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)

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)

Drawing on aspects of Foucauldian feminist theory Thomas Hardy, Femininity and Dissent offers original and detailed readings of six critically under-valued novels: Desperate Remedies, A Pair of Blue Eyes, The Hand of Ethelberta, A Laodicean, Two on a Tower and The Well-Beloved, demonstrating Hardy's peculiarly modern appreciation of how individuals negotiate the forces which shape their sense of self. Tracing his interest in the evolutionary debate and the woman question this book reveals a new politically engaged rather than a (...) grimly pessimistic Hardy. (shrink)

It has been posited that persuasive cues impart Evolution Wars communications with persuasive force extending beyond the merits of their communicated arguments. Additionally, it has been observed that the array of cues displayed throughout proevolutionist materials is exceeded in both the number and nuance of Darwin-skeptic persuasion techniques. This study reassesses these findings by exploring how persuasive cues in the Evolution Wars are being articulated with reference to the Cultural Cognition Thesis and Moral Foundations Theory. Observations of Institute for Creation (...) Research, Answers in Genesis, and the Center for Science and Culture media are reevaluated. These findings are juxtaposed with data pertaining to Richard Dawkins Foundation for Reason and Science, National Center for Science Education, and BioLogos Foundation broadcasts. The outcomes reveal how values claims and morally charged language are concentrated within the works of antievolutionists and New Atheist media makers, who collectively promote some manner of religion-science conflict. (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)

Locke's Essay concerning Human Understanding has generally been read as primarily concerned with epistemology. In particular, it has been claimed that the Essay attempts to defeat epistemological skepticism, but fails in this enterprise because of the veiling character of Locke's ideas. By way of reexamination of the texts in question I show that epistemological skepticism is not the topic of the Essay, and that there is not sufficient reason to claim that Locke's account of knowledge leads to epistemological skepticism. I (...) argue, moreover, that the motivating topic of the Essay is moral skepticism, and I explain the central role of ch. 8, book 2 in Locke's argumentation for the claim that we may achieve a science of morality. I conclude with an account of some of practical consequences of a science of morality, as conceived by Locke. (shrink)

A competent patient has the right to refuse treatment necessary to sustain life. However, for many end-of-life decisions, we lack direct access to the wishes of a competent patient. Some treatment decisions near the end of life involve patients with severely diminished mental capacity, some involve patients who are unable to communicate, and some involve patients who are simply unable or unwilling to participate in decisionmaking due to the nature or severity of their illness.

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

To get an initial grip of what is and, in particular, what is not at stake in the Phenomenology of SE, it is helpful to distinguish four dimensions of the sociality of emotions. As we shall see, the Phenomenology of emotions, in the sense in which I will [aut]Walther, Gerda’s account, is primarily, though certainly not exclusively, concerned with the fourth dimension. Roughly, the three first layers or levels in which social relations and facts come into play in the affective (...) life of individuals and groups are i) the interpersonal, ii) the Group and intergroup, and iii) the sociological and sociocultural dimensions. Whereas most phenomenologists, and [aut]Walther, Gerda, touch upon the interpersonal and Group-level dimensions and analyzing various collective and GroupPhenomena), the intergroup and sociological and sociocultural levels have been mined extensively by sociologists, as well as cross-cultural and social psychologists. Here is how the social [aut]Parkinson, Brian, [aut]Fischer, Agneta[aut]Manstead, Antony S. R. concisely delineate these dimensions. (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)

The Developmental Systems Theory (DST) presented by its proponents as a challenging approach in biology is aimed at transforming the workings of the life sciences from both a theoretical and experimental point of view (see, in particular, Oyama [1985] 2000; Oyama et al. 2001). Even though some may have the impression that the enthusiasm surrounding DST has faded in very recent years, some of the key concepts, ideas, and visions of DST have in fact pervaded biology and philosophy of biology. (...) It seems crucial to us both to establish which of these ideas are truly specific to DST, and to shift through these ideas in order to determine the criticisms they have drawn, or may draw (e.g., Sterelny et al. 1996; Griesemer 2000; Sterelny 2000; Kitcher 2001; Keller 2005; Waters 2007). (shrink)

