ursula Goldenbaum and Douglas M. Jesseph, (Berlin: De Gruyter, 2008), 31–52. 6 Anthony Milton, “A Qualified Intolerance: The Limits and Ambiguities of Early Stuart Anti-Catholicism” in Marotti, Catholicism and Anti-Catholicism, 85-115. The quotation is from 86. Milton identifies Suárez as an example of a Catholic scholar whose works enjoyed a particularly favourable reception in early modern England (Milton, “A Qualified Intolerance,” 91-92).

129 potential to challenge Catholic interests.7

I will substantiate this claim by drawing attention to the impact of anti-Catholic sentiment on Wallis’s works that seem to have little to do with theology. In the first section below, I will describe the extent of Wallis’s anti-Catholicism compared to his opinions of other people that he viewed with suspicion, such as Turks and heathens. This section will also address the well-known case of Wallis’s resistance to the adoption of the Gregorian calendar in England. In the next section, the first of three in-depth case studies, I will show that the debate on calendar reform was not a unique episode in Wallis’s career. Indeed, we will see that Wallis had been resisting ideas that might subtly support a Catholic agenda since the time of his first publication, Truth Tried

(1643). In the second case study, I will consider how anti-Catholicism might have caused Wallis not only to reject certain ideas, but to embrace ones that otherwise did not seem to appeal to him.

This section will focus on his involvement in the publication of a Latin translation of Francis

Potter’s Interpretation of the Number 666. I argue that the attraction to this text for Wallis was most likely its fiercely anti-Catholic argument that the pope was the Antichrist. Finally, I will revisit Wallis’s well-known animosity toward Descartes, whose algebra he maligns as derivative

7 A note about terminology is needed here. Throughout this chapter I refer to “anti-Catholicism” to encompass Wallis’s antipathy toward the Roman Church. However, certain factors complicate the notions of Catholicism and anti-Catholicism in the context of seventeenth-century England. First, the identification of the Roman Church as “Catholic” is anachronistic. When seventeenth-century English Protestants referred to the “Catholic church,” they generally meant the entirety of their own Church. When they meant to describe what today we would call Roman Catholicism, they typically used words like “papist” and “popery.” In addition, much of Wallis’s animosity was directed not at the entire Roman Church, but in particular at the pope, as well as the Jesuits, who were viewed by many Protestants as the pope’s most dangerous agents and were frequently assigned blame for conspiracies such as the Gunpowder Treason (see Hinds, The Horrid Popish Plot, 168-197; John Kenyon, The Popish Plot [London: Heinemann, 1972], 1-13; Jonathan Scott, England’s Troubles: Seventeenth-Century Political Instability in European Context [Cambridge: Cambridge University Press, 2000], 185-186). At times, then, Wallis’s attitude is more anti- papist than anti-Catholic (although his opposition of the doctrine of transubstantiation, discussed below, is an important exception). This distinction helps to explain why he could enjoy productive relationships with certain Catholic colleagues at the same time that he promoted the idea that the pope was the Antichrist. Despite these complications, it remains useful to refer to Wallis’s “anti-Catholicism,” with due caution, as a way to describe his wariness of several different elements of the Roman Church.

130 and plagiarized.8 I suggest that Wallis’s attacks on Descartes’ mathematics were motivated in part by theological and confessional differences, not merely nationalistic rivalry as has been assumed.9

Dissenters, Heathens, Catholics, Turks: Wallis and the rivals to the Church of

England

As a Presbyterian compelled to conform to the Anglican Church after the Restoration, Wallis had to be careful about whom he criticized outside of his own confession. Catholics, however, were a safe target, and Wallis seems genuinely to have believed that they posed a greater threat to the

Church of England than Episcopalians or even non-Christians. Wallis was not one of the true firebrand Puritans of seventeenth-century England. For instance, he claims in his autobiographical letter of 1696/7 that Presbyterians should not be understood as entirely opposed to episcopacy.10

8 Although I have used the word “plagiarized” here, it should be noted that contemporaries would almost certainly not have used this word in reference to Descartes stealing material from the English mathematician, Thomas Harriot, as alleged by Wallis. According to the Oxford English Dictionary, the noun “plagiarism” and the verb “plagiarize” were rare in the seventeenth century, but the related word “plagiary,” which could refer either to the act of unacknowledged literary borrowing or the person who committed it, was widely used. Linguistic differences notwithstanding, all sorts of early modern writers were concerned about plagiarism. See Hall Bjørnstad, ed., Borrowed Feathers: Plagiarism and the Limits of Imitation in Early Modern Europe (Oslo: Unipub, 2008); Paulina Kewes, ed., Plagiarism in Early Modern England (New York: Palgrave Macmillan, 2003); Laura J. Rosenthal, Playwrights and Plagiarists in Early Modern England: Gender, Authorship, Literary Property (Ithaca: Cornell University Press, 1996). 9 This chapter builds on the findings of Jacqueline Stedall in her article, “John Wallis and the French,” which describes the gradual development of Wallis’s antipathy toward French mathematicians over the course of his career. Beginning with Gilles de Roberval’s accusation that Wallis’s had committed plagiarism in his Arithmetica infinitorum (1656), Wallis had a series of unpleasant exchanges with French mathematicians including Pierre de Fermat, Blaise Pascal, and François Dulaurens. These disputes, which carried strong nationalistic overtones, led Wallis to despise French mathematicians in general. This includes Descartes, whom he rather unfairly charged with plagiarizing the works of the English mathematician Thomas Harriot (Jacqueline Stedall, “John Wallis and the French: His Quarrels with Fermat, Pascal, Dulaurens and Descartes,” Historia Mathematica 39 [2012]: 265-279). Stedall is right to point to Wallis’s nationalistic motivations in his disputes with French mathematicians. What I would like to emphasize here, however, is Wallis’s general anti-Catholic attitude, of which his distaste for the French might be merely one particular manifestation. For Wallis, the danger of Catholic intrusions into England was at least as great a threat as the possibility that England would lose ground to France in mathematics. 10 Reflecting on the Westminster Assembly nearly a half-century after it dissolved, Wallis claimed that the Presbyterians at the Assembly were not “Anti-Episcopal” but rather “Anti-Independent,” meaning they opposed those who rejected a central church government altogether (see Christoph Scriba, “The Autobiography of John Wallis, F.R.S.,” Notes and Records of the Royal Society of London 25 [1970]: 34-35; the quotations are from 35; italics in original). That being said, it is possible that by 1697 Wallis simply hoped to downplay his erstwhile connections to

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And in a letter of 1700 to George Keith, a former Quaker who had enthusiastically joined the

Anglican clergy earlier that year, Wallis urges toleration of dissenters. He explains to Keith that dissenters are not really so different from those ministers who conform to the Anglican Church and its Book of Common Prayer:

. . . however, as to some of the particulars, they may be unsatisfied; yet they do not disclaim communion with the Church of England. They come to our Churches; they hear our sermons; they join occasionally in our Publike Prayers; they be Orthodox in Doctrine; they do not renounce our Baptism; they do not disclaim our communion at the Lords Table . . . they [do] not disclaim our Ministers, as not lawfull Ministers of the Word of God.11

Presumably Wallis made this argument partly out of self-interest––at that time Presbyterians were considered dissenters––but this is consistent with his generally latitudinarian attitude.

Elsewhere, Wallis admitted that even heathens might not be entirely irreligious. In his posthumously published sermons, he explains that some heathens who lived before Christ’s time had “the Spirit of God working in them” although they were not aware of it. Such heathens could even “tast[e] the powers of the world to come.”12 Heathens could achieve “a very great height of morality” with God guiding them via “the light of nature.”13 Some of them even seemed to have genuine knowledge about God, creation, immortal souls, and the afterlife.14 Wallis also notes that

the Puritans who had flourished during the Interregnum. 11 Most of this letter is printed in the preface to Wallis’s posthumous collection of sermons. See John Wallis, Sermons: Now First Printed from the Original Manuscripts of John Wallis, D. D., ed. W. Wallis (London, 1791), cix-cxiii. The quotation is from cx-cxi. Not included in this version, or the other printed version in The Gentleman’s Magazine from 1789, is Wallis’s derision of Quakers and Anabaptists at the end of the letter, which appears in the manuscript copy at the Bodleian Library. Referring to “Quakers and Anabaptists with other looser sects,” Wallis notes that Keith seems to be “sufficiently convinced” of their “Errors” (Bodleian MS Add. D. 105, f. 118r; cf. John Wallis, “Liberal Letter of Dr. Wallis, Describing the Dissenters,” The Gentleman’s Magazine 59 [1789]: 294). In a private communication regarding her unpublished archival research, Louisiane Ferlier informed me that Wallis was a committed opponent of the Quakers; after he received some anti-Quaker tracts from Keith, Wallis had them bound and donated them to the Bodleian Library. 12 Wallis, Sermons, 55. 13 Wallis, Sermons, 359. 14 Wallis suggests, however, that the heathens must have learned of these things through contact with the ancient Jews. He writes, “it doth not appear by what means they could come by it without some ancient tradition of divine revelation, handed down by their forefathers” (Wallis, Sermons, 255-256; the quotation is from 256).

132 because salvation is a gift freely given, “it signifies not whether we are of this, or of that religion, as to salvation.” Thus even a “man in a wilderness” who has never been “a member of the visible church” can be saved if God decides to bestow grace on him.15 As we will see below in the section on Descartes, Wallis was not always so charitable toward heathens who stumbled upon knowledge of God without revelation, but clearly he did not think it was impossible that some of them might be saved.

If dissenters and heathens were no real threat to the Church of England, Roman Catholics were another matter entirely. For Wallis, as for many of his countrymen, Catholics were not

Christians. He makes this distinction in his Defense of Infant-Baptism as he explains, “The Child of a Jew is reputed a Jew; of a Christian, a Christian; of a Heathen, a Heathen; of a Papist, a Papist; and so of others.”16 Anything “popish,” “papist,” or “Romish” might represent a threat to

Protestantism. Indeed, in a letter to his friend Thomas Smith written in 1698, Wallis notes that not even the Turks were as great a threat to true Christianity as the papists:

I concur with you in condoling the hardship of the Greek Church under the Turkish oppression. And heartyly [sic] wish them a more happy condition. But if they should change the Turkish slavery for that of the Romish, I doubt [i.e., suspect] they would change for the worse. For, certainly, the Protestants in Hungary, are in much worse circumstances, under the Christian Emperor, than they were under the Turkish. And like oppressions there are in Poland, France & elsewhere, especially where the Jesuites rule.17

15 Wallis, Sermons, 216-218. 16 John Wallis, A Defense of Infant-Baptism. In Answer to a Letter (here Recited) from an Anti-Pædo-Baptist (Oxford, 1697), 13. 17 Bodleian MS Smith 54, p. 55. Wallis was not the only Protestant to claim that Catholic rule would be worse than Turkish rule. For instance, Martin Szentiványi, a Slovak Jesuit, relayed a story of a Calvinist town under attack by the Turks in 1660, whose inhabitants rejected support from the Catholic Habsburgs because they “prefer to hear the Turkish Halla rather than the Catholic Hallelujah” (se malle Varadini audire Turcicum Halla, quam Catholicum Alleluja; Martin Szentiványi, Consulatio saluberrima de reducenda stabili ac constanti tranquillitate & pace in Hungaria, per ejusdem adductionem in Unitatem Fidei ac Religionis [Trnava, 1704], 5-6). Many thanks to Svorad Zavarsky for informing me about this source. See also Wallis’s letter to Daniel Finch, the Earl of Nottingham, of 2 November 1689, wherein he expresses his concern about the possibility that the Princess of Hanover will marry a papist (Bodleian MS Add. D 105, f. 88r). Wallis had learned of Louis XIV’s plan to arrange this marriage from a letter he had decoded for Finch (British Library MS 32499, f. 55v).

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Here we see Wallis expressing typical English anti-Catholic sentiments, including the reference to the Jesuits. He was also typical in explicitly rejecting the doctrine of transubstantiation. In a letter to Arthur Charlett of 1696 he noted with approval that, since the Test Act had been passed in 1673, anyone entering the clergy or taking up a university position in England had to subscribe to a declaration against transubstantiation. To Wallis this seemed to be an effective means of keeping Catholics out of positions of influence.18

The main question addressed in this chapter is how Wallis’s strong anti-Catholic sentiments affect his judgement of ideas about mathematics and philosophy. One important case, which has been discussed in depth by other historians, is his opposition to the Gregorian calendar reform.19 In 1699, Wallis weighed in on a debate about whether England should adopt the

Gregorian calendar in order to correct the length of the year. The Julian calendar, developed in ancient Rome, slightly miscalculated the length of the year, and as a result it had drifted eleven days from the astronomical calendar by the close of the seventeenth century. This created major problems for the dating of Easter which involves precise astronomical observations and calculations. The reform sponsored by Pope Gregory XIII and adopted by Catholic Europe in

1582 corrected this error and ensured that the dating of Easter remained accurate.

While Protestant nations across Europe prepared to adopt the Gregorian calendar in 1700,

Wallis strove to ensure that England would not join them. As he wrote to the Archbishop of

Canterbury, Wallis felt that assenting to the calendar reform would constitute “a kind of tacit submission to the Pope’s Supremacy, or owning his Authority.”20 In letters to the archbishop, the

18 Bodleian MS Ballard 24, f. 3r. 19 For discussions of the anti-Catholicism in Wallis’s opposition to the Gregorian calendar, see Philip Beeley and Siegmund Probst, “John Wallis (1616-1703): Mathematician and Divine,” in Mathematics and the Divine: A Historical Study, eds. T. Koestier and L. Bergmans (Amsterdam: Elsevier, 2005), 453-457; Robert Poole, Time’s Alteration: Calendar Reform in Early Modern England (London: UCL Press, 1998), 86-87. 20 John Wallis, “An Extract of Two Letters, from Dr. John Wallis, (Professor of Geometry in Oxford.) The One to His

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Secretary of the Royal Society, and other prominent members of his society, Wallis opposed the

Gregorian reform, partly because he viewed it as unnecessary and potentially confusing, and partly because the new calendar represented “a latent Popish interest” in England’s ecclesiastical affairs.21 Wallis advises the archbishop that England could correct the dating of Easter according to astronomical data without adopting the Gregorian system. In any case, he notes, the annual observance of Easter as a “solemn commemoration of Christ’s resurrection” is more important than the precise date.22 Robert Poole notes that Wallis’s letter to the archbishop, which was printed in the Royal Society’s Philosophical Transactions, swayed many readers and helped to tip the scales against the Gregorian reform. As it turned out, England did not adopt the new calendar until

1752.23

The literature on Wallis’s opposition to the Gregorian calendar has paid little attention to his more general anti-Catholic attitude. But the case studies below will show that this well-known episode was not unique in Wallis’s career. Indeed, his letters on calendar reform, written at the end of his career, adopt the same anti-Catholic tone that characterizes his earliest publication, a philosophical treatise entitled Truth Tried. As I will discuss in the next section, in this text Wallis argues for a metaphysics of time and place that explicitly leaves no room for the Catholic doctrine of transubstantiation. Truth Tried and the calendar debate bookend a career in which Wallis strove

Grace the Lord Arch-Bishop of Canterbury. The Other to the Lord Bishop of Worcester,” Phil Trans 21 (1699): 345. 21 Wallis, “Extract of Two Letter,” 345. Wallis’s letters to Hans Sloane, Secretary of the Royal Society, on calendar reform are found in Royal Society Early Letters MS W.2, nos. 66, 74, 84. 22 Wallis, “Extract of Two Letters,” 345-346. Here Wallis echoes a position, articulated by English opponents of calendar reform as early as the Elizabethan period, that Easter was among the “things indifferent” which, as Poole explains, “were to be treated as commemorations rather than reenactments of sacred events.” This doctrine applied to other festivals such as Christmas, as well as the communion. According to this argument, the Nicene Council had not been concerned with identifying the “true” date for festivals when it established rules of the dating of Easter; the council’s concern was only to ensure that Easter did not fall on the same date as the Jewish observance of Passover. By the time Wallis expressed this view in 1699, it would have been familiar to readers well-versed in the issue of calendar reform (Poole, Time’s Alteration, 42). 23 Poole, Time’s Alteration, 88-89.

135 to defend English intellectual culture from hidden Catholic agendas.24

The metaphysics of the Eucharist in Truth Tried

Wallis’s Truth Tried was printed in 1643, before the start of his mathematical career. At that time, he was working as a chaplain for the Darleys, a noble Puritan family in Yorkshire.25 Henry Darley enlisted his chaplain to provide a commentary on a book by his friend Robert Greville, 2nd Baron

Brooke, a Parliamentarian general in the Civil War with an interest in philosophy and theology.

Greville’s Nature of Truth (1641), a muddled metaphysical treatise apparently inspired by his reading of biblical prophecy and Neoplatonic philosophy, attempts to obviate philosophical and theological debates by appealing to a vague notion of “unity.” Greville claims that, since God is the source of everything in Creation, many things that we consider distinct are really identical, and many things that we consider different in kind are only different in degree. Nature is characterized by a unity that reflects its Creator. Thus, for example, “the Understanding, the Soul,

Light, [and] Truth” are all one, so philosophers have no need to argue over their precise definitions.26 Similarly, natural phenomena such as gravity and magnetism are to be explained simply in terms of objects seeking “to improve their unity by mutuall imbraces.”27 For Greville, recognizing the unity in nature is enough to reconcile the philosophies of Aristotle, Plato, Hermes

24 Although Wallis consistently adopts an anti-Catholic attitude, it should be noted that he sought to keep his fellow Protestants honest about what Catholics actually did and believed. A good example is found in the Bodleian Library’s copy of a book claiming on the title page to be the Spanish Inquisition’s Index of Prohibited Books (Bernardo de Sandoval y Rojas, Index librorum prohibitorum et expurgatorum ill.mi ac r.mi D. D. Bernardi de Sandoval et Roxas [Madrid, 1612-1614]). In a marginal note, Wallis confirms that, when he learned that the book appeared to be a counterfeit produced by Calvinists in Geneva, he recommended that it be removed from the Bodleian’s collection of theological books. The shelf mark of this book is 4º V 46 Th. Thanks to Louisiane Ferlier for informing me about this source. 25 On Wallis’s service to the Darley family, see Rampelt, “Distinctions of Reason,” 47-49. 26 Robert Greville, The Nature of Truth: Its Union and Unity with the Soule, Which is One in its Essence, Faculties, Acts; One with Truth (London, 1641), 22. 27 Greville, Nature of Truth, 32, 39. The quotation is from 39.

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Trismegistus, and the moderns, and to align each of them with Scripture.28 “Unity,” Greville argues, can instantly resolve the divisive issues that have fractured the intellectual community since antiquity.

Greville was killed in battle before Wallis’s response was ready for publication.

Nevertheless, Wallis had it printed under the title Truth Tried: or, Animadversions on a Treatise published by the Right Honorable Robert Lord Brook, Entituled, The Nature of Truth. Although he maintains a respectful tone toward his patron’s late friend, it soon becomes clear that Wallis is entirely unconvinced by Greville’s arguments. The philosophical debates that Greville had tried to dismiss with sweeping declarations about unity were ones that Wallis took seriously and on which he had expended considerable energy. One part of The Nature of Truth that particularly concerned Wallis was Greville’s attempt to subsume time and place under his conception of unity.

Greville argues that distinctions between times and places are only apparent, which is why philosophers’ efforts to define them turn out to be nothing but tautology and sophistry. In reality,

Greville claims, time and place exist in the way that God sees them: everything is coeternal and coincident.29

In Truth Tried, Wallis points out various problems with the metaphysics of time and place described in The Nature of Truth. Greville compares time and place with other things that, in his view, only appear to have distinct parts. For instance, a stream might contain many springs that seem distinct, but they are all part of the same stream.30 According to Wallis, all that Greville has shown with these similitudes is that different times and places exist on a continuum. This, Wallis explains, is not the same as unity: distinctions between points on a continuum are real, not merely

28 See Greville, Nature of Truth, especially 142-143. 29 Greville, Nature of Truth, 92-98. 30 Greville, Nature of Truth, 91. See also 90, 105.

137 apparent. He writes, “every Continuum, be it Magnitude, Distance, Time, Place, Duration,

Motion, Action, or whatever . . . [is] equally divisible in semper divisibilia.”31 Even though the points on a continuum are connected, they are still distinct. According to Wallis, Greville has confused connectedness between things with unity.

Wallis’s concern, however, is not only the weaknesses in Greville’s reasoning. In fact,

Wallis makes no effort to disguise his anti-Catholic (and anti-Lutheran) motivation. He explicitly argues that Greville’s theory is unacceptable because it would undermine common arguments against the Catholic doctrine of transubstantiation and the Lutheran doctrine of consubstantiation.

According to the doctrine of transubstantiation, the substances of the bread and wine of the

Eucharist are transformed into the substances of Christ’s body and blood. Consubstantiation, on the other hand, holds that the substances of the body and blood exist alongside the substances of the bread and wine: there is no transformation either of bread into Christ’s body or of wine into

Christ’s blood. Following Calvin, early modern Anglicans typically rejected both of these doctrines, insisting that Christ was spiritually present at the Eucharist but not physically present.32

According to Wallis, the Calvinists have the advantage of rejecting both doctrines as absurd. One objection to each of these doctrines is that many communions take place among many different congregations at one time. How could Christ’s body and blood be present at all of these communions simultaneously? And as for consubstantiation in particular, it is absurd to believe

31 John Wallis, Truth Tried: or, Animadversions on a Treatise published by the Right Honorable Robert Lord Brook, Entituled, The Nature of Truth, Its Union and Unity with the Soule. Which (Saith he) is One in its Essence, Faculties, Acts; One with Truth (London, 1643), 71. 32 On Calvinists’ rejection of transubstantiation and consubstantiation in early modern England, see Horton Davies, Worship and Theology in England: From Andrewes to Baxter and Fox, 1603-1690, vol. 1 (Princeton: Princeton University Press, 1970), 76-123; Eleanor McNess, “John Donne and the Anglican Doctrine of the Eucharist,” Texas Studies in Literature and Language 29 (1987): 95-96; Alec Ryrie, “The Strange Death of Lutheran England,” The Journal of Ecclesiastical History 53 (2002): 64-92. It should be noted that “consubstantiation” is a pejorative term used by Calvinists to refer to the Lutheran position; Lutherans rejected this label for their doctrine. See Gene Edward Veith, Jr., “The Religious Wars in George Herbert Criticism: Reinterpreting Seventeenth-Century Anglicanism,” George Herbert Journal 11 (1998): 30.

138 that two substances could exist in the same place at once. However, Wallis argues, the Calvinists would lose this advantage if there were no meaningful distinction between different times and places:

. . . I desire to know, wherein the strength of that argument consists, which is by us so often urged against Papists and Lutherans, concerning their Transubstantiation, and Consubstantiation; viz. How Christs body can be at the Same Time in Severall Places? For, that it might be successively in all these Places at severall Times, we deny not: Now, if at Severall Times it may be in divers Places; why may it not be so, at the Same Time, if Time and Place be Nothing? Againe, Severall Places at the same Time may contein severall Bodies (v. g. Bread, and Christs Body;) now why may not the Same place conteine them, if Place be nothing? Why not Together, as well as successively, if Time be nothing?33

If Greville were right, Christ’s body and blood could be in many places at once, and in the same place as other things, so the metaphysical objections to the Catholic and Lutheran theology of the

Eucharist lose their force. Thus, Wallis suggests, Greville’s theory is dangerous as well as wrong.

In fact, he notes in the conclusion to Truth Tried that Greville’s metaphysics not only permits but actually requires that the Catholics (and Lutherans) are right about the physical presence of

Christ’s body and blood:

. . . if difference of Time and Place be only imaginary; then why do we deny to the Papists, that Christs Body is corporeally present in the Sacrament? since if it be any where, it must be every where, all places being indeed the same, admitting onely of an imaginary difference.34

The body and blood would be physically present at the Eucharist because they are present everywhere and always. For Wallis, a metaphysics that includes real distinctions between times and places is required not only by reason, but also by theology.

We see here that Wallis jumps at the opportunity to defend a Calvinist position against both Catholic and Lutheran doctrine, but it is likely that the papists were his primary target. In the

33 Wallis, Truth Tried, 71. 34 Wallis, Truth Tried, 106.

139 quotation above from the end of Truth Tried, Wallis focuses on Catholics in particular.

Furthermore, appended to the text are three theses that Wallis defended while studying at

Cambridge in the 1630s. The third thesis (which he composed at Cambridge but did not defend publicly) seeks to demonstrate that Francisco Suárez, a Spanish Jesuit, had unwittingly developed a metaphysics that makes transubstantiation impossible.35 In addition, the anti-Catholic motivation of Truth Tried is supported by the fact that Greville himself tried to challenge the metaphysics of transubstantiation in The Nature of Truth. Protestants had long objected that transubstantiation seems to require that an accident can exist without its substance, since the accidents of bread and wine (their taste, appearance, texture, and so on) are still present after the substances have been transformed into Christ’s body and blood. Predictably, Greville argues that substances are not actually distinct from their accidents, so it is impossible for one to exist without the other.36 In Truth Tried, Wallis suggests that Greville’s goal of challenging the metaphysics of transubstantiation was admirable but ultimately counterproductive. Yet he seems to have appreciated Greville’s intentions. Although Greville had died, Wallis still used his first publication to show that a robust metaphysics could meet the demands of reason and anti-

Catholicism at once.

