Gnomes in the Fog: The Reception of Brouwer's Intuitionism in the 1920s (Science Networks. Historical Studies, 28) [Hardcover]

Dennis E. Hesseling (Author)

Book Description

Publication Date: January 12, 2004 | ISBN-10: 3764365366 | ISBN-13: 978-3764365363 | Edition: 1

The significance of foundational debate in mathematics that took place in the 1920s seems to have been recognized only in circles of mathematicians and philosophers. A period in the history of mathematics when mathematics and philosophy, usually so far away from each other, seemed to meet. The foundational debate is presented with all its brilliant contributions and its shortcomings, its new ideas and its misunderstandings.

Editorial Reviews

Review

"L.E.J. Brouwer is best known to many mathematicians for his seminal contributions to topology. He is also the founder of mathematical intuitionism, and a key player in the debate on foundations of mathematics that raged for a brief decade in the 1920s, and then subsided. Gnomes in the Fog tells the story of that important and influential episode in the history of mathematics, in fascinating and delicious detail.... [A]nyone with an interest in mathematics and its history and philosophy, should enjoy this book. Mathematicians (especially logicians) may find some surprises in the first chapter, on Brouwer's predecessors; philosophers and science study scholars should especially appreciate the final chapter on the cultural context of the debate.... One of the many treasures to be discovered in reading this book is the rich collection of original quotes in the many languages in which the debate took place, along with the author's translations." —MAA Online

Product Details

• Hardcover: 470 pages
• Publisher: Birkhäuser Basel; 1 edition (January 12, 2004)
• Language: English
• ISBN-10: 3764365366
• ISBN-13: 978-3764365363
• Product Dimensions: 9.3 x 6.5 x 1.2 inches
• Shipping Weight: 2.2 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #3,425,927 in Books (See Top 100 in Books)

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3 of 3 people found the following review helpful:

5.0 out of 5 stars fascinating and excellent book, June 18, 2008

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Rudolph V. Dusek "Val Dusek" (Scarborough ME USA) - See all my reviews
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This review is from: Gnomes in the Fog: The Reception of Brouwer's Intuitionism in the 1920s (Science Networks. Historical Studies, 28) (Hardcover)

This is a unique, thorough, and excellent treatment of the reception of intuitionist mathematics and philosophy of mathematics. It presents the views of the semi-intuitionists such as Kronecker and Poincare. It extensively discusses the various foundational debates and opinions of intutionism by various mathematicians,including several less well known ones, but it goes far beyond that. For instance, it includes parallels to similar currents such as constructivism in art to the popularity of appeals to "constructivism" by not only the mathematical intuitionists, but by the formalist Hilbert and the logicist Carnap. Also mentioned is the case of a high school text of the period that included some discussion of intuitionist mathematics. It also discusses parallels between Weyl's defense of intuitionism and Spengler's "Decline of the West" and the influences of Brouwer on Wittgenstein. This is all and all a fascinating book. It doesn't develop the conceptual points as far as it might, but it lays out numerous suggestions and alternative accounts of the relation of mathematical intuitionism to lebensphilosophie, Weimar culture and other cultural currents of the time.