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Synthetic Philosophy of Contemporary Mathematics, by Fernando Zalamea
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Synthetic Philosophy of Contemporary Mathematics is a unique and unprecedented book, and a much needed one. Fernando Zalamea (Professor of Mathematics at the Universidad Nacional de Colombia) offers a synthetic perspective on the vast spectrum of contemporary mathematics, together with an analysis of the new philosophical problems originating therein. The book makes available to the inquisitive non-specialist the conceptual transformations and intellectual orientations of modern and contemporary mathematics, and their significance for speculative philosophical thought. The first part of the text discusses the specificity of modern (1830-1950) and contemporary (1950 to the present) mathematics, and offers an extensive review of how philosophy of mathematics addressed it (or failed to). In the second part, thirteen detailed case studies examine the greatest creators in the field, compiling a map of the central advances accomplished in mathematics over the last half-century. Drawing on these concrete examples, the third part proposes some generic outlines for synthesis. Zalamea's book serves as a conceptual introduction to mathematical themes rarely discussed outside specialist circles, and as a critical lens by means of which today's mathematics may aid us in the configuration of new cultural perspectives. If analytic philosophy was forged in the fires of set theory and classical logic at the beginning of the twentieth century, then today, at the dawn of the twenty-first, and around the scaffolding of category theory and the logic of sheaves, it is time for a complementary, synthetic philosophy to be built.
- Sales Rank: #1119308 in Books
- Published on: 2013-01-15
- Dimensions: 6.89" h x .79" w x 4.53" l,
- Binding: Paperback
- 394 pages
Review
This is a weighty and daring book. It proposes a new philosophy of mathematics, based on a detailed knowledge of the most recent work in advanced mathematics, and constructed in explicit contrast with the traditional analytical approach…this new synthetic and open-minded approach is no doubt worthy of attention, and philosophers who dare to make an effort will surely reap the reward. --Paloma Pérez-Ilzarbe, American Mathematical Society s MathSciNet
Zalamea is clearly on the cutting edge of theorizing potential intersections between networks, math, and philosophy. Few thinkers are able to bring together insights from as diverse fields in such as exciting manner as Zalamea. --Christopher Vitale, Assistant Professor, Media Studies, Pratt Institute, NY
With high professional competence in mathematics and philosophy and written in masterful prose, Zalamea opens up a breathtaking insight into advanced contemporary mathematics by enlightening its magical power with the powerful paradigm of gestural dynamics as developed by Valéry, Merleau-Ponty and Châtelet. --Guerino Mazzola, Professor of Mathematical Music Theory and Creativity, School of Music, University of Minnesota
About the Author
Fernando Zalamea is professor of Mathematics at the Universidad Nacional de Colombia. He is author of Ariadna y Penélope: Redes y mixturas en el mundo contemporáneo (Asturias: Ediciones Nobel,2004), América, una trama integral: Transversalidad, bordes y abismos en la cultura americana,siglos xix y xx (Bogotá: Universidad Nacional de Colombia, 2009), and Razón de la Frontera y Fronteras de la razón: Pensamiento de los límites en Peirce, Florenski, Marey, y limitantes de la expresión en Lispector,Vieira da Silva, Tarkovski (Bogotá: Universidad Nacional de Colombia, 2010). He is also editor and translator of the Spanish edition of the works of Albert Lautman, Ensayos sobre la dialéctica, estructrura y unidad de las matemáticas modernas (Bogotá:Universidad Nacional de Colombia, 2011).
Most helpful customer reviews
20 of 21 people found the following review helpful.
Fantastic exploration of contemporary math
By Peter
Great book, completely interesting. Most of the math was over my head, but the clarity and correctness he brought to the parts that i did understand made me believe the rest. He's a good writer and doesn't waste time or fluff up his vocabulary unnecessarily. Really, really made me want to learn some new math. Also, a very attractive, well-designed and well-edited volume. Two thumsb up. His basic thesis is that until now philosophy (particularly analytic philosophy) has treated mathematical logic and ZFC set theory as the universe of all possible maths, which is crazily parochial and doesn't even bite the tip of the iceberg of contemporary math. Zamalea does a great job using words to describe the ways in which contemporary mathematics is simply incommensurable with early-20th-century math, and just can't be meaningfully reduced to it. Totally new things start happening when you start hitting the level of connectedness and complexity that is the starting point for doing contemporary math. The book is a call for philosophers to shut up, put down the frege and the quine (but maybe not cohen), and pick up grothendieck, serre, connes, zilber, etc.
Anyway, great book.
0 of 3 people found the following review helpful.
Completely satisfied!
By Driftwin Books
Arrived very quickly! Completely satisfied!
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