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Plato's Ghost: The Modernist Transformation of Mathematics First Edition Edition

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ISBN-13: 978-0691136103
ISBN-10: 0691136106
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Editorial Reviews


One of Choice's Outstanding Academic Titles for 2009

"In Plato's Ghost, he has . . . present[ed] us with an ambitious and in many respects remarkable synthesis of the modern transformation of mathematics via structural and set-theoretic notions, together not only with its logic and philosophy but also with related developments in artificial languages and psychology. . . . I can certainly recommend Plato's Ghost highly as a rich resource and point of departure for readers who want to learn more about this exciting period in the development of modern mathematics."--Solomon Feferman, American Scientist

"This accessible, rigorous volume belongs in every serious library."--J. McCleary, Choice

"In a book aimed at the educated public, the author presents an impressive amount of data--both of the kind mathematicians with some awareness of the history of their subject may be aware of, and of an entirely different kind, coming from the outskirts of mathematics, from philosophy, from physics, or from the popularization of mathematics, which will likely be new even to historians of mathematics."--Victor V Pambuccian, Mathematical Reviews

"It is . . . no small assertion to say that the book under review, Plato's Ghost, is [Gray's] most far-reaching and ambitious work to date. . . . [T]here is a wealth of valuable data here which, if not fully processed and pigeonholed, is at least tagged and cataloged in a helpful way. Plato's Ghost provides an insightful and informative resource for anyone doing mathematics today who has wondered how (and perhaps why) the subject has come to possess the features it has today. The book gives us a lot to think about, which is exactly what a good history should do."--Jeremy Avigad, Mathematical Intelligencer

"In this book Jeremy Gray offers us the fruit of more than a decade reading and thinking about modernism in mathematics. He presents it, in very well written form, to a broad audience interested in mathematics, its history and philosophy."--Erhard Scholz, Metascience

"What we have here . . . is an excellent and detailed survey of how modernism took root in mathematics. Plato's Ghost provides the launching pad for future ruminations on the modernist thesis."--Calvin Jongsma, Perspectives on Science and Christian Faith

"I commend Gray for writing an extraordinarily detailed and fascinating history of modernist mathematics, whose philosophical fruits remain ripe for the picking. The sections on geometry shine with clarity and convey the drama of modernism in a compelling and page-turning way. The treatments of less-studied actors are fascinating and promise to be of much use in incorporating their work into ongoing scholarship. The book could be fruitfully used as a supplement to a variety of courses in philosophy, including philosophy of mathematics and logic, history of analytic philosophy, and philosophy of science. It is a monument of scholarship and will reward careful study."--Andrew Arana, Philosophia Mathematica

"In the course of this study Gray uncovers many new and unexpected things. . . . Gray's book offers a rich and . . . balanced account of how modernist ideas gradually gained inroads within pure mathematics."--David E. Rowe, Bulletin of the American Mathematical Society

From the Back Cover

"In this impressive synthesis, Gray brings, in a largely nontechnical way, the technical development of mathematics from the 1880s to the 1930s into the broader historical analysis of the concept of modernity. His argument promises not only to challenge historians of mathematics but also, finally, to bring mathematics into wider discussions of cultural history."--Karen Hunger Parshall, author of James Joseph Sylvester: Jewish Mathematician in a Victorian World

"A major addition to scholarship in the history of mathematics and in the history of science in general. Gray throws light on a major cultural transformation of mathematics. The book is written for a large readership of historians of science, philosophers, and scientists. It will have repercussions in broader debates on scientific culture, and will remain a reference work for many years to come."--Moritz Epple, Johann Wolfgang Goethe University

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Product Details

  • Hardcover: 528 pages
  • Publisher: Princeton University Press; First Edition edition (September 22, 2008)
  • Language: English
  • ISBN-10: 0691136106
  • ISBN-13: 978-0691136103
  • Product Dimensions: 1.5 x 7.2 x 10 inches
  • Shipping Weight: 2.8 pounds (View shipping rates and policies)
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #471,975 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

42 of 58 people found the following review helpful By Viktor Blasjo on November 25, 2009
Format: Hardcover
This book has nothing in particular to say. It fills its pages with unimaginative, thoroughly neutral, semi-encyclopaedic surveys of one branch of mathematics after another, one philosophical debate after another, and so on, while offering next to nothing by way of synthesis or interpretation.