Anti-Catholic calculations: Wallis and the Interpretation of the Number 666

In both Truth Tried and the letters on calendar reform, Wallis made his anti-Catholic intentions obvious. He again involved himself in anti-Catholic polemics when he produced a Latin translation (1677) of Francis Potter’s Interpretation of the Number 666, a text on biblical prophecy

35 See Rampelt, “Distinctions of Reason,” 32, 36. 36 Greville, Nature of Truth, 164.

140 that uses mathematical calculations to show that the pope is the Antichrist.37 But in this case his motivation is less clear: Wallis initially concealed his involvement in the project before eventually mentioning it in the first volume of his Opera mathematica (1695). Potter, a cleric and Fellow of the Royal Society who was more than twenty years Wallis’s senior, published his Interpretation in 1642 amid a career otherwise focused on natural philosophy and medicine. The Interpretation found a receptive audience among Potter’s friends in the Hartlib circle, a group inclined toward millenarianism, and scholars interested in biblical prophecy continued to read and comment on

Potter’s work well into the eighteenth century.38 The first Latin translation of Potter’s

Interpretation was published in Basel in 1656 under the title Explicatio numeri bestiae DCLXVI.39

Just over two decades later, in the year before Potter’s death, Wallis had a new Latin translation published in Amsterdam with a more direct translation of the title: Interpretatio numeri 666.40

Wallis’s name appears nowhere in this publication.

The Interpretation focuses on Potter’s calculations involving two numbers that appear in

37 Francis Potter, An Interpretation of the Number 666: wherein, Not Onely the Manner, How This Number Ought to Be Interpreted, is Clearely Proved and Demonstrated: but It Is Also Shewed [That] This Number is an Exquisite and Perfect Character, Truly, Exactly, and Essentially Describing That State of Government to [Which] All Other Notes of Antichrist Doe Agree: with All Knowne Objections Solidly and Fully Answered [That] Can Be Materially Made against It (Oxford, 1642). 38 Potter’s text benefited from the support of Joseph Mede, one of the most influential writers on biblical exegesis in the period, who wrote a prefatory note to the Interpretation lauding Potter’s effort (Potter, Interpretation, sig. *1r). On Potter’s Interpretation and its contemporary readers, see Jed Z. Buchwald and Mordechai Feingold, Newton and the Origin of Civilization (Princeton: Princeton University Press, 2013), 137-138; Mordechai Feingold, “‘And Knowledge Shall Be Increased’: Millenarianism and the Advancement of Learning Revisited,” The Seventeenth Century 28 (2013): 367; Christopher Hill, Antichrist in the Seventeenth Century, revised ed. (London: Verso, 1990; orig. pub. 1971), 28; Charles Webster, The Great Instauration: Science, Medicine and Reform 1626-1660, 2nd ed. (Peter Lang: Oxford, 2002), 14, 33. On the book’s eighteenth-century readers, see Stephen J. Stein, “Cotton Mather and Jonathan Edwards on the Number of the Beast,” Proceedings of the American Antiquarian Society 84 (1974): 293-315. 39 Francis Potter, Explicatio numeri bestiae DCLXVI. Qua tum vera eius exponendi ratio ostenditur; tum Characteres exquisitissimi, quibus Antichristus, omnisque eius Hierarchia, advivum depingitur, perspicue solideque eruuntur, trans. J. S. B. [Johann Schönau] (Basel, 1656). 40 Francis Potter, Interpretatio numeri 666: quâ, tum modus unicus, quo numerus hic interpretandus est, perspicuè probatur et demonstratur; tum ostenditur, numerum hunc perfectum esse et accuratum characterem, quo verè, exactè et essentialiter, describitur status ille et regimen, cui reliquae omnes Antichristi notae conveniunt: simulque omnibus, hactenus notis, objectionibus, solidè et plenè respondetur, quae alicujus momenti in contrarium videantur, trans. [John Wallis] (Amsterdam, 1677).

141 the Book of Revelation: 666, the Number of the Beast, and 144, the measure of the number of cubits in the wall surrounding the New Jerusalem. These calculations are the basis of Potter’s elaborate argument that the pope is the Antichrist and that the entire history of the Catholic Church is tainted by the Antichrist’s influence. Potter’s position is typical of English texts discussing the

Antichrist in the first half of the seventeenth century. Puritans in particular emphasized the pope-

Antichrist identification, but it appears in works by all sorts of English Protestants, and there were precedents in the works of Martin Luther.41 As Christopher Hill has discussed, in England between the reign of Elizabeth I and the Civil War, the “orthodox” position was that the pope was the Antichrist. And among the most enthusiastic proponents of this claim were mathematicians who developed chronologies detailing the rise and fall of the Antichrist, and who performed calculations on the Number of the Beast in an effort to pinpoint its significance.42

Potter adopted these conventions with enthusiasm in his Interpretation. What makes his work distinctive, though, is its emphasis on square roots. According to Potter, just as the Number of the Beast represents the Antichrist––an identification accepted by most Protestants43––so the number 144 is “Gods number.”44 However, Potter argues, the reason that 144 represents Christ and 666 represents the Antichrist is their square roots. He notes numerous passages of Scripture wherein 12, the square root of 144, indicates holy things: “For there were 12 Tribes, not 144; and

12 gates in Jerusalem, not 144; and 12 Apostles, not 144.” The true number of God, then, is 12 rather than 144.45 Likewise, Potter argues, the true Number of the Beast is not 666 but its square

41 On Luther’s adoption of this position see David M. Whitford, “The Papal Antichrist: Martin Luther and the Underappreciated Influence of Lorenzo Valla,” Renaissance Quarterly 61 (2008): 26-52. 42 Hill, Antichrist in Seventeenth Century, 1-40. The quotation is from 34. On works by mathematicians that discuss the papal Antichrist see 25-29. 43 See Hill, Antichrist in the Seventeenth Century, 3-4. 44 Potter, Interpretation, 7. 45 Potter, Interpretation, 8.

142 root, which he claims is 25. This claim requires more rhetorical maneuvering than the identification of 12 as God’s number, since the square root of 666 is approximately 25.8 rather than 25 exactly. Potter claims that the symbolic importance of 666 lies in the greatest whole number contained in its square root. At the same time, though, the fractional square root of 666 corresponds to what the number represents: “as the number 666 is neither a square nor perfect number, nor built upon the number 12: so neither is the Romish Hierarchy a square and perfect building, neither is it built upon the doctrine of the 12 Apostles.”46 Potter proceeds to show that the number 25 can be found throughout the structure and history of the Catholic Church. The cardinals are a sort of anti-apostle, and as there were twelve apostles, so there were twenty-five members in the first College of Cardinals. Similar examples abound: “there were 25 Gates in

Rome according to the sense literall, & 25 Churches for Baptisme according to the sense spirituall, and 25 Pastors placed at these Churches, and 25 Cardinals sitting and ruling in them, and 25 Titles,

Tribes, or Parishes belonging to them.”47 In short, Potter builds an entire anti-Catholic apparatus on the foundation of his dubious calculation of the square of 666.48

Wallis’s Latin translation was printed in 1677, twenty-five years after the original publication of the Interpretation. Appended at the end of many copies of this translation is a much shorter Latin text entitled Alarm to All Protestant Princes. The Alarm was written in 1603 by

Francis Broccard, the secretary to Pope Clement VIII who defected to Protestantism. Broccard warns readers about the pope’s plot to infiltrate Europe’s Protestant lands with crypto-Catholic

46 Potter, Interpretation, 44. Italics in original. 47 Potter, Interpretation, 117. On the twenty-five members of the College of Cardinals see 97, 101. 48 Potter was aware that his method of biblical exegesis was unusual, and he acknowledges that square roots might seem to be “humane and heathenish inventions” unworthy of “such divine mysteries.” But he argues that God can convey knowledge to humanity by whatever means he wants, and what better means than mathematics, “by which so many, and so famous mysteryes have been, and dayly are revealed” (Potter, Interpretation, 45-46). Before moving on to his demonstration of the square root of 666, Potter notes that “Mathematicall learning [is] called wisedome [sic] in the Scriptures,” and in a marginal note he adds that Moses learned mathematics from the Egyptians (Potter, Interpretation, 64).

143 spies. Once in place, these papist agents will proceed to stir up conflicts among Protestants, all the while making preparations for invasion by a Catholic Holy League.49 Broccard’s Alarm was translated into English and published in 1679, complete with a preface wherein the translator blames the Civil War and the Popish Plot (which will be discussed below) on “Jesuitical

Counsels.” The translator also alerts his Protestant readership to “the present Popish Design, for killing our King, subverting our Government, murdering his People, destroying the Protestant

Religion, and introducing Popery amongst us.”50 Some evidence suggests that it was Wallis himself who translated Broccard’s Alarm into English, which would also make him the author of this strongly anti-Catholic introduction.51 In any case, the translator’s preface of Potter’s

Interpretation removes all doubt that the work was intended as an anti-Catholic polemic.

Still, we can only speculate on what exactly convinced Wallis to translate Potter’s

Interpretation into Latin and to pair it with Broccard’s Alarm. This was one of few occasions on which Wallis did not advertise one of his publications, and the circumstances surrounding his involvement are mysterious. Although Wallis’s name does not appear in the published text, he mentioned it seventeen years later in his Opera mathematica. The Interpretation appears at the end of the table of contents where Wallis lists his works that will not be included in the Opera.

49 Francis Broccard, His Alarm to All Protestant Princes. With a Discovery of Popish Plots and Conspiracies, After his Conversion from Popery to the Protestant Religion (London, 1679). 50 Broccard, Alarm to All Protestant Princes, ii. 51 In his Athenæ Oxonienses, Anthony à Wood identifies Wallis as the translator of Broccard’s Alarm. However, this appears in his entry on the ejected minister Thomas Gilbert, whom Wood claims to be the translator of Potter’s Interpretation rather than Wallis (Anthony à Wood, Athenæ Oxonienses: An Exact History of All the Writers and Bishops Who Have Had Their Education in the University of Oxford: to Which Are Added the Fasti, or Annals of the Said University, vol. 4, ed. Philip Bliss [London, 1820], 408). As noted below, Wood makes this same attribution in his entry on Potter. Wood appears to be mistaken here, so his attribution of the Broccard translation to Wallis seems unreliable, and I am aware of no other source that identifies Wallis as the translator of Broccard’s Alarm. Furthermore, Wallis does not include the English translation of the Alarm on the list of his works in his Opera mathematica, whereas he does include the Latin translation of the Interpretation. The translator of the Alarm does notes that he based the translation on the 1677 printing of Broccard’s Alarm, that is, the text appended to Wallis’s translation of Potter (Broccard, Alarm to All Protestant Princes, ii). Perhaps when Wallis was sent a copy of his translation of the Interpretation, he found the Alarm appended to it and decided to translate the latter text as well. Many thanks to Jason Rampelt for drawing my attention to this information.

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The list is divided into mathematical and theological works; Wallis identifies the Interpretation as mathematical.52 The Opera contain no other indication of Wallis’s thoughts on Potter’s

Interpretation or his involvement in the translation. Nor does it seem that his contemporaries knew he had produced the translation. Anthony à Wood, an Oxford antiquarian and an enemy of

Wallis, either did not know that the Savilian Professor had translated the Interpretation or chose to exclude it from the biography of Potter that he included in his Athenae Oxonienses. Instead,

Wood attributes the 1677 translation to Thomas Gilbert, a Presbyterian minister who was ejected from his living in Oxford after the Restoration.53 Furthermore, in the nineteen English and Latin copies of the Interpretation that I examined in various archives in Oxford, not a single reader has left any indication that they knew Wallis (or Gilbert, for that matter) was the translator.

There is no surviving correspondence between Wallis and Potter, and no references to

Potter in Wallis’s texts that would shed light on the Savilian Professor’s decision to translate the

Interpretation.54 This is surprising, not least because Potter experimented on blood transfusion, a procedure that was the subject of an intense priority dispute during the 1660s; Wallis wrote in defense of England’s claim to priority but did not mention Potter.55 Certainly, the two men ran in

52 OM I, sig. b4r-b4v. 53 Wood, Athenæ Oxonienses, vol. 3, 1156. Wood had inquired about Potter’s Interpretation in 1663, asking his friend John Aubrey to write to John Pell for information about any translations of the text. This, of course, was long before the publication of Wallis’s translation. In addition, Wood died less than a year after the first volume of Wallis’s Opera was published, so it is somewhat unlikely that he would have learned about it there. See British Library Add. MS 4365, f. 34r, 41r. Wood’s animosity toward Wallis stems from the Savilian Professor restricting his access to materials in the university archives. See Rampelt, “Distinctions of Reason,” 19-22; idem, “The Last Word: John Wallis on the Origin of the Royal Society,” History of Science 46 (2008): 189-191. 54 As a possible exception, the editors of the Oldenburg Correspondence note that, in a letter from 1675, Wallis asks Oldenburg to forward a letter to “Mr Potter,” and the editors suggest that this might be Francis Potter (A. Rupert Hall and Marie Boas Hall, eds., The Correspondence of Henry Oldenburg, vol. 12 [Madison: University of Wisconsin Press, 1986], 4, 6). One other tenuous connection between Wallis and Potter is that they used the same publisher. The Oxford-based Lichfield family published the original English version of Potter’s Interpretation, and among Wallis’s works they published were Operum mathematicorum pars altera (1656), Due Correction for Mr Hobbes (1656), Hobbianae puncti dispunctio (1657), Hobbius Heauton-timorumenos (1662), and Defense of Infant-Baptism (1697). 55 See WC II, 324, 544. On Potter’s transfusion experiments see Charles Webster, “The Origins of Blood Transfusion: A Reassessment,” Medical History 15 (1971): 387-392.

145 some of the same intellectual circles, but no record of a personal relationship between them has survived. The few marginalia in the copies of Potter’s Interpretation throughout Oxford only deepen the mystery. The most significant example appears in a copy of Wallis’s translation at the

Bodleian Library, which contains corrections of errata and some dog-eared pages, but only one substantive marginal note (see Figure 8). Written in what appears to be Wallis’s hand, the note is located at the top of the first page of Broccard’s Alarm, which is appended to this copy, and reads,

“Ex Manuscripto Codice Jacobi––Usserij, Archi Episcopi Armaschani.”56 Here Wallis has evidently recorded where he found the copy of either Potter or Broccard that he used as his source: among the manuscripts of James Ussher, Archbishop of Armagh, the Irish Royalist who had briefly lived in Oxford during the early 1640s.

As with Potter, there is little evidence linking Wallis directly to Ussher. Each of them lived at Exeter College at different times, Ussher during his brief stay at Oxford during the early 1640s and Wallis upon his arrival in Oxford in 1649 until he secured more permanent accommodations.

In fact, they may have lived in the same house.57 But Ussher lived there while Oxford was a

Royalist stronghold during the Civil War. Wallis––a supporter of Parliament installed in Oxford by Cromwell’s regime––had little in common with the former resident of Exeter. What they did share was a strong anti-Catholic streak. Ussher was convinced that the Catholic Church was an enduring threat to Protestantism on the British Isles. During his Oxford period, for instance, he claimed in a letter to his Huguenot friend, André Rivet, that to seek a reconciliation with the

56 This is one of several copies of Potter’s Interpretation at the Bodleian. The shelf mark of this copy is 8ºL 116 Th. Wallis’s marginal note appears on p. 189. 57 Ussher’s move to Exeter College is discussed in Richard Parr, The Life of the Most Reverend Father in God, James Usher, Late Lord Arch-Bishop of Armagh, Primate and Metropolitan of All Ireland (London, 1686), 48. Ussher lived in the Foreigner’s House at Exeter, and circumstantial evidence suggests that Wallis lived there too. In private correspondence, Philip Beeley explained to me that although Wallis identified Exeter College as his address, there is no record at Exeter that he had a fellowship or any other position there. This means he probably stayed as a visitor in the Foreigner’s House.

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Catholic Church was not only futile but also “a dangerous work: since it cannot be that iron will coalesce with clay by any human art.”58 Indeed, Ussher identified the pope as Antichrist in numerous published and unpublished texts.59 Although there are few material connections between Wallis, Ussher, and Potter, we can be sure that they shared a conviction that Protestants were under a constant threat from Catholic machinations.

It seems likely, then, that Wallis would have appreciated the anti-Catholic thrust of

Potter’s argument. On the other hand, although Wallis used the numbers recorded in Scripture for mathematical exercises and to calculate the age of the Earth (as discussed in Chapter 4 above), he usually showed no interest in the sort of numerology and interpretation of biblical prophecy featured in Potter’s text. Furthermore, Potter’s imprecise calculation of a square root is unlikely to have impressed Wallis, a man who mentally calculated irrational square roots, and the square roots of numbers with dozens of digits, during bouts of insomnia.60 For Wallis, then, the value of a Latin translation of Potter’s Interpretation was presumably not its mathematical and exegetical insights, but rather its anti-Catholic argument.

Wallis’s translation was published during a resurgence of anti-Catholicism in England during the late 1670s. Political developments contributed to the rising tension: English Protestants agonized over the looming succession of Charles II’s Catholic brother James, as rumours spread about James’s plan to restore the Catholic Church in England with help from Louis XIV of

58 Elizabethanne Boran, ed., The Correspondence of James Ussher, 1600-1656, vol. 3 (Dublin: Irish Manuscripts Commission, 2015), 870. Ussher’s criticism was directed against the irenic efforts of Hugo Grotius, which are described in Henk Nellen, “Minimal Faith and Irenic Ideals in Seventeenth-Century Scholarly Circles: Hugo Grotius as a Guardian of Isaac Casaubon’s Legacy,” Church History and Religious Culture 94 (2014): 444-478. 59 See Alan Ford, James Ussher: Theology, History, and Politics in Early-Modern Ireland and England (Oxford: Oxford University Press, 2007), 73-83, 124-127; Hill, Antichrist in the Seventeenth Century, 21, 38-39. 60 See John Wallis, “Two Extracts of the Journall of the Phil. Soc. of Oxford: One Containing a Paper, Communicated March 31, 1685, by the Reverend Dr Wallis, President of the Soc. concerning the Strength of Memory when Applied with Due Attention: The Other, Dated Dec. 15th, 1685, Describing a Large Stone Voided by Way of Urine,” Phil Trans 15 (1685): 1269-1271.

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France.61 Anti-Catholic fears boiled over with the “Popish Plot” scare in 1678, as many English

Protestants bought into a fabricated Jesuit conspiracy to overthrow the government and the

Anglican Church. Although the Popish Plot apparently had no basis in fact, the anti-Catholic fears that accompanied it were enough to provoke the execution of dozens of alleged conspirators.62 In short, a new edition of a strongly anti-Catholic text like Potter’s Interpretation would have attracted an avid readership in England in the late 1670s. And since Wallis had it published in

Latin, he evidently also hoped to fan the flames of anti-Catholicism abroad.

But why publish a translation of Potter rather than an original anti-Catholic work? Despite the vigorous anti-Catholicism of the late 1670s, Hill explains that by then the identification of the pope as the Antichrist was not unanimous in England as it had been earlier in the seventeenth century. One reason for this is that writers in the middle decades of the century had found new enemies to identify as the Antichrist––Bishops or Puritans, Royalists or Cromwellians, depending on one’s political inclinations––so the pope-Antichrist connection had been diluted. Furthermore, after the Restoration, discussion of the Antichrist in general recalled the radicalism of the

Interregnum, so fewer writers wrote about the subject at all.63 Although it has been cogently argued that Hill overstates the decline of apocalyptic writing in the Restoration period,64 he rightly observes that the pope-Antichrist identification was no longer treated as a matter of fact in the late seventeenth century. Accordingly, Wallis may have published his translation of Potter’s

Interpretation in an effort to refocus anti-Catholic sentiment and to revive the idea of the papal

Antichrist. A new edition of Potter’s text, especially when paired with Broccard’s Alarm to All

61 See Scott, England’s Troubles, 169-173, 184-186. 62 On the Popish Plot and general anti-Catholicism in England during the 1670s and 1680s, see Hinds, The Horrid Popish Plot; Warren Johnston, “The Anglican Apocalypse in Restoration England,” Journal of Ecclesiastical History 55 (2004): 487-490; Kenyon, The Popish Plot. 63 Hill, Antichrist in the Seventeenth Century, 41-174. 64 See Johnston, “The Anglican Apocalypse,” esp. 467-468.

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Protestant Princes, would remind Protestant readers about the threat of papist interference in the affairs of Protestant nations. Perhaps the Latin text would also encourage international cooperation against the Church of Rome, a dream that had thrived early in the seventeenth century but had faded as the pope became less powerful, and thus less threatening, as a political figure in later decades.65

Yet the fact that Wallis concealed his involvement in the new publication of Potter and

Broccard for nearly two decades suggests that his enthusiasm for these anti-Catholic polemics was tempered by other considerations. His precise reasons are a matter of speculation. If, as Hill argues, the publication of a text on the Antichrist could be considered dangerous and radical, this helps to explain why Wallis neglected to include his name in the text and had it published in

Amsterdam. On the other hand, he may simply have wanted to avoid alienating his Catholic colleagues. From its inception, the Royal Society included a few Catholics, such as Kenelm

Digby.66 Furthermore, although Catholics are sparse in Wallis’s correspondence, he did take advantage of his relationships with certain members of the Roman Church. During the 1670s his

Catholic correspondents included the Jesuit mathematician Jean Bertet, with whom he discussed mathematical problems and arranged for books to be sent from France, and the Jansenist theologian Pasquier Quesnel, regarding his plan to publish the works of St. Augustine.67 These are not contacts whom Wallis would have viewed as expendable.

In addition to these factors, however, we should bear in mind that Potter’s Interpretation is a work of numerology and exegesis of a prophetical text. Wallis himself explored connections between mathematics and biblical interpretation, but he never did so in the manner of Potter and

65 See Hill, Antichrist in the Seventeenth Century, 172-173. 66 On Digby’s contributions to the early Royal Society before his death in 1665, see R. T. Petersson, Sir Kenelm Digby: The Ornament of England, 1603-1665 (Cambridge, MA: Harvard University Press, 1956), 294-301. 67 See WC III, 420, 426-427, 452, 529-535, 549-554; WC IV, xliii, 20-23, 49-51.

149 other apocalyptic writers, and he evidently had no interest in the millenarian pursuits that attracted many of his contemporaries. In any case, despite his apparent ambivalence, Wallis ultimately chose to reveal his involvement with Potter’s Interpretation in his Opera mathematica, a collection intended to secure his mathematical legacy in the final years of his life.68 It seems that, for Wallis, a clear anti-Catholic message was worth a departure into the more esoteric aspects of mathematical inquiry.

Plagiarized algebra and speculative theology: Wallis and Descartes revisited

What remains to be considered is the unusual case of Wallis’s attitude toward one of the greatest philosophical and mathematical minds of early modern Europe, René Descartes. Historians or mathematics recognize Descartes as, among other things, the progenitor of analytic geometry, which employs algebraic symbols to solve geometrical problems. It was Descartes who demonstrated the utility of treating mathematics not as a purely deductive process as it appears from reading of ancient Greek sources. Rather, his symbolic approach is based on exploration and discovery. The development of analytic geometry is regarded as one of the most important achievements in the history of modern mathematics.69 Yet, in his Treatise of Algebra (1685) and elsewhere, Wallis claimed that the groundbreaking algebraic methods that Descartes published in his Géometrie (1637) were nowhere near as novel as most readers assumed. He argued that

68 In 1690, Wallis wrote to his friend Thomas Salmon regarding his plans to publish his collected mathematical works. He asks Salmon for help in finding a publisher in Holland like the ones that handled the works of Viète, Descartes, and van Schooten. Wallis suggests that his works might still interest mathematically-inclined scholars abroad, “my name being pretty well known in most parts of Europe to such as follow these studies.” But he emphasizes that the project must be undertaken soon, since he is getting old and might not have a chance to finish it if he waits (MS Add. D. 105, f. 92r). 69 On the massive contribution of Descartes’ Géometrie to the development of algebra and its application to geometry, see Craig Fraser, “Mathematics,” in History of Modern Science and Mathematics, vol. 1, ed. Brian S. Baigrie (New York: Charles Scribner’s Sons, 2002), 89-90; Paolo Mancosu, Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century (Oxford: Oxford University Press, 1996), 65-91.

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Descartes had stolen his methods from the English mathematician and astronomer, Thomas

Harriot, whose work was published posthumously under the title Artis analyticae praxis in 1631.70

The reason for Wallis’s negative opinion of Descartes seems to be overdetermined:

Descartes was French, he was Catholic, he was known for a rationalist epistemology, and eventually his system of natural philosophy was in competition with that developed by Wallis’s countryman, Isaac Newton. However, historians have typically discussed Wallis’s antipathy toward Descartes simply in terms of xenophobia and nationalistic rivalry, often suggesting that

Wallis invented the plagiarism charge in a shameless attempt to promote English mathematicians over their French rivals. For instance, in an article on Wallis’s disputes with French mathematicians, Jacqueline Stedall describes Wallis’s claims about Descartes’ algebra as “at best misleading, and at worst deliberately duplicitous.” According to Stedall, Wallis’s unjust treatment of Descartes is the most egregious part of Wallis’s Treatise of Algebra, a text whose purpose was

“to trumpet the contributions of English mathematicians from the medieval period onwards.”71

Here Stedall echoes a long-standing position on Wallis’s disparagement of Descartes. As early as

1939, I. Bernard Cohen described the historical section of Wallis’s Treatise as “one of the greatest distortions in the history of the history of science.”72

I am not suggesting that such incredulous responses to Wallis’s charges against Descartes are mistaken. As we will see below, Wallis bases his argument entirely on similarities that he detects in the styles, methods, and results of Harriot’s and Descartes’ algebra; he offered no

70 Wallis’s accusation that Descartes was a plagiarist is discussed in Katherine Neal, From Discrete to Continuous: The Broadening of Number Concepts in Early Modern England (Dordrecht: Klewer, 2002), 39-40, 64; Jacqueline A. Stedall, A Discourse concerning Algebra: English Algebra to 1685 (Oxford: Oxford University Press, 2002), 210; idem, “Wallis and the French,” 274-276. 71 Stedall, “Wallis and the French,” 274-276. 72 I. Bernard Cohen, Review of The Mathematical Works of John Wallis, D. D., F. R. S. (1616-1703) by J. F. Scott, Isis 30 (1939): 531.

