Download or read book Starry Reckoning Reference and Analysis in Mathematics and Cosmology written by Emily Rolfe Grosholz and published by Springer. This book was released on 2016-11-25 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with a topic that has been largely neglected by philosophers of science to date: the ability to refer and analyze in tandem. On the basis of a set of philosophical case studies involving both problems in number theory and issues concerning time and cosmology from the era of Galileo, Newton and Leibniz up through the present day, the author argues that scientific knowledge is a combination of accurate reference and analytical interpretation. In order to think well, we must be able to refer successfully, so that we can show publicly and clearly what we are talking about. And we must be able to analyze well, that is, to discover productive and explanatory conditions of intelligibility for the things we are thinking about. The book’s central claim is that the kinds of representations that make successful reference possible and those that make successful analysis possible are not the same, so that significant scientific and mathematical work typically proceeds by means of a heterogeneous discourse that juxtaposes and often superimposes a variety of kinds of representation, including formal and natural languages as well as more iconic modes. It demonstrates the virtues and necessity of heterogeneity in historically central reasoning, thus filling an important gap in the literature and fostering a new, timely discussion on the epistemology of science and mathematics.
Download or read book Humanizing Mathematics and its Philosophy written by Bharath Sriraman and published by Birkhäuser. This book was released on 2017-11-07 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift contains numerous colorful and eclectic essays from well-known mathematicians, philosophers, logicians, and linguists celebrating the 90th birthday of Reuben Hersh. The essays offer, in part, attempts to answer the following questions set forth by Reuben himself as a focus for this volume: Can practicing mathematicians, as such, contribute anything to the philosophy of math? Can or should philosophers of math, as such, say anything to practicing mathematicians? Twenty or fifty years from now, what will be similar, and what will, or could, or should be altogether different: About the philosophy of math? About math education? About math research institutions? About data processing and scientific computing? The essays also offer glimpses into Reuben’s fertile mind and his lasting influence on the mathematical community, as well as revealing the diverse roots, obstacles and philosophical dispositions that characterize the working lives of mathematicians. With contributions from a veritable “who’s who” list of 20th century luminaries from mathematics and philosophy, as well as from Reuben himself, this volume will appeal to a wide variety of readers from curious undergraduates to prominent mathematicians.
Download or read book Great Circles written by Emily Rolfe Grosholz and published by Springer. This book was released on 2018-11-13 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume explores the interaction of poetry and mathematics by looking at analogies that link them. The form that distinguishes poetry from prose has mathematical structure (lifting language above the flow of time), as do the thoughtful ways in which poets bring the infinite into relation with the finite. The history of mathematics exhibits a dramatic narrative inspired by a kind of troping, as metaphor opens, metonymy and synecdoche elaborate, and irony closes off or shifts the growth of mathematical knowledge. The first part of the book is autobiographical, following the author through her discovery of these analogies, revealed by music, architecture, science fiction, philosophy, and the study of mathematics and poetry. The second part focuses on geometry, the circle and square, launching us from Shakespeare to Housman, from Euclid to Leibniz. The third part explores the study of dynamics, inertial motion and transcendental functions, from Descartes to Newton, and in 20th c. poetry. The final part contemplates infinity, as it emerges in modern set theory and topology, and in contemporary poems, including narrative poems about modern cosmology.
Download or read book The Making of Mathematics written by Carlo Cellucci and published by Springer Nature. This book was released on 2022-03-07 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an alternative to current philosophy of mathematics: heuristic philosophy of mathematics. In accordance with the heuristic approach, the philosophy of mathematics must concern itself with the making of mathematics and in particular with mathematical discovery. In the past century, mainstream philosophy of mathematics has claimed that the philosophy of mathematics cannot concern itself with the making of mathematics but only with finished mathematics, namely mathematics as presented in published works. On this basis, mainstream philosophy of mathematics has maintained that mathematics is theorem proving by the axiomatic method. This view has turned out to be untenable because of Gödel’s incompleteness theorems, which have shown that the view that mathematics is theorem proving by the axiomatic method does not account for a large number of basic features of mathematics. By using the heuristic approach, this book argues that mathematics is not theorem proving by the axiomatic method, but is rather problem solving by the analytic method. The author argues that this view can account for the main items of the mathematical process, those being: mathematical objects, demonstrations, definitions, diagrams, notations, explanations, applicability, beauty, and the role of mathematical knowledge.
