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Geometry as Objective Science in Elementary School Classrooms: Mathematics in the Flesh (Routledge International Studies in the Philosophy of Education)
by Wolff-Michael RothThis study examines the origins of geometry in and out of the intuitively given everyday lifeworlds of children in a second-grade mathematics class. These lifeworlds, though pre-geometric, are not without model objects that denote and come to anchor geometric idealities that they will understand at later points in their lives. Roth's analyses explain how geometry, an objective science, arises anew from the pre-scientific but nevertheless methodic actions of children in a structured world always already shot through with significations. He presents a way of understanding knowing and learning in mathematics that differs from other current approaches, using case studies to demonstrate contradictions and incongruences of other theories – Immanuel Kant, Jean Piaget, and more recent forms of (radical, social) constructivism, embodiment theories, and enactivism – and to show how material phenomenology fused with phenomenological sociology provides answers to the problems that these other paradigms do not answer.
Geometry for the Artist
by Catherine A. GoriniGeometry for the Artist is based on a course of the same name which started in the 1980s at Maharishi International University. It is aimed both at artists willing to dive deeper into geometry and at mathematicians open to learning about applications of mathematics in art. The book includes topics such as perspective, symmetry, topology, fractals, curves, surfaces, and more. A key part of the book’s approach is the analysis of art from a geometric point of view—looking at examples of how artists use each new topic. In addition, exercises encourage students to experiment in their own work with the new ideas presented in each chapter. This book is an exceptional resource for students in a general-education mathematics course or teacher-education geometry course, and since many assignments involve writing about art, this text is ideal for a writing-intensive course. Moreover, this book will be enjoyed by anyone with an interest in connections between mathematics and art. Features Abundant examples of artwork displayed in full color Suitable as a textbook for a general-education mathematics course or teacher-education geometry course Designed to be enjoyed by both artists and mathematicians
Geometry in History
by Athanase Papadopoulos S. G. DaniThis is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.
The Geometry of Choice: Language, Culture, and Education
by Marek KuźniakThis book offers a cognitive-semantic insight into the roots of the human decisionmaking process, using the metaphor of CHOICE as CUBE. The areas of key interest are language, culture, and education as forms of social organization. This book addresses issues relevant to a number of fields, including social epistemology, cognitive linguistics, cognitive anthropology, philosophy, culture and education studies, and will be of interest to readers in these and related disciplines.
The Geometry of René Descartes: with a Facsimile of the First Edition
by René DescartesThis is an unabridged republication of the definitive English translation of one of the very greatest classics of science. Originally published in 1637, it has been characterized as "the greatest single step ever made in the progress of the exact sciences" (John Stuart Mill); as a book which "remade geometry and made modern geometry possible" (Eric Temple Bell). It "revolutionized the entire conception of the object of mathematical science" (J. Hadamard).With this volume Descartes founded modern analytical geometry. Reducing geometry to algebra and analysis and, conversely, showing that analysis may be translated into geometry, it opened the way for modern mathematics. Descartes was the first to classify curves systematically and to demonstrate algebraic solution of geometric curves. His geometric interpretation of negative quantities led to later concepts of continuity and the theory of function. The third book contains important contributions to the theory of equations.This edition contains the entire definitive Smith-Latham translation of Descartes' three books: Problems the Construction of which Requires Only Straight Lines and Circles; On the Nature of Curved Lines; and On the Construction of Solid and Supersolid Problems. Interleaved page by page with the translation is a complete facsimile of the 1637 French text, together with all Descartes' original illustrations; 248 footnotes explain the text and add further bibliography.
Geometry of the Passions: Fear, Hope, Happiness: Philosophy and Political Use (Lorenzo Da Ponte Italian Library)
by Remo Bodei Gianpiero W. DoeblerThe passions have long been condemned as a creator of disturbance and purveyor of the temporary loss of reason, but as Remo Bodei argues in Geometry of the Passions, we must abandon the perception that order and disorder are in a constant state of collision. By means of a theoretical and historical analysis, Bodei interprets the relationship between passion and reason as a conflict between two complementary logics. Geometry of the Passions investigates the paradoxical conflict-collaboration between passions and reason, and between individual and political projects. Tracing the roles passion and reason have played throughout history, including in the political agendas of Descartes, Hobbes, and the French Jacobins, Geometry of the Passions reveals how passion and reason may be used as a vehicle for affirmation rather than self-enslavement.
Geometry Through History: Euclidean, Hyperbolic, And Projective Geometries
by Meighan I. DillonPresented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises.For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the field.
