About

Jason Richards is an Assistant Professor of Neurology and a Clinician Educator at Brown University. He received his undergraduate degree in mathematics and chemistry from Tufts University and earned his medical degree from Tufts University School of Medicine. Following medical school, he completed an internship in internal medicine and residency training in adult neurology at the University of North Carolina Hospitals in Chapel Hill. He further specialized by completing a fellowship in clinical neurophysiology at Duke University Medical Center in Durham, North Carolina. Dr. Richards is a member of the American Academy of Neurology and the American Epilepsy Society. He is board certified by the American Board of Psychiatry and Neurology in both neurology and epilepsy. His research includes work on epileptic encephalopathy associated with ATP1A3 mutation and seronegative myasthenia gravis associated with malignant thymoma.

Research topics

• Philosophy
• History
• Sociology
• Political Science
• Classics
• Literature
• Art
• Epistemology
• Theology
• Religious studies
• Genealogy
• Law

Selected publications

• 9. De Morgan’s Family

  Open Book Publishers · 2024-09-04

  book-chapterOpen access1st authorCorresponding

  This chapter places Augustus De Morgan in his familial context. Focusing on his wife Sophia, it explores her fascination with the development of her offspring’s powers of reasoning, underlining that interest in education was the preserve of both husband and wife, not of Augustus De Morgan alone. The chapter also balances De Morgan’s intellectual legacy with his biological legacy through his children’s achievements: we learn of their second son George, a budding mathematician and co-founder of the London Mathematical Society, who fell victim to an early death; their youngest daughter Mary, who became a published author of fairy tales and short stories; and their eldest son William, who, although best known in his lifetime as a successful novelist, is remembered today for his innovative work as a ceramic artist, particularly his creation of ‘De Morgan tiles’, via which the name of De Morgan continues to live on.