151 concrete evidence to suggest that Descartes had plagiarized Harriot. It was also typical of Wallis to promote dubious claims of English priority in mathematics and natural philosophy. But there is no reason to assume that Wallis was only motivated by nationalistic anti-French fervour.73

Based on evidence from Wallis’s correspondence, I will argue in this section that Wallis’s animosity toward Descartes stems in part from theological concerns. As we will see, when Wallis reflected on Descartes’ philosophy, and he found it wanting and potentially dangerous. He was particularly troubled by the reliance on reason alone in Descartes’ epistemology, which seemed to overlook the importance of sensory perceptions and experimental evidence. Accordingly,

Wallis was highly skeptical toward Descartes’ effort to prove the existence of God by this rationalist method. Considering that Wallis was alert to harmful ideas from Catholic sources, his negative view of Descartes as a philosopher and theologian may help to explain why he repeatedly made what is, frankly, a flimsy and unfair charge of plagiarism. Whether the French philosopher’s adherence to Catholicism was a factor in Wallis’s judgement remains unclear. But I will suggest below that Wallis’s objections to Descartes’ epistemology should be understood in the context of an association, promoted by Wallis’s colleagues in the Royal Society, between Protestantism and experimentalism on the one hand, and between Catholicism and neglect of experiments on the other.

What I would like to suggest is that, when Wallis criticized Descartes mathematics, he sought to use a mathematical dispute to undermine an opponent’s credibility. This is the same

73 It should be noted, however, that Wallis may have been particularly suspicious of the French because of his work as a codebreaker. He was repeatedly enlisted to decode intercepted French intelligence after the Restoration. In many cases this occurred during wars between England and France such as the Nine Years’ War (1688-1697). Numerous French letters that Wallis decoded are contained in British Library MS 32499, including one in which he discovered the plans of Louis XIV of France and John III of Poland to start a war with Prussia (see ff. 55v-57v). In addition, Wallis evidently considered it crucial for an English cryptanalyst to understand French: he instructed his grandson, William Blencowe, whom he trained as his successor in codebreaking, to “study the French Tongue” (see John Wallis “Original Anecdotes and Letters of Dr. John Wallis, &c.,” The Gentleman’s Magazine 58 [1788]: 380, which contains a partial excerpt of Wallis’s account of his codebreaking career from a letter written in 1702).

152 strategy that he employed in his protracted conflict with Thomas Hobbes. As Douglas Jesseph has argued, Wallis attacked Hobbes’s mathematics in order to reveal the weaknesses in his reasoning and thus diminish his reputation. The goal of this ad hominem approach was to weaken Hobbes’s credibility and thus make his works on other subjects––namely politics, theology, and philosophy––seem less appealing.74 In texts criticizing Hobbes’s mathematics published between the 1650s and 1670s, Wallis’s ultimate goal was to prove that Hobbes, as he wrote to Bishop

Thomas Tenison in 1680, “was not a man of strong Reason; but onely of a bold daring phansy” who used “his magisterial way of speaking” to encourage his readers to “be Atheiste.”75 By chipping away at Hobbes mathematical reputation, Wallis sought to prevent readers from being swayed by the philosopher’s dangerous combination of faulty reasoning and radical thought.

Given Wallis’s concern about Descartes’ theology, we might consider him to be engaged in a similar sort of campaign against the French philosopher. This helps to explain why he would be so outspoken with his disparaging remarks about Descartes’ ability and character, remarks that he presumably recognized as unsubstantiated.

According to Wallis’s own account, his first encounter with Descartes’ mathematics left him with a favourable impression. In a letter to John Collins written mid-1670s, Wallis explains that he was deeply impressed by the Géometrie when he borrowed it from a friend in 1648. Having read no other works of algebra except William Oughtred’s Clavis mathematicae (1631), Wallis found Descartes’ method to be original and useful. He especially admired the technique of moving all the elements of an equation to one side and making them equal to zero.76 Wallis exchanged

74 Douglas M. Jesseph, Squaring the Circle: The War between Hobbes and Wallis (Chicago: University of Chicago Press, 1999), 69-72, 293-339. 75 Bodleian MS Add. D 105, f. 70v. 76 WC IV, 173-175. For Wallis’s full assessment of Descartes’ Géometrie compared to the work of other algebraists, see also WC IV, 169-173, 176-187.

153 letters about Descartes’ methods with at least two correspondents in the late 1640s––John Smith of Queens’ College, Cambridge, who had lent the Géometrie to Wallis, and Frans van Schooten, who published the first Latin translation of the book––but these letters have not survived.77

Despite his initial enthusiasm, as he explained to Collins, Wallis changed his mind about

Descartes when he compared his works to those of Harriot and concluded that the Frenchman was a fraud. Based on similarities between the Géometrie and Harriot’s Praxis, Wallis could only conclude that Descartes had stolen his algebraic material from Harriot without acknowledging the source. According to Wallis, the Praxis must have been Descartes’s source not only for the method of moving all elements of an equation to one side, but also for the notation that uses lowercase letters for variables. Within months of his first encounter with the Géometrie, Wallis changed his mind and concluded that Descartes had borrowed everything useful he had written about algebra “without taking any notice of the fountaine” from which they sprung.78

Wallis’s evidence is entirely circumstantial, and his argument may well have been disingenuous. Indeed, as late as 1656, when he published his Arithmetica infinitorum—the work that established his reputation as a mathematician—Wallis includes Descartes on a list of the great modern mathematicians and refers to him uncritically throughout the text. The esteem he shows for Descartes here does not fit with the timeline he describes in his letter to Collins.79 In addition,

77 See WC I, 8-9, 12-13. 78 WC IV, 175. For Wallis’s full assessment of Descartes’ Géometrie compared to the work of other algebraists, see also pp. 169-173, 176-187. 79 John Wallis, The Arithmetic of Infinitesimals, trans. Jacqueline A. Stedall (New York: Springer-Verlag, 2004), 82, 161, 180-181. See also Stedall, “Wallis and the French,” 266. Already by this time, however, Wallis had hinted at his suspicions about Descartes in print. In De sectionibus conicis (1655) Wallis wrote in the epistle dedicatory to Seth Ward that he had sometimes used the notation of William Oughtred and sometimes that of Descartes, “unless you would prefer that I name our Dr. Harriot, who in these things entirely preceded Dr. Descartes on the path” (nisi velitis potius ut D. Harriotum nostratem nominem, qui in eadem fere semita D. Cartesio præivit; John Wallis, “De sectionibus conicis, nova methodo expositis, tractatus,” in Operum mathematicorum pars altera [Oxford, 1656], sig. I2v-I3r). Still, the suggestion that Harriot preceded Descartes does not necessarily imply that the Frenchman had plagiarized his English counterpart. Perhaps at this point Wallis was less convinced, or less bold, than he was by the time that he wrote his letter to Collins.

154 as Stedall, Cohen, and others have noted, Wallis rarely missed an opportunity to promote the contributions of English mathematicians at the expense of their continental rivals when he discussed the history of mathematics.

In any case, by the late seventeenth century, Wallis was committed to exposing Descartes’ supposed plagiarism. He intended for his letters on mathematics and natural philosophy to be shared and often printed, and indeed part of his letter to Collins was copied into the records of the

Royal Society.80 Wallis made his position even more public in his Treatise of Algebra, which contains an overview of the history of algebra beginning in antiquity. The Treatise was first published in English in 1685, and in 1693 it was reprinted in Latin as part of Wallis’s Opera mathematica. Wallis argues in the preface that there is “scarce any thing of (pure) Algebra in Des

Cartes, which was not before in Harriot; from which Des Cartes seems to have taken what he hath (that is purely Algebra) but without naming him.”81 He goes on to deprive Descartes of credit for his famous “Rule of Signs” for determining the number of roots of a polynomial; Wallis calls this “Harriot’s Rule” and claims that Descartes’ use of it is only a “concurrence.”82

These claims convinced some contemporaries that Descartes’ apparent innovations in algebra could be traced back to Harriot. Wallis’s friend Thomas Smith, for instance, expressed his sympathy with Wallis’s position in a letter of 1691. Smith explains that he agrees with Wallis despite what had recently been written Jean Prestet, a “bold & insolent” French author who had reproached Wallis for his accusations.83 In another letter, Smith thanked Wallis for sending a copy

80 Collins himself criticized Descartes at length—not for plagiarism, but for arrogance and unoriginality—in an essay of 1675. This essay survives in manuscript form in the archives of the Royal Society (Royal Society MS 81, No. 28). A partial transcription of Wallis’s letter to Collins is included on p. 18 of that manuscript. The transcription has been printed in WC IV, 173. 81 John Wallis, A Treatise of Algebra Both Historical and Practical, Shewing the Original, Progress, and Advancement Thereof from Time to Time, and by What Steps It Hath Attained to the Heighth at Which Now It Is (London, 1685), sig. a4r. 82 See Stedall, “Wallis and the French,” 274-276. 83 Bodleian MS Smith 66, f. 9.

155 of the volume of the Opera mathematica containing the Treatise of Algebra, adding that it would help him to defend Harriot and other English mathematicians “against the unjust cavils” of French writers.84 And it was not only Wallis’s friends who believed his claims. Indeed, Stedall notes that even in the twenty-first century she was asked by a historian of mathematics where to find the

Rule of Signs in Harriot’s works.85

For Stedall, Wallis’s accusations mark the culmination of his increasingly closed-minded attitude toward all things French in mathematics, which by the time he wrote the Treatise of

Algebra had reached the level of “unreasoning bitterness.”86 However, there seems to be more to

Wallis’s antipathy toward Descartes than rampant nationalism. The problem with Descartes was not merely that he was French; for one thing, he was also a Roman Catholic. As Ian Stewart notes, in the mid-seventeenth century, Descartes’ Catholic background troubled many English divines who observed the growing popularity of his natural philosophy and felt that it was inappropriate for their Protestant students.87 In terms of Wallis’s anti-Catholic motivations, though, this case is unusual on account of the Descartes’ complicated relationship with the Roman Church. Although he was trained in a Jesuit college and identified himself as a Catholic throughout his life, some critics accused Descartes of crypto-Calvinism. Furthermore, on one occasion he advised his patron, Princess Elizabeth of Bohemia, that it made no difference whether one was a Protestant

84 Bodleian MS Smith 66, f. 15. In addition, although it preceded the publication of Wallis’s Treatise of Algebra, Wallis might also be the source of John Flamsteed’s claim that Harriot “preceded De Chartes and was not much his Inferior in Geometry” (Eric G. Forbes, Lesley Murdin, and Frances Willmoth, eds., The Correspondence of John Flamsteed, The First Astronomer Royal, vol. 2 [Bristol: Institute of Physics, 1997], 15; see also 16 n. 11). On the reactions of other contemporaries to Wallis’s claims, see Stedall, “Wallis and the French,” 276; Philip Beeley, “Wallis, Leibniz und der Fall von Harriot und Descartes. Zur Geschichte eines vermeintlichen Plagiats im 17. Jahrundert',” Acta Historica Leopoldina 45 (2005): 115-129. 85 Stedall, “Wallis and the French,” 276. 86 Stedall, “Wallis and the French,” 266. 87 Ian Stewart, “‘Fleshy Books’: Isaac Barrow and the Oratorical Critique of Cartesian Natural Philosophy,” History of Universities 16 (2000): 36.

156 or a Catholic.88 Modern biographers of Descartes remain undecided about whether he was, at heart, a faithful Catholic, but he maintained an identity as such and resisted pressure to convert to

Protestantism while he lived in Holland.89

Although I am not aware of any source in which Wallis discusses Descartes’ relationship with the Catholic Church, he does address Descartes’ theology in his correspondence with the non-juror cleric Edmund Elys. Their discussion concerns Descartes’ rationalist argument for the existence of God in his Meditations on First Philosophy (1641), whose full title promises to demonstrate the existence of both God and immortal souls.90 In the epistle dedicatory to the

Meditations, Descartes argues “that God’s existence can be proved by natural reason,” which is precisely what he proceeds to attempt.91 In the first two Meditations, Descartes engages in a mental exercise of systematic doubt and concludes that everything he knows might be an illusion or a deception. The one exception is that he is certain of his own existence as a thinking being: cogito ergo sum, I think therefore I am.92 The second truth that he establishes as certain, in the

Third Meditation, is the existence of God. Descartes claims that God, which he considers to mean

“an infinite, independent, supremely powerful substance,” must exist for the very reason that one can conceive of such an entity. A finite being could not conceive of an infinite being like God on its own: this conception must have come from without, that is, from the infinite being itself.

Indeed, Descartes claims, he can only understand himself as an imperfect being in comparison to

88 See Stephen Gaukroger, Descartes: An Intellectual Biography (Oxford: Clarendon Press, 1995), 406. 89 See Desmond M. Clarke, Descartes: A Biography (Cambridge: Cambridge University Press, 2006), 180-181; Gaukroger, Descartes, 3, 187-188, 291-292, 386, 443 n. 4 90 René Descartes, Renati Des-Cartes, Meditationes de prima philosophia, in qua dei existentia et animæ immortalitas demonstratur (Paris, 1641). 91 René Descartes, Meditations on First Philosophy with Selections from the Objections and Replies, trans. Michael Moriarty (Oxford: Oxford University Press, 2008), 3. 92 Descartes, Meditations on First Philosophy, 17-24. Although Descartes articulates this argument, cogito ergo sum, in the Meditations, he does not convey it in this famous Latin formulation. That first appeared in his Principles of Philosophy (1644).

157 a perfect being, so God’s existence is logically prior to his own. Descartes treats this argument for the existence of God as a product of reason alone: his mind has proven that God exists without reference to any potentially deceptive sense perceptions or experiences.93

In general, English philosophers were ambivalent toward Descartes’ epistemology in the second half of the seventeenth century. Prominent scholars such as Thomas Sprat, Joseph

Glanvill, and John Locke declared his methodology inadequate and emphasized the importance of empirical evidence.94 Yet throughout this period, Descartes’ works were read, discussed, and sometimes defended by certain English writers. One such defender was Elys, who declared his admiration for the French philosopher in a letter to Wallis written in 1691. Elys had been following the series of letters that Wallis had recently published defending the doctrine of the

Trinity, and he wrote to the Savilian Professor in 1691 to express his approval of the latest letter.

The only part of the letter he could not accept, Elys explains, was a digression on epistemology where Wallis claims that people “have no Notions in our Mind, other than what we derive,

Mediately or Immediately, from Sensible Impressions of Finite Corporeal Beings.”95 Elys insists knowledge of God is prior to such sensible impressions, and he explicitly links this to some tracts he wrote “in Vindication of Des Cartes.” The one thing that is not known through the senses, either mediately or immediately, is “the Notion of the ONE INFINITE ESSENCE.”96 According to Elys, Wallis was right to claim that knowledge comes through the senses, but he should have made an exception for knowledge of God.

93 Descartes, Meditations on First Philosophy, 32-33. 94 On the reception of Descartes in seventeenth-century England, see G. A. J. Rogers, “Descartes and the English,” in The Light of Nature: Essays in the History and Philosophy of Science Presented to A. C. Crombie, eds. J. D. North and J. J. Roche (Dordrecht: Martinus Nijhoff, 1985), 281-301. 95 John Wallis, “A Seventh Letter, concerning the Sacred Trinity; Occasioned by a Second Letter from W. J.,” in Theological Discourses; Containing VIII Letters and III Sermons concerning the Blessed Trinity (London, 1692), 15. 96 Bodleian MS Eng. th. e. 22, f. 228r.

158

In his reply, Wallis objects to Elys’s suggestion that the existence of God could be proven solely on the basis of a rationalistic argument. He also takes the opportunity to attack Descartes’ effort to build an epistemology and a theology on his famous argument, cogito ergo sum. Wallis suggests that if Elys reconsiders the matter he will realize that one needs sensory experience to achieve knowledge of God, just like anything else. He asks Elys to “suppose a man in such circumstances, as neither to have seen or Heard, or Felt any thing: I doubt whether he would have any thoughts of God, more than an Embryo yet unborn.”97 Wallis goes on to explain that (except for Revelation, presumably) humanity can only come to know God by observing the world:

The Heavens declare the Glory of God; but not without being seen, or at lest heard of, or some way made known to me by sensible Impressions. The Invisible things of him (even his Eternal Power & Godhead) are clearly seen (which is by the Creation of the World; being understood by the things that are made. But if we never see, nor hear of, or have any Notion of the things that are Notions antecedent to that of One Infinite Essence, (which cannot be derived from sensible Impressions of Corporeal Beings.)98

The senses, Wallis suggests, are the means by which God makes himself known to humanity, so

Elys’s insistence on a priori knowledge of God is mistaken.

Wallis goes on to suggest that Elys’s mistake was trusting Descartes’ flawed philosophical method. Indeed, Descartes overlooked the sensory experience he needed to conclude cogito ergo sum in the first place, so his move to demonstrating the existence of God on the basis of that principle is doubly problematic. Wallis writes,

As to Des Chartes; there must be a great many Notions, or Simple Apprehensions, which he must presume, before he commence to the complex Notion, of Deus est. And a great many Illative Notions (from Natural Logick) before he can Argue, Cogito, Ergo Sum. He must at lest [sic] have a Notion of Simple Apprehension, of what is meant by Cogito; and what is meant by Sum: and then a Complex Notion, that What Is not, cannot Think. And then this Illative Notion, (or Natural Syllogism;) But I think; Therefore I am: And I doubt, he cannot come at all this, without some use of his Senses.99

97 Bodleian MS Eng. th. e. 22, f. 229r. Underlining in original. 98 Bodleian MS Eng. th. e. 22, f. 229v. Underlining in original. 99 Bodleian MS Eng. th. e. 22, f. 229v. My italics. Underlining in original. Another possible reason why Wallis was wary of Descartes’ cogito argument was its association with the controversial Trinitarian theology of William

159

Evidently, Wallis considers Descartes’ epistemology and theology as fraudulent as his mathematics: the entire rationalist structure of the Meditations is a fiction that obscures the fundamental role of sensory perceptions in the formation of a person’s most basic ideas. Without the senses, one cannot establish his own existence, much less the existence of God.

This letter to Elys was not the first time that Wallis warned against trusting reason at the expense of sensory experience. He made a similar case in Truth Tried, which was published in

1643, only two years after Descartes’ Meditations. In fact, in a postscript to his letter to Elys, he notes that he is also sending a copy of Truth Tried, in order to show his friend that the problems with Descartes’ sort of rationalism had been apparent nearly fifty years earlier.100 Descartes is not mentioned in Truth Tried, presumably because the text is a point-by-point response to Greville’s

Nature of Truth in which Descartes is also absent. But by referring Elys to Truth Tried in a letter that addresses Descartes’ epistemology, Wallis suggests that he might have had the French philosopher in mind while writing in the early 1640s. Following Greville, Wallis addresses these matters in terms of the doctrines of ancient Greek philosophers. Greville had adopted the Platonic position that “Knowledge [is] nothing but a Remembrance” of ideal forms, whereas Wallis explains that he prefers “Aristotle’s Rasa Tabula.” For Wallis, as for Aristotle, the mind is a blank slate on which knowledge is inscribed by experience.101 In particular, matters of fact must be

Sherlock, whom Wallis and Elys referred to several times in their correspondence. Sherlock viewed the persons of the Trinity as three distinct, infinite minds, a view that struck many contemporaries as tending toward the heresy of tritheism. At least two critics of Sherlock, Robert South and Stephen Nye, argued in their published works that Descartes’ cogito argument was at the heart of Sherlock’s theology: Sherlock conceived of a person as that which thinks, and this led him to regard the Father, Son, and Holy Spirit as three distinct minds. See Maria Rosa Antognazza, Leibniz on the Trinity and the Incarnation: Reason and Revelation in the Seventeenth Century, trans. Gerald Parks (New Haven: Yale University Press, 2007), 94-97, 101. On Wallis’s response to Sherlock’s theology, see Chapter 6 below. 100 Wallis notes that he is sending two books to Elys: one was a collection of his sermons in defense of the Trinity, and the other was a book “concerning the Lord Brooke.” The latter must have been Truth Tried, his response to Robert Greville, Lord Brooke (Bodleian MS Eng. th. e. 22, f. 229v). 101 Wallis, Truth Tried, 45 [49]. Italics in original.

160 learned from experience rather than reason:

What Principle is there implanted in nature to enform me, Whether there ever were such a City as Troy? Whether it were so destroyed? Whether this or that were Plato’s or Aristotle’s Opinion? What Principle to enform, that it rained yesterday & is faire to day? Certainly, matters of Fact have not such Idea’s implanted in Nature; for then might they by Discourse be known to have been or not to have been, without the help of either Sense or Information.102

Here, as in his letter to Elys, Wallis suggests that sense perceptions form the foundation of knowledge, despite authorities such as Plato or Descartes insisting on the epistemological primacy of reason.

Later in Truth Tried, Wallis connects his empiricism to his theology. He argues that

“Experimentall Knowledge,” the sort of thing we believe because “we Tast and See it to be so,” is fundamental to our knowledge of God. Even “Devils” share in “Speculative Knowledge, whereby we assent to the Truth reveiled.” “Experimental” evidence, however, is the basis for

“Knowledge peculiar to Gods children . . . whereby no man knows him but he that hath him; That

Knowledge which is Life Everlasting.” The knowledge that leads to salvation, then, is based on

“this spiritual Tast, this Experimentall Knowledge” that accompanies faith.103 It is one thing to know about God abstractly, as any intelligent being can do; it is another thing to experience God, as righteous people do. As Wallis explains, “A wicked man may Know that God is good, (as a blind man knows that the Sun shines, by the report of others; or as an Astronomer knows of an

Eclipse before it come, by Calculation, or rationall Discourse and Illation;) But he Sees it not, he

Tasts it not.”104 According to Wallis, to stumble upon some truths about God by reason alone, as

Plato or Descartes might have done, is not really to have knowledge of God.

102 Wallis, Truth Tried, 45 [49]. Italics in original. 103 Wallis, Truth Tried, 60. Italics in original. For biblical support of this notion of experimental theology, Wallis cites Hebrews 5:14, which refers to people who “have trained themselves to distinguish good from evil,” and Philippians 1:9, wherein Paul prays that God will increase his “knowledge and depth of insight.” 104 Wallis, Truth Tried, 60.

161

Wallis claims, then, that experimental knowledge of God is exclusive to his children (a category that presumably includes only Protestants). Certainly, there is a metaphorical element to

Wallis’s description of spiritual taste and sight. Furthermore, for much of the seventeenth century the word “experiment” was used almost interchangeably with “experience,” and Puritans frequently described their personal religious experiences as “experimental” in contrast to what could be described in purely rational terms.105 So Wallis might not have meant to invoke the new natural philosophy when he referred to experimental knowledge of God. Nevertheless, as he links

Truth Tried to his critique of Descartes’ epistemology in his letter to Elys, Wallis seems to suggest that only an empiricist epistemology befits a true believer. Descartes’ supposed demonstration of the existence of God was a speculative rather than experimental approach to theology, the sort of thing of which wicked men and even devils are capable. Similarly, in a published sermon entitled

The Life of Faith, Wallis distinguishes between Christians who have come to know God through revelation, and the heathens whose understanding of God is merely “Conjectural, and Groping in the dark.” Such conjecture led some heathens to believe that the world was eternal and uncreated, and others to believe that it was merely “a Fortuitous Concurse of Atomes.”106 Considering that

Descartes’ philosophy drew extensively on ancient Greek atomic theories,107 it is no wonder that

Wallis was concerned about the implications of his rationalist theology. It seems that he intended to warn Elys that following the French philosopher might lead him to the sort of dangerous and

105 See Peter Harrison, “Experimental Religion and Experimental Science in Early Modern England,” Intellectual History Review 21 (2011): 413-433. Harrison specifically identifies Anthony Burgess, who tutored Wallis at Cambridge, as typical in his references to “experimental” knowledge of God; see Harrison, “Experimental Religion,” 418-419. 106 John Wallis, The Life of Faith. In Two Sermons to the University of Oxford, at St. Mary’s Church There; on the 6th. of January, 1683/4. and June the 29th. following (London, 1684), 29. 107 See Catherine Wilson, Epicureanism at the Origins of Modernity (Oxford: Clarendon Press, 2008), 23-24, 55, 112- 121; idem, “Soul, Body and World: Plato’s Timaeus and Descartes’ Meditations” in Platonism at the Origins of Modernity: Studies on Platonism and Early Modern Philosophy, eds. Douglas Hedley and Sarah Hutton (Dordrecht: Springer, 2007), 177-191.

162 dubious theology that results from excessive reliance on reason.108

Wallis’s harsh judgement of Descartes’ theology and philosophy provides an important context for his attack on the Frenchman’s mathematics. Perhaps Wallis, fearing that Descartes had promoted potentially dangerous ideas about the nature of knowledge and its relation to theology, decided to do his part to damage Descartes’ reputation, and so promoted a flimsy charge of plagiarism. Since we do not know what precisely motivated Wallis’s attack on Descartes’ mathematics, it is a matter of speculation whether Descartes’ adherence to the Catholic Church was a factor. An important factor to consider, though, is the notion, promoted by the Royal

Society, that an empirical and experimental philosophy would help Protestants in their fight against the Catholic Church. When Thomas Sprat declared in his History of the Royal-Society

(1667) that the founding of the Society would effect a second Reformation, he was not only portraying experimentalism as a radical departure from earlier natural philosophy. Sprat suggests that Catholics only pretend to embrace experimental philosophy, just as they only pretend to follow the literal text of the Bible. According to Sprat, “it is likely [the Catholics] have cherish’d some Experiments, not out of zeal to the continuance of such Studies, but that the Protestants might not carry away all the glory, and thence withal get new strength to oppose them.”109

Experimentation was fundamentally Protestant, then, despite Catholic attempts to appropriate it.

