Deleuze and the History of Mathematics

Deleuze and the History of Mathematics
Author: Simon Duffy
Publisher: A&C Black
Total Pages: 225
Release: 2013-05-09
Genre: Philosophy
ISBN: 1441113894

Gilles Deleuze's engagements with mathematics, replete in his work, rely upon the construction of alternative lineages in the history of mathematics, which challenge some of the self imposed limits that regulate the canonical concepts of the discipline. For Deleuze, these challenges provide an opportunity to reconfigure particular philosophical problems - for example, the problem of individuation - and to develop new concepts in response to them. The highly original research presented in this book explores the mathematical construction of Deleuze's philosophy, as well as addressing the undervalued and often neglected question of the mathematical thinkers who influenced his work. In the wake of Alain Badiou's recent and seemingly devastating attack on the way the relation between mathematics and philosophy is configured in Deleuze's work, Simon B.Duffy offers a robust defence of the structure of Deleuze's philosophy and, in particular, the adequacy of the mathematical problems used in its construction. By reconciling Badiou and Deleuze's seemingly incompatible engagements with mathematics, Duffy succeeds in presenting a solid foundation for Deleuze's philosophy, rebuffing the recent challenges against it.

Time and History in Deleuze and Serres

Time and History in Deleuze and Serres
Author: Bernd Herzogenrath
Publisher: A&C Black
Total Pages: 214
Release: 2011-12-15
Genre: Philosophy
ISBN: 1441185704

For Gilles Deleuze, time is 'out of joint'. For Michel Serres, it is 'a crumpled handkerchief'. In both of these concepts, explicit references are made to the non-linear dynamics of Chaos and Complexity theory, as well as the New Sciences. The groundbreaking work of these key thinkers has the potential to instigate a radical break from traditional existentialist theories of time and history, affording us the opportunity to view history and historical events as a complex, non-linear system of feedback-loops, couplings and interfaces. In this collection, the first to address the comparative historiographies of Deleuze and Serres, twelve leading experts - including William Connolly, Eugene Holland, Claire Colebrook and Elizabeth Grosz - examine these alternative concepts of time and history, exposing critical arguments in this important and emerging field of research.

Mathematics, Ideas and the Physical Real

Mathematics, Ideas and the Physical Real
Author: Albert Lautman
Publisher: A&C Black
Total Pages: 354
Release: 2011-06-02
Genre: Philosophy
ISBN: 1441146547

Albert Lautman (1908-1944) was a French philosopher of mathematics whose work played a crucial role in the history of contemporary French philosophy. His ideas have had an enormous influence on key contemporary thinkers including Gilles Deleuze and Alain Badiou, for whom he is a major touchstone in the development of their own engagements with mathematics. Mathematics, Ideas and the Physical Real presents the first English translation of Lautman's published works between 1933 and his death in 1944. Rather than being preoccupied with the relation of mathematics to logic or with the problems of foundation, which have dominated philosophical reflection on mathematics, Lautman undertakes to develop an understanding of the broader structure of mathematics and its evolution. The two powerful ideas that are constants throughout his work, and which have dominated subsequent developments in mathematics, are the concept of mathematical structure and the idea of the essential unity underlying the apparent multiplicity of mathematical disciplines. This collection of his major writings offers readers a much-needed insight into his influence on the development of mathematics and philosophy.

The Fold

The Fold
Author: Gilles Deleuze
Publisher: A&C Black
Total Pages: 219
Release: 2006-05-16
Genre: Philosophy
ISBN: 082649076X

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Making and Breaking Mathematical Sense

Making and Breaking Mathematical Sense
Author: Roi Wagner
Publisher: Princeton University Press
Total Pages: 250
Release: 2017-01-10
Genre: Mathematics
ISBN: 0691171718

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.

What is a Mathematical Concept?

What is a Mathematical Concept?
Author: Elizabeth de Freitas
Publisher: Cambridge University Press
Total Pages: 301
Release: 2017-06-22
Genre: Education
ISBN: 1107134633

Leading thinkers in mathematics, philosophy and education offer new insights into the fundamental question: what is a mathematical concept?

Synthetic Philosophy of Contemporary Mathematics

Synthetic Philosophy of Contemporary Mathematics
Author: Fernando Zalamea
Publisher: National Geographic Books
Total Pages: 0
Release: 2012-09-01
Genre: Philosophy
ISBN: 0956775012

A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest. A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest, this book gives the inquisitive non-specialist an insight into the conceptual transformations and intellectual orientations of modern and contemporary mathematics. The predominant analytic approach, with its focus on the formal, the elementary and the foundational, has effectively divorced philosophy from the real practice of mathematics and the profound conceptual shifts in the discipline over the last century. The first part discusses the specificity of modern (1830–1950) and contemporary (1950 to the present) mathematics, and reviews the failure of mainstream philosophy of mathematics to address this specificity. Building on the work of the few exceptional thinkers to have engaged with the “real mathematics” of their era (including Lautman, Deleuze, Badiou, de Lorenzo and Châtelet), Zalamea challenges philosophy's self-imposed ignorance of the “making of mathematics.” In the second part, thirteen detailed case studies examine the greatest creators in the field, mapping the central advances accomplished in mathematics over the last half-century, exploring in vivid detail the characteristic creative gestures of modern master Grothendieck and contemporary creators including Lawvere, Shelah, Connes, and Freyd. Drawing on these concrete examples, and oriented by a unique philosophical constellation (Peirce, Lautman, Merleau-Ponty), in the third part Zalamea sets out the program for a sophisticated new epistemology, one that will avail itself of the powerful conceptual instruments forged by the mathematical mind, but which have until now remained largely neglected by philosophers.

Deleuze, Whitehead, Bergson

Deleuze, Whitehead, Bergson
Author: K. Robinson
Publisher: Springer
Total Pages: 248
Release: 2008-12-19
Genre: Philosophy
ISBN: 0230280730

This volume explores the relations between the work of Gilles Deleuze, Alfred North Whitehead and Henri Bergson. It examines the articulation between their concepts, methods and modes of philosophy. Themes are examined in the context of the contrasts, differences and conjunctions - the rhizomatic connections - between their shared concepts.