  PublisherOA PDFDOI

• Generations of Reason: A Family's Search for Meaning in Post-Newtonian England

  Perspectives on Science and Christian Faith · 2023 · 6 citations

  1st authorCorresponding
  • Literature
  • Philosophy
  • Classics

  GENERATIONS OF REASON: A Family's Search for Meaning in Post-Newtonian England by Joan L. Richards. New Haven, CT: Yale University Press, 2021. 456 pages, with 21 b/w illustrations, 1,218 endnotes, and a 35-page index. Hardcover; $45.00. ISBN: 9780300255492. *The title gives no clue who this book is about. Nor does the publisher's description on its website, the abbreviated blurb inside the book jacket, the four endorsements posted on the jacket's back ("beautifully written," "epic masterpiece," "magnificent study," "compelling and wide-ranging"), or even the chapter titles. The reader first learns whom the book is about and how it came into focus in the author's Acknowledgments. In studying the divergent interests of Augustus De Morgan and his wife, Sophia, the importance of De Morgan's father-in-law William Frend's thinking became apparent. This is turn led Richards to delve into the lives and beliefs of two ancestors from the previous generation, Francis Blackburne and Theophilus Lindsey, who felt compelled by their commitment to "reasoned conclusions about matters of faith" (p. x) to move away from orthodox Anglicanism and establish the first Unitarian church in England. Thus the book eventually evolved into chronicling the lives of three generations over a century and a half during (roughly) the Enlightenment era. *A central motif running through the experiences, beliefs, and work of these families was their steadfast commitment to a form of enlightened rationality that provided coherence and foundational meaning for their lives. Reason informed their ecclesiastical commit-ment to Unitarianism, their views of science and mathematics, and their public activity favoring social and educational reforms. But also, paradoxically, their search for reason led to the beliefs and practices (of some family members) that today would be considered pseu-do-scientific--mesmerism, phrenology, and spiritism, among others. *As Richards notes in the book's opening sentence, for her, Generations of Reason is "the culmination of a life devoted to understanding the place of mathematics in modern European cultural and intellectual history." The mathematics and logic of early- to mid-nineteenth-century Britain has been an ongoing research interest for Richards during her forty-year tenure as a historian of mathematics at Brown Universi-ty. It is this that largely drew me to the book and which I will focus on here: it climaxes in a substantive treatment of the progressive mathematics of De Morgan, whose work contributed to transforming British algebra and logic. This is in stark contrast with the radical ideas of Frend, who refused to admit negative numbers into mathematics. *A central figure behind the developments under investigation is John Locke, whose Essay Concerning Human Understanding (1689) and The Reasonableness of Christianity, as Delivered in the Scriptures (1695) exercised a tremendous influence over and challenge for eighteenth- and nineteenth-century British thinkers. Locke's ideas defined and emphasized rationality in relation to knowledge generally and to scientific and religious knowledge in particular, providing dissenters with a rationale for combatting traditional theology and conformist science and philosophy. For Locke, however, a literal reading of scripture was still authoritative for religious beliefs. This was true for Frend and De Morgan also, even though they held tolerant attitudes toward a wide latitude of thinkers. *Locke's view of Reason also affected period reflections on mathematics. Like others in the early modern and Enlightenment eras, Locke had held up mathematics as a model of absolutely certain knowledge because of the clarity of its ideas and the supposed self-evidence of its axiomatic truths. Of course, this characterization applied more to Euclidean geometry than to the burgeoning domains of analytic mathematics, such as calculus, which, as Berkeley charged, still lacked a sound theoretical basis. As for logic, Locke had an acute antipathy toward traditional argument forms and proposed that one should reason with ideas rather than words, assessing their agreement or disagreement in less convoluted ways than in a syllogism. In expressing such relations with language, though, one should use meaningful and unambiguous terms. This was somewhat problematic in algebra and calculus, where symbolic expressions were manipulated to produce useful and important results, even when their meaning was less than clear. *Around the turn of the nineteenth century, Frend campaigned to bring algebra in line with Lockean reasoning: algebra was conceptualized at that time as universal arithmetic, containing such laws as the transposition rule if a + b = c then a = c - b. Thus, no expression should be employed if its meaning was unintelligible. In the above equations, one must assume the condition b < c to rule out negative values, since numbers, which represent quantities of discrete things, cannot be less than 0. Excising negative quantities from mathematics was extreme but necessary in order to adhere to a literalistic view of rationality. *British mathematicians largely resisted following Frend down this path of purity, though they were unsure how to rationally justify their use of negative and imaginary quantities without going outside mathematics and appealing to things like debts. Robert Woodhouse, in an 1803 work, was one of the first Cambridge mathemati-cians to propose a more formalistic algebraic approach in calculus. This agenda was furthered a decade later by members of Cambridge's Analytical Society, one of whom was George Peacock. His and others' attempts to convert Cambridge analysis from Newtonian to Leibnizian calculus were waged through translating a French textbook and making notational changes in Cambridge's mathematical examinations. *In 1830 Peacock's Treatise on Algebra introduced a more formalistic approach in algebra. Richards argues, drawing upon some fairly recent research, that Peacock's position was grounded in a progressivist view of history: arithmetic developed naturally out of fluency with counting, and algebra out of familiarity with arithmetic. Arithmetic suggests equivalent forms (equations, or symbolic assertions like the above rule) that can also be accepted as equiva-lent/valid in algebra without being constrained by restrictions appropriate to arithmetic. Such transitions, he thought, constitute genuine historical progress. Algebra thus splits into two parts for Peacock, arithmetical algebra and symbolical algebra, the latter based upon his principle of the permanence of equivalent forms, as found in his 1830 A Treatise on Algebra. *Peacock's approach to algebra set the stage for later British mathematicians such as De Morgan (Peacock's student), Boole, and others. Initially inclined to follow his future father-in-law's restrictive approach in algebra, De Morgan was soon won over to Peacock's point of view, even going beyond it in his own work. In a series of articles around 1840, De Morgan identified the basic rules governing ordinary calculations, but he also began entertaining the notion of a symbolical algebra less tightly tied to arithmetical algebra. By more completely separating the interpretation of algebra's operations and symbols from its axioms, symbolical algebra gained further independence from arithmetic. This gave algebra more flexibility, making room for subsequent developments such as the quaternion algebra of William Rowan Hamilton (1843) and Boole's algebra of logic (1847). *After exploring the foundations of algebra, De Morgan turned his attention to analyzing forms of reasoning, a topic made popular by the resurgence of syllogistic logic instigated at Oxford around 1825 by Richard Whately. Traditional Aristotelian logic parsed valid arguments into syllogisms containing categorical statements such as every X is Y. De Morgan treated such sentences exten-sionally, using parentheses to indicate total or partial inclusion between classes X and Y. Thus, every X is Y was symbolized by X)Y since the parenthesis opens toward X; to be more precise, one should indicate whether X and Y are coextensive or X is only a part of Y. By thus quantifying the predicate, as it was called, De Morgan allowed for these two possibilities to be symbolized respectively by X)(Y and X))Y, in compact symbolic form as ')(' and '))'. Combining the two premises of a syllogistic argument using this notation, one could then apply an erasure rule to draw its conclusion. De Morgan enthusiastically elaborated his symbolic logic by adopting an abstract version of algebra that paved the way for operating with formal symbols in logic. De Morgan's symbolism is not as inaccessible as Frege's later two-dimensional concept-writing (though the full version of De Morgan's notation is more complex than indicated here), but it is still rather forbid-ding and failed to find adherents. *In addition to expanding Aristotelian forms by quantifying the predicate, yielding eight basic categorical forms instead of the standard four, by 1860 De Morgan was generalizing the copula "is" in such sentences to other relations, such as "is a brother of" or "is greater than." He began to systematically investigate the formal properties of such relations and the ways in which relations might be compounded. Though intended as a way to generalize categorical statements and expand syllogistic logic, his treatment of relations was later recognized as an important contribution that could be incorporated into predicate logic. Richards's treatment gives the reader a fair sense of what De Morgan's logic was like, and while a detailed comparison is not developed, the reader can begin to see how De Morgan's system compares to Aristotelian logic, Boole's algebra of logic, and contemporary mathematical logic. *However, as indicated at the outset, exploring De Morgan's algebraic and logical work is only a subplot of

