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Fernando Zalamea
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Synthetic Philosophy of Contemporary Mathematics Illustrated Edition

by Fernando Zalamea (Author), Zachery Luke Fraser (Translator)
4.6 4.6 out of 5 stars 23 ratings
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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.

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  1. ISBN-10
    0956775012
  2. ISBN-13
    978-0956775016
  3. Edition
    Illustrated
  4. Publisher
    Urbanomic/Sequence Press
  5. Publication date
    September 1, 2012
  6. Language
    English
  7. Dimensions
    4.63 x 0.8 x 6.94 inches
  8. Print length
    380 pages
  9. See all details
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Editorial Reviews

Review

This book, elegantly and clearly translated by Z.L. Fraser provides, for the Anglophone world, insight into Zalamea's renewal of philosophy through mathematical (and synthetical) means.—Tzuchien Tho, MUTE—

Zalamea's book is thematically vast. It is truly astounding to behold the rich range of mathematical themes that are touched upon, arguably including all of the most important objects of contemporary exploration.

—Giuseppe Longo, Speculations—

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, MathSciNet—

About the Author

Fernando Zalamea is Professor of Mathematics at the Universidad Nacional de Colombia.

Product details

  • Publisher ‏ : ‎ Urbanomic/Sequence Press; Illustrated edition (September 1, 2012)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 380 pages
  • ISBN-10 ‏ : ‎ 0956775012
  • ISBN-13 ‏ : ‎ 978-0956775016
  • Item Weight ‏ : ‎ 10.4 ounces
  • Dimensions ‏ : ‎ 4.63 x 0.8 x 6.94 inches
  • Customer Reviews:
    4.6 4.6 out of 5 stars 23 ratings

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Fernando Zalamea

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Customer reviews

4.6 out of 5 stars
4.6 out of 5
23 global ratings

Top reviews from the United States

Peter
5.0 out of 5 stars Fantastic exploration of contemporary math
Reviewed in the United States on February 25, 2013
Verified Purchase
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.
28 people found this helpful
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Pablo I. Altieri, II, M.D.
5.0 out of 5 stars Must read
Reviewed in the United States on August 24, 2020
Verified Purchase
This is such an important piece of work. Anyone interested in mathematics, philosophy, the theory of mind, and the real and imagined should read it.
One person found this helpful
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Driftwin Books
5.0 out of 5 stars Completely satisfied!
Reviewed in the United States on July 24, 2015
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Arrived very quickly! Completely satisfied!
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Top reviews from other countries

Rahul
5.0 out of 5 stars the voice of things
Reviewed in India on August 18, 2022
Verified Purchase
FZ's SPCM is a great contributor to philosophy. As he writes on the back cover, "The heart of mathematics has its reasons, of which linguistic reason knows nothing... the philosopher of mathematics must confront the 'wild heart' of mathematics". Many non-mathematicians cannot intuitively listen to this heartbeat, in fact, more often than not, the mathematical heart beats them up. This book just might break that groove. FZ makes things lucid in an uncompromising manner for experts, beginners, and those who can listen to the voice of things. Just one reminder - mathematics takes the shape of order, not the other way round.
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Rahul
5.0 out of 5 stars the voice of things
Reviewed in India on August 18, 2022
FZ's SPCM is a great contributor to philosophy. As he writes on the back cover, "The heart of mathematics has its reasons, of which linguistic reason knows nothing... the philosopher of mathematics must confront the 'wild heart' of mathematics". Many non-mathematicians cannot intuitively listen to this heartbeat, in fact, more often than not, the mathematical heart beats them up. This book just might break that groove. FZ makes things lucid in an uncompromising manner for experts, beginners, and those who can listen to the voice of things. Just one reminder - mathematics takes the shape of order, not the other way round.
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Prof L. S. Smith
5.0 out of 5 stars Excellent update to philosophy of Mathematics
Reviewed in the United Kingdom on August 17, 2013
Verified Purchase
This book is an accessible entry to new ideas in the philosophy of Mathematics. It moves away from the relatively trivial philosophical view of Mathematics being based on logic to a completely different view based on recent developments in Mathematics. It needs a degree of knowledge of Mathematics, but most of the more difficult parts are in footnotes, which makes it possible to read without a detailed knowledge of recent developments in Mathematics. The book is in three parts. The first part explains the general background, including the scope and purpose of the book. The second part is a review of recent Mathematics, concentrating on a baker's dozen of 20th century Mathematicians. Three different approaches to Mathematics are outlined, which the author calls eidal (transfusions of form: very much pure Mathematics, including mathematics of mathematics), quiddital (transfusions of the real, mathematics based in physics), and archaeal (decantations of the Universal). These chapters provide a very clear description of the moving forces in Mathematics, and allow the author to develop a philosophy of Mathematics in the third part that is much more relevant to mainstream research in Mathematics than existing mainstream philosophies of Mathematics. Zalamea does not come to this on his own, but bases his approach on the earlier work of the French philosopher of Mathematics, Lautmann, as well as Badiou. In particular, he is scathing of the approach in The Oxford Handbook of Philosophy of Mathematics and Logic (S. Shapiro (ed) 2007) - and he is also scathing of the lack of reading of non-English texts by native English speakers. I recommend this book to those seeking a deeper understanding the overall range of contemporary Mathematics, and to those seeking a better, more useful and more relevant philosophy of Mathematics than the mainstream approach.
11 people found this helpful
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