The Polymath Project is an online collaborative enterprise that was initiated in 2009, when Timothy Gowers asked whether and how groups could work together to solve mathematical problems that “do not naturally split up into a vast number of subtasks.” Gowers proposed to answer this question himself by actually trying to set up such a collaboration, based on interactions taking place in the comment-threads of a series of posts on a WordPress blog. Hence, the first project officially started in (...) early 2009, to be proclaimed successful only 6 weeks later (Gowers and Nielsen 2009). From its inception until April 2018, 15 more Polymath problems (and a handful of smaller or related ones) have been launched. These projects have attracted attention from different scholarly communities, including the philosophy of mathematical practices, from the perspective of which the Polymath Project can be seen as a vast repository of mathematics in action. This chapter continues previous work by its authors on the topic in question and topics related. More specifically, for the purposes of this volume, it is our aim to both summarize and expand upon these earlier contributions. The starting point is the above observation that in the past decade, the issue of “massively collaborative mathematics” (to be qualified below) has drawn quite some attention. However, does it also warrant intensive philosophical attention in particular? For, as exciting as these developments might be from mathematical and other points of view, the enhanced possibilities that have come with it do not per se give rise to any philosophical import. In Van Bendegem (2011), one of us has indeed tentatively argued for the philosophical relevance of these new dynamics of proof construction flowing from the wide availability and efficiency of Internet technology. We shall below briefly rehearse and update the argument given there. (shrink)

James Pickett’s much-anticipated book derives from his 2015 Princeton Ph.D. dissertation, and the comparatively slim end product only hints at the wealth of res.

Spirituality is deeply important, especially for contemporary times, because it’s such an alienating time. And at the end of the day I am a believing Muslim. I am a sceptical Muslim, in the sense that I believe in asking questions and I would ask those questions that many Muslims would not even dream of asking. But that doesn’t make me a non-believer. So in that sense I’m not a secularist. Religion plays a very important part in my life, in what (...) I believe, how I look at the world, what I do and how I behave. (shrink)

Spirituality is deeply important, especially for contemporary times, because it’s such an alienating time. And at the end of the day I am a believing Muslim. I am a sceptical Muslim, in the sense that I believe in asking questions and I would ask those questions that many Muslims would not even dream of asking. But that doesn’t make me a non-believer. So in that sense I’m not a secularist. Religion plays a very important part in my life, in what (...) I believe, how I look at the world, what I do and how I behave. (shrink)

A review of Jordy Cat & Adam Tamás Tuboly (eds.), Neurath Reconsidered: New Sources and Perspectives (Springer 2019).

Mark Geller is well known to everyone in his field and, unsurprisingly, his Festschrift is a bulging volume of contributions—from thirty-four scholars in a variety of different specialties. Like most Festschriften, it is of uneven quality, but there are some very fine articles, including useful text editions and offerings that raise interesting scholarly questions. Although there is nothing here on economics, there are articles that engage historical and/or anthropological questions, exegetical issues, and matters of composition of literary texts, including one (...) offering on Akkadian grammar. None of these would be expected from a volume entitled Mesopotamian Medicine and Magic, but their presence is a testimony to the very broad interests of the honoree. (shrink)

Green Mass is a meditation on—and with—twelfth-century Christian mystic and polymath Saint Hildegard of Bingen. Attending to Hildegard's vegetal vision, which greens theological tradition and imbues plant life with spirit, philosopher Michael Marder uncovers a verdant mode of thinking. The book stages a fresh encounter between present-day and premodern concerns, ecology and theology, philosophy and mysticism, the material and the spiritual, in word and sound. Hildegard's lush notion of viriditas, the vegetal power of creation, is emblematic of her deeply (...) entwined understanding of physical reality and spiritual elevation. From blossoming flora to burning desert, Marder plays with the symphonic multiplicity of meanings in her thought, listening to the resonances between the ardency of holy fire and the aridity of a world aflame. Across Hildegard's cosmos, we hear the anarchic proliferation of her ecological theology, in which both God and greening are circular, without beginning or end. Introduced with a foreword by philosopher Marcia Sá Cavalcante Schuback and accompanied by cellist Peter Schuback's musical movements, which echo both Hildegard's own compositions and key themes in each chapter of the book, this multifaceted work creates a resonance chamber, in which to discover the living world anew. The original compositions accompanying each chapter are available free for streaming and for download at www.sup.org/greenmass. (shrink)