Download or read book Lakatos and the Historical Approach to Philosophy of Mathematics written by Donald Gillies and published by Cambridge University Press. This book was released on 2023-12-31 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Element begins by claiming that Imre Lakatos (1922–74) in his famous paper 'Proofs and Refutations' (1963–64) was the first to introduce the historical approach to philosophy of mathematics. Section 2 gives a detailed analysis of Lakatos' ideas on the philosophy of mathematics. Lakatos died at the age of only 51, and at the time of this death had plans to continue his work on philosophy of mathematics which were never carried out. However, Lakatos' historical approach to philosophy of mathematics was taken up by other researchers in the field, and Sections 3 and 4 of the Element give an account of how they developed this approach. Then Section 5 gives an overview of what has been achieved so far by the historical approach to philosophy of mathematics and considers what its prospects for the future might be.
Download or read book Making and Breaking Mathematical Sense written by Roi Wagner and published by Princeton University Press. This book was released on 2017-01-10 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: In line with the emerging field of philosophy of mathematical practice, this book pushes the philosophy of mathematics away from questions about the reality and truth of mathematical entities and statements and toward a focus on what mathematicians actually do—and how that evolves and changes over time. How do new mathematical entities come to be? What internal, natural, cognitive, and social constraints shape mathematical cultures? How do mathematical signs form and reform their meanings? How can we model the cognitive processes at play in mathematical evolution? And how does mathematics tie together ideas, reality, and applications? Roi Wagner uniquely combines philosophical, historical, and cognitive studies to paint a fully rounded image of mathematics not as an absolute ideal but as a human endeavor that takes shape in specific social and institutional contexts. The book builds on ancient, medieval, and modern case studies to confront philosophical reconstructions and cutting-edge cognitive theories. It focuses on the contingent semiotic and interpretive dimensions of mathematical practice, rather than on mathematics' claim to universal or fundamental truths, in order to explore not only what mathematics is, but also what it could be. Along the way, Wagner challenges conventional views that mathematical signs represent fixed, ideal entities; that mathematical cognition is a rigid transfer of inferences between formal domains; and that mathematics’ exceptional consensus is due to the subject’s underlying reality. The result is a revisionist account of mathematical philosophy that will interest mathematicians, philosophers, and historians of science alike.
Download or read book The Map and the Territory written by Shyam Wuppuluri and published by Springer. This book was released on 2018-02-13 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents essays by pioneering thinkers including Tyler Burge, Gregory Chaitin, Daniel Dennett, Barry Mazur, Nicholas Humphrey, John Searle and Ian Stewart. Together they illuminate the Map/Territory Distinction that underlies at the foundation of the scientific method, thought and the very reality itself. It is imperative to distinguish Map from the Territory while analyzing any subject but we often mistake map for the territory. Meaning for the Reference. Computational tool for what it computes. Representations are handy and tempting that we often end up committing the category error of over-marrying the representation with what is represented, so much so that the distinction between the former and the latter is lost. This error that has its roots in the pedagogy often generates a plethora of paradoxes/confusions which hinder the proper understanding of the subject. What are wave functions? Fields? Forces? Numbers? Sets? Classes? Operators? Functions? Alphabets and Sentences? Are they a part of our map (theory/representation)? Or do they actually belong to the territory (Reality)? Researcher, like a cartographer, clothes (or creates?) the reality by stitching multitudes of maps that simultaneously co-exist. A simple apple, for example, can be analyzed from several viewpoints beginning with evolution and biology, all the way down its microscopic quantum mechanical components. Is there a reality (or a real apple) out there apart from these maps? How do these various maps interact/intermingle with each other to produce a coherent reality that we interact with? Or do they not? Does our brain uses its own internal maps to facilitate “physicist/mathematician” in us to construct the maps about the external territories in turn? If so, what is the nature of these internal maps? Are there meta-maps? Evolution definitely fences our perception and thereby our ability to construct maps, revealing to us only those aspects beneficial for our survival. But the question is, to what extent? Is there a way out of the metaphorical Platonic cave erected around us by the nature? While “Map is not the territory” as Alfred Korzybski remarked, join us in this journey to know more, while we inquire on the nature and the reality of the maps which try to map the reality out there. The book also includes a foreword by Sir Roger Penrose and an afterword by Dagfinn Follesdal.
