As a history of algebra in England and Scotland from the early seventeenth century to the mid-eighteenth century, this book considers not only technical algebra but also the personal, philosophical, religious, and institutional factors that affected the introduction, elaboration, and reception of the subject. The first chapter sets the scene for the study by discussing the new algebra that emerged in continental Europe in the sixteenth and early seventeenth centuries. This algebra – which I call “early modern algebra” – included new results (the solutions of the cubic and quartic equations), a new language (the symbolical), an expanded algebraic universe (with negative and, tentatively, imaginary numbers), a new emphasis on analysis as the special method of algebra, and a changing relationship between algebra and geometry. Chapters 2 through 10, the heart of the book, explore British algebra from the introduction of early modern algebra into England by William Oughtred and Thomas Harriot in 1631 through the post-Newtonian formulations of algebra by Colin MacLaurin and Nicholas Saunderson.

There is no book-length history of British algebra of the seventeenth and eighteenth centuries. Historians of British mathematics have concentrated on later algebra, since it was Great Britain of the late eighteenth and early nineteenth centuries that produced “symbolical algebra,” in which algebra began to take its modern, abstract form. While the present book centers on what was in itself as exciting and important an era in the development of algebra, it also provides essential background for the study of the emergence of nineteenth-century symbolical algebra.

In the preceding chapters, I have shown how Boyle's views on reason's limits in the context of theology were reflected in his views on the limits of reason in the context of natural philosophy. The entire point of this book, indeed, has been the extent to which Boyle expected to find parallels between what might be known about the secrets of revelation and what might be known about the secrets of nature. Boyle approached his studies of theology and nature with certain assumptions about reason's limits, and then interpreted his findings in such a way as to reinforce those assumptions: His God had deliberately chosen to limit the power and scope of human reason, leaving human beings in something of a state of perpetual blindness concerning the ultimate truths of both nature and Christianity.

This picture of Boyle differs markedly from our traditional picture of him as a confident and single-minded advocate of both the corpuscularian philosophy and rational religion. The image of Boyle as emphasizing a more rational approach to both nature and theology than he in fact did has its roots in the way he was portrayed in the early and highly selective accounts of his life given by Gilbert Burnet in Boyle's funeral sermon on the second of January, 1692, and by Thomas Birch in the biography of Boyle accompanying the first edition of his Works (1744). This view of him has been perpetuated since by scholars who have taken the canonical image of Boyle at face value, finding it all too easy to elide various aspects of his thought and personality that violate twentiethcentury conceptions of religious and scientific rationality.

Robert Boyle as Lay Theologian

Robert Boyle's status as a lay theologian was recognized in the seventeenth century and has been acknowledged ever since. In the sermon preached at Boyle's funeral in 1692, Gilbert Burnet, Bishop of Salisbury and one of Boyle's confessors, characterized him as one of those individuals who

In 1701, Jeremy Collier, in his Great Dictionary, placed more emphasis on Boyle as a lay theologian than on Boyle as a natural philosopher. And in his Memoirs of the Lives and Characters of the Illustrious Family of the Boyles, Eustace Budgell described the relationship between Boyle's theological writings and his scientific writings much as had Burnet, noting that he had “often blended Religion and Philosophy happily enough together; and made each serve to illustrate and embellish the other.”

Boyle's Discourse of Things above Reason (1681) was not his first sustained treatment of the relationship between reason and religion, but it was his most complete and most sophisticated treatment. He devoted two earlier works to the topic, however, and it is appropriate to consider them briefly before moving on to Things above Reason. In addition, there were other works in which Boyle touched on the subject, and I incorporate passages from those works into the discussion in this chapter when doing so helps to flesh out Boyle's views. (I have already discussed similar passages from works prior to 1660 in the Introduction and in chapters 2 and 3.)