Geopolitical Transformations in Higher Education: Imagining, Fabricating and Contesting Innovation (Educational Governance Research #17)
by Marcelo Parreira do Amaral Christiane ThompsonThis book discusses the central role education and research play in generating both value and comparative advantages in the (imageries of) global competition, competitiveness and transnational value chains. They are seen as assets placed at the forefront of developments that are arguably reshaping individuals, society and economy. This edited volume explores these developments in terms of changing relations between society, economy, science and individuals. The idea that we live in global knowledge societies and knowledge-based economies or that present-day productive systems constitute an industry 4.0 have gained currency as descriptions of contemporary society that are said to bear direct and indirect consequences for political, economic, and social orders. In this context, innovation, science and education are central themes in contemporary discussions about the future of modern societies. Innovation is enthusiastically embraced as the panacea for all sorts of societal issues of our times; science is equally deemed to play a decisive role in solving current problems and in heralding a bright future with more wealth and more welfare for all citizens; education is conferred the task to producing individuals equipped with both skills and competences considered key to innovation but also displaying the attitudes and dispositions that will secure continuous innovation and economic growth.
Geopolitics and the Quest for Dominance
by Jeremy M. BlackHistory and geography delineate the operation of power, not only its range but also the capacity to plan and the ability to implement. Approaching state strategy and policy from the spatial angle, Jeremy Black argues that just as the perception of power is central to issues of power, so place, and its constraints and relationships, is partly a matter of perception, not merely map coordinates. Geopolitics, he maintains, is as much about ideas and perception as it is about the actual spatial dimensions of power. Black's study ranges widely, examining geography and the spatial nature of state power from the 15th century to the present day. He considers the rise of British power, geopolitics and the age of Imperialism, the Nazis and World War II, and the Cold War, and he looks at the key theorists of the latter 20th century, including Henry Kissinger, Francis Fukuyama and Samuel P. Huntington, Philip Bobbitt, Niall Ferguson, and others.
Geopolitics in the Era of Globalisation: Mapping an Alternative Global Future
by Yogendra KumarThis book presents an alternative roadmap for a world characterised by geopolitical uncertainty. The surging expectations about a future world of democratic values and high economic growth, born out of superpower bonhomie at the end of the Cold War, did not lead to the promised outcomes. Instead we are faced with deeply destabilising challenges, like climate change, widespread state fragility, terrorism, arms race, disruptive newer technologies, global economic volatility, and ineffectiveness of multilateral institutions, old and new. The volume: surveys the intellectual discourse, the attempts to redesign the global institutions, and the geopolitical trends since the end of the Cold War for an understanding of the contemporary geopolitics, analyses the characteristics of the contemporary geopolitics, the seeming intractability of the global challenges, and the ongoing discourse about preventing their further deterioration, foregrounds the Gandhian praxis and IR theory for managing power transitions anchored in non-violent mobilisation of empowered masses, ensuring institutional resilience, and illustrates them through ongoing conflicts in Iraq and Afghanistan, outlines an approach, based on the Gandhian experience of managing political change, towards conflict, geopolitical uncertainties, and institutional ineffectiveness for securing a better future globally, including South Asia. Accessibly written, this volume will be indispensable for foreign policy experts, government think tanks, and career bureaucrats. It will also be essential for scholars and researchers of international relations, foreign policy, politics, and governance and public policy.
Georg Christoph Lichtenberg: Philosophical Writings (SUNY series in Contemporary Continental Philosophy)
by Georg Christoph LichtenbergAdmired by philosophers such as Schopenhauer, Nietzsche, Kierkegaard, Freud, Benjamin, and Wittgenstein, Georg Christoph Lichtenberg (1742–1799) is known to the English-speaking world mostly as a satirist. An eminent experimental physicist and mathematician, Lichtenberg was knowledgeable about the philosophical views of his time, and interested in uncovering the philosophical commitments that underlie our common beliefs. In his notebooks (which he called his Waste Books) he often reflects on, challenges, and critiques these philosophical commitments and the dominant views of the Enlightenment, German idealism, and British empiricism. This scholarly collection of Lichtenberg's philosophical aphorisms contains hundreds of trenchant observations drawn from these notebooks, many of which have been translated into English here for the first time. It also includes a historical and philosophical introduction to his writings, situating him in the history of philosophy and ideas, and is supplemented with a chronology, suggestions for further reading, and extensive introductory and textual notes explaining his references.
