the architecture of modern mathematics essays in history and philosophy

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The Architecture Of Modern Mathematics

Author : José Ferreirós Domínguez
ISBN : 9780198567936
Genre : Mathematics
File Size : 39. 23 MB
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Aimed at both students and researchers in philosophy, mathematics and the history of science, this edited volume, authored by leading scholars, highlights foremost developments in both the philosophy and history of modern mathematics.

New Perspectives On Mathematical Practices

Author : Bart Van Kerkhove
ISBN : 9789812812230
Genre : Electronic books
File Size : 64. 83 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.

Epistemology Versus Ontology

Author : P. Dybjer
ISBN : 9789400744356
Genre : Philosophy
File Size : 75. 61 MB
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This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice (ZFC). This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics?

From Riemann To Differential Geometry And Relativity

Author : Lizhen Ji
ISBN : 9783319600390
Genre : Mathematics
File Size : 71. 17 MB
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This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. It features contributions from a range of fields, historical expositions, and selected research articles that were motivated by Riemann’s ideas and demonstrate their timelessness. The editors are convinced of the tremendous value of going into Riemann’s work in depth, investigating his original ideas, integrating them into a broader perspective, and establishing ties with modern science and philosophy. Accordingly, the contributors to this volume are mathematicians, physicists, philosophers and historians of science. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.

Mathematical Knowledge And The Interplay Of Practices

Author : José Ferreirós
ISBN : 9781400874002
Genre : Science
File Size : 43. 10 MB
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This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, José Ferreirós uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results. Describing a historically oriented, agent-based philosophy of mathematics, Ferreirós shows how the mathematical tradition evolved from Euclidean geometry to the real numbers and set-theoretic structures. He argues for the need to take into account a whole web of mathematical and other practices that are learned and linked by agents, and whose interplay acts as a constraint. Ferreirós demonstrates how advanced mathematics, far from being a priori, is based on hypotheses, in contrast to elementary math, which has strong cognitive and practical roots and therefore enjoys certainty. Offering a wealth of philosophical and historical insights, Mathematical Knowledge and the Interplay of Practices challenges us to rethink some of our most basic assumptions about mathematics, its objectivity, and its relationship to culture and science.

The Bulletin Of Symbolic Logic

Author :
ISBN : UOM:39015072619839
Genre : Logic, Symbolic and mathematical
File Size : 25. 72 MB
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Visualization Explanation And Reasoning Styles In Mathematics

Author : Paolo Mancosu
ISBN : 1402033346
Genre : Mathematics
File Size : 24. 31 MB
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This book contains groundbreaking contributions to the philosophical analysis of mathematical practice. Several philosophers of mathematics have recently called for an approach to philosophy of mathematics that pays more attention to mathematical practice. Questions concerning concept-formation, understanding, heuristics, changes in style of reasoning, the role of analogies and diagrams etc. have become the subject of intense interest. The historians and philosophers in this book agree that there is more to understanding mathematics than a study of its logical structure. How are mathematical objects and concepts generated? How does the process tie up with justification? What role do visual images and diagrams play in mathematical activity? What are the different epistemic virtues (explanatoriness, understanding, visualizability, etc.) which are pursued and cherished by mathematicians in their work? The reader will find here systematic philosophical analyses as well as a wealth of philosophically informed case studies ranging from Babylonian, Greek, and Chinese mathematics to nineteenth century real and complex analysis.

Crossroads History Of Science History Of Art

Author : Kim Williams
ISBN : 3034801394
Genre : Mathematics
File Size : 30. 41 MB
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A follow-up to the volume "Discovering the Principles of Mechanics 1600-1800. Essays by David Speiser" (Birkhäuser 2008), this volume contains the essays of David Speiser on relationships between science, history of science, history of art and philosophy.

Sets For Mathematics

Author : F. William Lawvere
ISBN : 0521010608
Genre : Mathematics
File Size : 79. 77 MB
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In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.

Mathematical Reviews

Author :
ISBN : UOM:39015076649881
Genre : Mathematics
File Size : 57. 4 MB
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