Was Silvanus Phillips Thompson primarily a physicist, electrical engineer, biographer, or teacher? His obituarists could not agree. I argue Thompson was in fact a polymathic generalist who, as a philanthropic Quaker, worked not to promote his own expertise but rather to ensure the public was swiftly informed of the most important techno-scientific research and applications of his contemporaries. I illustrate this in a comparison of Thompson and his longer-lived friend Oliver Lodge: working in closely-related areas, they had contrasting profiles and (...) commitments. After inspecting Thompson's work as textbook author and bibliophile, I resolve his apparently paradoxical status as both radical critic and figurehead of multiple institutions. Finally, to flesh out his friends' representation of him as a “many-sided crystal,” I analyse Thompson's multi-facetted posthumous reputation, especially in reviews of the Life and Letters written by his widow Jane and daughter Helen exactly 100 years ago. (shrink)

Asia, America, and Europe have been intellectually intertwined for centuries. Several studies have been published revealing European scholars’ interest in the “exotic” languages of Asia and America, as well as in ethnographic and anthropological aspects. Some scholars such as Polymath Leibniz (1646–1716), were interested in these languages in an attempt to construct a universal language, while others tried to establish language families, like the Jesuit Hervás y Panduro (1735–1809). However, all acknowledge the importance of language and the circulation of (...) knowledge. This paper analyzes the dissemination of the compilation of eighteenth‐century multilingual lexical compilations for comparative purposes as an early globalized project. These compilations were designed by European scholars and subsequently elaborated in different languages by missionaries, explorers, and scientists in the Philippines and America. Taking the correspondence and relations between botanist Mutis (1732–1808) and bureaucrats, European scientists such as polymath Humboldt (1769–1859) and Botanist Linnaeus (1707–1778) among others, and navy officers of the scientific exploration commanded by Malaspina (1754–1809) and Bustamante y Guerra (1759–1825) into consideration, I will analyze how simultaneous projects followed a unified aim, and illustrate their substantial contribution to the study of language in the late eighteenth century. (shrink)

The polymath Michael Polanyi first made his mark as a physical chemist, but his interests gradually shifted to economics, politics, and philosophy, in which field he would ultimately propose a revolutionary theory of knowledge that grew out of his firsthand experience with both the scientific method and political totalitarianism. In this sixth entry in ISI Books’ Library of Modern Thinkers’ series, Mark T. Mitchell reveals how Polanyi came to recognize that the roots of the modern political and spiritual crisis (...) lay in an errant conception of knowledge that served to foreclose any possibility of making meaningful statements about truth, goodness, or beauty. Polanyi’s theory of knowledge as ineluctably personal but also grounded in reality is not merely of historical interest, writes Mitchell, for it proposes an attractive alternative for anyone who would reject both the hubris of modern rationalism and the ultimately nihilistic implications of academic postmodernism. (shrink)

The polymath Michel de Certeau is traditionally seen as one of a group of French poststructuralist thinkers who reject constructs in the social sciences in favor of the diversity of the everyday or the past. However, in this paper I will show that, as a historian, Certeau did not discard these constructs, but rather valued them as a means of doing justice to the “strangeness” of the past. The position that Certeau adopts can be seen most clearly from his (...) theoretical debate with Paul Veyne, which is the starting point of this article. I then show how Certeau’s first major historical work, The Possession at Loudun, exemplifies his theoretical position. An analysis of this work demonstrates how the historian’s active reconstruction of interactions between exorcists, medical doctors, state officers, and possessed nuns helps us to perceive the complexity of the past in a way that can be seen as a microhistory avant la lettre. I will suggest that during his writing of the history of Loudun, Certeau implicitly raises more theoretical and epistemological problems, and in so doing he “practices” a theory of history. The most elusive aspect of the story at Loudun turns out to be the drama around the priest Grandier. This article demonstrates how Certeau pays tribute to Grandier by using “scientific” methods, thus showing the “limits of representation” through disciplinary means. Finally, the article explores the implications of Certeau’s theory and practice of the writing of history for understanding historiography at large. The historian not only appears as a tramp who looks for remains that are forever lost to us, but is also a “scientist” who uses both models and concepts in order to put them to the test. (shrink)

A polymath and author of dozens of books including The Death of Tragedy, After Babel and In Bluebeard's Castle examines two thousand years of Western culture, philosophy and literature and discusses how great thought and great style are ...