I shall criticise Gray for being rather more uncritical than befits a historian in his acceptance of party-line modernism. The tenet of party-line modernism that I shall focus on is the myth that history shows that intuition must be abandoned since it leads to "false" results. It is an important task for historians to reject such propaganda abuses of history as the fabrications that they are; but unfortunately Gray is somewhat rubbing the back of the establishment in this case.

A typical statement of the myth in question is the following passage, where Gray is supposedly quasi-paraphrasing Perron:

"Spatial intuition is a very frequent source of error, especially when it is used to supplant proofs, as, for example, in proofs of the intermediate value theorem. 'Intuition is a crude instrument that lets us make out true relationships only imprecisely' (p. 204), and this is particularly so of our understanding of curves, which may fail in all sorts of ways to have the intuitive properties one suspects." (p. 275)

The propaganda myth is that intuition leads one to suspect that curves should have certain properties while they really don't. Rather, the problem is that the intuitive notion of "curve" does not correspond precisely to the formal mathematical notion. So the "error" referred to above is not at all an error of intuition; it is the error of stupidly taking intuition to apply to formal objects.
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3 of 4 people found the following review helpful By Kodiak on April 28, 2013
Format: Hardcover Verified Purchase
Plato's Ghost covers the development of mathematics from 1880 to 1920, which is a topic that would normally challenge even the very best writers of science. Yet, Gray handles the material with ease in a manner that allows both mathematicians and non-mathematicians to grasp the significance of the key events and players in this field. At the same time, this subject matter is well-documented, so the reader can easily follow up on anything he or she might have a greater interest in pursuing. Gray is such a good writer on science and mathematics, that I have decided that I must consider reading anything he writes in these disciplines. I am now reading his next book, Henri Poincare, A Scientific Biography on the French mathematician and physicist. Poincare, like David Hilbert the German mathematician, each came very close to discovering relativity; so it is interesting to compare their work on a layman's level to that of Albert Einstein's. If anything, Gray is handling even more complex subject matter than in Plato's Ghost, yet once again with great ease. I highly recommend Plato's Ghost to anyone who is looking for an excellent introduction to this period in the development of mathematics; and I highly recommend that you consider reading Jeremy Gray, if you have an interest in mathematics and science. Gray sets a standard that will be hard for other writers in these disciplines to achieve.
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4 of 7 people found the following review helpful By Sam Adams on February 15, 2011
Format: Hardcover Verified Purchase
Gray's thesis, subdued through much of the book, is that the rise of modern mathematics not only coincided with the rise of what historians call Modernism in the arts, but that mathematics in its own way shared with Modernism an analogous change in viewpoints, values, and intellectual concerns. He doesn't propose any specific influences from the arts upon mathematics or particular mathematicians, although he does briefly note influences going the other way.

In philosophy, however, the stature of Immanuel Kant (1724-1804) and therefore of Kant's views on cognition and intuition in mathematics, especially in the light of the later discoveries of non-Euclidean geometry, stimulated mathematicians' thinking about mathematics as being within the purview of cognition and about mathematicians' own notions of the cognitive status and role of so-called mathematical intuition in mathematical knowledge. This scrutiny of epistemological concepts in relation to mathematics included, and indeed required, a critical examination of the pivotal notions of logic, definition, and proof. Here, the philosophical convictions of Gottfried Leibniz (1646-1716) on the nature of logic and on the relation of mathematics to logic stimulated mathematicians' thinking.

The development of mathematics had reached a point where mathematicians were concerned to find the unequivocal and comprehensive epistemological basis of mathematics. That basis, if it was not found in some form external to mathematics, be it as Kant traced it or otherwise, would be found within the anatomy of mathematics itself. This left open the question of the cognitive relations of mathematics to the physical world.
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Plato's Ghost: The Modernist Transformation of Mathematics
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