This volume assembles ten studies of the life and work of Thomas Harriot (1560-1621). These are based on lectures that have been given annually at Oriel College, Oxford since 1990, by such authorities as Hugh Trevor Roper, David Quinn and John D. North. The contributions to Thomas Harriot. An Elizabethan man of science shed new light on all the main aspects of Harriot's life and stand as an important contribution to the re-evaluation of one of (...) the most gifted and intriguing figures in early modern British science. (shrink)

Thomas Harriot was the finest English mathematician before Isaac Newton, but his work on the coinage of his country is almost unknown, unlike Newton’s. In the early 1600s Harriot studied several aspects of the gold and silver coins of his time. He investigated the ratio between the values of gold and silver, using data derived from the official weights of the coins; he used hydrostatic weighing to determine the composition of the coins; and he studied the methods (...) used to calculate how metals should be combined in order to produce the required standard of purity. This work required not only arithmetical skill, but also great insight into the relationships between the various quantities, and here his ‘greate invention of algebra’ played its part. The gold and silver coins were critically important in the national economy at that time, because they had intrinsic value and represented the country’s store of wealth. In his lifetime Harriot was supported by the patronage of Henry Percy, the Earl of Northumberland, who was a member of the Privy Council in 1604 when great changes to the English coinage were being made. After Harriot’s death his papers remained under the control of one of his executors, Sir Thomas Aylesbury, who became Master of the Tower Mint in 1635. These facts suggest that his work on the coins was considered to be important for practical reasons, not just academic ones. In this article the interplay between the scholarly work and its application to matters of national significance will be analysed in depth. The conclusions also throw some light on the long-standing mystery surrounding the fate of Harriot’s papers. (shrink)

Some time in the late 1590s, the Welsh amateur mathematician John Bulkeley wrote to Thomas Harriot asking his opinion about the properties of a truly gargantuan (but totally imaginary) plano-spherical convex lens, 48 feet in diameter. While Bulkeley’s original letter is lost, Harriot devoted several pages to the optical properties of “Mr Bulkeley his Glasse” in his optical papers (now in British Library MS Add. 6789), paying particular attention to the place of its burning point. Harriot’s (...) calculational methods in these papers are almost unique in Harriot’s optical remains, in that he uses both the sine law of refraction and interpolation from Witelo’s refraction tables in order to analyze the passage of light through the glass. For this and other reasons, it is very likely that Harriot wrote his papers on Bulkeley’s glass very shortly after his discovery of the law and while still working closely with Witelo’s great Optics; the papers represent, perhaps, his very first application of the law. His and Bulkeley’s interest in this giant glass conform to a long English tradition of curiosity about the optical and burning properties of large glasses, which grew more intense in late sixteenth-century England. In particular, Thomas Digges’s bold and widely known assertions about his father’s glasses that could see things several miles distant and could burn objects a half-mile or further away may have attracted Harriot and Bulkeley’s skeptical attention; for Harriot’s analysis of the burning distance and the intensity of Bulkeley’s fantastic lens, it shows that Digges’s claims could never have been true about any real lens (and this, I propose, was what Bulkeley had asked about in his original letter to Harriot). There was also a deeper, mathematical relevance to the problem that may have caught Harriot’s attention. His most recent source on refraction—Giambattista della Porta’s De refractione of 1593—identified a mathematical flaw in Witelo’s cursory suggestion about the optics of a lens (the only place that lenses appear, however fleetingly, in the writings of the thirteenth-century Perspectivist authors). In his early notes on optics, in a copy of Witelo’s optics, Harriot highlighted Witelo’s remarks on the lens and della Porta’s criticism (which he found unsatisfactory). The most significant problem with Witelo’s theorem would disappear as the radius of curvature of the lens approached infinity. Bulkeley’s gigantic glass, then, may have provided Harriot an opportunity to test out Witelo’s claims about a plano-spherical glass, at a time when he was still intensely concerned with the problems and methods of the Perspectivist school. (shrink)

From the early eighteenth century onward, primacy for the invention of binary numeration and arithmetic was almost universally credited to the German polymath Gottfried Wilhelm Leibniz (1646–1716). Then, in 1922, Frank Vigor Morley (1899–1980) noted that an unpublished manuscript of the English mathematician, astronomer, and alchemist Thomas Harriot (1560–1621) contained the numbers 1 to 8 in binary. Morley’s only comment was that this foray into binary was “certainly prior to the usual dates given for binary numeration”. Almost thirty (...) years later, John William Shirley (1908–1988) published reproductions of two of Harriot’s undated manuscript pages, which, he claimed, showed that Harriot had invented binary numeration “nearly a century before Leibniz’s time”. But while Shirley correctly asserted that Harriot had invented binary numeration, he made no attempt to explain how or when Harriot had done so. Curiously, few since Shirley’s time have attempted to answer these questions, despite their obvious importance. After all, Harriot was, as far as we know, the first to invent binary. Accordingly, answering the how and when questions about Harriot’s invention of binary is the aim of this short paper. (shrink)

