the philosophy of mathematical practice

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The Philosophy Of Mathematical Practice

Author : Paolo Mancosu
ISBN : 9780199296453
Genre : Philosophy
File Size : 76. 72 MB
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This book gives a coherent and unified presentation of a new direction of work in philosophy of mathematics. This new approach in philosophy of mathematics requires extensive attention to mathematical practice and provides philosophical analyses of important novel characteristics of contemporary (twentieth century) mathematics and of many aspects of mathematical activity-such as visualization, explanation, understanding etc.-- which escape purely formal logicaltreatment.The book consists of a lengthy introduction by the editor and of eight chapters written by some of the very best scholars in this area. Each chapter consists of a short introduction to the general topic of the chapter and of a longer research article in the very same area. Theeight topics selected represent a broad spectrum of the contemporary philosophical reflection on different aspects of mathematical practice: Diagrammatic reasoning and representational systems; Visualization; Mathematical Explanation; Purity of Methods; Mathematical Concepts; Philosophical relevance of category theory; Philosophical aspects of computer science in mathematics; Philosophical impact of recent developments in mathematical physics.

Philosophy Of Mathematics And Mathematical Practice In The Seventeenth Century

Author : Paolo Mancosu
ISBN : 9780195132441
Genre : Drama
File Size : 76. 6 MB
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The seventeenth century saw dramatic advances in mathematical theory and practice than any era before or since. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, analytic geometry, the geometry of indivisibles, the arithmetic of infinites, and the calculus had been developed. Although many technical studies have been devoted to these innovations, Paolo Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Beginning with the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relationship between empiricist epistemology and infinitistic theorems in geometry, and the debates concerning the foundations of the Leibnizian calculus In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics.

Model Theory And The Philosophy Of Mathematical Practice

Author : John Baldwin
ISBN : 9781107189218
Genre : Mathematics
File Size : 70. 26 MB
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Recounts the modern transformation of model theory and its effects on the philosophy of mathematics and mathematical practice.

Mathematical Practice And The Philosophy Of Mathematics

Author : Audrey Yap
ISBN : STANFORD:36105128106320
Genre :
File Size : 77. 46 MB
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New Perspectives On Mathematical Practices

Author : Bart Van Kerkhove
ISBN : 9789812812230
Genre : Electronic books
File Size : 70. 24 MB
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This volume focuses on the importance of historical enquiry for the appreciation of philosophical problems concerning mathematics. It contains a well-balanced mixture of contributions by internationally established experts, such as Jeremy Gray and Jens Hoyrup; upcoming scholars, such as Erich Reck and Dirk Schlimm; and young, promising researchers at the beginning of their careers. The book is situated within a relatively new and broadly naturalistic tradition in the philosophy of mathematics. In this alternative philosophical current, which has been dramatically growing in importance in the last few decades, unlike in the traditional schools, proper attention is paid to scientific practices as informing for philosophical accounts.

Perspectives On Mathematical Practices

Author : Bart van Kerkhove
ISBN : 9781402050343
Genre : Science
File Size : 72. 70 MB
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In the eyes of the editors, this book will be considered a success if it can convince its readers of the following: that it is warranted to dream of a realistic and full-fledged theory of mathematical practices, in the plural. If such a theory is possible, it would mean that a number of presently existing fierce oppositions between philosophers, sociologists, educators, and other parties involved, are in fact illusory.

Mathematics In Kant S Critical Philosophy

Author : Lisa Shabel
ISBN : 9781135370633
Genre : Mathematics
File Size : 36. 97 MB
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First published in 2003. Routledge is an imprint of Taylor & Francis, an informa company.

The Argument Of Mathematics

Author : Andrew Aberdein
ISBN : 9789400765344
Genre : Philosophy
File Size : 81. 49 MB
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Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. The book begins by first challenging the assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics. ​

New Directions In The Philosophy Of Mathematics

Author : Thomas Tymoczko
ISBN : 0691034982
Genre : Mathematics
File Size : 61. 17 MB
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The traditional debate among philosophers of mathematics is whether there is an external mathematical reality, something out there to be discovered, or whether mathematics is the product of the human mind. This provocative book, now available in a revised and expanded paperback edition, goes beyond foundationalist questions to offer what has been called a "postmodern" assessment of the philosophy of mathematics--one that addresses issues of theoretical importance in terms of mathematical experience. By bringing together essays of leading philosophers, mathematicians, logicians, and computer scientists, Thomas Tymoczko reveals an evolving effort to account for the nature of mathematics in relation to other human activities. These accounts include such topics as the history of mathematics as a field of study, predictions about how computers will influence the future organization of mathematics, and what processes a proof undergoes before it reaches publishable form. This expanded edition now contains essays by Penelope Maddy, Michael D. Resnik, and William P. Thurston that address the nature of mathematical proofs. The editor has provided a new afterword and a supplemental bibliography of recent work.

The Philosophy Of Mathematics Education

Author : Paul Ernest
ISBN : 9783319405698
Genre : Education
File Size : 52. 51 MB
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This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its overall importance and use? It provides overviews of critical mathematics education, and the most relevant modern movements in the philosophy of mathematics. A case study is provided of an emerging research tradition in one country. This is the Hermeneutic strand of research in the philosophy of mathematics education in Brazil. This illustrates one orientation towards research inquiry in the philosophy of mathematics education. It is part of a broader practice of ‘philosophical archaeology’: the uncovering of hidden assumptions and buried ideologies within the concepts and methods of research and practice in mathematics education. An extensive bibliography is also included.

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