The identification of empiricism as a distinctively English epistemology is a gross

108 It should be noted that Wallis also warns against excessive trust of the senses in Truth Tried. Defending the Copernican hypothesis, he notes that sensory experience on its own is misleading in this case, since we seem to perceive a moving Sun and a stationary Earth. See Wallis, Truth Tried, 73-74. 109 See Thomas Sprat, The History of the Royal-Society of London, for the Improving of Natural Knowledge (London, 1667) 363[371]-366[374]. Italics in original. The quotation is from 373. Nevertheless, there was a small Catholic contingent in the early Royal Society, as well as some nonconformists and Quakers, a fact that required some careful rhetorical maneuvering by Sprat. See Michael Hunter, Establishing the New Science: The Experience of the Early Royal Society (Woodbridge, NH: Boydell Press, 1989), 59-61; idem, The Royal Society and Its Fellows 1660-1700: The Morphology of an Early Scientific Institution (Chalfont St. Giles: British Society for the History of Science, 1994; orig. pub. 1982), 9.

163 oversimplification,110 but this characterization is rooted in the rhetoric of the seventeenth century.

In order to cast experimental philosophy as an English achievement, Sprat and others promoted a crude association between Catholicism and an inattention to experiments. Like the Catholics, the natural philosophers of the past relied on reason alone, never bothering to investigate things for themselves, and so they inherited the mistakes of their ancestors. In contrast, Protestants

(particularly those in the Church of England) and experimentalists “both suppose alike, that their

Ancestors might err.” Protestants and experimentalists, unlike Catholics and rationalists, reject

“corrupt Copies” and turn to “perfect Originals.”111 On this account, Catholic theology is like a philosophy that relies entirely on reason: each of them neglects the evidence that should serve as the foundation of knowledge, whether in Scripture or the natural world.

As Sprat rhetorically aligns right knowledge with right religion, he suggests that each of the two Reformations is a weapon against the false religion of the Catholic Church. And what

Sprat describes rhetorically, Wallis puts into practice: his mathematics and philosophy are anti-

Catholic, and often explicitly so. Whether this is a crucial factor in the specific case of Wallis’s attitude toward Descartes remains difficult to discern. In any case, I argue that Wallis judged

Descartes’ mathematics so harshly in part because he had considered the theological implications of Cartesian philosophy. There were many reasons for Wallis to dislike Descartes, and his being a Catholic was only one of them. But this antipathy certainly fits Wallis’s usual pattern of judging works of mathematics and philosophy in light of their relation to undesirable theological ideas––

110 See David Fate Norton, “The Myth of ‘British Empiricism’,” History of European Ideas 1 (1981): 331-344. 111 Sprat, History of the Royal-Society, 363[361]. Italics in original. Sprat also directly addressed Descartes’ epistemology based on systematic doubt his History. Sprat refers to him as “the excellent Monsieur des Cartes” but suggests that his philosophical method will only satisfy “his own delight” (Sprat, History of the Royal-Society, 95- 96). According to Sprat, a system of knowledge based on the contents of one’s own mind inevitably confuses what is particular to a person with what is universal, and so leads to “many gross mistakes” (Sprat, History of the Royal- Society, 96; see also Rogers, “Descartes and the English,” 295-296).

164 of which Catholic doctrines were only one prominent example.

Conclusion

In February 1699/1700, Wallis wrote to the mathematician David Gregory about the ongoing issue of calendar reform. He insists in his letter that the new calendar “hath no foundation but Pope

Gregorie’s Bull” and adds that if those who favour reform “cannot see the force of my Argument; it is not my Fault.”112 Over three centuries later, one can still sense Wallis’s exasperation. Did the

English supporters of the Gregorian calendar not see the danger in letting the pope dictate their ecclesiastical and civil practices? Wallis, now in his eighty-fourth year, seems weary of having to warn his countrymen about the intrusion of Catholic ideas into England for so many years. The calendar debate was Wallis’s final battle against Catholic influence in England. It seems that he won, as he helped to delay England’s adoption of the Gregorian calendar for another half-century.

I have argued in this chapter that anti-Catholic sentiment shaped Wallis’s works at several points throughout his career. Long before he wrote on calendar reform, Wallis discouraged Robert

Greville from promoting a metaphysics that could accommodate transubstantiation (and consubstantiation) in his first publication, Truth Tried. Three decades later, at the height of his career at Oxford, Wallis translated Francis Potter’s work of numerology and prophetical interpretation into Latin. With this translation of Interpretation of the Number 666, Wallis provided an international Protestant audience with an argument, based on the application of mathematics to numbers in the Bible, that the pope was the Antichrist. For reasons that are unclear,

Wallis initially concealed his involvement in the translation of Potter’s book, but he chose to reveal his role in publishing this anti-Catholic polemic in his Opera mathematica in 1695. Finally,

112 Bodleian MS Tanner 114, f. 48r.

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Wallis publicly accused René Descartes of plagiarism in his works of mathematics, a move which seems to have been motivated in part by Wallis’s objections against Descartes’ theology and, perhaps, Descartes’ role as a prominent Catholic thinker.

In light of these case studies, we can conclude that Wallis’s assessment of ideas in mathematics and philosophy was often swayed by theological concerns, and that these concerns typically took the form of anti-Catholicism. At times, Wallis’s attitude toward Catholics seems just as important as other factors—including his patriotism and his empiricism—that affect how he responds to ideas about nature and mathematics. Wallis’s career suggests that confessional differences play a significant role in theory selection, a possibility that merits additional historical research. Moreover, my findings further challenge the notion of the “autonomy” of science––the idealization of science as entirely dispassionate, apolitical, secular, and value-free––which historians of science have endeavoured to problematize in the last several decades. As David

Lindberg has written,

. . . totally autonomous science is an attractive ideal, but we do not live in an ideal world. And many of the most important developments in the history of science have been produced by people committed not to autonomous science, but to science in the service of some ideology, social program, or practical end; for most of its history, the question has not been whether science will function as a handmaiden, but which mistress it will serve.113

The case of Wallis shows us that seventeenth-century English science was hardly autonomous from political and religious affiliations. As we have seen, Wallis’s anti-Catholicism—like his

English nationalism and his sympathy with the political goals of the Royal Society—plays a key role in his scientific activities. Nor can we dismiss Wallis as a marginal or eccentric scholar who does not reflect this period fairly: he was a productive, well-respected, and fairly typical member

113 David C. Lindberg, The Beginnings of Western Science: the European Scientific Tradition in Philosophical, Religious, and Institutional Context, Prehistory to A.D. 1450, 2nd ed. (Chicago: University of Chicago Press, 2007), 150.

166 of the Royal Society and the mathematical community. There is no “pure science” in the period unaffected by prejudice.114 For all the rhetoric of dispassionate and democratic study of nature in works promoting the new philosophy––rhetoric that featured in Wallis’s own accounts of the origins of the Royal Society115––the history of science features as much prejudice as the rest of history in this period. In England, this meant that science was anti-Catholic. Steven Shapin generalizes this phenomenon in his essay on prejudice in science: “Knowledge free of prejudice has not been obtained in historical practice, and, it is probably impossible to obtain in principle.

The Republic of Science seems rather to reflect the most widely distributed prejudices of its times and citizens.” Throughout the history of science, Shapin argues, prejudice has been built into knowledge, even if contemporaries do not recognize that prejudice as such.116 Evidently Wallis did not perceive the tension between the Royal Society’s ideals and his own taken-for-granted opposition to Catholicism.

As long as the history of science has been a profession, researchers have investigated how the Protestant Reformation changed the study of nature, and what was distinctive about Protestant science in the early modern period.117 What has generally been overlooked is that Protestant

114 I am suggesting here that the anti-Catholicism in Wallis’s science challenges not only the notion of the autonomy of science—its independence from political, religious, educational, and other institutions and their ideologies—but also the related notion of the purity of science, a subject of ongoing philosophical debate. Especially during the “science wars” of the 1990s, many writers have tried to defend the idea of a “pure science” that can be separated from its applications. According to this view, pure science is strictly a matter of discovering truth, and only the applications of science have moral, social, and political implications (see Philip Kitcher, Science, Truth, and Democracy [Oxford: Oxford University Press, 2001], 85-91). I contend that it is very difficult—and contrary to the historical evidence— to separate the anti-Catholic (and other ideological) applications of Wallis’s works from the “science” itself, with the possible exception of some of his work on pure mathematics. 115 For instance, in his autobiographical letter, Wallis wrote that the London experimentalist group of the 1640s, which eventually evolved into the Royal Society, “preclud[ed] matters of Theology and State Affairs” from its meetings (Scriba, “Autobiography of John Wallis,” 40). 116 Steven Shapin, “Science and Prejudice in Historical Perspective,” in Never Pure: Historical Studies of Science as if It Was Produced by People with Bodies, Situated in Time, Space, Culture, and Society, and Struggling for Credibility and Authority (Baltimore: Johns Hopkins University Press, 2010), 54. 117 For a useful overview of historiographical arguments linking the Scientific Revolution to the Reformation or to certain types of Protestantism see Peter Harrison, The Bible, Protestantism and the Rise of Natural Science (Cambridge: Cambridge University Press, 1998), 5-8.

167 science meant anti-Catholic science. Throughout his career, Wallis directed his knowledge of nature and mathematics, as well as his knowledge of theology and ecclesiastical history, toward the impediment of Catholic interests. England’s rivalry with France was also a rivalry with a

Catholic power, and both aspects of this rivalry spilled over into the intellectual activities of

Wallis and the Royal Society. Additional case studies will reveal whether Wallis’s colleagues in

England and abroad were as dedicated and successful as he was in the pursuit of anti-Catholic science.

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Chapter 6: Wallis’s Hammer: Language, Rhetoric, and Their Applications

In 1678, John Wallis published a thirty-three-page treatise entitled A Defence of the Royal Society.

The title is misleading: if the book was written to defend anyone, it was Wallis himself. William

Holder, a fellow cleric and member of the Royal Society, had recently accused Wallis of conspiring to deprive him of credit for a major achievement. Holder claimed that it was he, not

Wallis, who had taught Alexander Popham, the son of a minor noble family who had been deaf since birth, to speak. But in 1670 an article in the Philosophical Transactions noted that Wallis had successfully taught “a young Gentleman . . . who did from his birth want his Hearing” to speak clearly.1 Realizing that this referred to Popham, Holder published a Supplement to the

Philosophical Transactions wherein he complained that Wallis had stolen credit for Holder’s achievement: he was an “Invader” whose “subtle practices” had been “contrived to abuse and mislead the Reader” about who had taught Popham to speak.2

Wallis’s response in his Defence of the Royal Society is unapologetic, and makes Holder out to be incompetent and paranoid. He explains that Popham’s family, having heard of his success with another deaf patient named Daniel Whaley, brought Popham to him after Holder had failed to teach him and given up. Wallis claims that Popham came to him with no ability to speak, but under his guidance Popham learned to speak and to communicate with other people. In his account printed in the Philosophical Transaction, Wallis explains, he had left Holder out for fear of embarrassing him. He writes, “I thought it best . . . to say nothing of it; rather than to say, That,

1 Wallis, “A Letter of Dr. John Wallis to Robert Boyle Esq, Concerning the Said Doctor’s Essay of Teaching a Person Dumb and Deaf to Speak, and to Understand a Language; together with the Success Thereof: Which Letter Though Written Many Years Since, Was but Lately Obtain’d to be Inserted Here, It Being Esteemed Very Well Worth to be Preserv’d and Communicated for Publick Use,” Phil Tran. 5 (1670): 1098-1099. 2 William Holder, Supplement to the Philosophical Transactions of July, 1670. With Some Reflexions on Dr. John Wallis, His Letter There Inserted (London, 1678).

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What Dr. Holder had Attempted, but Given over; I had undertaken with Success.” But Holder, jealous of Wallis’s success and having distorted the events in his head, began to “imagin[e] Plots, and Practises, Designs, and Subtil Contrivances, And a great many more Fansies of his own Brain, which never came into my Thoughts.”3

Although the rhetorical skills that Wallis demonstrates here were ones that he used throughout his career, it was highly unusual for him to direct them against a fellow member of the

Royal Society and Anglican minister such as Holder. In fact, these publications were the result of a conflict between the two clerics that threatened to divide the Royal Society into two feuding parties.4 Wallis was normally an active promoter of the Society’s interests, so what was at stake in this dispute that was worth jeopardizing the Society’s future? As far as Wallis is concerned, the answer is clear. He did not view his work with Whaley and Popham as merely an exercise in pedagogy. He also treated this work as a successful application of his abilities as both an experimental philosopher and as a linguist, an achievement that he showed off by bringing Whaley to speak before the Royal Society and the court of King Charles II in 1662. Wallis’s success with

Whaley, the result of over a year’s worth of hard work,5 produced some of the strongest

3 Wallis, A Defence of the Royal Society, and the Philosophical Transactions, Particularly Those of July, 1670. In Answer to the Cavils of Dr. William Holder (London, 1678), 20, 24. Italics in original. 4 Mordechai Feingold provides a useful synopsis of the events leading to these polemical publications. As Feingold explains, Holder claimed priority for his work with Popham in the Philosophical Transactions in 1668. Thereafter Wallis and his friends mentioned the Savilian Professor’s work with Popham and Whaley in a series of publications, neglecting to mention Holder each time. This infuriated Holder, who confronted Henry Oldenburg about publishing an account partial to Wallis in the Transactions in 1670, and enlisted the support of such prominent Fellows as Robert Hooke and Christopher Wren. Wallis, on the other hand, had the support of the Society’s President, William Brouncker. In the end, Brouncker lost his presidency over the dispute, but neither Holder nor Wallis suffered any serious consequences (Mordechai Feingold, “The Origins of the Royal Society Revisited,” in The Practice of Reform in Health, Medicine, and Science, 1500-2000: Essays for Charles Webster, eds. Margaret Pelling and Scott Mandelbrote [Aldershot: Ashgate, 2005], 168-175). See also Jonathan Rée, I See a Voice: Deafness, Language and the Senses––A Philosophical History (London: HarperCollins, 1999), 106-19. 5 In his autobiographical letter of 1696/7, Wallis mentions that it took “little more than a year” to teach Whaley to speak clearly (Christoph J. Scriba, “The Autobiography of John Wallis, F.R.S.,” Notes and Records of the Royal Society of London 25 [1970]: 41).

170 experimental evidence to date that deaf people could understand and communicate with spoken language, which had long been considered impossible.6

Wallis had been able to give speech to these deaf patients on account of his intimate knowledge of how language works, not only grammatically and historically, but also physiologically. In 1653, Wallis had displayed this range of linguistic knowledge in his Latin text on English grammar, the Grammatica linguae Anglicanae. Printed along with the Grammatica was his treatise De loquela, which describes how the organs of speech are manipulated to produce sounds. This, Wallis notes, was apparently “the first Book ever Published in that kind.”7 Wallis took pride in this achievement, as well as his work with Whaley and Popham, which depended on these earlier linguistic studies.8

These examples aside, relatively few of Wallis’s texts deal directly with language or grammar. Those that do, however, stand as prominent examples of the importance of words in his broader philosophy. The experimentalist culture in which Wallis participated has typically been associated with a renewed emphasis on things rather than words—or, in the standard Latin formulation, on res rather than verba. Much credit for this shift is given to Francis Bacon, who famously writes in The Advancement of Learning (1605), “the first distemper of learning, [is] when men studie words, and not matter”; this sort of vain philosophy, which is more concerned with philology and rhetoric than with things themselves, is what Bacon hopes to replace with his

6 See Rée, I See a Voice, 108-109. Rée notes, however, that later in his life, Wallis attached less importance to speech as a means of communication for deaf people. In a letter of 1699 to Joseph Conrad Amman, a fellow educator of the deaf, Wallis claimed that, while it was now clearly possible to teach deaf people to speak, it would be more useful to teach them to read and write, which they could do just as well as a person who could hear. Amman printed this letter in his treatise on teaching the deaf, Dissertatio de loquela (1700) (Rée, I See a Voice, 115-116; see also James Knowlson, Universal Language Schemes in England and France 1600-1800 [Toronto: University of Toronto Press, 1975], 216). 7 Wallis, “Letter to Boyle,” 1099. 8 In his letter to Boyle that was published in the Philosophical Transactions, Wallis explicitly connects his work with Whaley to the method he described in De loquela (Wallis, “Letter to Boyle,” 1096).

171 empirical methodology.9 But regardless of how much Bacon’s aspirations might have inspired activities of the Royal Society, the case of Wallis helps to show that the study of words was not necessarily in tension with the emerging experimental philosophy. Indeed, as I will argue below,

Wallis treats his language studies as one of his most important contributions as an experimentalist.

In fact, the deeper one looks into his works, the more one finds that Wallis was a devoted student of language, even though this was not his main profession. He never misses an opportunity to show off his knowledge of etymology, grammar (including that of English and a range of other languages), phonetics, or the physiology of speech—in short, every aspect of human language.

Although the focus on language in Wallis’s works has rarely been addressed by historians, it recurs in his writings on a wide range of topics. In the Defence of the Royal Society, for example,

Wallis not only defends his achievements with Whaley and Popham, but also makes several digressions that demonstrate his linguistic expertise. He notes that John Wilkins had consulted him while working on his “real character,” a project supported by the Royal Society to produce an artificial language with words that correspond exactly to things in the natural world. As Wallis explains, “There [was] scarce any part, in all that Discourse, wherein I was not advised with.” 10

9 Francis Bacon, The Two Bookes of Francis Bacon. Of the Proficience and Aduancement of Learning, Diuine and Humane. To the King (London, 1605), 18. A. C. Howell’s classic article argues that Bacon’s Advancement of Learning articulates a new meaning of res as opposed to verba. Classical writers had distinguished the res or subject matter of a text from verba, its words, whereas seventeenth-century scholars redefined res as things in the world, and so reconceived the res/verba distinction as one between words and things (A. C. Howell, “Res et verba: Words and Things,” ELH 13 [1946]: 131-142). More recent scholarship on Bacon has emphasized that the Advancement of Learning should not be viewed in isolation from Bacon’s other writing, which generally does not take such a negative view of language and rhetoric. See, for example, Pavneet Aulakh, “Seeing Things through ‘Images Sensible’: Emblematic Similitudes and Sensuous Words in Francis Bacon’s Natural Philosophy,” ELH 81 (2014): 1149-1172; Francis Wilson, “Such Words in His Things: The Poetry in Bacon’s New Science,” Language and Literature 11 (2002): 195-215; Brian Vickers, “Bacon and Rhetoric,” in The Cambridge Companion to Bacon, ed. Markku Peltonen (Cambridge: Cambridge University Press), 200-231. 10 Wallis, Defence of the Royal Society, 17. Wilkins’ Essay towards a Real Character (1668) was the most influential of the several universal language projects by British scholars in this period. These artificial languages were meant to be not only universal, but also “philosophical,” meaning that they would be constructed on a foundation of logic and natural philosophy, so that the words would convey the precise meanings of the things that they represent. Other notable examples include the language schemes of George Dalgarno and Francis Lodwick. For detailed accounts of each of these projects, see Umberto Eco, The Search for the Perfect Language, trans. James Fentress (Oxford:

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The examples noted above reflect the linguistic knowledge and rhetorical abilities that

Wallis relied on time and again throughout his career. This chapter investigates the purpose of language studies and rhetoric in Wallis’s corpus as a whole. I have two main goals in this chapter.

The first is to describe the nature of Wallis’s linguistic studies which, I argue, he conceived as a part of experimental philosophy. This has important implications for historians’ understanding of the relationship between language and science in seventeenth-century England. The second goal is to describe some of the applications of Wallis’s linguistic knowledge, as well as his rhetorical techniques. I will argue that these abilities allowed Wallis to write with authority not only about words and phrases, but also about the referents of those words and phrases. As I will discuss below, Wallis relied on a combination of rhetorical savvy and linguistic knowledge during debates over terminology. This applies to his dispute over mathematical terminology with Thomas

Hobbes, and also to his forays into theological controversies. In the seventeenth century, such controversies hinged on the contested meaning of terms commonly used in Christian theology since the patristic period, such as “person” and “substance.” As he claimed to know exactly what was meant by such terms—grammatically, etymologically, and historically—he could speak with authority on exactly what they referred to, and he could insist on interpretations of those words that would support his own positions. The texts discussed below are interspersed with long digressions on grammar and etymology that might seem bizarre and excessive to the modern reader. But their purpose becomes clear when we consider the central role of words in Wallis’s works: by means of rhetoric and linguistic knowledge, Wallis seeks to control the meanings of crucial terminology in natural philosophy, in mathematics, and perhaps especially in theology.

Blackwell, 1995), 228-268; Rhodri Lewis, Language, Mind and Nature: Artificial Languages in England from Bacon to Locke (Cambridge: Cambridge University Press, 2007), 49-63, 85-100, 108-109, 146-221; M. M. Slaughter, Universal Languages and Scientific Taxonomy in the Seventeenth Century (Cambridge: Cambridge University Press, 1982), 85-125.

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This account of Wallis’s language and rhetorical skills helps to demonstrate the extent to which seventeenth-century writers were concerned with verba as well as res. Wallis emphasized the use of appropriate language in his works on subjects ranging from mathematics to theology.

This was not merely a matter of describing things accurately. Rather, his linguistic investigations themselves constitute a major part of his novel contributions to these fields. In natural philosophy he investigated the mechanics of speech; in grammar he empirically described how people use words and connect them to each other; in mathematics he sought precise definitions for fundamental concepts; and in theology he mirrored his efforts in mathematics, marshalling his wide range of linguistic (and rhetorical) skills in an effort to define the boundaries of theological terms.11

I will substantiate these claims in three sections below. The first describes Wallis’s lifelong interest in language and its relation to his natural philosophy. As this section will show, if we can allow the anachronistic label “scientific” for any of Wallis’s activities, it should surely apply to his study of languages, including his interest in their history and grammatical structure as well as the physiology of speech. The second section considers the role of rhetoric and language in Wallis’s conflict with Hobbes. I argue that the first stage of the dispute was largely about the meaning of words—philosophical, mathematical, and religious ones. This contest over the use

11 My emphasis on the importance of language studies is informed by James J. Bono’s analysis of language and science in early modern Europe. Bono argues that, as modern science emerged, it was accompanied by new ways of using and studying language. These developments were not a “mere discursive reflection” of the transformation of science, not “an epiphenomenon of some larger, totalizing, paradigmatic perspectival shift.” Rather, new theories and uses of language actually changed how natural philosophers studied nature; language is “an agent or site of scientific change” (James J. Bono, The Word of God and the Languages of Men: Interpreting Nature in Early Modern Science and Medicine, vol. 1 [Madison: University of Wisconsin Press, 1995], 9). Thus, for example, Bacon’s emphasis on studying things rather than words is informed by his belief that human language had been forever changed by the confusion of tongues at Babel. In an effort to recover the natural knowledge that Adam had had in the Garden of Eden, many scholars sought to recover his language, which was supposed to have described knowledge perfectly. But according to Bacon, the effects of Babel had made the “Adamic” language permanently inaccessible. The only way to recover Adam’s knowledge, then, was to study nature itself (Bono, Word of God, 209-246). See also n. 32 below.

174 and propriety of language gave Wallis the opportunity he needed to assert his authority in linguistic matters, and it helps to explain his and Hobbes’s otherwise puzzling preoccupation with grammatical minutiae in a debate ostensibly about mathematical method. Finally, in the third section, I return to Wallis’s engagement in the Trinitarian controversy of the 1690s. I argue that this, too, was in part a contest over the meaning of terminology, and accordingly Wallis’s rhetorical and linguistic skills were indispensable. The conclusion to this chapter reflects on what

Wallis’s language studies reveal about the science-religion relationship in the seventeenth century. I argue that Wallis conceived of his language studies as part of natural philosophy, but the applications of his linguistic skills served theological ends.

Language studies and experimental philosophy in Grammatica and De loquela

In his popular logic textbook, Institutio logicae (1687), Wallis defined knowledge of languages as one of the “acquired habits” gained through repeated exposure and practice. A rare historical exception was the “knowledge of languages instilled in the Apostles of Christ from heaven” during Pentecost, as described in Chapter 2 the Book of Acts.12 But since this miraculous Gift of

Tongues was a unique historical event, people in Wallis’s time had to acquire linguistic knowledge through study and practice. This is how Wallis approached languages in his own life, honing his skills and exposing himself to new foreign languages whenever he could. His

Grammatica encourages readers to take the same approach, especially the fourth edition of 1674, the first to include translation exercises in an appendix entitled “Praxis grammatica.”13 The study

12 “Habituum . . . Acquisiti”; “linguarum peritia Christi Apostolis Cœlitùs indita” (Wallis, Institutio logicae, ad communes usus acommodata, 1st ed. [Oxford, 1687], 35). Wallis also refers to speech as a habit in his Defence of the Royal Society when he challenges Holder’s claim to have taught Alexander Popham to speak. According to Wallis, “Habits so well acquir’d, do not use to be so quickly lost” (Wallis, Defence of the Royal Society, 4; italics in original). 13 See Wallis, “Praxis grammatica,” in Grammatica linguae Anglicanae, 4th ed. (Oxford, 1674), 135-190.

