Intuitionistic analysis a constructive frame of mind Dirk van Dalen, Mark van Atten, Craig Smoryński

Format:

Book

Author/Creator:

Dalen, D. van (Dirk), 1932- author.

Atten, Markus Sebastiaan Paul Rogier van, 1973- author.

Smoryński, C., author.

Series:

Springer undergraduate mathematics series

SUMS Readings

Springer undergraduate mathematics series 2197-4144

SUMS readings

Language:

English

Subjects (All):

Brouwer, L. E. J. (Luitzen Egbertus Jan), 1881-1966.

Mathematical analysis--Philosophy.

Physical Description:

1 online resource

Place of Publication:

Cham, Switzerland Springer [2026]

Summary:

"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"-- Springer Nature Link

Contents:

Logic

Natural numbers, integers, and rationals

Real numbers

Functions and continuity

Going forth

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (Springer Nature Link, viewed May 6, 2026)

Other Format:

Print version Dalen, D. van (Dirk), 1932- Intuitionistic analysis

ISBN:

9783032164919

3032164915

OCLC:

1588213140

Access Restriction:

Restricted for use by site license