  PublisherDOI

• Robert Leslie Ellis: An Almost Perfect Moral Nature

  Studies in history and philosophy of science · 2022-01-01

  book-chapterOpen access1st authorCorresponding

  Abstract Sophia De Morgan met Robert Ellis when he was a student at Cambridge, and ever-after remembered him to possess an “almost perfect moral nature.” Her response to the sickly young man was typical of the ways Victorians responded to invalids like John Keats or Elizabeth Barrett Browning. But Ellis was neither a poet nor a woman. In the case of Ellis, the evidence of his moral character lay in the facility with which he practiced mathematics. Throughout the eighteenth century, the success of Newtonian cosmology served the English as a guarantee that in mathematics they could align their thoughts with the mind of God and by so doing truly understand the world in which they lived. As they moved into the nineteenth century, however, this assurance of unity between the human and the divine was being challenged on many fronts. When Sophia attributed “an almost perfect moral character” to the sickly young man, she was recognizing him as an ally in a battle for England’s soul that centered on the nature of mathematics.

  PublisherOA PDFDOI

• Beyond Reason

  Yale University Press eBooks · 2021-10-26

  book-chapter1st authorCorresponding

  In 1860, the De Morgans moved to a house farther from town, and began to develop their ideas in new directions. De Morgan stopped writing his column for the <italic>Companion to the Almaniac,</italic> and drew back from the RAS. He spent some time supporting the work of the Indian mathematician Yesudas Ramchandra, began writing a signed column for the <italic>Atheneum</italic> called “A Budget of Paradoxes,” and became the first president of the London Mathematical Society (LMS), which his son George was instrumental in founding. But in 1867 he became convinced that UCL had abandoned the secular principles on which it was founded, and he resigned his position as mathematics professor there. Four months later George De Morgan died; Christiana De Morgan died in 1870. The combination of these events overwhelmed Augustus, who died on March 18, 1871. Sophia defended his life of reason in a <italic>Memoir of Augustus De Morgan,</italic> published in 1882. She died in 1895.

  PublisherDOI

• Unitarian Women

  Yale University Press eBooks · 2021-10-26

  book-chapter1st authorCorresponding

  In the late 1820s and 1830s, William Frend and his former pupil Lady Byron were deeply involved in efforts to improve the condition of the poorer people of England. Central to their efforts, were attempts to establish and support the development of Mechanics Institutes as envisioned by Henry Brougham. As she grew into adulthood, Sophia Frend was also drawn into Lady Byron’s philanthropic orbit and became active in the Children’s Frend Society. Joined by the literalist view reason they had each learned from Frend, the two women together examined the implications of the literalist view of reason for their world of early Victorian womanhood, and aspired to understand the nature of what they called ‘Truth with a capital T.” As they did so, both were deeply affected by the ideas of Ramouhan Roy, albeit in somewhat different ways.

  PublisherDOI

• Generations of Reason

  Yale University Press eBooks · 2021 · 1 citations

  1st authorCorresponding
  • Sociology
  • Political Science
  • Classics

  <italic>Generations of Reason</italic> recounts the story of three Cambridge-educated Englishmen and the women with whom they chose to share their commitment to reason in all parts of their lives. In the first generation, Theophilus and Hannah Lindsey founded the Unitarian Church in 1774. In the second, William Frend, with the support of his wife Sarah, lived a complicated life as a radical political thinker and writer through the Napoleonic era. In the third, Augustus De Morgan pursued mathematics and logic while his wife Sophia explored the world of spiritualism in early Victorian England. These couples were members of a non-traditional family formed when a man married the daughter or niece of the mentor, who had taught him the ways of reason. This dynamic supported a commitment to reason that profoundly shaped the lives of three generations of men, women and children. The reason this family embraced was an essentially human power with the potential to generate true insight into all aspects of the world. Recognizing the role reason played in their lives casts new light on key developments in English cultural and political history, from the religious conformism of the eighteenth century through the upheavals of the Napoleonic era into the industrial prosperity of the Victorian age. At the same time, it restores the rich world of the essentially meditative, rational sciences of theology, astronomy, mathematics, and logic to their proper place in the English intellectual landscape.