175 of languages was an ongoing project throughout Wallis’s life, as it was for many of his contemporaries. This began in the grammar schools that he attended in his youth and continued with the various intellectual endeavours of his adulthood, which almost always included a linguistic element.14

Although language studies were never the main focus of Wallis’s career, his works reflect extensive linguistic abilities and a keen interest in foreign tongues. The Grammatica became one of the most popular and influential accounts of the English language, reaching its sixth edition in

1765. In fact, modern scholars still appreciate its insights into the structure of the English language.15 Apart from English and Latin, the languages in which he composed his works, Wallis demonstrated a deep knowledge of Greek—which allowed him to produce modern translations of works by Ptolemy, Archimedes, Aristarchus, and Pappus––as well as a competency in French, and at least a familiarity with Hebrew, Persian, Arabic, and Chinese.16 On occasion, colleagues consulted Wallis on linguistic matters. For example, he helped Wilkins to test out his artificial

14 In his autobiographical letter to Thomas Smith, Wallis fondly recalls attending grammar school in Kent and Essex in his early years before he matriculated at Cambridge in 1632; he learned Latin, Greek, and some Hebrew (Scriba, “Autobiography of Wallis,” 24-26). 15 On the content and impact of Grammatica, see Ilinca Constantinescu, “John Wallis (1616–1703): A Reappraisal of His Contribution to the Study of English,” Historiographia Linguistica 1 (1974): 297-311; J. A. Kemp, trans., John Wallis’s Grammar of the English Language (London: Longman Group, 1972), 27-73; A. B. Melchior, “Sir Thomas Smith and John Wallis: The Problem of the Early Modern [y:] Re-Examined,” English Studies 53 (1972): 210-223; Vivian Salmon, “Effort and Achievement in 17th-Century British Linguistics”, in Language and Society in Early Modern England: Selected Essays 1981-1994, ed. Konrad Koerner (Amsterdam and Philadelphia: John Benjamins, 1996), 19-23. 16 Wallis’s Greek translations are listed in OM I, sig. b4r. In an unpublished manuscript, Wallis comments on the challenges of publishing ancient Greek texts that result from the changes in the language over time. He notes that the translator must modernize the language of the text, just as someone would need to do in order to publish a new edition of Chaucer for modern English readers (MS. Ballard 24, ff. 11r-12r). As for other languages, Wallis repeatedly shows off his knowledge of Hebrew and Persian in Grammatica, comparing the grammatical rules of these language to those of English (Kemp, John Wallis’s Grammar, passim). In addition, as Jacqueline Stedall has discussed, Wallis’s study of the adoption of Hindu-Arabic numerals in Europe led him to make some comments on the Arabic language, particularly in relation to the origins of such mathematical terms as “algebra” and “algorithm”; see Jacqueline A. Stedall, “Of Our Own Nation: John Wallis’s Account of Mathematical Learning in Medieval England,” Historia mathematica 28 (2001): 75, 78. Finally, Wallis comments on Chinese grammar in his letter to Boyle on his work with deaf students, and also in a letter to Edmond Halley (ESO XII, 114; Wallis, “Letter to Boyle,” 1091). These examples constitute only a small sample of Wallis’s extensive engagement with foreign languages.

176 language by exchanging letters written in Wilkins’ “real character.”17 Similarly, when approached by Robert Boyle for comments on his book, Some Considerations Touching the Usefullnesse of

Experimental Natural Philosophy (1663), Wallis advised him on word choices and spelling as much as on matters of natural philosophy.18

The circumstances surrounding Wallis’s publication of a textbook on grammar remain unknown. Presumably, though, Wallis appreciated the study of languages not only because it was dynamic and challenging, but also because it fit well with his other interests. Like most fields of inquiry, language studies underwent dramatic changes in the seventeenth century, and one consequence of these changes was that natural philosophy and linguistics became more and more closely intertwined. In this period, the history of language intersects with the history of science in at least two important ways, and Wallis’s works offer good examples of each. Firstly, writers developed new rhetorical techniques and new styles of discourse, which they used both within science and to talk about science. The members of the early Royal Society in particular are known for creating a new, dispassionate style of scientific writing to describe their experiments and observations, a style that, as Shapin and Schaffer put it, was “plain, ascetic, unadorned (yet convoluted) . . . [and] functional.”19 On the other hand, while this style of discourse left little room for the classical techniques of persuasive rhetoric, those works that promoted the Royal Society,

17 Wallis’s translation of Wilkins’ letter and drafts of his own letter survive in his copy of Wilkins’ Essay (Bodleian Savile A 4, iii-vi; see WC II, 493-494, 496). In addition, there is some evidence that Wallis contributed to George Dalgarno’s artificial language project. Samuel Hartlib mentions this in his Ephemerides, noting that Seth Ward helped as well, and Wallis himself claims to have helped Dalgarno in Defence of the Royal Society. Dalgarno, however, did not acknowledge Wallis’s help when he published his Ars Signorum. See Lewis, Language, Mind and Nature, 85- 87. 18 WC II, 91-98. 19 Steven Shapin and Simon Schaffer, Leviathan and the Air-Pump: Hobbes, Boyle, and the Experimental Life, 2nd ed. (Princeton: Princeton University Press, 2011), 66. Italics in original. For a focused discussion of how and why the Fellows developed this new style, see Peter Dear, “Totius in verba: Rhetoric and Authority in the Early Royal Society,” in Rhetoric and the Early Royal Society: A Sourcebook, eds. Tina Skouen and Ryan J. Stark (Leiden and Boston: Brill, 2015), 53-76.

177 such as Thomas Sprat’s History, openly and skillfully employed these techniques in order to convince people of the value of experimental philosophy.20 Wallis wrote effectively in each of these two styles, the dispassionate and the highly rhetorical. His experimental reports fit in well among those of Boyle, Hooke, and others, but he was also among the most rhetorically gifted of the Society’s early members. And as we will see below, he seems to have delighted in crafting passionate rhetorical attacks against Hobbes and his other enemies. For the modern reader, it is often breathtaking to observe Wallis’s ability to describe every development in mathematics or natural philosophy in a way that serves his own interests, or the interests of England, Oxford, or the Royal Society. These instances show that Wallis truly had a rhetorical gift.

The second important connection between language and science in the seventeenth century was the flourishing scientific study of languages themselves. English scholars in this period devoted unprecedented attention to the form and function of their own language and others, ranging from those of the Americas to those of the Far East.21 Many major figures in natural philosophy engaged in linguistic studies, collecting a wealth of data on languages just as they did with natural phenomena, and again Wallis is one of the foremost examples. He had two separate accounts of his work with the deaf published in the Philosophical Transactions: a letter of 1661/2 to Boyle—the printing of which sparked his dispute with Holder—and a letter of 1698 to the

Independent minister Thomas Beverley. Each of these letters is written like an experimental

20 See Richard Nate, “Rhetoric in the Early Royal Society,” in Skouen and Stark, Rhetoric and the Early Royal Society, 77-93. On Sprat’s rhetorical techniques in particular, see Tina Skouen, “Science versus Rhetoric: Sprat’s History of the Royal Society Reconsidered,” in Skouen and Stark, Rhetoric and the Early Royal Society, 237-264. 21 For an overview of the major developments in language studies in seventeenth-century England, see Salmon, “Effort and Achievement,” 3-29. English scholars often had religious motivations for studying the grammars of other languages, including a desire to convert the speakers of those languages to Christianity—or more specifically to Protestantism. Boyle, for instance, supported projects to translate the Bible into Algonquian, Turkish, Lithuanian, and Irish, so that native speakers could be converted. See Gabriel Glickman, “Protestantism, Colonization, and the New England Company in Restoration Politics,” The Historical Journal 59 (2016): 372-373; Noel Malcolm, “Comenius, Boyle, Oldenburg, and the Translation of the Bible into Turkish,” Church History and Religion Culture 87 (2007): 327-362.

178 report. In the letter to Beverley, for example, Wallis offers a series of step-by-step instructions based on his own experiences, with the explicit goal of allowing readers to replicate his method.

He wrote, “I have taken pains to draw-up this method . . . as apprehending it may be of use to some others when I am dead. And I am not desirous it should dy with me.”22 Here, as elsewhere,

Wallis links these educational techniques to De loquela, which was published forty-five years earlier. Evidently, with this second account in the Philosophical Transactions, he wanted to ensure that his techniques for teaching language to deaf students would form part of his legacy within the natural philosophical community.23

De loquela approaches the physiology of speech with what J. A. Kemp calls an

“articulatory system”––that is, a system organized not in terms of the sounds produced, but rather in terms of how the various organs of speech are manipulated in order to produce those sounds.

Wallis’s articulatory system, Kemp explains, was not the first of its kind, but it was the most sophisticated such system to date.24 Describing De loquela in his autobiographical letter of

1696/7––another sign that Wallis considered this work an important part of his legacy––he explains that he “Philosophically considered the Formation of all Sounds used in Articulate

Speech, (as well of our own, as of any other Language that I know;) By what Organs, and in what

Position each sound was formed.” This was a project that “some Grammarians” had undertaken before, but only partially and “very imperfectly.”25 Wallis describes his system in similar terms

22 Wallis, “A Letter of Dr. John Wallis, (Geom. Prof. Oxon., and F. R. S.) to Mr. Thoma’s [sic] Beverly; concerning his Method for Instructing Persons Deaf and Dumb,” Phil Trans 20 (1698): 359. 23 Wallis was by no means the only member of the early Royal Society who considered language studies to be connected to natural philosophy. For instance, David Cram identifies such connections in the work of John Wilkins, who had undertaken his philosophical language project at the request of the Royal Society. As Cram explains, Wilkins believed that God had created language and given it to Adam, but more recent developments—particularly since the confusion of tongues at the Tower of Babel—had to be explained in terms of natural causes, just as the Royal Society explained natural phenomena (David Cram, “Linguistic Eschatology: Babel and Pentecost in Seventeenth-Century Linguistic Thought,” Language and History 56 [2003]: 48). 24 Kemp, John Wallis’s Grammar, 40. 25 Scriba, “Autobiography of Wallis,” 41.

179 in Defence of the Royal Society, claiming that he believes it to be “the first attempt” to identify

“with what Organs, in what Positions, and by what Motions, all Sounds used in Speech are

Formed.” Here Wallis notes that, to the nine organs of speech that are traditionally identified— the throat, tongue, palate, two lips, and four front teeth—he added another, namely, the nostrils, which open to different widths in the production of certain sounds, “[w]hich (I think) no body, before me, had taken notice of. But I am since followed by others.”26 This comprehensive articulatory system, Wallis evidently believed, constituted one of his most original and important achievements as an experimental philosopher.

Wallis’s description of his system as philosophical, and his suggestion that it can accommodate the sounds made in any language, indicate that he saw his contribution to the physiology of speech much like his work in physics. The articulatory system could in principle be totally comprehensive, accommodating all utterances in the same way that his laws of motion accommodate the motions of any solid body (as discussed in Chapter 3 above). But it is not only

De loquela that Wallis treats as a comprehensive set of rules comparable to those affecting natural phenomena. The Grammatica, to which De loquela was prefixed, is the product of Wallis’s careful collection of an enormous amount of data about how the English language is used, and how it compares to other languages. As A. B. Melchior has argued, “For Wallis it is the facts of the spoken language that matter.” 27 Thus spelling, for instance, should be adapted to common pronunciations. Furthermore, Wallis emphasizes his intention to describe the English language on its own terms, rather than fitting it into a framework based on Latin grammar as previous English grammarians had done. His predecessors had

26 Wallis, Defence of the Royal Society, 16. Italics in original. 27 Melchior, “Smith and Wallis,” 220. Melchior notes, however, that Wallis sometimes steps outside the boundary of actual, spoken English and identifies alternative “theoretical, non-existing pronunciations” for words, which would correspond more directly to how they are commonly spelled (Melchior, “Smith and Wallis,” 219).

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. . . all forced English too rigidly into the mould of Latin (a mistake which nearly everyone makes in descriptions of other modern languages too), giving many useless rules about the cases, genders and declensions of nouns, the tenses, moods and conjugations of verbs, the government of nouns and verbs, and other things of that kind, which have no bearing on our language, and which confuse and obscure matters instead of elucidating them.28

Conversely, Wallis views his own system of English grammar as “a completely new method, which has its basis not, as is customary, in the structure of the Latin language but in the characteristic structure of our own.”29

Thus, rather than conforming to classical ideas about grammar, Wallis bases his account on direct observation, so to speak, of how the language is used. It is perhaps his insistence on direct observation and his rejection of ancient precedent that prompt Vivian Salmon to describe Wallis’s

Grammatica as “the first genuinely ‘scientific’ grammar of English.”30 While it is unclear what criteria Salmon uses to designate a grammatical system “scientific,” this descriptor does reflect the fact that Wallis’s approach in the Grammatica seems to resonate with the ideas of Francis

Bacon. In “De dignitate et augmentis scientiarum” (1623), Bacon calls for a new sort of grammar informed by natural knowledge that would “diligently inquire, not the analogy of words with one another, but the analogy between words and things, or reason.” Such a grammar would include a comparative study of the strengths and weaknesses of different languages, so that “not only may languages be enriched by mutual exchanges, but the several beauties of each may be combined

. . . for the right expressing of the meanings of the mind.” In addition, Bacon envisioned this grammar to be complemented by a separate investigation of “[t]he primary formation of simple letters . . . (that is, by what percussion of the tongue, by what opening of the mouth, by what meeting of the lips, by what effort of the throat, the sound of each letter is produced).” Strictly

28 Kemp, John Wallis’s Grammar, 109-111. 29 Kemp, John Wallis’s Grammar, 111. 30 Salmon, “Effort and Achievement,” 23.

181 speaking, this is not a part of grammar, but instead is “to be handled under Sense and the

Sensible.”31 Bacon’s ideal grammar, then, would be developed in conjunction with reason and natural philosophy: words should match ideas exactly, and the structure of the grammar should be informed by a parallel study of the physiology of speech.

Salmon rightly observes that the various universal language projects in England during the late seventeenth century were a response to Bacon’s call for a grammar developed in tandem with a reformed natural philosophy.32 As for Wallis, although the Royal Society appointed him to a committee that would discuss how to improve Wilkins’ Essay towards a Real Character (1668),33 he felt that these artificial languages were impractical and he doubted that they would catch on.

He wrote to Henry Oldenburg that he “judged well of” Wilkins’ Essay, conceding that the creation of a philosophical language was “fesible,” but he added that he had “but very slender

31 Francis Bacon, “De dignitate et augmentis scientiarum,” in The Philosophical Works of Francis Bacon: Baron of Verulam, Viscount St. Albans, and Lord High Chancellor of England, ed. John M. Robinson (New York: E. P. Dutton, 1905), 523-524. 32 Salmon, “Effort and Achievement,” 22. See also Joseph L. Subbiondo’s argument that Wilkins’ Essay toward a Real Character was directly inspired by Bacon’s New Atlantis (Joseph L. Subbiondo, “Francis Bacon’s New Atlantis and John Wilkins’ Essay: Educational Reform and Philosophical Language in 17th-Century England,” in Linguists and Their Diversions: A Festschrift for R. H. Robins on His 75th Birthday, eds. Vivien Law and Werner Hüllen [Münster: Nodus, 1996], 123-139. Many seventeenth-century scholars argued that the creation of a universal language could help to reverse the detrimental effects of the Fall of Man and the Confusion of Tongues. It was generally believed that, in the Garden of Eden, Adam had spoken a philosophical language whose words corresponded exactly with the nature of things. Adam’s Fall, however, not only permanently weakened humanity’s cognitive abilities but also removed access to this philosophical language. Subsequently, as a punishment for construction of the Tower of Babel, God created a Confusion of Tongues and forced humanity to speak a variety of language. This not only made communication more difficult, it also further distanced humanity from the language spoken by Adam in the Garden of Eden. The seventeenth-century scholars involved in universal language projects differed on the relative importance that they assigned to the Fall and Babel in the history of human languages, but they had in common the goal of either recovering or emulating the prelapsarian, philosophical, “Adamic” language. In England, Bacon’s call for an “instauration” of Adam’s prelapsarian knowledge included plans for such a philosophical language, which set an important example for later English language scholars. See Bono, Word of God, 214-244; Jaap Maat and David Cram, “Universal Language Schemes,” in The Cambridge History of Linguistics, eds. Linda R. Waugh and Monique Monville-Burston (Cambridge: Cambridge University Press, forthcoming); William Poole, “The Divine and the Grammarian: Theological Disputes in the 17th-Century Universal Language Movement,” Historiographia Linguistica 30 (2003): 273-300. Wallis himself believed that the Fall had damaged humanity’s cognitive abilities, but he resisted describing the history of languages in terms of the biblical narrative. 33 Rhodri Lewis discusses this committee, noting that its members never submitted a report, and probably never even met (Rhodri Lewis, “The Efforts of the Aubrey Correspondence Group to Revise John Wilkins’ Essay [1668] and Their Context,” Historiographia Linguistica 28 [2001]: 331-332; idem, Language, Mind and Nature, 194-200).

182 expectations” that any language could ever be universally adopted.34

Perhaps Wallis envisioned his Grammatica as a more realistic way to reform grammar along the same lines as natural philosophy. The Grammatica was “universal” in a different sense: it was meant to teach English to foreigners so they could appreciate the achievements of English writers.

As Wallis explains in his autobiographical letter, he wrote the Grammatica “chiefly to gratify strangers, who were willing to learn it: (because of many desirable things published in our

Language) but complained of its difficulty for want of a Grammar, suited to the propriety and true

Genius of our Language.”35 The Grammatica is replete with comparisons between English and other languages in both phonics and grammar, as well as comments on their respective advantages. Discussing the letter c, for instance, Wallis explains that in English it could be hard or soft depending on the letter that followed it, whereas “[t]he French sometimes write soft c with the symbol ç, and I think this symbol could well be used by us too.”36 He also compares English phonics and grammar to Latin, Greek, Hebrew, German, and other languages, as if responding to

Bacon’s call thirty years earlier for a grammar based on a comparative study of languages.

Furthermore, although he was careful not to blur the boundary between grammar and physiology,

Wallis published his research on these subjects together so that they could be easily compared.

Again, although Wallis does not refer to Bacon directly, his work again seems to answer Bacon’s expectations: he produced a “philosophical” treatment of language to match the grammatical one.

34 WC II, 481. Italics in original. Wallis concluded that universal, philosophical language projects were impractical because he was convinced that language by its very nature is arbitrary and imprecise. Words can never correspond directly to ideas and objects, Wallis argued, so a new artificial language would truly be no more precise than existing languages. Furthermore, scholars would not agree on how a new language should be constructed, so no new language would appeal to everyone (Wallis, Defence of the Royal Society, 16). See David Cram, “Universal Language, Specious Arithmetic and the Alphabet of Simple Notions,” Beiträge zur Geschichte der Sprachwissenschaft 4 (1994): 213–233; Rhodri Lewis, “John Evelyn, The Early Royal Society, and Artificial Language Projection: A New Source,” Notes and Queries 51 (2004): 33; Jason Michael Rampelt, “Distinctions of Reason and Reasonable Distinctions: The Academic Life of John Wallis (1616-1703)” (PhD diss., Cambridge, 2005), 220-224. 35 Scriba, “Autobiography of Wallis,” 41. 36 Kemp, John Wallis’s Grammar, 215. Italics in original.

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In any case, in its form as well as its content, the Grammatica reflects the close connection between language and natural philosophy in the work of Wallis and his contemporaries.

The Grammatica is impressive on account of both its depth and breadth, which Wallis improved in each new edition. After his death, the book continued to be one of Wallis’s most enduring works, with further editions and two partial translations into English published in the eighteenth century.37 More than any of his other works, the Grammatica showcases Wallis’s formidable linguistic abilities—mostly in English and Latin, but to a lesser extend also in an assortment of other languages that he compares to English throughout the book. These linguistic abilities also had important practical applications. For instance, his work as a codebreaker depended on at least a familiarity with certain foreign languages (especially French, in which many of the intercepted letters that he decoded were written), and also on his insights into how language works in general. Indeed, in his letter to Boyle, Wallis explicitly compares Daniel

Whaley’s acquisition of knowledge to codebreaking. He notes that Whaley might eventually be able to read lips well enough to pick up part of what a person is saying, and then to fill in the blanks mentally “by a probable conjecture, (as when we Decipher Letters written in Cipher).”38

Wallis was reticent about his codebreaking techniques, even in his manuscript essay on the subject, but John Davys, who prepared the posthumous publication of that essay, suggests that linguistic knowledge was crucial to Wallis’s codebreaking even though he neglected to mention it. Davys writes,

It is requisite, that the Decypherer should know, or have probable Reason to believe, in what Language the Letter is written; and that he should also be at least moderately skill’d in that

37 The two eighteenth-century translations of the Grammatica attest to its lasting influence. Both James Greenwood and John Brightland published texts on English grammar in 1711 that largely consisted of translations of the Grammatica. Several more editions of each text were published during the eighteenth century. Greenwood is upfront about borrowing most of his material from Wallis, but Brightland downplays how much material he has taken from the Grammatica. See Kemp, John Wallis’s Grammar, 68-69. 38 Wallis, “Letter to Boyle,” 1095.

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Language. I can no otherwise account for Dr. Wallis’s Silence on this Head, than by supposing, that he took the Thing for granted.39

To be sure, Wallis’s codebreaking work had more transferrable skills with mathematics than with the study of languages. As Peter Pesic has discussed, for Wallis and other codebreakers, cryptanalysis involved many of the same problem-solving skills as algebra.40 Nevertheless, as

Davys’s remarks suggest, codebreaking represents one of the many practical applications of

Wallis’s extensive knowledge of languages. Indeed, linguistic knowledge is an important asset in practically all of Wallis’s intellectual pursuits. His interest in languages is at once scientific, philological, philosophical, and—as we will see in the next two sections—theological. Especially when paired with his formidable rhetorical abilities, linguistic knowledge was one of Wallis’s most useful resources in any sort of intellectual dispute.

The rhetoric and grammar of mathematics and theology: Wallis versus Hobbes

Shortly after the Grammatica was first published, Wallis was drawn into a controversy that would see him challenged on matters of mathematics, theology, and language all at once. Wallis’s two- decade dispute with Hobbes began in 1655. This is one of the most well-studied episodes in

39 John Davys, An Essay on the Art of Decyphering. In Which is Inserted a Discourse of Dr. Wallis Now First Publish’d from His Original Manuscript in the Publick Library at Oxford (London, 1737), 40. Italics in original. In the essay, Wallis makes the dubious claim that he has no general method for codebreaking. Instead, he suggests, a handful of people (including Wallis himself) simply have an aptitude for it, which they can cultivate with the virtues of “Patience and Sagacity” (Davys, Art of Decyphering, 14). In an article on Wallis’s cryptanalytical career, Philip Beeley discusses Wallis’s efforts to advertise his uncommon ability as a codebreaker while keeping his methods secret. This ensured that he would remain valuable to the patrons who called on his codebreaking services. As Beeley puts it, “Wallis’s indispensability, his status, and his reputation inevitably rested on the inscrutability of his methods” (Philip Beeley, “Breaking the Code: John Wallis and the Politics of Concealment,” in G. W. Leibniz und der Gelehrtenhabitus. Anonymitaet, Pseudonymitaet, Camouflage, eds. Wenchao Li and Simona Noreik [Cologne: Böhlau, 2016], 72). In addition to his aptitude for codebreaking, Wallis understood cryptography well enough to devise his own method for creating ciphers, although he apparently had no occasion to use it. See Alan Marshall, Intelligence and Espionage in the Reign of Charles II, 1660-1685 (Cambridge: Cambridge University Press, 1994), 91-92. 40 Peter Pesic, “Secrets, Symbols, and Systems: Parallels between Cryptanalysis and Algebra, 1580-1700,” Isis 88 (1997): 674-692. On Wallis’s techniques in cryptanalysis and algebra, see 688-692.

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Wallis’s career, but I wish to emphasize an element of the dispute that has received relatively little attention, namely, the linguistic and rhetorical contest between the two writers. The Wallis-

Hobbes dispute was largely about mathematical definitions, at least during the first stage, which spanned from 1655 to 1657. Each disputant recognized that the legitimacy of their techniques and results depended on precise definitions of mathematical entities. Wallis and Hobbes were mainly concerned about mathematical method, and the related question of whether Hobbes had succeeded in squaring the circle and solving other famous mathematical problems. Nevertheless, the dispute had many facets, and the emphasis on definitions allowed Wallis to flex his rhetorical and linguistic muscles. As Wallis and Hobbes argued about the language surrounding mathematics in addition to methods—the verba as well as the res—each of them found opportunities criticize the other’s use of language, particularly in terms of grammar and rhetoric.

In addition, the focus on definitions connects to the theological dimension of the Wallis-

Hobbes dispute. As we will see below, just as Wallis attacked Hobbes’s fundamental mathematical definitions to weaken his credibility, so Hobbes took aim at crucial definitions in

Wallis’s Mens sobria, a work on theology and ecclesiology, in order to challenge his authority as a minister. Based on these exchanges between Wallis and Hobbes dispute, I will argue in this section that, during controversies on both secular and divine matters in the seventeenth century, contests over words in at least three senses—definitions, grammar, and rhetoric—could be decisive. Polemical disputes such as that between Wallis and Hobbes were about verba as much as res.

Reflecting on the dispute in 1680, the year after Hobbes’s death, Wallis mentions two sorts of language that Hobbes was known to use. In the draft of a letter to Thomas Tenison, the future

Archbishop of Canterbury, Wallis explains that Hobbes would describe himself with “magisterial language,” even though he had “scarce any thing to commend him . . . save that he had the

186 confidence to talk profoundly, which Atheistical persons call Witt.” 41 In other words, Hobbes’s writing was witty, but ultimately empty: his was the language of an arrogant atheist. The second sort of language that Wallis attributes to Hobbes better suited who he truly was: “he was Morose,

Supercilious, highly opinionated of himself, & impatient of contradiction: (which when he mett with, it would putt him upon great passion, & very foul language).”42 In light of the printed exchanges between Wallis and Hobbes that are discussed below, I suggest that Wallis regarded

Hobbes’s language as “foul” in two senses: it was rude and unbecoming of a gentleman, and it was also the imprecise, vacuous language of a mediocre mind. He tells Tenison that the more

Hobbes wrote to try to prove he was a brilliant mathematical thinker, the more he revealed that he was, in truth, a bitter old atheist who had a dull mind despite all his witticisms. Indeed, Wallis claims, it was through mathematics that God chose to reveal Hobbes’s intellectual weakness:

And truly, I look upon it as a great providence, that God should leaven him to so great a degree of infatuation, in that which he did so much pride himself [i.e., mathematics]. For whereas in discourses on other subjects, mistakes may easily be shuffled off with a multitude of great words: In Mathematicks it cannot be so.43

In mathematics, no amount of wit could cover up Hobbes’s muddled reasoning and “foul” language.