"Displaying a masterful grasp of the texts, the author shows how otherness forces itself upon the existentialist Sartre, gradually constraining him to modify his understanding of consciousness as omnipotent. The issue is Sartre’s discovery of the social and its conceptual assimilation into his individualistic, consciousness-oriented philosophy." —Thomas R. Flynn "This very successful and accessible scholarly book... is simultaneously a succinct and clear overview of Sartre’s philosophical works.... and a fresh consideration of Sartre’s body of work." —Choice "Busch’s admirably clear (...) and compact discussion is essential reading for Sartre scholars, since it powerfully addresses many issues dividing them... " —Ethics "... a useful overview of the evolution of Sartre’s thought... " —Review of Politics "... a thought provoking reassessment of Sartre's philosophical career." —Man and World "... succinct, richly documented survey... " —International Studies in Philosophy. (shrink)

Have humans been sharing the planet with other intelligent life for millions of years without realizing it? _In Defense of Dolphins_ combines accessible science and philosophy, surveying the latest research on dolphin intelligence and social behavior, to advocate for their ethical treatment. Encourages a reassessment of the human-dolphin relationship, arguing for an end to the inhuman treatment of dolphins Written by an expert philosopher with almost twenty-years of experience studying dolphins Combines up-to-date research supporting the sophisticated cognitive and emotional capacities (...) of dolphins with entertaining first-hand accounts Looks at the serious questions of intelligent life, ethical treatment, and moral obligation Engaging and thought-provoking. (shrink)

Iconicity, or the resemblance between form and meaning, is often ascribed to a special status and contrasted with default assumptions of arbitrariness in spoken language. But does iconicity in spoken language have a special status when it comes to learnability? A simple way to gauge learnability is to see how well something is retrieved from memory. We can further contrast this with guessability, to see (1) whether the ease of guessing the meanings of ideophones outperforms the rate at which they (...) are remembered; and (2) how willing participants’ are to reassess what they were taught in a prior task—a novel contribution of this study. We replicate prior guessing and memory tasks using ideophones and adjectives from Japanese, Korean, and Igbo. Our results show that although native Cantonese speakers guessed ideophone meanings above chance level, they memorized both ideophones and adjectives with comparable accuracy. However, response time data show that participants took significantly longer to respond correctly to adjective–meaning pairs—indicating a discrepancy in a cognitive effort that favored the recognition of ideophones. In a follow‐up reassessment task, participants who were taught foil translations were more likely to choose the true translations for ideophones rather than adjectives. By comparing the findings from our guessing and memory tasks, we conclude that iconicity is more accessible if a task requires participants to actively seek out sound‐meaning associations. (shrink)

Hegemony is one of the most widely diffused concepts in the contemporary social sciences and humanities internationally, interpreted in a variety of ways in different disciplinary and national contexts. However, its contemporary relevance and conceptual coherence has recently been challenged by various theories of ‘posthegemony’. This article offers a critical assessment of this theoretical initiative. In the first part of the article, I distinguish between three main versions of posthegemony – temporal, foundational and expansive – characterized by different understandings of (...) the temporal and logical implications of hegemony. I then offer a critical assessment of the shared presuppositions of these theories, including their ‘pre-Gramscianism’, their indebtedness to Laclau and Mouffe’s formulation of hegemony, and their characterization of hegemony in terms compatible with modern theories of sovereignty. I conclude by arguing that the contradictions and oversights of the debate on posthegemony encourage us to undertake a reassessment of the real historical complexity of hegemonic politics and its different traditions of conceptualization. (shrink)

F. Thomas Burke believes that pragmatism, especially as it has been employed in politics and social action, needs a reassessment. He examines the philosophies of William James and Charles S. Peirce to determine how certain maxims of pragmatism originated. Burke contrasts pragmatism as a certain set of beliefs or actions with pragmatism as simply a methodology. He unravels the complex history of this philosophical tradition and discusses contemporary conceptions of pragmatism found in current US political discourse and explains what (...) this quintessentially American philosophy means today. (shrink)