Recent influential criticisms attack the reputation of Thomas Harriot by citing the contents of his ethnographic and economic survey, A briefe and true report of the new found land of Virginia, first published in 1588. This interpretation makes Harriot, together with Shakespeare and others, agents of a colonialist project. But profound differences are indicated in the comparison of the relatively unbiased depiction and analysis by Harriot and his artist collaborator John White with the interpretations of America (...) and Americans by some of their contemporaries. A briefe and true report conveys, and John White's drawings support, insight into particular non-European features of the cultural and economic lives of the Algonquian peoples. On the contrary, Captain Arthur Barlowe's Discourse and the illustrations by Theodore de Bry for the 1600 edition of Harriot's book instance romanticizing, stereotyping, and unanalytic condescension very unlike Harriot's and White's. These differences prove the faultiness of the recent assessment. (shrink)

Many scientists and philosophers of science think that beauty should play a role in theory selection. Physicists like Paul Dirac and Steven Weinberg explicitly claim that the ultimate explanations of the physical world must be beautiful. And philosophers of science like Peter Lipton say that we should expect the loveliest theory to also be the most likely. In this paper, I contend that these arguments from loveliness bear a striking similarity to Thomas Aquinas’ arguments from fittingness; both seem to (...) presume that the most beautiful theory is also the most probable. To do this, I first explain the explanatory virtues that are commonly thought to be constitutive of a lovely theory. Second, I elucidate Aquinas’ arguments from fittingness and show how they work in light of his account of beauty. Lastly, I connect the two kinds of aesthetic arguments and show the extent to which they overlap. (shrink)

Discussion of real cases encountered by medical students has been advocated as a component of medical ethics education. Suggested benefits include: a focus on the actual problems that medical students confront; active learner involvement; and facilitation of an exploration of the meaning of their own values in relation to professional behaviour. However, the approach may also carry risks: students may focus too narrowly on particular clinical topics or show a preference for discussing legal problems that may appear to have clearer (...) solutions. Teaching may therefore omit areas generally considered to be important components of the curriculum. In this paper, the authors present an analysis of the moral problems raised by medical students in response to a request to describe ethically problematic cases they had encountered during two clinical attachments, for the purpose of educational discussion at case-based seminars. We discuss the problems raised and compare the content of the cases to the UK Consensus Statement on core content of learning. The authors also describe the approaches that the students used to undertake an initial analysis of the problems raised, and consider possible implications for the development of medical ethics education. (shrink)

This is a book review-article. No abstract is required by me.

Summary This paper investigates the fate of Thomas Harriot's algebra after his death in 1621 and, in particular, the largely unsuccessful efforts of seventeenth-century mathematicians to promote it. The little known surviving manuscripts of Nathaniel Torporley have been used to elucidate the roles of Torporley and Walter Warner in the preparation of the Praxis, and a partial translation of Torporley's important critique of the Praxis is offered here for the first time. The known whereabouts of Harriot's mathematical (...) papers, both originals and copies, during the seventeenth century and later are summarised. John Wallis's controversial 1685 account of Harriot's algebra is examined in detail and it is argued that John Pell's influence on Wallis was far more significant than has previously been realised. The paper ends with a reassessment of Harriot's underrated and important contribution to the development of modern algebra. (shrink)

There are at least a few plausible grounds for our use of the term Beta in our title, notwithstanding that there is a key departure, in our framework, from classical Beta Existential Graphs. The situation, in brief, is as follows.The reader accustomed to Peirce’s graphical development of quantificational logic may, if desired, continue to think of formulas being written on a “sheet of assertion.” We retain the “cut” notation for negation and continue to represent conjunction simply by juxtaposition of diagrams. (...) However, on the side of departure, we dispense with the sometimes problematic “lines of identity” of classical Beta and instead represent a quantification by a.. (shrink)