The Victorian polymath William Stanley Jevons is generally and rightly venerated as one of the great innovators of economic theory and method in what came to be known as the 'marginalist revolution'. This book is an investigation into the cultural and intellectual resources that Jevons drew upon to revolutionize research methods in economics. Jevons's uniform approach to the sciences was based on a firm belief in the mechanical constitution of the universe and a firm conviction that all scientific knowledge (...) was limited and therefore hypothetical in character. Jevons's mechanical beliefs found their way into his early meteorological studies, his formal logic, and his economic pursuits. By using mechanical analogies as instruments of discovery, Jevons was able to bridge the divide between theory and statistics that had become more or less institutionalized in mid nineteenth-century Britain. (shrink)

The Viennese-born polymath Otto Neurath died on 22 December 1945 in Oxford, a few months after the end of World War Two. A social engineer and sociologist of happiness, Neurath was not only a socially sensitive educator, advocating for any institute and organization that was concerned with the well-being of people; he was also a trained scientist and philosopher. Studying mathematics, economics, history, philosophy, and physics in Vienna and then in Berlin during the early years of the long twentieth (...) century, Neurath became involved in many of the disputes among social and natural scientists that shaped the course of the fields. This short introduction provides the context and describes the aims of the volume. Short summaries of the chapters are also included. (shrink)

William Whewell (1794–1866), polymathic Victorian scientist, philosopher, historian, and educator, was one of the great neologists of the nineteenth century. Although Whewell's name is little remembered today except by professional historians and philosophers of science, researchers in many scientific fields work each day in a world that Whewell named. "Miocene" and "Pliocene," "uniformitarian" and "catastrophist," "anode" and "cathode," even the word "scientist" itself—all of these were Whewell coinages. Whewell is particularly important to students of the historical sciences for another word (...) he coined, one that was unfortunately not as successful as many of his others because it is difficult to pronounce. This word, "palaetiology," was the name Whewell gave to the class of sciences that are concerned with historical causation: the class we might today refer to as historical sciences. Although the disciplines Whewell included under the heading of palaetiology might seem to cut across conventional academic boundaries of his day and ours—his exemplary palaetiological sciences were geology and comparative philology—all these fields may be examined together, Whewell argued, because of their common interest in reconstructing the past. ¶ This paper is an essay in the palaetiological sciences, dedicated to Whewell on the bicentennial of his birth, an essay that examines some of the principles, maxims, and rules of procedure that these sciences have all in common. Its first purpose is to demonstrate the continuing validity of Whewell's classification of these sciences through a study of historical representation in three different palaetiological fields: systematics, historical linguistics, and textual transmission. Its second purpose is to continue the development of an extended analogy between historical representation and cartographic representation that I began in an earlier paper (O'Hara, 1993, Systematic Biology), an analogy that makes especially clear the common representational practices that are found throughout palaetiology. (shrink)

The Belgian polymath Lambert Adolphe Jacques Quetelet pioneered social statistics. Applying his training in mathematics to the physical and psychological dimensions of individuals, he identified the 'average man' as characterised by the mean values of measured variables that follow a normal distribution. He believed that comparing the features of individuals against this average would allow scientists to better explore the processes that determine normal and abnormal qualities. Quetelet's methods influenced many, among them Florence Nightingale, and his simple measure for (...) classifying a person's weight, dividing it by the square of their height, is widely known as the body mass index. First published in French in 1835 and reissued here in the 1842 English translation, this is his most influential work and includes a new preface that succinctly states his aim to be 'the analysis of normal man through his actions and of intellectual man through his productions'. (shrink)

Charles S. Peirce, polymath, philosopher, logician, lived a life of often wild extremes and, when he died in 1914, had earned a vile reputation as a debauched genius. Yet he created a unified, profound and brilliant work, both published and unpublished, a fact difficult to explain. In my 1993 biography, I proposed three hypotheses to account for his Jekyll-Hyde character: his obsession with the puzzle of meaning, two neurological pathologies, trigeminal neuralgia and left-handedness, and the powerful influence of his (...) father. After publication, further research has led me to propose two additional hypotheses to explain his extraordinary life: manic-depressive illness and mystical experience, the last greatly influencing the development of his doctrine of semeiotic, of which his logic of science is a part. (shrink)

Porphyry, the Phoenician polymath, having studied with Plotinus when he was thirty years old, was a well-known Hellenic philosopher, an opponent of Christianity, and was born in Tyre, in the Roman Empire. We know of his anti-Christian ideology and of his defence of traditional Roman religions, by means of a fragment of his Adversus Christianos. This work incurred controversy among early Christians. His Adversus Christianos has been served as a critique of Christianity and a defence of the worship of (...) the traditional gods, so it is inevitable that his texts involved Biblical culture and religious Hellenism. Augustine, in his De Civitate Dei 10. 28, reproves Porphyry for wasting so much time in learning the theurgic arts and rites. This paper does not inquire into whether Porphyry’s philosophical monistic theology is shown in Plotinus’ Enneads, but focuses on his anti-Christian thought through the fragments that we have, particularly Augustine’s De Civitate Dei. (shrink)