Georg Lukacs: From Romanticism to Bolshevism
by Michael LöwyOn the 100th anniversary of the publication of History and Class Consciousness, a new edition of this indispensable guide to Lukacs's thought and politicsThe philosophical and political development that converted Georg Lukács from a distinguished representative of Central European aesthetic vitalism into a major Marxist theorist and Communist militant has long remained an enigma.In this this now classic study, Michael Löwy for the first time traced and explained the extraordinary mutation that occurred in Lukács's thought between 1909 and 1929. Utilizing many as yet unpublished sources, Löwy meticulously reconstructed the complex itinerary of Lukács's thinking as he gradually moved towards his decisive encounter with Bolshevism.The religious convictions of the early Lukács, the peculiar spell exercised on him and on Max Weber by Dostoyevskyan images of pre-revolutionary Russia, the nature of his friendships with Ernst Bloch and Thomas Mann, were amongst the discoveries of the book.Then, in a fascinating case-study in the sociology of ideas, Löwy showed how the same philosophical problematic of Lebensphilosophie dominated the intelligentsias of both Germany and Hungary in the pre-war period, yet how the different configurations of social forces in each country bent its political destiny into opposite directions. The famous works produced by Lukács during and after the Hungarian Commune—Tactics and Ethics, History and Class Consciousness and Lenin—were analysed and assessed. A concluding chapter discussed Lukács's eventual ambiguous settlement with Stalinism in the thirties, and its coda of renewed radicalism in the final years of his life.In this new edition, Löwy has added a substantial new introduction which reassess the nature of Lukacs's thought in the light of newly published texts and debates.
Georg Lukács (Routledge Revivals)
by G.H.R. ParkinsonFirst published in 1977, Georg Lukács gives an outline of Lukács’ views and explains how they are related to the relevant cultural traditions of his epoch. The author covers the whole range of Lukács’ thought, from his earliest literary criticism to the posthumous Ontology of Social Existence. Lukács’ early writings in particular are frequently obscure in style and impregnated with the language and thought of Hegel. Professor Parkinson has elucidated Lukács’ principal writings in systematic fashion, and the book includes a detailed exposition of Lukács’ influential but difficult book History and Class Consciousness. This should be an indispensable book for all those who seek a clear, comprehensible introduction to the writings of one of the most influential Marxist thinkers of our time.
Georg Simmel: Critical Assessments (Key Sociologists)
by David FrisbyUntil recently little of Simmel's work was available in translation and certain key texts were unknown outside Germany. David Frisby, the eminent Simmel scholar, provides not only an introduction to the major sociological writings of this important figure, but also an argument for a reconsideration of his work. The author outlines the cultural and historical context in which Simmel worked; reviews Simmel's most important writings; and examines his legacy to sociology by illuminating his links with Weber's theories and his influential relationship with Marxism.Simmel, a central figure in the development of modern sociology, and a contemporary of Weber and Durkheim, was one of the first to identify sociology as a separate discipline. His ideas influenced Weber, the Chicago School, and many later sociologists. His introduction of a number of basic concepts to sociology, such as exchange, interaction and differentiation, attest to his intellectual stature and the far-reaching significance of his work.
Georg Simmel: On Individuality and Social Forms
by Donald N. Levine Georg Simmel"Of those who created the intellectual capital used to launch the enterprise of professional sociology, Georg Simmel was perhaps the most original and fecund. In search of a subject matter for sociology that would distinguish it from all other social sciences and humanistic disciplines, he charted a new field for discovery and proceeded to explore a world of novel topics in works that have guided and anticipated the thinking of generations of sociologists. Such distinctive concepts of contemporary sociology as social distance, marginality, urbanism as a way of life, role-playing, social behavior as exchange, conflict as an integrating process, dyadic encounter, circular interaction, reference groups as perspectives, and sociological ambivalence embody ideas which Simmel adumbrated more than six decades ago. "—Donald N. Levine Half of the material included in this edition of Simmel's writings represents new translations. This includes Simmel's important, lengthy, and previously untranslated "Group Expansion and Development of Individuality," as well as three selections from his most neglected work, Philosophy of Money; in addition, the introduction to Probleme der Geschichtsphilosophie, chapter one of the Lebensanschauung, and three essays are translated for the first time.