'The Greate Invention of Algebra' casts new light on the work of Thomas Harriot, an innovative thinker and practitioner in several branches of the mathematical sciences, including navigation, astronomy, optics, geometry, and algebra. Although on his death Harriot left behind over four thousand manuscript sheets, much of his work remains unpublished. This book focuses on one hundred and forty of Harriot's manuscript pages, those concerned with the structure and solution of equations. The original material has been (...) carefully ordered, translated, and annotated to provide the first complete edition of his work on this subject, and an extended introduction provides the reader with a lucid background to the work and explains its contents. Illustrations from the manuscripts provide fascinating reference material. The appendix discusses correlations between Harriot's manuscripts and the texts of his contemporaries Viète, Warner, and Torporley. The clear and concise exposition makes this an excellent reference volume for historians of mathematics and those interested in the history of science. This is an important new resource for understanding the development of algebra in seventeenth-century England. (shrink)

Late in a career of more than sixty years, Thomas Burch, an internationally known social demographer, undertook a wide-ranging methodological critique of demography. This open access volume contains a selection of resulting papers, some previously unpublished, some published but not readily accessible [from past meetings of The International Union for the Scientific Study of Population and its research committees, or from other small conferences and seminars]. Rejecting the idea that demography is simply a branch of applied statistics, his work (...) views it as an autonomous and complete scientific discipline. When viewed from the perspective of modern philosophy of science, specifically the semantic or model-based school, demography is a balanced discipline, with a rich body of techniques and data, but also with more and better theories than generally recognized. As demonstrated in this book, some demographic techniques can also be seen as theoretical models, and some substantive/behavioral models, commonly rejected as theory because of inconsistent observations, are now seen as valuable theoretical models, for example demographic transition theory. This book shows how demography can build a strong theoretical edifice on its broad and deep empirical foundation by adoption of the model-based approach to science. But the full-fruits of this approach will require demographers to make greater use of computer modeling [both macro- and micro-simulation], in the statement and manipulation of theoretical ideas, as well as for numerical computation. This book is open access under a CC BY license. (shrink)

Torporley's ‘Congestor analyticus’, completed in 1627 in the library of the Earl of Northumberland at Petworth, was seen by Rigaud in the 1830s among the mathematical manuscript collection of the Earl of Macclesfield. Torporley's additional copy of the introductory part, preserved at Sion College, has been used for the present report. Torporley's prime objective was the presentation of some of Harriot's work. His first example concerns a classical problem in number theory. The complete solution, by an inductive process based (...) on tables of differences, is given in a few folios of the British Library collection of Harriot manuscripts. Torporley's transcription and commentary contrast forcibly today with the immediate illuminating impact of Harriot's original. (shrink)

This article examines Jacques Derrida’s work of self-reflection on his own teaching practice by using as a guiding thread the problematics of reproduction in the seminars of the 1970s. The first part of the article examines the sequence of seminars taught by Derrida at École normale supérieure from 1971 to 1977 to show how the concept of reproduction is deconstructed by Derrida across several seminars. Derrida systematically demonstrates, across several themes and fields (sociology and economy, biology and sexuality, art, technique, (...) ontology, and so on), that the critical recourse to the concept of reproduction (for instance, in its Marxist form) risks being complicit in the reproductive system it criticizes. The deconstructive motif of débordement is introduced to problematize this onto-logic of re-production. The second part of the article analyzes more specifically the unpublished seminar “GREPH, le concept de l’idéologie chez les idéologues français” (1974–75), in which Derrida examines the seminar function, his role as a teacher, and his own situation within the French educational system. In particular, Derrida offers a deconstructive critique of the reproductive effects of teaching, and of the institution of philosophy inasmuch as it functions as a reproductive machine. This work of deconstruction is done in the seminar notably through readings of Marx, Engels, and Althusser, with special attention to the concepts of ideology, reproduction, and sexual difference. (shrink)

This collection of essays came from an NEH Summer Seminar in 1995 at the University of Chicago.

