Dirk van Dalen - Böcker

Dirk van Dalen’s popular textbook Logic and Structure, now in its fifth edition, provides a comprehensive introduction to the basics of classical and intuitionistic logic, model theory and Gödel’s famous incompleteness theorem. The discussion of classical logic is concluded with a concise exposition of second-order logic.

Dirk van Dalen’s biography studies the fascinating life of the famous Dutch mathematician and philosopher Luitzen Egbertus Jan Brouwer. It appeals to mathematicians and anybody interested in the history of mathematics in the first half of the twentieth century.

Dirk van Dalen’s biography studies the fascinating life of the famous Dutch mathematician and philosopher Luitzen Egbertus Jan Brouwer. It appeals to mathematicians and anybody interested in the history of mathematics in the first half of the twentieth century.

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.

This book constitutes the strictly refereed post-workshop proceedings of the 10th International Workshop on Computer Science Logic, CSL'96, held as the 5th Annual Conference of the European Association of Computer Science Logic (EACSL), in Utrecht, The Netherlands, in September 1996.The volume presents 26 revised full papers selected from a total of initially 75 papers submitted; also included are two refereed invited contributions. The volume addresses all current issues in the area of computer science logic research, and is thus a unique record of recent progress in the area.