Style of the Scriptures

The first work that Boyle devoted to the relationship between reason and religion was Style of the Scriptures (1661). Originating from his unpublished manuscript “Essay of the holy Scriptures” (written c. 1651–1652 and discussed in chapter 2), Style was written to defend scripture from objections that it is obscure, that it is unmethodical, and that it is self-contradictory. In this defense, Boyle relied heavily on various considerations concerning the application of human reason to scripture, and because his intent was to foster the reading and study of scripture, his emphasis was for the most part on reason's competence to understand the content of scripture and on the importance of human learning to prepare reason to understand. There is a heavy emphasis on the importance of the study of languages and historical context, as well as on Boyle's claim that doctrines fundamental to salvation are “expressed with an evidence proportionable to the degree of assent that they exact, and are as far forth intelligible to pious and industrious readers, as they are necessary to be understood by them.”

The Protestant insistence that scripture alone was to be the rule of faith – and the accompanying claim that the laity was competent to interpret scripture – brought with it the inevitable consequence of the proliferation of alternative and conflicting interpretations of scripture, and hence the proliferation of sects. In this chapter, I examine the claims of one of those sects, the Socinians, with an emphasis on their claim that there is nothing in scripture that contradicts human reason. I also examine some of the responses to Socinianism published in England prior to the publication of Boyle's Things above Reason (1681), for it is in these responses to Socinian claims that the rough outlines of the themes developed in Things above Reason are to be found.

The Protestant Background

The claim that scripture contains doctrines that are above reason, but none contrary to reason, was one of the battle cries of the Reformation in England. William Chillingworth (1602–1644), for example, stressed that each individual must use his God-given reason to make a conscious choice between Roman Catholicism and Protestantism. In advocating the study of scripture alone as a rule of faith, Chillingworth observed that although nothing in scripture is contrary to reason, some doctrines of Roman Catholicism require a person to believe things (such as Transubstantiation) that are impossible.

When confronted with the charge that the doctrine of Christ's Incarnation was irrational, the African Church Father Tertullian (c. 160–c. 220) cheerfully responded, “And the Son of God died; it is by all means to be believed, because it is absurd. And He was buried, and rose again; the fact is certain, because it is impossible.” It is likely that his claim was based on a passage in Aristotle's Rhetoric, where Aristotle explored a position that could be taken in response to the charge that certain beliefs are incredible: “We may argue that people could not have believed them if they had not been true or nearly true: even that they are the more likely to be true because they are incredible.”

Most likely, with his “I believe because it is absurd,” Tertullian meant nothing more than that the objects of faith, even if incomprehensible to human understanding, are by virtue of their being revealed most certainly true. As Étienne Gilson observed in commenting on this passage, “Ever since the time of Athenagoras, theologians have been most anxious always to establish at least the rational possibility of the Christian faith.” This anxiety led to the claim that although some Christian doctrines may be above reason, none are contrary to reason, a claim that had become a commonplace expression by the seventeenth century. “Above but not contrary to reason,” however, has meant different things to different Christian thinkers at different times and in different contexts.

Being considered one of the “great” thinkers of the past has all too often resulted in a highly selective presentation of an individual's thought. In what has come to be known as a “Whiggish” interpretation of history, aspects of an individual's thought that are judged to have contributed to some perceived line of progress from the past to the present have been emphasized, while those that might be considered “embarrassing” from a twentieth-century point of view, such as a belief in witchcraft or alchemy, have been glossed over as vestiges of the past that unfortunately marred the otherwise progressive thought of the individual. One of the most encouraging aspects of recent Boyle studies is that Boyle scholars today are attempting to see his thought as a unified whole rather than selecting only those aspects that might be considered “modern.”

“The father of modern chemistry” was not a scientist who dabbled in alchemy on the side. Boyle had a remarkably unified worldview, a worldview in which truths in chemistry, physics, alchemy, and theology were but different aspects of one unified body of knowledge. Boyle himself was quite aware that the individual aspects of his thought were but a part of a unified whole, and expressed his conception of the whole in The Excellency of Theology (1674):

I do not cover all aspects of Boyle's empirical epistemology in detail in this book because there have already been a number of excellent studies on the topic. In this chapter, therefore, I limit myself to a discussion of the various ways in which Boyle believed he could attain knowledge of the created world. Specifically, I discuss Boyle's views on scriptural revelation, personal revelation, abstract reason (including innate ideas, which, having their origin in God, might be construed as a form of revelation), and sensory perception as possible sources of knowledge about the created world.