Hobbes, for his part, makes the same association between poor reason and poor language, both of which he detects in Wallis’s writing. In Six Lessons to the Professors of Mathematiques

(1656), the first text that he wrote against Wallis and his fellow Savilian Professor, Seth Ward,

41 Bodleian MS. Add. D. 105, f. 70r. Wallis crossed out the section of the draft quoted here, rewording much of it later in the letter. Cf. the letter itself (Lambeth Palace Library MS 930, item 55) which does not include the section quoted here. 42 Bodleian MS. Add. D. 105, f. 71r. My italics. 43 Bodleian MS. Add. D. 105, f. 71r. Tenison himself published a lengthy book, written in dialogue format, denouncing Hobbes’s religious views, entitled The Creed of Mr. Hobbes Examined; in a Feigned Conference between Him, and a Student of Divinity (1670). See Samuel I. Mintz, The Hunting of Leviathan: Seventeenth-Century Reactions to the Materialism and Moral Philosophy of Thomas Hobbes (Cambridge: Cambridge University Press, 1962), 72-73.

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Hobbes ridicules Wallis in particular for using “so much contumelious language grounded upon arrogance and ignorance.”44 Indeed, in the early stage of their dispute, Hobbes seems to be just as preoccupied with words as Wallis. Each of them was concerned with precise definitions, especially in mathematics, but also in natural philosophy and theology. In addition, they expend a surprising amount of energy arguing over proper Latin and Greek usage. For each of these thinkers, authority over linguistic matters supports one’s authority in other areas, including their debates on whose mathematical techniques were legitimate and whose theology was more reasonable.

The high stakes of their linguistic contest help to explain why, for instance, Wallis spends seven pages of his Due Correction for Mr Hobbes (1656) arguing that Hobbes is wrong to claim that the Latin verb ducere, and other verbs of which ducere is the root, can only take direct objects that are animate, rather than inanimate.45 Douglas Jesseph rightly points out that such grammatical squabbles are typical of the rhetorical conventions of seventeenth-century controversies: it was a standard rhetorical technique to point out an opponent’s grammatical errors and other linguistic weaknesses in order to reveal an opponent’s lack of eloquence, erudition, and wit.46 I contend, however, that rhetorical conventions are not sufficient to explain the sheer volume of words that the disputants expend on seemingly trivial grammatical minutiae. Rather, Wallis and Hobbes belabour these grammatical points to such an extent because they were part of a larger contest for authority over language. This contest also involved their competing interpretations of terminology

44 Thomas Hobbes, Six Lessons to the Professors of the Mathematiques, one of Geometry, the Other of Astronomy: in the Chaires Set Up by the Noble and Learned Sir Henry Savile, in the University of Oxford (London, 1656), 35. 45 Wallis, Due Correction for Mr Hobbes. Or Schoole Discipline, for Not Saying His Lessons Right. In Answer to His Six Lessons, Directed to the Professors of Mathematicks (Oxford, 1656), 14-21. 46 Douglas Jesseph, Squaring the Circle: The War between Hobbes and Wallis (Chicago: University of Chicago Press, 1999), 327-333.

188 that was fundamental to mathematical and other kinds of knowledge.47 Each of the two disputants seeks to show that the other’s flawed use of language was a reflection of flawed thinking, but

Wallis in particular argues that a good mathematician must be a good grammarian.48 After Hobbes objected to Wallis’s use of the phrase “Mathematicall definition,” claiming that definitions are matters of language rather than mathematics, Wallis insists in his Due Correction that definitions are the very foundation of mathematical knowledge. He asks Hobbes, “Do you think, nothing is

Mathematicall, wherein a man makes use of Grammar? Can a man teach Mathematicks, in any language, without Grammar?” Indeed, Euclid himself appreciated the dependence of mathematics on clear language, for “if not his Definitions, what then is it, in Euclide, that is Mathematicall?”49

As Wallis recognized, his dispute with Hobbes was mathematical in character, but mathematical issues were inseparable from linguistic ones.

Wallis appreciated, as did Hobbes, that an attack on his opponent’s definitions could be devastating to his mathematics. Each of them reasoned that clear thinking produces clear definitions, and clear definitions in turn produce clear mathematical demonstrations. Thus it was

47 Jason Rampelt briefly discusses Hobbes and Wallis’s emphasis on precise definition during their dispute (Rampelt, “Distinctions of Reason,” 177-179). The definitions in question are mainly mathematical ones, until Hobbes challenges Wallis on religious definitions in ΣΤΙΓΜΑΙ, but at times they also dispute terminology in natural philosophy. Hobbes, for example, objects to the references to condensation and rarefaction by Wallis, Ward, Boyle, and other proponents of the existence of the vacuum. The vacuists claimed that condensation and rarefaction referred to a change in the amount of empty space between the particles in a substance: when air was condensed, its particles were forced closer together, and when it was rarefied, the particles were farther apart. Hobbes, as a plenist, thought it was impossible for the same quantity of a substance to occupy more or less space. The words “condensation” and “rarefaction” are so meaningless, Hobbes quips, that they might as well be replaced with “Wardensation” and “Wallifaction.” Hobbes means to suggest that these “empty” words are products of “empty” minds. See Simon Schaffer, “Wallifaction: Thomas Hobbes on School Divinity and Experimental Pneumatics,” Studies in the History and Philosophy of Science 19 (1988): 275-298. 48 As for Hobbes, Ted H. Miller notes that the connection he established between flawed language and flawed reasoning was not restricted to his polemical tracts directed against Wallis. In both Leviathan (1651) and De homine (1658), Hobbes argues that imprecise language only leads to confusion, and is often used by deceptive writers who want to hide the absurdity of their ideas. He also notes that the careful way that geometers use definitions sets an important example of right reasoning, which explains his urgent need to refute Wallis’s critiques of his mathematical definitions (Ted H. Miller, Mortal Gods: Science, Politics, and the Humanist Ambitions of Thomas Hobbes [University Park: Pennsylvania State University Press, 2011], 38-41, 227). 49 Wallis, Due Correction, 25-26. Italics in original.

189 just as effective to challenge the definitions supporting the demonstrations as to challenge the demonstrations themselves: either way, the goal is to show that the other’s mathematics is founded on flawed reasoning. Indeed, in Elenchus geometriæ Hobbianæ (1655), his initial attack on

Hobbes, the first step that Wallis takes to dismantle Hobbes’s geometry is to dispute his definitions of mathematical objects. While he grants individual mathematical discretion to define objects in a way that suits them,50 he insists that the definitions must be clear and precise. If they do not meet these criteria, then the entire edifice built on them will be unstable. Accordingly,

Wallis attacks Hobbes’s mathematics by disputing his definitions of such basic elements of geometry as points and lines in De corpore (1655), his treatise on mathematics and natural philosophy. Wallis writes,

But truly who among the mortals ever hoped for such a definition of “Point”: A point is a body that is moved, even if the magnitude that is always somewhat there is not considered? . . . Who before you has ever considered a point to be a body? Who (that was sober) ever declared the magnitude of any (mathematical) point?51

According to Wallis, it is obvious that a point has no magnitude, so Hobbes’s definition reflects his misconception of even this most basic element of geometry. Wallis argues that Hobbes is similarly confused about lines, which he defines as “the way that passes through [a body] in a single or simple direction.” In Wallis’s view, Hobbes’s definition diverges from the entire mathematical tradition because he unnecessarily involves motion in his definitions. Surely a line is still a line when at rest, so why does Hobbes insist on making his definitions depend on

50 Rampelt links this attitude to Wallis’s discussion of definitions in Institutio logicae. There Wallis grants mathematicians more latitude in their definitions than natural philosophers, since mathematicians do not describe actual objects in the world. Wallis adds, however, that no definition can capture every aspect of a thing, so natural philosophers, too, are necessarily selective about what they include in their definitions (Rampelt, “Distinctions of Reason,” 177-178, 205-207). 51 “At verò quis unquam mortalium hujusmodi definitionem Puncti speraret, Punctum est Corpus quod movetur, cujusq[ue] magnitudo etsi semper aliqua sit, non consideratur? . . . Quis unquam, ante te definvit punctum esse corpus? Quis unquam (sobrius) puncti (mathematici) ullam esse magnitudinem asseruit?” (Wallis, Elenchus geometriæ Hobbianæ. Sive, geometricorum, quæ in ipsius Elementis Philosophiæ, à Thoma Hobbes Malmesburiensi proferuntur, refutatio [Oxford, 1655], 6-7; italics in original).

190 motion?52 In addition to these most basic definitions, Wallis objects to Hobbes’s definition of equal bodies as those that may occupy the same space: any two bodies may occupy the same space if their shapes are changed, such as by condensation or rarefaction. Hobbes’s definition, Wallis claims, threatens to dissolve the difference between equal and unequal, which would render the whole of mathematics useless.53

Responding to Wallis in his Six Lessons, Hobbes defends his definitions and makes it clear that he and Wallis hold fundamentally different views on the nature of mathematical objects.

Hobbes’s materialist mathematics entails certain peculiarities that set him apart from the mainstream mathematical community in the seventeenth century. For instance, he insists that the objects of geometry must be defined in terms of the motion used in their construction, since they only exist once the geometer has constructed them. In addition, Hobbes excludes the possibility of objects that have no magnitude. Conversely, Wallis accepts several kinds of mathematical objects that either have no magnitude (which he sometimes calls “non-quantum”) or are infinitely small, such as points, indivisibles, and the angle of contact between a curve and a tangent.54

Accordingly, in Six Lessons Hobbes takes aim not only at Wallis’s Elenchus, but also at three texts on which Wallis founded his reputation as a mathematician in the mid-1650s—namely, De

52 “. . . via per quam transit, Linea, sive dimensio una & simplex dicitur” (Wallis, Elenchus, 6). Italics in original. 53 See Wallis, Elenchus, 7-13, esp. 13. Having critiqued Hobbes’s mathematics in Latin in the Elenchus, Wallis repeats each of these challenges to Hobbes’s mathematical definitions for English readers in Due Correction for Mr Hobbes (cf. Wallis, Due Correction, 52-53, 55-56). On Hobbes’s criticisms of the concepts of condensation and rarefaction, see n. 47 above. 54 On Wallis’s use of indivisibles—Cavalieri’s concept of infinitely thin lines which, when multiplied by infinity, can be used to determine the area or volume of a body—see Philip Beeley, “Infinity, Infinitesimals, and the Reform of Cavalieri: John Wallis and His Critics,” in Infinitesimal Difference: Controversies between Leibniz and his Contemporaries, eds. Ursula Goldenbaum and Douglas M. Jesseph, (Berlin: De Gruyter, 2008), 31–52. On Wallis’s definition of the angle of contact as null or infinitely small, see Philip Beeley and Christoph Scriba, “Controversy and Modernity: John Wallis and the Seventeenth-Century Debate on the Nature of the Angle of Contact,” Acta Historica Leopoldina 54 (2008): 431-450; see 440 for the role of the angle of contact in the Wallis-Hobbes dispute. As Beeley and Scriba explain, for most of his career, Wallis vacillated on whether the angle of contact was infinitely small or a true non-quantum. He could get away with this until Newton and Leibniz developed calculus and demonstrated the need for a more precise definition of the infinitesimal; then he decided that the angle of contact was a non-quantum (Beeley and Scriba, “Controversy and Modernity,” 445-449).

191 sectionibus conicis, (1655), Arithmetica infinitorum (1656), and De angulo contactus (1656)—all of which employed mathematical entities with null or infinitely small magnitudes. Following

Wallis’s lead, Hobbes emphasizes the flaws in his opponent’s definitions of mathematical objects.

For instance, regarding De sectionibus conicis, he objects to Wallis’s definition of an indivisible as an infinitely small parallelogram, one with so little height that it “is scarce anything else but a

Line.” On this definition Hobbes remarks, “Is this the Language of Geometry? How do you determine this word scarce? The least Altitude, is Somewhat or Nothing.”55 For Hobbes, Wallis’s treatment of indivisibles lacks the precision required for a good mathematical definition: it is not written in “the Language of Geometry.”56 And the problem is not only with his definitions of complex and novel mathematical concepts such as indivisibles, but also with the simplest and most fundamental mathematical concepts: Wallis does not understand “what is Quantity, nor

Measure, nor Straight, nor Angle, nor Homogeneous, nor Heterogeneous, nor Proportion.”57 This attack is meant to be devastating to Wallis’s entire mathematical oeuvre. For Hobbes, as for

Wallis, mathematical errors are a sign of improper definitions, which in turn are a sign of flawed reasoning.58

55 Hobbes, Six Lessons, 46. Italics in original. 56 Hobbes also objects to Wallis’s use of another sort of mathematical “language,” namely, algebraic symbols. He notes that De sectionibus conicis in particular is “covered over with the scab of Symboles [sic]” that do not correspond to real things, and so fail to inform readers about anything meaningful. Indeed, symbols make it harder for a reader to understand a mathematician’s meaning: “For the conception of Lines and Figure (without which a man learneth nothing) must proceed from words, either spoken or thought upon. So that there is a double labour of the mind, one to reduce your Symboles to words (which are also Symboles) another to attend to the Ideas which they signifie.” This, Hobbes argues, is why the ancients almost never used symbols: they realized that symbols make mathematics more difficult, not less (Hobbes, Six Lessons, 49, 54). 57 Hobbes, Six Lessons, 34. 58 Hobbes’s great concern about the meaning that Wallis assigns to words is not surprising in light of his philosophy of language. According to Stephen K. Land, Hobbes believed that the names we give to things, while arbitrary, are absolutely essential to reasoning. Adopting a nominalist metaphysics, Hobbes argues that particular things are grouped only by the names that we assign to them, and not by any metaphysical relationship between them. The decision to include certain particular things in the category “tree,” for instance, is arbitrary: we decide what counts as a tree and name it accordingly. Reasoning, according to Hobbes, occurs at the level of these names: it is “primarily a formal, linguistic process,” a comparison between universals to determine whether they overlap entirely, partially, or not at all. Knowledge, then, depends entirely on the meanings of words in Hobbes’s view (Stephen K. Land, The

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While the focus on definitions is clearly related to the mathematical dispute between

Wallis and Hobbes, their grammatical squabbles seem to have nothing to do with mathematical method or squaring the circle. Each of the disputants points out the other’s failings in the usage of Greek and especially Latin, which by the mid-seventeenth century still retained its status as the language of learned discourse. In Six Lessons, for instance, Hobbes complains about a particular sentence in Wallis’s Elenchus, where he claims that Hobbes takes too many steps in his demonstrations and thus makes mathematical problems more difficult than they need to be. With his quip—Tu quasi malleum adducis quo occidas muscam, that is, “It is as if you bring a hammer to kill a fly”— Wallis unwittingly set off a protracted debate about which Latin verbs can take which kinds of direct objects.59 Hobbes insists that adducere, and other verbs based on the root ducere, should never take a direct object that is inanimate, such as malleum (hammer). He digresses in the middle of a series of complaints about Wallis’s definitions and algebraic symbols to address this grammatical error:

Before I proceed, I must put you in mind that these words of yours, Adducis malleum, ut occidas muscam, are not good Latine, Malleum affers, Malleum adhibes, Malleo uteris, are good. When you speak of bringing Bodies animate, Ducere and Adducere are good, for there to bring, is to guide or lead. And of Bodies inanimate Adducere is good for Attrahere, which is to draw to. But when you bring a hammer, will you say Adduco Malleum, I lead a hammer? A man may lead another man, and a ninny may be said to lead another ninny, but not a hammer.60

He would not have bothered quibble on this point, Hobbes adds, if he had not found Wallis

“nibling (but causelessly) at my Latine” when he wrote his Elenchus. Hobbes’s reference to

“nibling” might suggest that the finer points of Latin grammar were a trivial matter, but he and

Philosophy of Language in Britain: Major Theories from Hobbes to Thomas Reid [New York: AMS Press, 1986], 5- 29; the quotation is from 27). 59 Wallis, Elenchus, 94 60 Hobbes, Six Lessons, 51.

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Wallis repeatedly prove that they do not see it this way: neither one can let the other get away with accusations of grammatical incompetence.

Responding to Hobbes’s Six Lessons in his Due Correction for Mr Hobbes, Wallis devotes the first two chapters entirely to linguistic matters. First, he ridicules Hobbes for the rhetoric he seems to have learned in two notorious London neighbourhoods, Billingsgate and Turnbull Street

(i.e., from the fish merchants and prostitutes who work there). Next, he complains about Hobbes’s choice to write the Six Lessons in English in response to the Elenchus, which was written in

Latin—surely a sign of Hobbes’s incompetence as a Latin writer. Then he moves on to Hobbes’s latest grammatical errors.61 Later in the Due Correction, Wallis introduces dozens of classical examples to prove to Hobbes that ducere and similar verbs can be used with inanimate objects.62

This is the same text in which Wallis argued that “Mathematicall definitions” had been the core of mathematical knowledge since Euclid, and that nothing in mathematics could be taught without grammar, so he could hardly accept Hobbes’s suggestion that he had made an embarrassing grammatical error.63

As Hobbes challenged Wallis’s linguistic abilities, however, it was not only the Savilian

Professor’s mathematics that he sought to attack. Theology, too, was bound up in their contest for linguistic authority. Hobbes makes this clear in the final section of his Six Lessons, where he notes

61 Wallis, Due Correction, 1-4. 62 Wallis, Due Correction, 14-21. 63 The debate about ducere verbs continued at length. In his ΣΤΙΓΜΑΙ (1657), Hobbes challenges each of Wallis’s examples of ducere verbs taking inanimate direct objects in the Due Correction. He also includes a ten-page extract of a letter from his friend, Henry Stubbe, who sides with Hobbes on all the grammatical points debated by him and Wallis (Thomas Hobbes, ΣΤΙΓΜΑΙ Αγεωµετρίας, Αγποικίας, Αντιπολιτείας, or Markes of the Absurd Geometry, Rural Language, Scottish Church-Politicks and Barbarismes of John Wallis Professor of Geometry and Doctor of Divinity [London, 1657], 15-16, 20-31). Stubbe published his own treatise in 1657—spanning some seventy pages—showing Hobbes to be the superior grammarian. He makes clear how seriously he takes this matter when he writes, “I have spoken the more concerning adducis malleum, that so important a business might not be overruled, nor the university” that Wallis represents “debauched in their stile” (Henry Stubbe, Clamor, Rixa, Joci, Mendacia, Furta, Cachiny; or a Severe Enquiry into the Late Oneirocritica Published by John Wallis, Grammar-Reader in Oxon. [London, 1657], 1).

194 that what he despises in people like Wallis and Ward, who were trained in “Metaphysiques and

School-Divinity,” is their “Insignificant and absurd language.”64 He then connects this meaningless language to the professors’ absurd philosophy and “Incomprehensible” theology, which include immaterial substances and insoluble divine mysteries. Hobbes goes on to claim that the clergy use such obscure philosophical and theological language so that they alone seem capable of interpreting it. This is part of their effort to usurp authority that properly belongs solely to the sovereign: “both your Philosophy and your Language are under the Servitude . . . of the

Ambition of some other Doctors, that seek, as the Roman Clergy did, to draw all humane learning to the upholding of their Power Ecclesiasticall.”65 Thus Hobbes’s complaints about his opponent’s imprecise, mistaken, and empty language were tied into his whole overarching philosophy, with its materialism and opposition to the power of the clergy. It is no surprise, then, that Wallis employed his full range of linguistic and rhetorical abilities in his conflict with Hobbes.

Theological language did not become a prominent part of the dispute until 1657, when

Hobbes published his informatively titled ΣΤΙΓΜΑΙ [Stigmai] . . . or Markes of the Absurd

Geometry, Rural Language, Scottish Church-Politicks and Barbarismes of John Wallis Professor of Geometry and Doctor of Divinity. Here Hobbes took the opportunity to attack Wallis’s recently- published Mens sobria (1657), a theological collection that includes two of the three theses that

Wallis had defended in order to be granted his doctorate of divinity in 1654. This text was Wallis’s foray into the raging ecclesiological debates of the mid-seventeenth century. During the Civil

War, the Parliamentarian party included various kinds of opponents to the structure of the Church of England, which is arranged hierarchically with the Archbishop of Canterbury at the top.

64 Hobbes, Six Lessons, 56. Italics in original. 65 Hobbes, Six Lessons, 61. On Hobbes’s similar arguments about obscure language in Leviathan and elsewhere, see n. 48 above.

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However, after Parliament’s victory in the war, opponents of this Episcopalian structure remained divided on what should replace it, an issue that came to a head as Puritans rose to positions of prominence during the Interregnum. Puritan divines in this time can be roughly divided into two categories—Presbyterians and Independents—based on their preferred ecclesiology. As John

Spurr explains, a single definition can hardly cover all the various meanings ascribed to either

Presbyterianism or Independency in this period, but essentially they diverged on the question of how much autonomy should be granted to individual congregations.66 Whereas the Independents sought total autonomy for congregations, the Presbyterians wanted only partial autonomy with a central body overseeing the Church as a whole. In Mens sobria, Wallis signals his support for

Presbyterianism as he defends the view that a minister’s authority extends beyond his own congregation to the entire Church. Here he publicly diverged from the view of the Independents, including Oxford’s vice-chancellor, John Owen, who restricted the authority of a minister to his own congregation. The two parties also differed on the source a minister’s authority, the

Independents favouring the election of ministers by the congregation, and Presbyterians claiming that ministers should be appointed, continuing a succession that extends back to Christ’s appointment of the Apostles. Again, Wallis sides with the Presbyterians, arguing that a minister is appointed by other ministers in a chain that connects all the way back to Christ. Wallis offended

Owen when he defended these theses, and he did so again when he had them published three years later.67

As Wallis thus stoked the flames of the conflict between Presbyterians and Independents at

66 John Spurr, English Puritanism, 1603-1689 (New York: St Martin’s Press, 1998), 106-107, 119-120. 67 On the ecclesiological debates between Presbyterians and Independents, see Youngkwon Chung, “Ecclesiology, Piety, and Presbyterian and Independent Polemics During the Early Years of the English Revolution,” Church History 84 (2015): 345-368; Spurr, English Puritanism, 94-130. On Wallis’s ecclesiology in particular, see Jesseph, Squaring the Circle, 300-302; Rampelt, “Distinctions of Reason,” 118-123.

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Oxford, Hobbes was keen to point out the problems in the Presbyterian position as articulated by the Savilian Professor. Like the Independents, Hobbes opposed the Presbyterians’ claim that a minister has authority over the whole Church, not because he thought that individual congregations should be autonomous, but because he maintained that the sovereign alone has authority over the Church. So when Hobbes’s friend, Henry Stubbe, wrote to inform him of

Wallis’s conflict with the Independents, he eagerly seized the opportunity to condemn a text in which Wallis commits himself to Presbyterian principles.68 In terms of rhetoric, Hobbes attacks

Mens sobria in the same way that he and Wallis had been attacking each other’s mathematics.

Once again, he takes aim at key definitions used by his opponent, which in this case concern theological and ecclesiological ideas rather than mathematical ones. In the course of defending his theses, Wallis had defined such terms as “election,” a crucial concept in Calvinist soteriology, and “minister,” the ecclesiastical position that Wallis occupied and Hobbes so resented. What

Wallis had done to Hobbes’s mathematics, Hobbes now did to Wallis’s theology: he struck at the heart of his opponent’s ideas by attacking key definitions.

In particular, Hobbes takes Wallis to task for his account of what makes someone a minister.

Wallis defines a minister as a person whom Christ himself sets apart from ordinary Christians so that he can carry out duties such as preaching, administering the sacraments, ordaining other ministers, and so on.69 In the first place, Hobbes challenges Wallis on how, according to his definition, Christ is supposed to have appointed ministers. He writes:

. . . I desire to know in what manner you will be able out of this definition to prove your self a Minister? Did Christ himself immediately enjoyn you to preach, or give you orders? No. Who then, some Bishop, or Minister or Ministers? Yes; by what Authority? Are you sure they had Authority immediately from Christ? no. How then are you sure but that they might have none? At least, some of them through whom your Authority is derived might have

68 See Jesseph, Squaring the Circle, 303-304. 69 Wallis, Mens sobria seriò commendata: concione ad Baccalaureos Artium determinaturos, Latine abita Oxoniæ; in die cinerum dicto; Febr. 20. 1655. stile Anglia (Oxford, 1657), 136-137.

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none.70

Wallis holds that a minister is appointed by Christ, but he cannot prove that this is so, especially since as recently as 120 years ago, “you will finde your Authority derived from the Pope; which words have a sound very unlike to the voice of the Laws of England.”71 However, Hobbes’s main problem with the definition is not the reference to Christ, but the absence of the civil sovereign.

It is the sovereign, Hobbes insists, who has authority over the Church, who grants ministers their status, and who can remove that status if he so chooses. Accordingly, Hobbes proposes a revised definition:

Why then do you not put some such clause into your definition? As thus, Ministers of the Gospel are those to whom the preaching of the Gospel is enjoyned by the Soveraign power in the name of Christ. What harm is there in this definition, saving onely it crosses the ambition of many men that hold your principles?72

Hobbes suggests that Wallis’s conception of his own authority as a minister is mistaken, and less secure than he believes. With Hobbes’s attack on Mens sobria, then, the contest over definitions reached a new height: it now challenged Wallis’s identity as a minister.

Wallis responded to Hobbes’s ΣΤΙΓΜΑΙ with Hobbiani puncti dispunctio (1657), a text focused primarily on Latin and Greek usage. The epistle dedicatory concisely lists Hobbes’s grammatical errors, and some seventeen pages—more than a third of the text—support Wallis’s argument about adducere taking inanimate direct objects. However, Wallis suggests a link between these grammatical minutiae and the larger political and theological stakes of the debate: he claims that the reason he “brought a hammer” to the dispute in the first place was to smash

Hobbes’s whole philosophy. Wallis writes of the debate on adducere, “I confesse . . . I have bestowed more words upon it than the thing deserves: But it was not, you know, to kill a fly; but,

70 Hobbes, ΣΤΙΓΜΑΙ, 17. 71 Hobbes, ΣΤΙΓΜΑΙ, 17. 72 Hobbes, ΣΤΙΓΜΑΙ, 17-18.

198 to knock down leviathan, who would not be killed with a fillip on the forehead.”73 This remark reminds us that, as discussed in previous chapters, Wallis’s polemics against Hobbes’s mathematics were a means of indirectly discrediting his whole philosophy. He despised the

Leviathan for its absolutist political philosophy, its denouncement of the clergy as usurpers of the monarch’s authority, and its criticisms of university men as blind followers of Scholastic philosophy.74 And as Hobbiani puncti dispunctio makes clear, Wallis was aware that the linguistic dispute, too, was interconnected with matters of politics and philosophy: Hobbes had to be attacked on all sides so that his dangerous ideas would be discredited.

