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Intuitionistic Analysis: A Constructive Frame of Mind (Springer Undergraduate Mathematics Series) - Tapa blanda

Dalen, Dirk Van; Atten, Mark Van; Smory¿ski, Craig

 
9783032164902: Intuitionistic Analysis: A Constructive Frame of Mind (Springer Undergraduate Mathematics Series)
Tapa blanda
ISBN 10: 3032164907 ISBN 13: 9783032164902
Editorial: Springer-Verlag GmbH, 2026

Sinopsis

This book introduces the core ideas of L.E.J. Brouwer’s approach to constructivity in mathematics, focusing on analysis, set theory, and topology, while considering his philosophical motivations. Brouwer’s “intuitionism” offers a coherent alternative to classical (nonconstructive) mathematics.

Starting with the rejection of the Principle of the Excluded Middle, the book reconstructs number systems and analysis using Cauchy sequences. It compares constructive and classical methods, highlights where classical theorems fail through “weak counterexamples”, and examines Brouwer’s classical and constructive versions of the Fixed-Point Theorem. Intuitionistic concepts like choice sequences and the Creating Subject lead to surprising results, such as the continuity of all total real functions and the existence of effective but non-recursive functions. Brief but fundamental comparisons are made with the later alternatives of Markov and Bishop.

Intended as an introduction for undergraduates, this book is suitable for mathematics students interested in philosophy as well as philosophers with some mathematical background.

"Sinopsis" puede pertenecer a otra edición de este libro.

Acerca del autor

Dirk van Dalen is a professor emeritus of philosophy and history of mathematics and logic at Utrecht University. A former student of Arend Heyting, his research interests are intuitionism, constructive mathematics, and their philosophy and history. His publications include the textbook Logic and Structure (5th edition, Springer, 2013) and a biography of L.E.J. Brouwer (Oxford University Press, 1999 and 2005; Springer, 2013).

Mark van Atten is a senior researcher at CNRS, France and a member of the Archives Husserl in Paris. A former student of Dirk van Dalen, his field is the philosophy of mathematics, specifically the intersection of Brouwer's intuitionism and Husserl's phenomenology. Among his publications are On Brouwer (Wadsworth, 2004); Brouwer Meets Husserl (Springer, 2007); and Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer (Springer, 2015).

Craig Smoryński is a mathematician and independent scholar who earned his degree at the University of Illinois in Chicago and spent several years in the Netherlands, where his knowledge of intuitionism matured. He has made contributions to logic, proof theory, arithmetic, and their historiography. He is the author of several texts, including Self-Reference and Modal Logic (Springer, 1985), Logical Number Theory I (Springer, 1991), and Adventures in Formalism (College Publications, 2012).

De la contraportada

This book introduces the core ideas of L.E.J. Brouwer's approach to constructivity in mathematics, focusing on analysis, set theory, and topology, while considering his philosophical motivations. Brouwer's "intuitionism" offers a coherent alternative to classical (nonconstructive) mathematics.

Starting with the rejection of the Principle of the Excluded Middle, the book reconstructs number systems and analysis using Cauchy sequences. It compares constructive and classical methods, highlights where classical theorems fail through "weak counterexamples", and examines Brouwer's classical and constructive versions of the Fixed-Point Theorem. Intuitionistic concepts like choice sequences and the Creating Subject lead to surprising results, such as the continuity of all total real functions and the existence of effective but non-recursive functions. Brief but fundamental comparisons are made with the later alternatives of Markov and Bishop.

Intended as an introduction for undergraduates, this book is suitable for mathematics students interested in philosophy as well as philosophers with some mathematical background.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Springer-Verlag GmbH
Año de publicación
2026
Idioma
Inglés
ISBN 10 
3032164907
ISBN 13 
9783032164902
Encuadernación
Tapa blanda
Número de páginas
188
Contacto del fabricante
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