ABSTRACT This article examines the Fourierist reception of Owenism. In challenging the established historiography on Owen’s reception in France, the article draws on a wide range of Fourierist material – letters, unpublished draft manuscripts, and neglected articles in Fourierist and non-Fourierist periodicals – that previously not accessible to twentieth-century historians in order to reassess the Fourierist response to Owen and Owenism. The article pays special attention to the work of Fourier’s leading disciple, Victor Considerant. It contrasts Fourier’s highly critical evaluation (...) of Owen’s work, with Considerant’s more considered reading of Owen and conciliatory approach in dealing with other socialists, such as the Saint-Simonians and Owen’s French disciples. The article also examines the work of some of Fourier’s other followers, including Jules Lechevalier, Adrien Berbrugger, Alexandre Baudet-Dulary, and Amédée Paget and their evaluations of Owen and Owenism. (shrink)

Within half a century, the status of Duchamp’s readymades changed from iconoclastic object to iconic sculpture. This contribution focusses on two of Duchamp’s readymades, one from 1915 and thus dated at the very beginning of Duchamp’s occupation with this subject matter, while the other is dated 1967, the very last object to enter this particular category within Duchamp’s oeuvre. André Breton remarked that “future generations can do no less than make a systematic effort to go back the stream of Duchamp’s (...) thought and carefully describe its meanderings in search of the hidden treasure which was his mind.” It is with these suggestions in mind that, after the examination of an heretofore unknown readymade from the 1910’s and his collage Pollyperruque from the year before he passed away, final observations will examine the 100th anniversary of Duchamp’s Fountain to reassess the readymade’s potential as an analog object and social media phenomenon in the digital realm. (shrink)

This dissertation is a historical and critical study of a controversy that raged among all the great figures of Enlightenment natural philosophy. The issue at stake is the structure or internal architecture of matter. One the one hand, an array of a priori arguments seems to show that matter must be fundamentally discrete in its fine structure: it must resolve to metaphysical atoms or monads. On the other hand, an opposing battery of a priori arguments seems to show that it (...) must be fundamentally continuous and altogether without simple first elements. ;The conflict between these rival sets of arguments deeply unsettled natural philosophers of the Enlightenment. Since both incompatible sets of arguments seemed compelling, the clash between them appeared to expose a paradox or antinomy in the new world view pioneered by Galileo and Newton. The new science's account of a fundamentally geometrical Creation, mathematicizable and intelligible to the human inquirer, seemed to be under threat. ;In this dissertation I present a rational reconstruction of the Enlightenment debate that challenges the standard interpretation in the secondary literature. Contra that standard interpretation, I argue that the debate turns crucially on substantive metaphysical theses about the 'filling' or 'stuffing' of matter, not just on theses about its mathematically tractable form or structure. The early moderns were committed to a particular metaphysical doctrine concerning the stuffing of matter and it is this doctrine that lies behind the paradoxes of material composition. Having set out this new metaphysical reading of the Enlightenment debate, I then mobilize it in order to reassess the various early modern responses to the paradoxes of material structure. (shrink)

"The development of modern diagnostic neuroimaging techniques led to discoveries about the human brain and mind that helped give rise to the field of neurolaw. This new interdisciplinary field has led to novel directions in analytic jurisprudence and philosophy of law by providing an empirically-informed platform from which scholars have reassessed topics such as mental privacy and self-determination, responsibility and its relationship to mental disorders, and the proper aims of the criminal law. Similarly, the development of neurointervention techniques that (...) promise to deliver new ways of altering people's minds creates opportunities and challenges that raise important and rich conceptual, moral, jurisprudential, and scientific questions. The specific purpose of this volume is to make a contribution to the field of neurolaw by investigating the legal issues raised by the development and use of neurointerventions "--. (shrink)

Many believe that colleges of business have a role to play in improving the level of marketing ethics practiced in the business world, while others believe that by the time students reach the level of university education, their ethical beliefs are so ingrained as to be virtually unalterable. The purpose of this study is to add to the literature regarding university students' ethical value judgments. It utilizes scenario studies to assess base line ethical values of junior level undergraduate business administration (...) students, then techniques are employed to influence students' perceptions of the ethics of various marketing practices, and students' values are reassessed. A total of 667 junior and senior level students majoring in business administration participated in the pre-tests and 525 students participated in the post-tests. The results of the before/after studies indicate that some experimental techniques are more effective than others in affecting change, but it is difficult to affect long-run change in those predisposed to unethical behavior. (shrink)