However, despite his theological and political motivations in writing against Hobbes, Wallis appears reluctant to take Hobbes’s bait by disputing the meaning of “minister.” His response to that part of ΣΤΙΓΜΑΙ is brief and sandwiched between two sections on proper Greek usage. When he does address the meaning of “minister,” though, Wallis maintains his position that a minister’s power comes directly from God, without passing through the civil sovereign. He is especially curt in response to Hobbes’s critique of Mens sobria as he writes, “You aske now whether Christ do injoin those to preach, whose office is so to do? Yes, he doth.” As Wallis explains, his definition did not address the political questions that Hobbes referred to “because all this was nothing to the purpose” of defining a minister.75 With that, it seems, Wallis considers the matter closed.

So ends the first stage of the Wallis-Hobbes dispute; after the publication of Hobbiani puncti dispunctio, Hobbes did not respond with an attack on Wallis for three years. When the dispute

73 John Wallis, Hobbiani puncti dispunctio, or the Undoing of Mr. Hobbs’s Points; in Answer to M. Hobbs’s ΣΤΙΓΜΑΙ, id est, Stigmata Hobii (Oxford, 1657), 30. 74 See Jesseph, Squaring the Circle, passim; Miller, Mortal Gods, 156-158. In his brief account of the Hobbes-Wallis dispute, Miller argues that, Hobbes, too had political motivations. As Miller explains, Hobbes resented Wallis’s appointment as Savilian Professor of Geometry, which he believed was a reward for Wallis’s service to the Parliamentarians during the Civil War. After the Restoration, Hobbes was dismayed to discover that Wallis would keep his position despite his disloyalty. As Miller puts it, “Wallis represented the unjustified success of a faction following the Restoration that had betrayed the Crown” (Miller, Mortal Gods, 236-237). 75 Wallis, Hobbiani puncti dispunctio, 42-43. Italics in original.

199 resumed in the 1660s and 1670s, the tone shifted, especially on Wallis’s part.76 In this later stage, he typically wrote against Hobbes in treatises and brief articles in the Philosophical Transactions, which focused on particular mathematical demonstrations in Hobbes’s works that he found problematic. These texts betray Wallis’s growing impatience with the fact that he had to respond to Hobbes at all, since Hobbes seemed only to repeat ideas that Wallis had already addressed in the 1650s. Apart from a few brief skirmishes concerning etymology77 and definitions,78 the linguistic elements are less prominent during the rest of the dispute.

Nevertheless, the first part of the Wallis-Hobbes dispute cannot be properly understood without an emphasis on the disputants’ concern about many forms of language, including grammar, etymology, rhetoric, and definitions. Linguistic issues tie together Wallis’s and

Hobbes’s early debates over numerous topics ranging from mathematics to theology and ecclesiology. When we consider this first stage of the dispute, we should be careful not to lose sight of the fact that even the seemingly petty grammatical squabbles between Wallis and Hobbes matter—to the disputants and to the historian—as they constitute part of a broader contest that involved not only the disputants’ mathematical philosophies and methodologies, but also their rhetorical techniques and linguistic knowledge. Wallis thought that these resources would help him to bring down Hobbes’s Leviathan; Hobbes employed similar tactics in his attack on what he

76 For a timeline of the dispute, see Jesseph, Squaring the Circle, 10-16. 77 See Wallis, Hobbius Heauton-timorumenos. Or a Consideration of Mr Hobbes His Dialogves. In an Epistolary Discourse, Addressed to the Honourable Robert Boyle, Esq. (London, 1662), 38, 72-73. 78 In articles in the Philosophical Transactions, Wallis objects to how Hobbes defines infinity (Wallis, An Answer to Four Papers of Mr. Hobs, Lately Published in the Months of August, and This Present September, 1671,” Phil Trans 6 [1671]: 2241-2244) and air (Wallis, “An Extract of Letters from Dr. John Wallis to the Publisher, 1672. Sept. 26. &c. concerning the Suspension of Quick Silver Well Purged of Air, Much Higher than the Ordinary Standard in the Torricellian Experiment,” Phil Trans 7 [1672]: 5161). The debate about the nature of infinity extended back to Hobbes’s criticism of Wallis’s treatment of infinite series in Arithmetica infinitorum and other works. This discussion included passing comments by Wallis and Hobbes about the relationship between mathematical infinity and the infinitude of God. See Philip Beeley and Siegmund Probst, “John Wallis (1616-1703): Mathematician and Divine,” in Mathematics and the Divine: A Historical Study, eds. T. Koestier and L. Bergmans (Amsterdam: Elsevier, 2005), 444-449.

200 viewed as the pernicious institution of the clergy. In terms of understanding the importance that

Wallis attached to language in general, the point here is that Wallis focused on words in his dispute over Hobbes not merely because he was vain or pedantic. The stakes were much higher than personal prestige: Wallis could not let someone as subversive as Hobbes control the meaning of a minister or a mathematical point.

Language and authority in the Trinitarian controversy

On several other occasions, Wallis explored the linguistic aspects of theological topics. But he had to proceed carefully: theological language had been a source of heated religious and political controversy in England since the Reformation.79 Wallis witnessed firsthand some of the most important theological debates of his time, first as a secretary to the Westminster Assembly of

Divines beginning in 1643, and later as a Presbyterian delegate to the Savoy Conference of 1661 whose attendees decided how to revise the Book of Common Prayer. Thus he had been present at two crucial events that shaped the religious world of seventeenth-century England, not least because they included discussions about appropriate language to use in theology and prayer.80

79 Although by the mid-seventeenth century questions such as whether the Bible and liturgy should be available in the vernacular had been settled—the use of the King James Bible and the Book of Common Prayer was required by law—debates continued to rage over how to define terms used in the Bible and throughout Christian history. See Salmon, “Language Politics of the 16th and 17th Century English Church,” in Language and Society, 77-97. 80 On Wallis’s work at the Westminster Assembly, see Chad van Dixhoorn, ed., The Minutes and Papers of the Westminster Assembly 1643-1652, vol. 1 (Oxford: Oxford University Press, 2012), 16, 43, 134, 142-143; Rampelt, “Distinctions of Reason,” 53-60. On his participation in the Savoy Conference, see Horton Davies, Worship and Theology in England: From Andrewes to Baxter and Fox, 1603-1690, vol. 2 (Princeton: Princeton University Press, 1975), 367-368, 371-372. This is not the place for a full discussion of the terminological consequences of these two events, but an example will be helpful. The 1662 edition of the Book of Common Prayer, whose publication followed the Savoy Conference, changed the language of the “Declaration on Kneeling” with respect to Christ’s presence at the Eucharist. Whereas the 1552 edition denied the “real and essential presence” of Christ at the Eucharist, the later edition replaced this phrase with “corporeal presence” in order to emphasize that while Christ was not physically present in body, his presence was still real (Brian Douglas, “The 1662 Book of Common Prayer: Assessing Its Eucharistic Theology 350 Years On,” Pacifica 25 [2010]: 280). As for the Westminster Assembly, van Dixhoorn argues that although historians have focused on the ecclesiological debates, this was only one of the Assembly’s many concerns. They also spent days debating the meaning of language used by the early Church, such as the reference in the Apostles’ Creed to Christ’s descent (descensus) into hell: was this to be taken literally or did it refer,

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Such experiences served Wallis well when he wrote on matters of theological terminology.

This occurs in some surprising places in his corpus, such as the “Praxis” added to the fourth edition of the Grammatica, which contains exercises for readers to practise translating English texts into Latin. Wallis guides the reader through the translation of two texts which would have been familiar to nearly any reader, the Lord’s Prayer and the Apostles’ Creed. He also glosses the

English words, outlining their etymology and cognates. When he comes to the phrase “The Holy

Ghost” in the Apostles’ Creed, Wallis notes that “Ghost” is equivalent to the Latin word Spiritus, which is also the origin of the word “Spirit” in English. But the word “Ghost” has a certain practical advantage of “Spirit.” As Wallis explains, “The old expression Ghost is still maintained by an old custom, especially in the name The Holy Ghost; lest perhaps from this innovated name the vulgar consider the doctrine to have changed as well.” Wallis admits that this word choice is potentially confusing, since “Ghost” can also refer to demons, spectres, and “the wandering souls or spirits of the dead; especially those who were killed by murderers, or who had hidden treasures that were not yet found.”81 Nevertheless, Wallis declares that the convention should be maintained so that the “vulgar” do not become confused by a change in the language of the creed. Here Wallis shows his grasp of the linguistic issues involved in religious practice and, speaking with the authority of a minister and a linguistic expert, decides in favour of maintaining the word “Ghost” in the creed.

as Jean Calvin had argued, to Christ’s suffering on the cross? This debate included an extensive examination of the etymology of the words “descent” and “Hades.” The Assembly ultimately resolved to reject Calvin’s view and to maintain the position that Christ actually descended into hell after his crucifixion. Although this particular debate preceded Wallis’s appointment as secretary to the Assembly, it demonstrates the depth of the theological and terminological debates at Westminster (Chad B. van Dixhoorn, “New Taxonomies of the Westminster Assembly [1643-52]: The Creedal Controversy as Case Study,” Reformation & Renaissance Review 6 [2004]: 82-106, esp. 89- 95). 81 “Retinetur tamen, ab antiquâ consuetudine, præsertim in Spiritûs Sancti, appellatione, vox antiqua Ghost; ne forte ex innovato nomine putaret vulgas etiam doctrinam mutari”; “mortuorum Animas seu Spiritus palantes; præsertim qui ab homicidis mactati fuerant, aut Thesauros abscondiderant nondum repertos” (Wallis, “Praxis grammatica,” 153).

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In the “Praxis” Wallis demonstrates his expertise in etymology, which was an invaluable resource in theological controversies. It was crucial, for instance, in the controversy between

Trinitarians and anti-Trinitarians (or “Socinians”) during the 1690s. As discussed in Chapter 2 above, Wallis’s account of the relationship between the persons of the Trinity led him to discuss the nature of language, particularly the role of metaphors and the difficulty of describing God with human language. Just as important during the Trinitarian controversy were investigations of the etymology of particular Greek and Latin words traditionally applied to the persons of the

Trinity, such as persona, hypostasis, and οὐσία. Theologians argued over what these words meant and which of them the Church Fathers had used most often. Wallis himself wrote at length on the historical meaning of “person” (persona) in the fifth of his eight letters on the Trinity, in an effort to prove to his Socinian opponents that there could indeed be three persons in one God. “Person”

(persona), Wallis explains, does not mean the same thing as “man” (homo), since one man can be considered multiple persons: “the same Man may at once sustain the Person of a King and of a

Father.” A person, Wallis claims, most accurately means a “state, quality, or condition, whereby one Man differs from another.” This sense of “person” can be applied to the Father, Son, and Holy

Spirit, but only metaphorically, as divine relationships do not correspond exactly to human ones.82

Manuscript evidence shows that Wallis’s etymological investigations extended beyond what was published in the Trinity letters. The third letter addresses the references to Christ’s descent into hell in the Apostles’ Creed and the Athanasian Creed, two early Christian statements of Trinitarian theology. Here Wallis notes that the English word “hell” corresponds to the Greek

which do not necessarily refer to a place of ,(שְׁאוֹל) Hades (ᾅδης) and the Hebrew Sheol

82 Wallis, “A Fifth Letter concerning the Sacred Trinity; In Answer to What is Entituled, The Arians Vindication of Himself against Dr Wallis’s Fourth Letter,” in Theological Discourses; containing VIII Letters and III Sermons concerning the Blessed Trinity (London, 1692), 16. Italics in original.

203 punishment in the afterlife, but could instead “signifie, sometime the Grave, sometime, the Place,

State, or Condition of the Dead, whether good or bad.” Later commentators have disagreed about which sense of “hell” is meant in the creeds, as each of them can be supported by biblical references, so Wallis concludes that the original meaning of the creeds’ writers cannot be determined.83 In his own copy of this letter, Wallis adds a marginal note expanding on the relation between “hell” and its cognates. “Hell,” he explains, is a contraction of the Saxon word Heøl or

Heølle, which in turn might be a contraction of the Hebrew word Sheol, and the Saxon word, too, could mean something like a grave rather than “the place of the damned.” Collectively, all this linguistic evidence leaves Wallis wary to conclude that the creeds refer to Christ literally descending into hell.84 For Wallis, the interpretation of these key Trinitarian statements required etymological as well as theological expertise.

In terms of his rhetorical techniques and linguistic knowledge, Wallis’s foray into the

Trinitarian controversy closely resembles his early attacks on Hobbes. As in the dispute with

Hobbes, definitions are at the fore of the debate. And here, too, Wallis’s rhetorical strategy involves pointing out his opponent’s grammatical and etymological weaknesses. This is especially clear in his attack on the unorthodox Trinitarian theology of William Sherlock, dean of St. Paul’s

Cathedral in London, who created a scandal among English divines when he argued that the persons of the Trinity were three distinct, infinite minds or substances. Like the Wallis-Hobbes dispute, the attack on Sherlock is not primarily about language. But in this case, once again, Wallis shows that the verba are as important as the res. Since terminology was crucial to the debate,

Wallis again had many opportunities to employ his considerable rhetorical and linguistic abilities.

83 Wallis, “An Explication and Vindication of the Athanasian Creed. In a Third Letter Pursuant to Two Former, concerning the Sacred Trinity. Together with a Postscript, in Answer to Another Letter,” in Theological Discourses, 15-19. Italics in original. The quotation is from 16. 84 Bodleian MS. Eng. th. e. 22, f. 52v. Underlining in original.

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Sherlock intended his Vindication of the Doctrine of the Holy and Ever Blessed Trinity

(1690) to refute the anti-Trinitarians by offering a reasonable interpretation of how three persons could make up a single God. He argued that the Trinity consisted of three infinite minds, each of which has its own distinct consciousness in addition to the mutual consciousness that they all share. This doctrine both appalled orthodox Trinitarians and provoked the ridicule of anti-

Trinitarians. Critics on both sides agreed that Sherlock’s conception of the Trinity, by making too great a distinction between the persons of the Trinity, amounted to tritheism, or the belief in three gods.85 Among Sherlock’s most vociferous critics were his powerful opponents in Oxford, led by

Robert South, canon of Christ Church and the university’s public orator. In 1695, Sherlock’s account of the Trinity was denounced by Oxford’s Hebdomadal Board, a body consisting of the vice-chancellor and the college heads, established by Archbishop Laud in 1631 for the purpose of regulating religious views at the university. Following one of its weekly meetings, the

Hebdomadal Board issued a decree against Sherlock which was published as a single-page tract in both English and Latin.

This is a complicated episode with roots in the political and religious turmoil of the

Glorious Revolution (1688-9). Leading up to the Revolution, the Anglican clergy was in a state of crisis. Many ministers were torn between their belief in the divine right of kings, which required them to be loyal to James II, and their deep anxiety about the king’s increasingly apparent commitment to Catholicism. The removal of James and the placement of his Protestant nephew,

William III, on the throne brought this crisis to a head, forcing the clergy to swear oaths of allegiance to William in order to keep their livings. After months of dithering, Sherlock emerged

85 See Maria Rosa Antognazza, Leibniz on the Trinity and the Incarnation: Reason and Revelation in the Seventeenth Century, trans. Gerald Parks (New Haven, 2007), 94-102.

205 as a non-juror in the summer of 1689, meaning that he refused to swear the oaths of allegiance to the newly-crowned William III that were legally required of the clergy. He thus found himself opposed by South, his erstwhile friend, who had taken the oaths and felt surprised and betrayed by Sherlock’s decision. Although Sherlock had changed his mind again and sworn the oaths by

August 1690, he had by then made a permanent enemy in South, who became the most vocal critic of Sherlock’s theological views.86

Five years later, the rivalry between South and Sherlock was ongoing but had now come to focus the latter’s account of the Trinity.87 The occasion for the renewed hostilities was a sermon preached in October 1695 by Joseph Bingham, a young Oxford-based tutor and Master of Arts, at the University Church. Bingham argued that the Trinity is composed of three distinct substances, and that these substances are infinite minds, a view that he claimed did not deserve

“the heavy charge of Tritheism, which some have so liberally, but most unjustly bestowed” on it.88 His sermon largely consists of appeals to patristic writers who describe the Trinity as three numerically distinct substances. While he did not mention Sherlock by name, the language that

Bingham applied to the Trinity was unmistakeable—he described the Father, Son, and Holy Spirit as “three minds” and “three Infinite Beings”––and it would have been obvious to those who

86 See W. M. T. Dodds, “Robert South and William Sherlock: Some Unpublished Letters,” Modern Language Review 39 (1944): 215-224; Kenneth Padley, “Rendering unto Caesar in the Age of Revolution: William Sherlock and William of Orange,” Journal of Ecclesiastical History 59 (2008): 680-696. The divines who kept their livings and fellowships at Oxford after the Revolution were, of course, those who had sworn the oaths, but the university had an uneasy relationship with William III. As G. V. Bennett explains, Oxford had been “an essential pillar” supporting the king and the Church of England after the Restoration (G. V. Bennett, “Loyalist Oxford and the Revolution,” in The History of the University of Oxford, vol. 5, eds. L. S. Sutherland and L. G. Mitchell [Oxford: Clarendon Press, 1986], 9). But the Glorious Revolution changed the relationship between Oxford and the Crown, and the university became “a major centre of opposition to the government” under William (idem, “Against the Tide: Oxford under William III,” in Sutherland and Mitchell, History of Oxford, vol. 5, 31). 87 For a useful account of the theological dispute between Sherlock and South and its context, see Philip Dixon, “Nice and Hot Disputes”: The Doctrine of the Trinity in the Seventeenth Century (London: T & T Clark, 2003), 98-137. 88 Joseph Bingham, “A Sermon on the Doctrine of the Trinity, Preached at St. Mary’s Church, before the University of Oxford,” in Origines ecclesiasticæ: or the Antiquities of the Christian Church, and Other Works, of the Rev. Joseph Bingham, M.A., vol. 8, ed. Richard Bingham (London, 1834), 307.

206 attended that he meant to defend Sherlock’s conception of the Trinity.89 Scandalized, the members of the Hebdomadal Board issued their decree denouncing Bingham’s position, but again they did not mention Sherlock by name. Shortly thereafter, Sherlock was finally identified when the decree, which declares Bingham’s account of the Trinity “false, impious, and Heretical,” was published in English and Latin. A comment was added to the bottom of the page: “It may be noted,

That the Propositions above-mentioned, are Dr. S------k’s, in his Discourse of the Trinity, and the

Defenders of it; and wrote against by the Animadverter, &c.”90 The author in question was obviously Sherlock and the “Animadverter” was Robert South, who had published his

Animadversions upon Dr. Sherlock’s Book in 1693. The censure of Bingham’s sermon had now been explicitly framed in the context of the rivalry between Sherlock and South.91

Sherlock responded with his Modest Examination (1695) of the Hebdomadal Board’s decree. While he defends his theology, he also distances himself from Bingham’s sermon, claiming that South and his allies had shrewdly taken the opportunity to attack him when Bingham happened to use similar terminology to describe the Trinity. Sherlock explains that he does not know precisely what Bingham said, and if the young preacher suggested that the three infinite minds are “wholly divided and separate from each other” then this would indeed be “an Impious

Sense of these Words.”92 However, Sherlock argues, the terminology itself is not heretical when used properly, in a manner that does not treat the Father, Son, and Holy Spirit as distinct gods.

89 Bingham, “Sermon on the Trinity,” 301, 321. 90 An Account of the Decree of the University of Oxford, against Some Heretical Tenets. At a Meeting of Mr. Vice- Chancellour, and the Heads of Colledges and Halls, in the University of Oxford, the 25th of November, 1695 (London, 1695). 91 For an overview of these events see Yudha Thianto, “Three Persons as Three Individual Substances: Joseph Bingham and the Trinitarian Controversy at Oxford in the 1690s,” Fides et Historia 40 (2008): 67-86. On the dispute between Sherlock and South, see also Antognazza, Leibniz on the Trinity and the Incarnation, 96-101. 92 William Sherlock, A Modest Examination of the Authority and Reasons of the Late Decree of the Vice- Chancellor of Oxford, and Some Heads of Colleges and Halls; concerning the Heresy of Three Distinct Infinite Minds in the Holy and Ever-blessed Trinity (London, 1695), 10.

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Despite his opponents’ claims, he argues, the words themselves are by no means heretical: “Words may be new, unusual, inconvenient, and want the stamp of Ecclesiastical Authority, which are not

False, Impious, or Heretical. These are very different Crimes, to broach new Words, and new

Heresies, when the Words themselves are not manifestly Heretical.” Such words should not be condemned if “those who use them declare the Orthodox sense wherein they use them,” and this is what Sherlock proceeds to do in his Modest Examination.93

Sherlock proceeds to explain that he made his terminological innovation after concluding that the word “persons” had proven inadequate as a label for the Father, Son, and Holy Spirit.

Many theologians referring to persons had fallen into the heretical trap of modalism (or

Sabellianism), interpreting the three persons as three different aspects of God. According to this view, the distinction between the persons was not real, but merely apparent, existing only in the minds of humans trying to understand God’s nature. Since Trinitarian theology based on persons tended to “make no more of a Person, than a meer Mode,” Sherlock claims that it was necessary to clarify the real meaning of the doctrine with different language. Here he explains the logic supporting his new terminology: since there are three persons in God, there must also be three of

93 Sherlock, Modest Examination, 11. Italics in original. Sherlock supports his flexible position on theological language with references to patristic sources that show the importance of context. For instance, against the Arians, who made too great a distinction between the persons of the Trinity, the Nicene Council denied that the Trinity consisted of three substances, and accordingly they referred to a God of one substance in the Nicene Creed. But against the Sabellians, who made too little a distinction, the Church Fathers insisted that “three substances” were “very Catholick Words, and contain a true Catholick sense” as long as the words were not used in the mistaken way that the Arians used them. As St. Hilary of Poitiers had explained in the fourth century, the reference to God as “one substance” in the Nicene Creed meant one kind of substance, so the Sabellians were wrong to conclude that God did not consist of three distinct substances (Sherlock, Modest Examination, 38-39). Wallis responds to Sherlock’s point by arguing that, although the Church Fathers might have treated the word substantia as flexible, English theologians have long since adopted two different words—“substance” and “subsistence”—to correspond to these different meanings. God might have more than one subsistence, Wallis claims, but he certainly has only one substance ([Wallis], An Answer to Dr. Sherlock’s Examination of the Oxford Decree: In a Letter from a Member of That University, to His Friend in London [London, 1696], 18-19).

208 whatever is essential to a person. This means that there are three minds, spirits, and substances in the Godhead:

If then a Person be a Mind, a Spirit, a Substance, Three such Persons must be Three as distinct Minds, Spirits, or Substances, as they are distinct Persons; and Three such Personal Minds, Spirits, or Substances, are as reconcilable with the Unity of the Godhead, as Three substantial Persons.94

Far from being an admission of tritheism, Sherlock argues, his account of the three infinite minds saves the doctrine of Trinity from the equally heretical modalist interpretation.

Shortly after the publication of the Modest Examination, Wallis composed a letter reasserting the Oxford divines’ censure of Sherlock’s theology. He published the letter anonymously under the title An Answer to Dr. Sherlock’s Examination of the Oxford Decree

(1696). It is unclear exactly what led Wallis to respond to the Modest Examination and why he kept his name off the text,95 but his relationship with South offers some insights. Wallis supported a controversial decision to grant South the degrees of bachelor and doctor of divinity in 1663, and it was Wallis who presented South to the university on this occasion.96 Furthermore, Wallis had promptly sworn the oaths of allegiance to King William, so he might have been more sympathetic

94 Sherlock, Modest Examination, 17-18. Thianto argues that Sherlock’s and Bingham’s conceptions of the three persons was an application of John Locke’s philosophy to theology, the identification of persons with minds following from Locke’s view that self-consciousness is what constitutes personhood. According to Thianto, the conflict between Sherlock’s and South’s parties “was over what kind of philosophical language was most appropriate to understand the Godhead, that rooted in Platonism or that of a modern thinker like Locke” (Thianto, “Three Persons as Three Individual Substances,” 79). While I hesitate to accept Thianto’s interpretation, which relies on circumstantial evidence to frame the Trinitarian controversy as a contest between Platonic and Lockean philosophy, I agree with his point that a crucial element of the controversy was the question of what sort of philosophical language was appropriate in theology. 95 Wallis was not the only participant in the Trinitarian controversy to publish anonymously. Other examples include South’s Animadversions, Stephen Nye’s criticisms of Wallis, and Edward Wetenhall’s Earnest and Compassionate Suit for Forbearance (1691). What is curious is that Wallis had attached his name to the Trinity letters, but changed his approach with his Answer to Sherlock. Perhaps the comments made by Wetenhall and other weary observers of the controversy allowed him to see the advantage of publishing anonymously: since readers did not known for certain that he wrote the text, he could deflect any accusation of enthusiasm for controversy. 96 See Anthony à Wood, Athenæ Oxonienses: An Exact History of All the Writers and Bishops Who Have Had Their Education in the University of Oxford: to Which Are Added the Fasti, or Annals of the Said University, vol. 4, ed. Philip Bliss [London, 1820], 636-637.