Download or read book The Routledge International Handbook of Creative Cognition written by Linden J. Ball and published by Taylor & Francis. This book was released on 2023-08-31 with total page 835 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Routledge International Handbook of Creative Cognition is an authoritative reference work that offers a well-balanced overview of current scholarship across the full breadth of the rapidly expanding field of creative cognition. It contains 43 chapters written by world-leading researchers, covering foundational issues and concepts as well as state-of-the-art research developments. The handbook draws extensively on contemporary work exploring the cognitive representations and processes associated with creativity, whether studied in the laboratory or as it arises in real-world practice in domains such as education, art, science, entrepreneurship, design, and technological innovation. Chapters also examine the sociocognitive and cultural aspects of creativity in teams and organisations, while additionally capturing the latest research on the cognitive neuroscience of creativity. Providing a compelling synopsis of emerging trends and debates in the field of creative cognition and positioning these in relation to established findings and theories, this text provides a clear sense of the way in which new research is challenging traditional viewpoints. It is an essential reading for researchers in the field of creative cognition as well as advanced students wishing to learn more about the latest developments in this important and rapidly growing area of enquiry.
Download or read book The Poetry and Poetics of Olga Sedakova written by Stephanie Sandler and published by University of Wisconsin Press. This book was released on 2019-02-12 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Olga Sedakova stands out among contemporary Russian poets for the integrity, erudition, intellectual force, and moral courage of her writing. After years of flourishing quietly in the late Soviet underground, she has increasingly brought her considered voice into public debates to speak out for freedom of belief and for those who have been treated unjustly. This volume, the first collection of scholarly essays to treat her work in English, assesses her contributions as a poet and as a thinker, presenting far-reaching accounts of broad themes and patterns of thought across her writings as well as close readings of individual texts. Essayists from Russia, Ukraine, Germany, Italy, and the United States show how Sedakova has contributed to ongoing aesthetic and cultural debates. Like Sedakova's own work, the volume affirms the capacity of words to convey meaning and to change our understanding of life itself. The volume also includes dozens of elegant new translations of Sedakova's poems.
Download or read book A Companion to Simone de Beauvoir written by Laura Hengehold and published by John Wiley & Sons. This book was released on 2017-10-02 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: Winner of the 2018 Choice award for Outstanding Academic Title! The work of Simone de Beauvoir has endured and flowered in the last two decades, thanks primarily to the lasting influence of The Second Sex on the rise of academic discussions of gender, sexuality, and old age. Now, in this new Companion dedicated to her life and writings, an international assembly of prominent scholars, essayists, and leading interpreters reflect upon the range of Beauvoir’s contribution to philosophy as one of the great authors, thinkers, and public intellectuals of the twentieth century. The Companion examines Beauvoir’s rich intellectual life from a variety of angles—including literary, historical, and anthropological perspectives—and situates her in relation to her forbears and contemporaries in the philosophical canon. Essays in each of four thematic sections reveal the breadth and acuity of her insight, from the significance of The Second Sex and her work on the metaphysics of gender to her plentiful contributions in ethics and political philosophy. Later chapters trace the relationship between Beauvoir’s philosophical and literary work and open up her scholarship to global issues, questions of race, and the legacy of colonialism and sexism. The volume concludes by considering her impact on contemporary feminist thought writ large, and features pioneering work from a new generation of Beauvoir scholars. Ambitious and unprecedented in scope, A Companion to Simone de Beauvoir is an accessible and interdisciplinary resource for students, teachers, and researchers across the humanities and social sciences.
Download or read book A Clubbable Man written by Anthony W. Lee and published by Rutgers University Press. This book was released on 2022-06-17 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Samuel Johnson famously referred to his future biographer, the unsociable magistrate Sir John Hawkins, as “a most unclubbable man." Conversely, this celebratory volume gathers distinguished eighteenth-century studies scholars to honor the achievements, professional generosity, and sociability of Greg Clingham, taking as its theme textual and social group formations. Here, Philip Smallwood examines the “mirrored minds” of Johnson and Shakespeare, while David Hopkins parses intersections of the general and particular in three key eighteenth-century figures. Aaron Hanlon draws parallels between instances of physical rambling and rhetorical strategies in Johnson’s Rambler, while Cedric D. Reverand dissects the intertextual strands uniting Dryden and Pope. Contributors take up other topics significant to the field, including post-feminism, travel, and seismology. Whether discussing cultural exchange or textual reciprocities, each piece extends the theme, building on the trope of relationship to organize and express its findings. Rounding out this collection are tributes from Clingham’s former students and colleagues, including original poetry.