The English polymath Joseph Priestley wrote on a wide range of scientific, theological and pedagogical subjects. After the appearance of his influential Rudiments of English Grammar and A Course of Lectures on the Theory of Language and Universal Grammar, both of which are reissued in this series, Priestley produced in 1765 his Essay on a Course of Liberal Education, which is included and expanded on in this 1778 publication. Here he explains the reasons behind his decision to guide the (...) curriculum at Warrington Academy towards a greater focus on subjects with a more direct application to 'civil and active life'. He offers more general instruction on the cultivation of young men in various spheres, notably through foreign travel and developing 'knowledge of the world'. Priestley ends by outlining a suggested course of lectures on the history and laws of England. (shrink)

The polymathic Leibniz was surely one of the greatest and most enigmatic figures produced by the "century of genius." He is the only philosopher whom the renowned historian of the Prussian Academy of Sciences, Adolf von Harnack, would admit as a colleague to that august body, and Leibniz is universally admired by metaphysicians, theologians, advocates of cosmopolitanism and religious tolerance, students of international law, and, not the least, by philosophers of logic and language. Although efforts to canonize Leibniz as the (...) pure type of "harmonic synthesizer" have been under way for quite a long time, philosophers and historians are no longer so anxious as they once were to work out a synthetic unification of these and many other perspectives of Leibniz as was Mahnke, for instance, who characterized Leibniz’ philosophy as a synthesis of universal mathematics and individual metaphysics. (shrink)

The polymathic Leibniz was surely one of the greatest and most enigmatic figures produced by the "century of genius." He is the only philosopher whom the renowned historian of the Prussian Academy of Sciences, Adolf von Harnack, would admit as a colleague to that august body, and Leibniz is universally admired by metaphysicians, theologians, advocates of cosmopolitanism and religious tolerance, students of international law, and, not the least, by philosophers of logic and language. Although efforts to canonize Leibniz as the (...) pure type of "harmonic synthesizer" have been under way for quite a long time, philosophers and historians are no longer so anxious as they once were to work out a synthetic unification of these and many other perspectives of Leibniz as was Mahnke, for instance, who characterized Leibniz’ philosophy as a synthesis of universal mathematics and individual metaphysics. (shrink)

Garry Wills is the polymathic public intellectual bemoaned as missing from American letters. A professor emeritus at Northwestern University, he has built upon his early studies in classics and patristics, while bringing his considerable intellect to bear on American culture, politics, and religion, notably through provocative articles and books on wars, past and present presidents, and the Catholic Church Wills has distinguished himself in the crowded field of Civil War history; fearlessly taken on the legacies of Richard Nixon and Ronald (...) Reagan, among other presidents; and offered a critical voice in many fraught ethical discussions, especially in the areas of war and peace. Nation and World, Church and God gathers original critical reflections by leading writers and scholars on Garry Wills's life work. Organized around the themes of "Classics," "Civil War," "War and Peace," and "Theology, Church, and the Arts," the book reflects the cultural acumen, fine-grained political analysis, ethical candor, and theological wisdom of one of America's most prolific writers. (shrink)

Philosophy and religion were the two important sources of knowledge for medieval Arab Muslim polymaths. Owing to the difference between the nature of philosophy and religion, the interplay between philosophy and religion often takes the form of conflict in medieval Muslim thought as exemplified by the Al-Ghazali versus Averroes (Ibn Rusd) polemic. Unlike the Al-Ghazali versus Averroes (Ibn Rushd) polemic, the interplay between philosophy and religion in the political philosophy of Abu Nasr Alfarabi takes the form of harmonious co-existence. Although, (...) for Alfarabi, religion is an inferior form of knowledge as compared to philosophy, the present article will show that philosophy and religion play equally significant roles in Alfarabi’s virtuous city and that in the absence of either philosophy or religion, the political system proposed by Alfarabi cannot exist. (shrink)

George Spencer Brown, a polymath and author of Laws of Form, brought together mathematics, electronics, engineering and philosophy to form an unlikely bond. This book investigates Design with the NOR, the title of the yet unpublished 1961 typescript by Spencer Brown. The typescript formed through the author's experiences as technical engineer and developer of a new form of switching algebra for Mullard Equipment LTD., a British manufacturer of electronic components. Related essays contextualise the typescript drawing on a variety of (...) backgrounds from mathematics and engineering to philosophy and sociology. (shrink)

In 1847, the British polymath William Whewell pointed out that the sciences for which he, in 1837, had coined the term “palætiological” have much in common and that they may reflect light upon each other by being treated together. This recommendation is here put into practice in a specific way, to wit, not by comparing the palaetiological sciences that Whewell distinguished himself but by comparing the general historical development of the scientific study of the four broad palætiological domains that (...) he enumerated in 1847: the solar system, the Earth, its vegetable and animal creation, and man. For wide and various as their subjects are, it will be found that [the palætiological sciences] have all certain principles, maxims, and rules of procedure in common; and thus may reflect light upon each other by being treated together. William Whewell ( 1847, 1, p. 640). (shrink)