209 to South than to Sherlock on this point. On the other hand, to Wallis’s great irritation, in 1669

South publicly ridiculed the Royal Society and experimental philosophy during his speech at the opening of the Sheldonian Theatre.97 This might explain why Wallis was reluctant to attach his name to a document that seemed to support South’s campaign against Sherlock.

In any case, Sherlock made three moves in his Modest Examination that were sure to offend the Savilian Professor. First, he pretended to authority in grammar, pointing out an error in the Latin version of the Oxford decree—the translator had used eorum to mean “their” where he apparently should have used suae.98 He also proposed a grammatical rule for when words can be applied to God in the plural, not just in the singular, as a means to describe the Trinity.99

Second, by way of challenging their authority to condemn certain theological language as heretical, Sherlock criticized the Oxford divines as a group. He claimed that they “have a greater

Opinion of their Authority, than I can find the rest of the world has.”100 Evidently Wallis perceived this as a critique of the university itself, much like the one Hobbes had made in the 1650s, and his response suggests that he took great offense. Indeed, Sherlock echoes Hobbes when he scoffs at the theology of the “School-Men” at Oxford and ridicules their reliance on Scholastic philosophers.101

97 See Peter Harrison, The Fall of Man and the Foundations of Science (Cambridge: Cambridge University Press, 2007), 2; Felicity Henderson, “Putting the Dons in Their Place: A Restoration Oxford Terrae Filius Speech,” History of Universities 16 (2000): 35. 98 Sherlock, Modest Examination, 5. 99 This is permissible, Sherlock explains, only when the words are used as adjectives, rather than substantives. So the three persons can each be described as “Almighty,” but they should never be called “three Almighties” (Sherlock, Modest Examination, 45-46). 100 Sherlock, Modest Examination, 7-8. 101 Sherlock, Modest Examination, 32. Sherlock mocks the Oxford divines for relying on Thomas Aquinas and Duns Scotus to support their theology (Sherlock, Modest Examination, 22).

210

Third, and perhaps most importantly, although Sherlock does not name Wallis, he seems to imply that Wallis’s own Trinitarian terminology supports a modalist interpretation of the

Trinity. Wallis may have felt personally attacked when Sherlock wrote:

. . . is any other Trinity but a real substantial Trinity, the Object of religious Adoration? . . . is a Mode, a Posture, a Somewhat, without any name or notion belonging to it, the Object of Religious Worship? is it possible in the nature of the thing, for any man, who believes but one singular, solitary, divine Nature, to worship three with a distinct worship, without any conception of a real, substantial, distinction between them?102

The reference to “a Somewhat” was presumably directed at Wallis, who had argued that the

Father, Son, and Holy Spirit are most accurately described as three “Somewhats” in his letters on the Trinity. At the end of his Modest Examination Sherlock complains that his opponents have attacked “real Trinitarians” like him and have been silent about “the Nominal ones.”103 Evidently the latter category includes people who described the persons with terms no more precise than

Somewhats.

Wallis would surely have been sensitive about the implication that his Somewhats constituted three modes or aspects of God that were no more distinct than the divine attributes, which was tantamount to the ancient heresy of Sabellianism. His anti-Trinitarian opponent

Stephen Nye had accused him of this very heresy in his replies to the letters on the Trinity in the early 1690s, arguing that Wallis’s comparison of the divine persons to different “offices” held by a single man constituted modalism.104 Wallis, it seems, could not abide another association of his theological definitions with the Sabellian heresy. Although for some reason he was compelled to publish his response to Sherlock anonymously, he could at least defend himself by trying to destroy Sherlock’s credibility.

102 Sherlock, Modest Examination, 20. Italics in original. 103 Sherlock, Modest Examination, 46. Italics in original. On Wallis’s account of the Trinity, see Chapter 2 above. 104 See Antognazza, Leibniz on the Trinity and the Incarnation, 93-94.

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In his Trinity letters of the early 1690s, Wallis had been respectful toward Sherlock but careful not to endorse his ideas. It is Wallis’s correspondent, W. J., who brings up Sherlock, describing him as a “Learned and Ingenious Author” who “makes your three somewhats, not only three Substantial Beings . . . and three Infinite Minds.”105 Responding to W. J. in his second letter on the Trinity, Wallis declines to evaluate Sherlock’s theology since that is not the purpose of his letters.106 In his next letter, responding to Stephen Nye’s latest critique which mentions him and

Sherlock in the same breath, Wallis notes that “Dr. Sherlock says nothing contrary to what I defend.” While Sherlock’s conception of the Trinity is unusual, Wallis explains, at least he distinguishes between the three persons while recognizing them as one God.107 He elaborates a little in his seventh letter, after W. J.’s again brings up Sherlock’s theology. Wallis notes that he thinks Sherlock goes too far in treating the three persons as “Really Distinct, even as distinct as

Peter, James, and John; and One God onely as they are mutually Conscious.” However, although

Wallis notes that he would not use such language himself, he adds that he does not consider this view as dangerous as that of the Socinians, and concludes that Sherlock’s Trinitarian terminology is regrettable but not damning.108 In the early 1690s, then, Wallis seems to have regarded Sherlock as eccentric but harmless.

By 1696, however, Wallis had been provoked by a perceived attack on himself the other

Oxford divines. He responded by publishing a dismissive Answer to Sherlock’s Modest

Examination. To any historian familiar with Wallis’s polemical writing—and probably to

105 John Wallis, “A Second Letter concerning the Holy Trinity. Pursuant to the Former from the Same Hand; Occasioned by a Letter (There Inserted) from One Unknown,” in Theological Discourses, 3. Italics in original. 106 Wallis, “Second Letter,” 9-10. 107 Wallis, “Third Letter,” 42. Italics in original. 108 Wallis, “A Seventh Letter, concerning the Sacred Trinity; Occasioned by a Second Letter from W. J.,” in Theological Discourses, 17. Italics in original Wallis expresses essentially the same sentiments about Sherlock in his unpublished correspondence with Edmund Elys in the early 1690s: his choices of terminology are unfortunate, Wallis explains, but not so bad as to warrant a full rebuttal (Bodleian MS. Eng. th. e. 22, ff. 130r-v, 229r, 375v).

212 observant contemporaries—there is no mistaking who wrote this anonymous text. The haughty tone of Wallis’s Answer is remarkably similar to his attacks on Hobbes written decades earlier.

For instance, he employed his familiar rhetorical technique of identifying an opponent’s grammatical errors in order to suggest a lack of erudition. Sherlock unwittingly gave Wallis this opportunity when he pointed out a supposed grammatical error in the decree. Wallis responds in kind, noting a Latin spelling error in the Modest Examination: Sherlock wrote Prefectorum where he should have written “Præfectorum with an æ.”109 In addition, he refutes Sherlock’s claim that the Latin decree should have used suae instead of eorum to mean “their,” and he smugly discourages Sherlock from raising such grammatical objections since “his Talent doth not lie that way.”110 These are rather trivial grammatical points, even compared to a protracted argument on the proper direct objects of ducere and related verbs, but they demonstrate that Wallis remained alert to the importance of scoring rhetorical points against his opponents.

After briefly ridiculing Sherlock’s grammar, Wallis moves on to his opponent’s theology.

Just like in the dispute with Hobbes, here Wallis transitions seamlessly between grammatical and more substantive linguistic criticisms. He focuses his attack on Sherlock’s terminology, emphasizing his misunderstanding of words like “person” and “substance.” Whereas he had tactfully avoided outright criticism of Sherlock before, now Wallis is blunt in his judgement that

Sherlock’s terminology is of no value. Sherlock’s rejection of traditional Trinitarian language,

Wallis suggests, was the result of his own gross misunderstanding of theological terminology.

Typically, Wallis allowed a fair amount of latitude in descriptions of the Trinity, just as he did with mathematical definitions. As I discussed in Chapter 2, he did not insist that anyone else refer

109 Wallis, Answer to Sherlock’s Examination, 3. 110 Wallis, Answer to Sherlock’s Examination, 5.

213 to the Father, Son, and Holy Spirit as three Somewhats. However, writing as the anonymous defender of the Oxford divines, Wallis makes clear that Sherlock’s language, which is imprecise and opens the door to tritheism, falls outside the range of acceptable descriptions of the Trinity.

The main problem with Sherlock’s terminology, Wallis argues, is that he applies it carelessly and so conflates things that should be kept distinct. According to Wallis, it might be acceptable to identify “mind,” “spirit,” and “substance” with each other, but Sherlock goes too far in identifying all three of these with “person.” Indeed, the dean of St. Paul’s should not be surprised that his idea caused such a backlash: “he knows it will not be allowed him: Because

Mind, Spirit, Substance, are (in their proper signification) Absolute; but Person (in its proper signification) Is a Relative Term.” Wallis’s point here is that the distinction between minds, spirits, and substances is greater than that between persons. A man can be more than one person, but he cannot have more than one mind, spirit, or substance. Ignoring the fact that his own view does indeed seem like modalism, Wallis presses Sherlock further on his terminology, suggesting that it was reckless for him to introduce novel terms to describe the Trinity when he did not really understand them. If “mind,” “spirit,” and “substance” are indeed equivalent to person, “why cannot he content himself with (what is generally received) three Persons, but must impose upon us his New Terms of Three Distinct Minds, Three distinct Spirits, and Three distinct Substances?”

The description of the Trinity as three infinite minds, to which Sherlock had devoted years’ worth of theological writing, was an irredeemable mistake, and no amount of “Scorn and Flowncing” would smooth over the serious metaphysical issues underlying his terminological innovation.111

By the late 1690s, the controversy between Sherlock’s and South’s parties had become so fierce that the Crown had to intervene. Shortly after Wallis published his Answer to Sherlock,

111 Wallis, Answer to Sherlock’s Examination, 17-18. Italics in original.

214

Thomas Tenison—now Archbishop of Canterbury—persuaded King William to demand an end to the conflict and to ban the use of new terminology to describe the Trinity. In this respect, South and his supporters at Oxford got their way: traditional Trinitarian language would be maintained.

But the Oxford divines resented the king’s decision to intervene and thus to curtail their authority over religious matters. As for Sherlock and Bingham, far from being denounced as heretics, each of them went on to enjoy comfortable careers in their respective parishes, preaching and publishing for years after the swift conclusion of the controversy.112

What if the controversy had been allowed to continue? In this case, Sherlock might have published a response to Wallis and thus dragged him into another protracted polemical battle like the one he had fought with Hobbes. The Savilian Professor showed no signs of losing his passion for public disputes as he approached his eightieth birthday. He had retained the skills that he had relied on for decades, particularly his sharp wit, his extensive knowledge of history, and his considerable rhetorical and linguistic abilities. Although he published his Answer to Dr.

Sherlock’s Examination anonymously, it is likely that many contemporaries—at least those old enough to remember his vehement mid-century attack on all things Hobbesian—recognized

Wallis as the author.

Conclusion

Wallis’s career can help us to appreciate that intellectual controversies in the seventeenth century were often about words as much as things, verba as much as res. This is why it served Wallis well to demonstrate the extent of his linguistic abilities, and why, in part, it was so important to

112 On the end of the Trinitarian controversy, and on Bingham’s subsequent career, see G. V. Bennett, “University, Society, and Church, 1668-1714,” in Sutherland and Mitchell, History of Oxford, vol. 5, 397-398; Thianto, “Three Persons as Three Individual Substances,” 84-86.

215 establish that it was he, and not William Holder, who had taught the deaf mute Alexander Popham to speak. To be sure, Wallis and his colleagues took inspiration from major early modern figures like Bacon who emphasized the importance of studying things rather than mere words. Bacon’s emphasis on direct observation of nature was a major impetus for the reform of natural philosophy. Nevertheless, for Wallis, language was by no means a marginal aspect of more serious studies. On the contrary, his linguistic observations and arguments constitute a significant part of his contribution to the intellectual world of the seventeenth century. Even his discussions of grammar, phonetics, and etymology form part of his larger effort to pinpoint the meaning of important terms, ranging from the points, lines, and indivisibles of mathematics to the persons and substances of theology.

In this chapter I have shown that linguistic concerns, broadly conceived, are involved in practically every aspect of Wallis’s thought. A significant portion of his intellectual output consisted of the study of language itself—particularly grammar and the physiology of speech, which are the focus of the many editions of his Grammatica and De loquela. But Wallis’s linguistic expertise reaches far beyond these specific texts and intersects with his work in other fields of studies, often in surprising ways. Firstly, he treated linguistics as a part of natural philosophy, and accordingly sought to apply the empirical methods of the new experimental philosophy to the study of languages. Indeed, I have argued that Wallis’s work on languages represents one of his chief contributions to experimental philosophy. Secondly, Wallis deployed a range of linguistic skills in his dispute with Thomas Hobbes, primarily to assert control over the meaning of mathematical objects, but also to defend his identity as a minister of the Church of

England. Finally, Wallis used a remarkably similar set of linguistic techniques in his works on the

Trinity, again with the intention of controlling the meaning of terminology. Wallis evidently believed that his linguistic and rhetorical abilities would lend credibility to his work in

216 mathematics, natural philosophy, and theology, and it seems that he was right: he made a lasting impact on each of these fields that historians are increasingly coming to appreciate.

Wallis was far from the only figure in the seventeenth century for whom language studies form a thread running through various fields of study. As Rhodri Lewis argues, in a period before linguistics had emerged as a field in its own right, “early modern thinkers were concerned with grammar, poetics, rhetoric, philology, logic, law, natural philosophy, education, politics, theology and medicine . . . and studied language through, and in as much as it impacted on, these practices and concerns.”113 This remark, however, suggests a passive role for language studies in the seventeenth century, as if they were neglected except when pressed into the service of some other sort of inquiry. Through the above case studies, I have shown that, for Wallis at least, language studies played a more active role than Lewis suggests. His knowledge of grammar and etymology, his research on the physiology of speech, and his rhetorical prowess were among Wallis’s most trusted intellectual resources, ones that he knew how to mobilize in a variety of different contexts.

The case of Wallis demonstrates that language studies were central, not incidental, to a wide range of fields including mathematics, natural philosophy, and theology.

In each of the foregoing chapters, I have sought to identify the points of contact between

“science” and “religion” in Wallis’s thought. Few things bring together the natural and the divine in Wallis’s work like the study of languages. It is not too anachronistic, I believe, to describe

Wallis’s interest in languages as “scientific.” He sought explanations for how language works, not in terms of biblical narratives but in terms of natural causes. Using empirical methods, Wallis investigated questions such as how the organs of speech produce sounds in order to form words,

113 Lewis, Language, Mind and Nature, 9.

217 how people use those words, and how different languages have developed throughout the world.

His answers to these questions constitute one of the most successful projects of his career.

On the other hand, the uses of Wallis’s linguistic knowledge are typically religious in character. The article in the Philosophical Transactions about his work with deaf students mentions that he taught Daniel Whaley how to read the Bible,114 and in the “Praxis grammatica” he demonstrated to readers of the Grammatica how to translate and to interpret the Lord’s Prayer and the Apostles’ Creed.115 In addition, Wallis eagerly sought support for a project to produce a

Lithuanian vernacular translation of the Bible, without which he feared “the soules possibly of many thousands” of Lithuanian speakers might “perish, for want of the Bible in their own

Language.”116 Furthermore, his knowledge of etymology helped him to interpret the reference to

Christ’s descent into hell in the Athanasian Creed and the Apostles’ Creed. Finally, as discussed at length above, Wallis’s linguistic skills helped him to refute dangerous theological ideas, such as Hobbes’s materialism and Sherlock’s unorthodox conception of the Trinity. Linguistic knowledge was a “hammer” that Wallis could bring down upon the ideas of his religious and philosophical opponents. This is what it meant for an Anglican minister and experimental philosopher in the seventeenth century to take up the study of languages as one of his foremost

114 Wallis, “Letter to Boyle,” 1098. 115 Indeed, Linda C. Mitchell argues that Wallis and other writers of grammar textbooks were motivated, in part, by a desire to teach foreigners how to read the Bible in English, as well as English works on theology (Linda C. Mitchell, Grammar Wars: Language as a Cultural Battlefield in 17th and 18th Century England [Aldershot: Ashgate, 2001], 139). 116 WC I, 580. In the letter quoted here, written in 1658/9 to the theologian Matthew Poole, Wallis lamented that the translator, a Polish scholar named Samuel Boguslaus Chylinski, was struggling to raise enough money to finish the project (WC I, 580). Wallis also sought the support of Boyle who, as discussed in n. 21 above, promoted several such Bible translation projects (see WC II, 63-68). Chylinski never managed to get his translation printed, but he came close thanks to the support of Wallis, Boyle, and Hartlib. See Nicholas Hans, “Polish Protestants and Their Connections with England and Holland in the 17th and 18th Centuries,” The Slavonic and East European Review 37 (1958): 213-214; R. E. W. Maddison, The Life of the Honourable Robert Boyle F.R.S. (London: Taylor & Francis, 1969), 111-112; Michal J. Rozbicki, “Between East-Central Europe and Britain: Reformation and Science as Vehicles of Intellectual Communication in the Mid-Seventeenth Century,” East European Quarterly 30 (1996): 410-412.

218 intellectual projects: Wallis’s language studies were “scientific” in character, but “religious” in outlook.

219

Chapter 7: Conclusion

In the opening pages of her biography on Robert Hooke, Lisa Jardine reflects on the difficulty of writing the biography of a figure who was a prominent natural philosopher in his time, but who is not known for a particular discovery or invention—a figure “who almost made great discoveries now tied to the names and enduring fame of others.” Jardine writes,

Biography is the art of giving shape and coherence to the life of an individual. Where the subject has a major achievement to his or her name, a life can be crafted as a “before” and “after” around that beacon moment. Where an individual has been prolific and varied in his endeavours and achieved a breathtaking amount, yet without leaving his lasting mark on history in the form of a single significant discovery, it is far harder to give him his place in history. Hence Hooke’s shadowy presence—a man without a defining great work to give his life shape.1

The challenge that Jardine articulates so well is precisely the one facing the historian who tries to describe the life and works of John Wallis. While this dissertation is not meant to be a biography, my intention has been, in part, to answer the question posed in the introduction: Who was John

Wallis? As with Hooke, Wallis’s career does not offer any singular moment of discovery around which to structure a narrative. His discovery of the Wallis product as an expression of the value of π, and his introduction of the symbol ∞ for infinity, are surely significant in the development of algebra. But these represent brief moments near the beginning of Wallis’s mathematical career, and they offer little in terms of understanding Wallis, his times, and his legacy.

The best answers to such questions, I contend, are those based on the gradual accumulation of data from episodes spanning Wallis’s long career. This is what I have sought to accomplish in the preceding chapters. Wallis emerges from these in-depth studies as a dynamic and creative thinker, a voracious student of both ancient and modern ideas, a prolific writer and correspondent,

1 Lisa Jardine, The Curious Life of Robert Hooke: The Man Who Measured London (New York: Harper Perennial, 2004), 2. Italics in original.

220 and a witty and stubborn defender of his ideals. His career spanned most of the seventeenth century, and in many ways he is emblematic of that century. Wallis’s works bring out the many tensions shaping the thought of natural philosophers, mathematicians, theologians and other intellectuals in this period—tensions between tradition and innovation, empirical evidence and rational arguments, res and verba, decorum and polemics. His constant attention to the pressing intellectual issues of his time led him to engage with the ideas of contemporaries who achieved a more lasting fame—including Galileo, Hobbes, Descartes, Hooke, Boyle, Huygens, Leibniz, and

Newton—most of whom he engaged in personal correspondence with, at least intermittently.

Wallis’s vast corpus leaves no doubt that he was a prominent thinker and a forceful personality in the Republic of Letters, the Royal Society, the town and university of Oxford, and the Church of

England. For decades, he maintained his position as Savilian Professor and an ordained minister despite political upheavals and frequent attacks from his enemies and critics. In short, Wallis’s lack of name recognition today is out of proportion with his prominence among contemporaries, and it should not come as a surprise if, as the historian delves into the intellectual world of seventeenth-century England, she begins to find Wallis wherever she looks.

Among the documents that attest to Wallis’s prominence are his inscriptions in several alba amicorum. These are early modern autograph books whose owners solicited signatures from friends and noteworthy people. The inscriptions usually included the writer’s favourite pithy Latin and Greek dicta and quotations. According to the extant examples, Wallis typically included some combination of the same few phrases. These included two biblical quotations—“I am a stranger on earth” (Psalm 119:19) and “For here we do not have an enduring city” (Hebrews 13:14)

(NSRV)—which recall the impermanence of earthly things. Underneath these verses, though,

Wallis quotes Archimedes’ famous dictum, “Give me somewhere to stand and I will move the

221 earth.”2 In his signature he styles himself John Wallis, S. T. D. (Sacrae Theologiae Doctor, Doctor of Sacred Theology) and Savilian Professor of Geometry. These inscriptions are formulaic, but they capture an important element of Wallis’s philosophy. Wallis always had one eye on the world to come, but while on Earth he sought natural knowledge that, he believed, was capable of practically anything. He passionately pursued natural knowledge, even though he recognized the vanity of such mundane matters, and this is the aspect of his personality that he chose to record for posterity in the autograph books of his friends and acquaintances.

This attitude toward the natural and the divine helps to explain what makes Wallis such a valuable case study in the history of science and religion. While he appreciated his responsibility as a minister to care for people’s souls, this was evidently no deterrent from his lifelong commitment to secular studies, chiefly mathematics and natural philosophy. Furthermore, Wallis had the expertise and creativity to relate his knowledge of sacred and secular things in original ways, although these interactions were usually implicit. The subtlety of the links between science and religion in his works—namely, the recurrence of certain rhetorical strategies across multiple fields, the Scholastic principles he adopted, the nuanced way that he introduced biblical evidence into natural philosophy—is itself instructive. To relate natural and divine knowledge in Wallis’s time did not necessarily require a grand philosophical scheme explicating every aspect God’s interaction with the created world, of the sort articulated by Descartes, Newton, and Leibniz. For

Wallis, the relationship had more to do with the strategies that one adopts in both natural philosophy and theology, and the lessons that one field can offer the other. This sort of approach

2 Wallis included each of these quotations in the album amicorum of two German acquaintance: Johann Wülfer, in 1676/7 (Uppsala University Library MS. Y 147 k, f. 32r), and Andreas Arnold, in 1681 (Herzog August Library Cod. Guelf. 226 Blank., f. 36). See also Wallis’s inscriptions in two alba amicorum held by the National Széchényi Library in Budapest (Duod. Lat. 168, f. 116r; Oct. Lat. 121st, f. 93r). Many thanks to Steve Snobelen for drawing my attention to Wallis’s inscriptions in alba amicorum.

222 to the science-religion relationship allowed Wallis to flourish as a cleric, and also as a mathematician and natural philosopher.

To determine whether Wallis’s strategies had any lasting impact—whether they represent a significant part of the genealogy of science and religion—one must begin by comparing him with contemporaries and later figures, particularly those who might have been exposed to his ideas. In part, the goal of this thesis has been to create a point of reference for such comparisons.

A logical next step would be to consider other clerical practitioners—in seventeenth-century

England an beyond—who successfully studied both the natural and the divine, without any sign of the tension described in Mordecai Feingold’s account of clerical science (as discussed in

Chapter 1 above). It would be instructive to discover whether Wallis’s techniques for relating the natural and the divine are unique, or whether other scholars adopted them as well. For instance, a study of whether other clerical practitioners were informed by the Scholastic ideas that I have identified in Wallis’s work—the technique of identifying similitudes, and Grosseteste’s principle that “Nature doth not work by Election”—would help to clarify Wallis’s place in the broader picture of the history of science and religion. In addition, to determine whether Wallis was responsible for transmitting these ideas to others, or whether he is merely exemplary of them, it is crucial to establish how many other clerical practitioners read Wallis’s published works or were exposed to his ideas in other ways, perhaps through correspondence or by reading the works of his commentators and critics. We know, for instance, that Leibniz’s understanding of Wallis’s

Trinitarian theology was informed by his reading of Stephen Nye’s responses to the Trinity letters.3 The filtration of Wallis’s ideas through his commentators adds a layer of complexity that must be considered.

3 See Maria Rosa Antognazza, Leibniz on the Trinity and the Incarnation: Reason and Revelation in the Seventeenth

223

Likewise, it would be useful to compare Wallis to other figures, both clerical and lay, whose ideas might have been affected by antagonism toward the pope, the Jesuits, or Roman

Catholics in general. It seems likely that many Protestants would have similar reservations about ideas that might further Catholic interests, but perhaps Protestants who lived elsewhere or belonged to other churches responded differently to this problem. Alternately, additional studies might consider whether Catholic figures were affected by a similar antipathy toward Protestant thinkers and institutions. In general, the role of Protestant-Catholic relations in natural philosophy and mathematics remains a largely neglected avenue of research, and Wallis could serve as an important point of reference for further study.

In such ways, I hope that this case study of Wallis will serve as a departure point for other studies that will improve our understanding of the history of science and religion. But another goal of this work is to give some structure to Wallis’s diverse intellectual activities, to ensure that he becomes more than, as Jardine would put it, a “shadowy presence” lurking in the background of seventeenth-century historiography. I have sought to demonstrate that certain common answers to our initial question—Who was John Wallis?—are too simple, because they either make presentist assumptions or give too much credence to the derisive comments of Wallis’s critics.

The answer given by John Dunton, that Wallis was a precursor to Newton, has been echoed by many modern writers. So has the answer offered by enemies such as Anthony à Wood and Henry

Stubbe: that Wallis was a treacherous social climber whose success had more to do with ambition than talent. Neither answer reflects the complexity that emerges from an in-depth study of Wallis’s works. Likewise, the claim made by opponents such as Stephen Nye and Thomas Hobbes, that

Wallis’s ideas are devoid of any philosophical merit, is not a fair assessment of his contributions

Century, trans. Gerald Parks (New Haven: Yale University Press, 2007), 92, 102.

224 to the intellectual community. On the contrary, further study will likely confirm that Wallis’s thoughts on nature, mathematics, and the divine reverberated throughout and beyond the intellectual world of England in the seventeenth century.

225

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