Georg Simmel: Essays on Art and Aesthetics (Heritage Of Sociology Ser.)
by Georg SimmelGeorg Simmel is one of the most original German thinkers of the twentieth century and is considered a founding architect of the modern discipline of sociology. Ranging over fundamental questions of the relationship of self and society, his influential writings on money, modernity, and the metropolis continue to provoke debate today. Fascinated by the relationship between culture, society, and economic life, Simmel took an interest in myriad phenomena of aesthetics and the arts. A friend of writers and artists such as Auguste Rodin, Rainer Maria Rilke, and Stefan George, he wrote dozens of pieces engaging with topics such as the work of Michelangelo, Rembrandt, and Rodin, Japanese art, naturalism and symbolism, Goethe, “art for art’s sake”, art exhibitions, and the aesthetics of the picture frame. This is the first collection to bring together Simmel’s finest writing on art and aesthetics, and many of the items appear in English in this volume for the first time. The more than forty essays show the protean breadth of Simmel’s reflections, covering landscape painting, portraiture, sculpture, poetry, theater, form, style, and representation. An extensive introduction by Austin Harrington gives an overview of Simmel’s themes and elucidates the significance of his work for the many theorists who would be inspired by his ideas. Something of an outsider to the formal academic world of his day, Simmel wrote creatively with the flair of an essayist. This expansive collection of translations preserves the narrative ease of Simmel’s prose and will be a vital source for readers with an interest in Simmel’s trailblazing ideas in modern European philosophy, sociology, and cultural theory.
Georg Simmel and German Culture: Unity, Variety and Modern Discontents (Ideas in Context #135)
by Efraim PodoksikThe significance of the German philosopher and social thinker, Georg Simmel (1858–1918), is only now being recognised by intellectual historians. Through penetrating readings of Simmel's thought, taken as a series of reflections on the essence of modernity and modern civilisation, Efraim Podoksik places his ideas within the context of intellectual life in Germany, and especially Berlin, under the Kaiserreich. Modernity, characterised by the growing differentiation and fragmentation of culture and society, was a fundamental issue during Simmel's life, underpinning central intellectual debates in Imperial Germany. Simmel's thought is depicted here as an attempt at transforming the complexity of these debates into a coherent worldview that can serve as an effective guide to understanding their main parameters. Paying particular attention to the genealogy and usage of the concepts of Bildung, culture and civilisation in Germany, this study offers contextual analyses of Simmel's philosophies of culture, society, art, religion and the feminine, as well as his interpretations of Dante, Kant, Nietzsche, Schopenhauer, Goethe and Rembrandt.
Georg Simmel and the Disciplinary Imaginary
by Elizabeth GoodsteinAn internationally famous philosopher and best-selling author during his lifetime, Georg Simmel has been marginalized in contemporary intellectual and cultural history. This neglect belies his pathbreaking role in revealing the theoretical significance of phenomena—including money, gender, urban life, and technology—that subsequently became established arenas of inquiry in cultural theory. It further ignores his philosophical impact on thinkers as diverse as Benjamin, Musil, and Heidegger. Integrating intellectual biography, philosophical interpretation, and a critical examination of the history of academic disciplines, this book restores Simmel to his rightful place as a major figure and challenges the frameworks through which his contributions to modern thought have been at once remembered and forgotten.
Georg Wilhelm Friedrich Hegel: The Phenomenology of Spirit (Cambridge Hegel Translations)
by Michael Baur Georg Wilhelm Friedrich Hegel Terry PinkardHegel's Phenomenology of Spirit (1807) is one of the most influential texts in the history of modern philosophy. In it, Hegel proposed an arresting and novel picture of the relation of mind to world and of people to each other. Like Kant before him, Hegel offered up a systematic account of the nature of knowledge, the influence of society and history on claims to knowledge, and the social character of human agency itself. A bold new understanding of what, after Hegel, came to be called 'subjectivity' arose from this work, and it was instrumental in the formation of later philosophies, such as existentialism, Marxism, and American pragmatism, each of which reacted to Hegel's radical claims in different ways. This edition offers a new translation, an introduction, and glossaries to assist readers' understanding of this central text, and will be essential for scholars and students of Hegel.
Georg Wilhelm Friedrich Hegel: Encyclopaedia of the Philosophical Sciences in Basic Outline, Part 1, Logic
by Daniel O. Dahlstrom Klaus Brinkmann Georg Wilhelm Friedrich HegelHegel's Encyclopaedia Logic constitutes the foundation of the system of philosophy presented in his Encyclopaedia of the Philosophical Sciences. Together with his Science of Logic, it contains the most explicit formulation of his enduringly influential dialectical method and of the categorical system underlying his thought. It offers a more compact presentation of his dialectical method than is found elsewhere, and also incorporates changes that he would have made to the second edition of the Science of Logic if he had lived to do so. This volume presents it in a new translation with a helpful introduction and notes. It will be a valuable reference work for scholars and students of Hegel and German idealism, as well as for those who are interested in the post-Hegelian character of contemporary philosophy.
