Intuitionistic Analysis: A Constructive Frame of Mind
暫譯: 直觀分析：一種建設性的思維框架

Van Dalen, Dirk, Van Atten, Mark, Smoryński, Craig

Intuitionistic Analysis: A Constructive Frame of Mind
  • 出版商: Springer
  • 出版日期: 2026-05-04
  • 售價: $2,670
  • 貴賓價: 9.5 折 $2,536
  • 語言: 英文
  • 頁數: 167
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3032164907
  • ISBN-13: 9783032164902
  • 相關分類: 離散數學 Discrete-mathematics

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商品描述

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.

商品描述(中文翻譯)

本書介紹了L.E.J. Brouwer在數學中對於建構性的核心理念，重點關注分析、集合論和拓撲學，同時考慮他的哲學動機。Brouwer的「直覺主義」提供了一種與傳統（非建構性）數學相一致的替代方案。

本書從拒絕排中律（Principle of the Excluded Middle）開始，利用Cauchy序列重建數系和分析。它比較了建構性方法和傳統方法，突顯了傳統定理在「弱反例」下的失效，並檢視Brouwer的傳統和建構性版本的固定點定理（Fixed-Point Theorem）。直覺主義概念如選擇序列和創造主體導致了一些驚人的結果，例如所有總實函數的連續性以及有效但非遞歸函數的存在。與Markov和Bishop的後來替代方案進行了簡短但基本的比較。

本書旨在作為本科生的入門書籍，適合對哲學感興趣的數學學生以及具備一定數學背景的哲學家。

作者簡介

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).

作者簡介(中文翻譯)

Dirk van Dalen 是烏特勒支大學的哲學及數學與邏輯歷史名譽教授。他曾是 Arend Heyting 的學生，研究興趣包括直覺主義、建構數學及其哲學與歷史。他的出版物包括教科書 Logic and Structure（第五版，Springer，2013年）以及 L.E.J. Brouwer 的傳記（牛津大學出版社，1999年和2005年；Springer，2013年）。

Mark van Atten 是法國國家科學研究中心（CNRS）的高級研究員，也是巴黎 Husserl 檔案館的成員。他曾是 Dirk van Dalen 的學生，研究領域為數學哲學，特別是 Brouwer 的直覺主義與 Husserl 的現象學的交集。他的出版物包括 On Brouwer（Wadsworth，2004年）；Brouwer Meets Husserl（Springer，2007年）；以及 Essays on Gödel's Reception of Leibniz, Husserl, and Brouwer（Springer，2015年）。

Craig Smoryński 是一位數學家和獨立學者，他在伊利諾伊大學芝加哥分校獲得學位，並在荷蘭生活了幾年，期間他的直覺主義知識得到了成熟。他在邏輯、證明理論、算術及其歷史學方面做出了貢獻。他是幾本著作的作者，包括 Self-Reference and Modal Logic（Springer，1985年）、Logical Number Theory I（Springer，1991年）以及 Adventures in Formalism（College Publications，2012年）。

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