  PublisherDOI

• Gentleman of Reason

  Yale University Press eBooks · 2021-10-26

  book-chapter1st authorCorresponding

  In the early 1830s, Augustus De Morgan was deeply affected by the revolutionary changes that took place in the French political world and the English scientific one. In the summer of 1831 he resigned his position at the University of London, because he did not think the professoriate was being treated as gentlemen. He then turned his attention to educating his countrymen in reason by publishing with the Society for the Diffusion of Useful Knowledge (SDUK) that had been established by Henry Brougham. As he was beginning to organize his ideas for publication in the <italic>Penny Cyclopædia</italic> he was converted to a radically new interpretation of the implications of the Literalist view of reason in mathematics. To Frend’s chagrin he followed the lead of his former tutor, George Peacock, and accepted the legitimacy of negative numbers in algebra.

  PublisherDOI

• Faith in Reason

  Yale University Press eBooks · 2021-10-26

  book-chapter1st authorCorresponding

  This chapter focuses on a conversation between well-established Anglican rector of Richmond and archdeacon of Cleveland, Francis Blackburne, and the rising young minister Theophilus Lindsey. Both men were educated at Cambridge University, where they learned of reason through the writings of John Locke. Following the literalist view of reason they took from Locke into the Bible, left the two men struggling to reconcile the religion Jesus preached with doctrines set out in the Thirty-nine Articles of the Anglican Church. Over the course of a very difficult year the two of them arrived at a delicate truce that allowed both of them to keep their jobs in the Anglican Church. At the chapter’s end, their agreement was cemented when Lindsey married Blackburne’s stepdaughter, Hannah Elsworth.

  PublisherDOI

• Son of India

  Yale University Press eBooks · 2021-10-26

  book-chapter1st authorCorresponding

  Augustus De Morgan was born on June 26, 1806, in Madura India, and two months later his family sailed with him to England. His father, John De Morgan, who was a rather restless and dissatisfied officer in the East India Company, returned to India within the year, which left his mother, Elizabeth nee Dodson, to raise Augustus and his three siblings. Augustus’s father spent a couple of years in England when he was five and six, but then returned to India, where he died when his oldest son was ten. Augustus’s mother was the fourth of sixteen children, and his many uncles who formed a net of support for the family. Augustus was blind in one eye and very short-sighted in the other. Nonetheless he had a lively imagination, read prodigiously, drew constantly, and played the flute beautifully. After a rather haphazard education in a variety of dame schools, his mother sent him to a school run by Mr. Parsons in Redlands. As well as making a number of friends for life, Augustus discovered his love of mathematics at Mr. Parsons’s school.

  PublisherDOI

• Trials in London

  Yale University Press eBooks · 2021-10-26

  book-chapter1st authorCorresponding

  In the context of England in the early 1790s, the consequences Frend faced were mild. In the spring of 1794 Priestly fled the country; in the fall of that year several leaders of the radical London Corresponding Society were arrested and tried for high treason in the London Treason Trials. The radical William Godwin wrote an impassioned defense, based on a literalist reading of the statute of 1351 under which these men were charged. Some form of Godwin’s reasoned argument won the day and the men were released, but within the year new laws were passed that made groups like the London Corresponding Society illegal. In addition to facing him with a dangerous political landscape, Frend’s move from essentially monastic Cambridge forced him to rethink his relation to women. Mary Hays was a radical woman who fell in love with him. When Frend drew away, Hays turned for advice to William Godwin, who advised her to write out her feelings in a novel. The result was <italic>The Adventures of Emma Courtney</italic>, a passionately romantic novel with a thinly disguised William Frend at its center.

  PublisherDOI

Frequent coauthors

• Lorraine Daston

  University of Chicago

  6 shared

• Michael E. Hobart

  3 shared

• M. J. Hobart

  2 shared

• Dennis Guerrier

  2 shared

• Mary Jo Nye

  2 shared

• David A. Sullivan

  2 shared

• John Wood

  2 shared

• Roger H. Stuewer

  University of Minnesota

  2 shared

Education

• B.A.

  Tufts University

  2009

• M.D.

  Tufts University School of Medicine

  2013