The Mathematical Minister: John Wallis (1616-1703) at the Intersection of Science, Mathematics, and Religion by 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 © Copyright by Adam Richter 2018 The Mathematical Minister: John Wallis (1616-1703) at the Intersection of Science, Mathematics, and Religion 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 iv 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 v 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 vi 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