Download or read book From Eudoxus to Einstein written by C. M. Linton and published by Cambridge University Press. This book was released on 2004-08-12 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since man first looked towards the heavens, a great deal of effort has been put into trying to predict and explain the motions of the sun, moon and planets. Developments in man's understanding have been closely linked to progress in the mathematical sciences. Whole new areas of mathematics, such as trigonometry, were developed to aid astronomical calculations, and on numerous occasions throughout history, breakthroughs in astronomy have only been possible because of progress in mathematics. This book describes the theories of planetary motion that have been developed through the ages, beginning with the homocentric spheres of Eudoxus and ending with Einstein's general theory of relativity. It emphasizes the interaction between progress in astronomy and in mathematics, showing how the two have been inextricably linked since Babylonian times. This valuable text is accessible to a wide audience, from amateur astronomers to professional historians of astronomy.
Download or read book The History and Practice of Ancient Astronomy written by James Evans and published by Oxford University Press. This book was released on 1998-10-01 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: The History and Practice of Ancient Astronomy combines new scholarship with hands-on science to bring readers into direct contact with the work of ancient astronomers. While tracing ideas from ancient Babylon to sixteenth-century Europe, the book places its greatest emphasis on the Greek period, when astronomers developed the geometric and philosophical ideas that have determined the subsequent character of Western astronomy. The author approaches this history through the concrete details of ancient astronomical practice. Carefully organized and generously illustrated, the book can teach readers how to do real astronomy using the methods of ancient astronomers. For example, readers will learn to predict the next retrograde motion of Jupiter using either the arithmetical methods of the Babylonians or the geometric methods of Ptolemy. They will learn how to use an astrolabe and how to design sundials using Greek and Roman techniques. The book also contains supplementary exercises and patterns for making some working astronomical instruments, including an astrolabe and an equatorium. More than a presentation of astronomical methods, the book provides a critical look at the evidence used to reconstruct ancient astronomy. It includes extensive excerpts from ancient texts, meticulous documentation, and lively discussions of the role of astronomy in the various cultures. Accessible to a wide audience, this book will appeal to anyone interested in how our understanding of our place in the universe has changed and developed, from ancient times through the Renaissance.
Download or read book The Dark Matter Problem written by Robert H. Sanders and published by Cambridge University Press. This book was released on 2010-04-22 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most astronomers and physicists now believe that the matter content of the Universe is dominated by dark matter: hypothetical particles which interact with normal matter primarily through the force of gravity. Though invisible to current direct detection methods, dark matter can explain a variety of astronomical observations. This book describes how this theory has developed over the past 75 years, and why it is now a central feature of extragalactic astronomy and cosmology. Current attempts to directly detect dark matter locally are discussed, together with the implications for particle physics. The author comments on the sociology of these developments, demonstrating how and why scientists work and interact. Modified Newtonian Dynamics (MOND), the leading alternative to this theory, is also presented. This fascinating overview will interest cosmologists, astronomers and particle physicists. Mathematics is kept to a minimum, so the book can be understood by non-specialists.
Download or read book De Sphaera of Johannes de Sacrobosco in the Early Modern Period written by Matteo Valleriani and published by Springer Nature. This book was released on 2020-01-01 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book explores commentaries on an influential text of pre-Copernican astronomy in Europe. It features essays that take a close look at key intellectuals and how they engaged with the main ideas of this qualitative introduction to geocentric cosmology. Johannes de Sacrobosco compiled his Tractatus de sphaera during the thirteenth century in the frame of his teaching activities at the then recently founded University of Paris. It soon became a mandatory text all over Europe. As a result, a tradition of commentaries to the text was soon established and flourished until the second half of the 17th century. Here, readers will find an informative overview of these commentaries complete with a rich context. The essays explore the educational and social backgrounds of the writers. They also detail how their careers developed after the publication of their commentaries, the institutions and patrons they were affiliated with, what their agenda was, and whether and how they actually accomplished it. The editor of this collection considers these scientific commentaries as genuine scientific works. The contributors investigate them here not only in reference to the work on which it comments but also, and especially, as independent scientific contributions that are socially, institutionally, and intellectually contextualized around their authors.
Download or read book Poetry and mathematics written by Scott Buchanan and published by . This book was released on 1975 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fundamental Astronomy written by Hannu Karttunen and published by Springer Science & Business Media. This book was released on 2007-08-09 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamental Astronomy is a well-balanced, comprehensive introduction to classical and modern astronomy. While emphasizing both the astronomical concepts and the underlying physical principles, the text provides a sound basis for more profound studies in the astronomical sciences. This is the fifth edition of the successful undergraduate textbook and reference work. It has been extensively modernized and extended in the parts dealing with extragalactic astronomy and cosmology. You will also find augmented sections on the solar system and extrasolar planets as well as a new chapter on astrobiology. Long considered a standard text for physical science majors, Fundamental Astronomy is also an excellent reference work for dedicated amateur astronomers.