The relevant alternatives approach in epistemology1 arose some years ago partly out of the hope to be able to reconcile our ordinary claims of knowledge with our inability to answer the skeptic. It was supposed to give rise to an account of knowledge according to which our ordinary claims of knowledge are true, even though the claims about our lack of knowledge that the skeptics make in one of their more persuasive moments are also true. To know, according to such (...) an account, is to have evidence sufficient to rule out all the relevant alternatives. In ordinary life few alternatives are relevant. For example, whether or not we are brains in a vat is not a relevant alternative that we have to be able to rule out. In the debate with the skeptic it may become relevant, and accordingly we might not know something any more then, even though we have the same evidence as in ordinary life. The skeptics cleverly make more and more alternatives relevant, and that is how they succeed. But their success in the philosophy seminar is no threat to our ordinary claims of knowledge, or so the theory goes. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Editors' IntroductionThomas Cattoi and Kristin Johnston LargenIn 2018, Buddhist-Christian Studies published the proceedings of an international conference on Ippolito Desideri (1684–1733) that had been held in Pistoia in October 2017. Marking the two-hundredth anniversary of the arrival of the Tuscan Jesuit in Lhasa, the event explored from a variety of disciplinary perspectives the extraordinary contribution of a figure who effectively inaugurated the theological conversation between Tibetan Buddhism and Christianity. (...) Desideri, however, was neither the only nor the first Catholic missionary to reach Tibet—a number of other Jesuits and a few members of other religious orders had visited the Land of Snows or even settled there before his arrival. In this issue of the journal, we are therefore glad to open this issue with the translation of another report by a missionary—this time, the author is the Capuchin Domenico da Fano, who authored his memories of his time in Tibet in 1713. The translation is by Michael J. Sweet and Leonard Zwilling—names many of our readers will recognize as the translator and the editor of Desideri's Relazione. As Luciano Petech's collection Il Nuovo Ramusio contains quite a few more reports by Italian Catholic missionaries to Asia, this may not even be the last such translation that the journal is going to publish.Continuing our long-established tradition, the first part of the issue contains a number of papers that were initially presented at the annual meeting of the Society for Buddhist-Christian Studies. For the second year in a row, because of the global health emergency, the meeting was held remotely, but the energy and the enthusiasm of both speakers and audience ensured that the sessions were both compelling and inspiring. A first set of essays touches on the relationship between Buddhist-Christian dialogue and the environmental crisis, exploring perspectives as diverse as process thought, hybridity, the interface between environmental activism and spiritual practice, and the need to listen to the environmental wisdom of the marginalized voices from the Global South. The second section explores different facets of the exchange between Japanese Buddhism and Christianity. Two contributions map the contribution of the Jesuit scholar and practitioner William Johnston, SJ (1925–2010), who played an important role in laying the foundations of dialogue between Japanese Zen and Catholic Christianity; another piece—also presented at the SBCS meeting in November 2021—addresses the fraught question of different responses to US nationalism during the Japanese-American conflict in World War II, while a final essay introduces us to the way women practitioners respond to [End Page vii] challenging aspects of Shin Buddhist teachings. The third and the last section of the first part includes four essays that sketch the contours of a number of interreligious encounters; one explores monastic obedience in Franciscan spirituality and Theravada Buddhism, one touches on the spirituality of victim souls and the Tibetan practice of gcod, and a final one brings into conversation Dignāga, Dharmakīrti, and Lonergan.In 2016, members of the Research Center for World Buddhist Cultures at Ryukoku University started an interreligious project under the title "Conversations in Comparative Theology: Shin Buddhism, Christianity, Islam." The goal was to organize a series of events where a few scholars from these three traditions would present papers on shared themes and discuss points of shared concerns. This initiative led to a series of four meetings that concluded in 2019. Thanks to Dennis Hirota and Perry Schmidt-Leukel, Buddhist-Christian Studies is glad to publish a series of eight essays that emerged from these conversations. Readers will notice that some of these essays are of an interreligious nature, but do not actually discuss the intersection of Buddhism and Christianity. In line with the policy adopted with the publication of the proceedings from the 2019 Lotus Sutra seminar organized in Tokyo by Risshō-Kōsei-Kai, the editors decided to publish all the contributions from these events, so as to make sure that the proceedings of these important interreligious exchanges would all be available in the same place.On January 22, 2022, the Vietnamese Buddhist leader Thich Nhat Hahn reached the end of his life. Thich Nhat Hahn had devoted his... (shrink)

This mischievously artful essay plays out on several levels; think of them as storeys of an imaginary castle much like the real, solid, central Italian one it explores and expounds. On its own ground floor, the essay recounts a gruesome murder, a noble husband’s midnight revenge upon his wife and upon her bastard lover, his own half-brother, in her castle chamber, in bed. In sex. Of course. The murder itself is pure Renaissance, quintessential Boccaccio or Bandello, but the aftermath, in (...) fort and village, is more singular, more ethnographically delightful, as castle and village trace a ceremonious passage from frozen limbo to fluid grief and storytelling, finally set in motion by the arrival of the dead wife’s brother. Meanwhile, one flight up, the essay retells my own investigation of the real castle’s geometry, as I clambered through rooms, peered out windows, prowled the roof, and scanned blueprints seeking the places of the plotters’ plots. In an expository attic, I lodge reflections on my teaching stratagems, as I led a first-year seminar into detection’s crafts and exposition’s ploys. All the while, on its rooftop, this essay dances among fantastical chimneys and turrets of high theory and literary practice, musing on the patent irony of artful artifice, which evokes both the irony and the pathos of scholars’ cool histories about hot deeds and feelings. Art suggests we authors had best hide ourselves, unlike normal essayists, so as not to spoil the show. But, I posit, our self-effacement is so conspicuous that it proclaims our presence, as in fact it should, and, by so doing, trumpets the necessary tensions of our artifice and craft. Thus artfulness itself nicely both proclaims and celebrates the bittersweet frustrations of historians’ and readers’ quest for knowledge and, especially, for experience of a lost past. (shrink)

