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Author: Emily Rolfe Grosholz
Publisher: Springer
ISBN: 3319466909
Category : Philosophy
Languages : en
Pages : 187
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Book Description
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.
Author: Emily Rolfe Grosholz
Publisher: Springer
ISBN: 3319466909
Category : Philosophy
Languages : en
Pages : 187
Get Book
Book Description
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.
Author: Bharath Sriraman
Publisher: Birkhäuser
ISBN: 331961231X
Category : Mathematics
Languages : en
Pages : 363
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Book Description
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.
Author: Emily Rolfe Grosholz
Publisher: Springer
ISBN: 3319982311
Category : Mathematics
Languages : en
Pages : 274
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Book Description
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.
Author: Carlo Cellucci
Publisher: Springer Nature
ISBN: 3030897311
Category : Mathematics
Languages : en
Pages : 457
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Book Description
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.
Author: Donald Gillies
Publisher: Cambridge University Press
ISBN: 1009430572
Category : Science
Languages : en
Pages : 122
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Book Description
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.
Author: Roi Wagner
Publisher: Princeton University Press
ISBN: 1400883784
Category : Mathematics
Languages : en
Pages : 256
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Book Description
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.
Author: Shyam Wuppuluri
Publisher: Springer
ISBN: 3319724789
Category : Science
Languages : en
Pages : 641
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Book Description
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.
Author: Linden J. Ball
Publisher: Taylor & Francis
ISBN: 1000917282
Category : Psychology
Languages : en
Pages : 835
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Book Description
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.
Author: Stephanie Sandler
Publisher: University of Wisconsin Press
ISBN: 0299320103
Category : Literary Criticism
Languages : en
Pages : 437
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Book Description
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.
Author: Laura Hengehold
Publisher: John Wiley & Sons
ISBN: 1118796020
Category : Philosophy
Languages : en
Pages : 548
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Book Description
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.