Scriptural Revelation

In Defence of the Doctrine Touching the Spring and Weight of the Air … Against the Objections of Franciscus Linus (1662), Boyle stated that there are only two ways of obtaining knowledge of the created world: sense perception and revelation. Linus had attempted an explication of the “rota aristotelica” in which he appealed (among other things) to the motion of angels. To this Boyle, replied that

It is not clear whether by “immediate revelation” about the actions of angels Boyle meant personal revelation or scriptural revelation. Because he viewed these as two distinct sources of knowledge, I examine them separately, beginning with scriptural revelation.

Boyle believed that scripture revealed knowledge of the created world only about matters that are not knowable by other means, such as the origin and ultimate destiny of the world.

Theological controversies in seventeenth-century England show clearly the impact of the proliferating and often contradictory interpretations of scripture that accompanied the development of Protestantism. And one of the most passionate controversies of all was the apparently endless one over the correct interpretation of predestination. As a modern commentator has aptly observed, “the Calvinist-Arminian controversy placed great strain on Luther's doctrine of the perspicuity of Scripture.” With the fate of his or her soul at stake, it was crucially important that each individual discover which of the conflicting interpretations was uniquely correct, for surely God knew which was true and surely God would punish those who erred. Further, the fate of the nation itself was at stake, for surely God's pleasure or displeasure would affect the course of national and international events. Hence it was crucially important that the divines of the Church of England determine correct doctrine and establish styles of worship that would be pleasing to God.

In A Discourse of Things above Reason, Boyle refused to commit himself to any particular explanation as to exactly why he believed many of the mysteries of Christianity and the secrets of nature to be impervious to human understanding. As I showed in chapter 4, he suggested that the difficulty might be due to our “lapsed state,” or it might be related to the way in which the human soul was united to the human body. But he emphasized neither of these possibilities, being content most of the time to appeal more generally to the incommensurability between the understanding of finite beings and that of an infinite being. A careful study of Boyle's writings as a whole, however, reveals that he believed that God, as creator, had freely and deliberately chosen to limit the rational faculties of human beings (and the rational faculties of angels, as well). In creating the world commensurate with his own infinite understanding and in limiting the rational faculties of created beings, God had deliberately left “human understandings to speculate as well as they could upon those corporeal, as well as other things.”

Boyle's belief in the incommensurability between finite created understandings and a world created in accordance with God's infinite understanding had significant implications for his conception of the task of the natural philosopher. In chapter 7, I emphasized Boyle's refusal to make knowledge claims about the truth or falsehood of the various hypotheses available to explain the hidden mechanisms behind phenomena.

I have argued that Boyle's primary motivation for writing Discourse of Things above Reason was a theological one, and the work was in fact considered to be a theological work at the time. It was listed as a theological work in catalogues issued by his publishers in his later years, as well as classified as theological by subsequent compilers of collections of his works. Nevertheless, Boyle explicitly presented the work as a philosophical essay, not a theological one, claiming that the category of things transcending reason is not limited to revealed truths but extends to matters of natural philosophy as well.

Boyle's position here was certainly not original; as I pointed out in chapter i, it can be traced back at least as far as Irenaeus (born c. 126) who, arguing in a theological context not unlike that which prompted Boyle's Things above Reason, supported his claim that certain Christian doctrines are genuinely mysterious by pointing out that some natural phenomena are also mysterious. As Étienne Gilson has put it, this “insistence on the deficiency of natural knowledge introduced, if not for the first time, at least with a force that was then new, what will remain, up to the time of Montaigne's Apology for Raymond Sebond, the favorite theme of a certain type of Christian apologetics.” The deficiency of natural knowledge was certainly a favorite theme of Boyle's a hundred years after the publication of Montaigne's Apology in 1568. In the hands of one of the founders and foremost members of the Royal Society of England, it took on a new significance, and received an application that helped define the limits of the new natural philosophy.