This article analyzes the role played by Immanuel Kant's defense of the death penalty, in the first and the second years of Jacques Derrida's Death Penalty Seminars, delivered from 1999 to 2001. Regarding the first year, the initial part of this article charts how Derrida introduces Kant's writings that purport to elaborate the categorical imperative of the death penalty, not by Kant's primary arguments but rather precisely through Kant's concession of an exception to this categorical imperative, concerning the impunity of (...) a mother's infanticide. Derrida's lectures juxtapose Kant's philosophy of the death penalty with Victor Hugo's claim for the inviolability of life, and in doing so, the sessions introduce other examples of the applicability of the death penalty to mothers who have killed their children. What is at stake is the status of philosophy relative to the death penalty. Concerning the second year, the latter part of this article isolates the logic of Kant's categorical imperative, as deconstructed by Derrida, through recourse to the additions that Kant was obliged to append to his initial argument—those involving precisely sex crimes. The article follows how Derrida thoroughly takes apart both the simplicity of Kant's categorical imperative of the death penalty by means of the complications that are its abyssal foundation and the phallogocentrism of Freud's sexual oppositions through the extraction of insights into another thinking of sexual difference that Freud's categories foreclosed. (shrink)

Dieser Band bietet einen aktuellen, analytisch orientierten Querschnitt durch ein zentrales Thema der Philosophie. In den Originalbeitragen werden erkenntnistheoretische, sprachphilosophische, formallogische, historische, wissenschaftstheoretische und metaphysische Aspekte des Themas untersucht. Der Band ist als Grundlage fur Seminare und Ubungen ab dem zweiten Studienjahr konzipiert.

Tina Beattie has re‐read Aquinas in the light of Lacanian theory and found the later Lacan's transition to what he calls the register of “the Real” to be significant for a revitalised theology beyond traditional intellectual categories. She argues for a maternal Trinity which she believes to lie hidden in Thomas and, in support of this, she contends that Lacan left behind Freud's paternal preoccupations in favour of maternity. This response to Beattie will re‐examine Lacan's trajectory from “the Symbolic” (...) register to “the Real” through the lens of what he said in his year‐long seminars about Moses, whom he regarded as a representative of “the Symbolic”, and it will demonstrate that paternity remained a constant in Lacan, who even came to see “the Real” itself as a name of the father. (shrink)

I am pleased to participate in this joint Critical Notice, in part because it is an opportunity to pay a debt of gratitude. Thirteen years ago, as a Toronto undergraduate with interests in things like Hegelian metaphysics, I enrolled in an ethics seminar with Wayne Sumner. I had not done any ethics before, and took this course largely because I thought I ought to. But it turned out to be the best course of my undergraduate career, and permanently changed (...) my philosophical interests. Having learned what I did in the seminar I have been doing ethics ever since—so, thank you, Wayne. (shrink)

My paper proceeds in three stages: 1) the traditional relationship between philosophy and theology; 2) how the “foundationalist” issue affects this debate; 3) some final reflections. This essay, along with the previous one by Jack Bonsor, was originally presented to the “Theology in the Seminary Context” seminar at the Catholic Theological Society of America convention in June, 1995.

This essay adopts a semiotic perspective focused on practices of communication, movement, and translation to examine the global impact of A. J. Greimas and his oeuvre. The linguist and semiotician’s lecture trips abroad, the number and provenance of international students in his Paris seminar, and the chronology and linguistic geography of translations of his work help describe, gauge, and explain the dissemination and development of his ideas throughout the world. His project has engendered distinctive appropriations and at times productive (...) institutional structures in a number of cultural and linguistic contexts, notably Romance, Anglo-American, Germanic, Russian, Lithuanian, and Chinese. The broader historical relations between France and other lands, and the extent of each society’s use of the French language have conditioned, fostered, or impeded responses to his proposals. The conclusion’s discussion of the relative importance of personal contacts, socio-historical context, and the sociolinguistic and pedagogical status of French for his international reception aims to contribute to general methodological debates in the history of science and ideas and in transnational history. (shrink)