Georg Wilhelm Friedrich Hegel: The Science of Logic
by George Di Giovanni Georg Wilhelm Friedrich HegelThis new translation of The Science of Logic (also known as 'Greater Logic') includes the revised Book I (1832), Book II (1813), and Book III (1816). Recent research has given us a detailed picture of the process that led Hegel to his final conception of the System and of the place of the Logic within it. We now understand how and why Hegel distanced himself from Schelling, how radical this break with his early mentor was, and to what extent it entailed a return (but with a difference) to Fichte and Kant. In the introduction to the volume, George di Giovanni presents in synoptic form the results of recent scholarship on the subject, and, while recognizing the fault lines in Hegel's System that allow opposite interpretations, argues that the Logic marks the end of classical metaphysics. The translation is accompanied by a full apparatus of historical and explanatory notes.
Georg Wilhelm Friedrich Hegel: Journal Publications
by Brady Bowman Allen SpeightThis work brings together, for the first time in English translation, Hegel's journal publications from his years in Heidelberg (1816-18), writings which have been previously either untranslated or only partially translated into English. The Heidelberg years marked Hegel's return to university teaching and represented an important transition in his life and thought. The translated texts include his important reassessment of the works of the philosopher F. H. Jacobi, whose engagement with Spinozism, especially, was of decisive significance for the philosophical development of German Idealism. They also include his most influential writing about contemporary political events, his essay on the constitutional assembly in his native Württemberg, which was written against the background of the dramatic political and social changes occurring in post-Napoleonic Germany. The translators have provided an introduction and notes that offer a scholarly commentary on the philosophical and political background of Hegel's Heidelberg writings.
George Berkeley: A Philosophical Life
by Tom JonesA comprehensive intellectual biography of the Enlightenment philosopherIn George Berkeley: A Philosophical Life, Tom Jones provides a comprehensive account of the life and work of the preeminent Irish philosopher of the Enlightenment. From his early brilliance as a student and fellow at Trinity College Dublin to his later years as Bishop of Cloyne, Berkeley brought his searching and powerful intellect to bear on the full range of eighteenth-century thought and experience.Jones brings vividly to life the complexities and contradictions of Berkeley’s life and ideas. He advanced a radical immaterialism, holding that the only reality was minds, their thoughts, and their perceptions, without any physical substance underlying them. But he put forward this counterintuitive philosophy in support of the existence and ultimate sovereignty of God. Berkeley was an energetic social reformer, deeply interested in educational and economic improvement, including for the indigenous peoples of North America, yet he believed strongly in obedience to hierarchy and defended slavery. And although he spent much of his life in Ireland, he followed his time at Trinity with years of travel that took him to London, Italy, and New England, where he spent two years trying to establish a university for Bermuda, before returning to Ireland to take up an Anglican bishopric in a predominantly Catholic country.Jones draws on the full range of Berkeley’s writings, from philosophical treatises to personal letters and journals, to probe the deep connections between his life and work. The result is a richly detailed and rounded portrait of a major Enlightenment thinker and the world in which he lived.
George Berkeley: Three Dialogues Between Hylas and Philonous (Longman Library of Primary Sources in Philosophy)
by Daniel Kolak George B. Berkeley Michael B. MathiasPart of the “Longman Library of Primary Sources in Philosophy,” this edition of Berkeley's Three Dialogues Between Hylas and Philonous is framed by a pedagogical structure designed to make this important work of philosophy more accessible and meaningful for readers. A General Introduction includes biographical information on Berkeley, the work's historical context, and a discussion of historical influences, and a conclusion discusses how the work has influenced other philosophers and why it is important today. Annotations and notes from the editor clarify difficult passages for greater understanding. A bibliography gives the reader additional resources for further study.
George Berkeley: Religion and Science in the Age of Enlightenment
by Silvia ParigiGeorge Berkeley was considered "the most engaging and useful man in Ireland in the eighteenth century". This hyperbolic statement refers both to Berkeley's life and thought; in fact, he always considered himself a pioneer called to think and do new things. He was an empiricist well versed in the sciences, an amateur of the mechanical arts, as well as a metaphysician; he was the author of many completely different discoveries, as well as a very active Christian, a zealous bishop and the apostle of the Bermuda project. The essays collected in this volume, written by some leading scholars, aim to reconstruct the complexity of Berkeley's figure, without selecting "major" works, nor searching for "coherence" at any cost. They will focus on different aspects of Berkeley's thought, showing their intersections; they will explore the important contributions he gave to various scientific disciplines, as well as to the eighteenth-century philosophical and theological debate. They will highlight the wide influence that his presently most neglected or puzzling books had at the time; they will refuse any anachronistical trial of Berkeley's thought, judged from a contemporary point of view.