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Logic and Structure

  • Textbook
  • © 1980

Overview

Authors:
  1. Dirk Dalen

    1. Mathematisch Instituut, Rijksuniversiteit Utrecht, Utrecht, The Netherlands

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Part of the book series: Universitext (UTX)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-IX
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  2. Introduction

    • Dirk van Dalen
    Pages 1-3

  3. Propositional Logic

    • Dirk van Dalen
    Pages 4-57

  4. Predicate Logic

    • Dirk van Dalen
    Pages 58-105

  5. Completeness and Applications

    • Dirk van Dalen
    Pages 106-153

  6. Second-Order Logic

    • Dirk van Dalen
    Pages 154-164

  7. Appendix

    • Dirk van Dalen
    Pages 165-167

  8. Bibliography

    • Dirk van Dalen
    Pages 168-168

  9. Gothic Alphabet

    • Dirk van Dalen
    Pages 169-169

  10. Back Matter

    Pages 170-174
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Keywords

About this book

Logic appears in a 'sacred' and in a 'profane' form. The sacred form is dominant in proof theory, the profane form in model theory. The phenomenon is not unfamiliar, one observes this dichotomy also in other areas, e.g. set theory and recursion theory. For one reason or another, such as the discovery of the set theoretical paradoxes (Cantor, Russell), or the definability paradoxes (Richard, Berry), a subject is treated for some time with the utmost awe and diffidence. As a rule, however, sooner or later people start to treat the matter in a more free and easy way. Being raised in the 'sacred' tradition, I was greatly surprised (and some­ what shocked) when I observed Hartley Rogers teaching recursion theory to mathema­ ticians as if it were just an ordinary course in, say, linear algebra or algebraic topology. In the course of time I have come to accept his viewpoint as the didac­ tically sound one: before going into esoteric niceties one should develop a certain feeling for the subject and obtain a reasonable amount of plain working knowledge. For this reason I have adopted the profane attitude in this introductory text, reserving the more sacred approach for advanced courses. Readers who want to know more about the latter aspect of logic are referred to the immortal texts of Hilbert-Bernays or Kleene.

Reviews

From the reviews of the fourth edition:

"This book teaches logic to mathematicians in just the way I would have wished. … Beginning with the propositional calculus by means of truth-tables, i.e. the semantics, it proceeds to the syntactics in the form of Gentzen’s natural deduction. … this fourth edition has a long final chapter added, on Gödel’s incompleteness theorem. … The chapter follows traditional lines but preserves the excellent quality of the earlier chapters. This is a delightful textbook, with plenty of examples for the reader." (C.W. Kilmister, The Mathematical Gazette, Vol. 89(515), 2005)

"This is the fourth edition of van Dalen’s classic textbook on logic in the popular ‘Universitext’ -series. … this book explains clearly all aspects of logic which a novice in this matter should learn by heart. … Reading this book was a real delight. A lot of the fun was in the exercises … heartily recommend this excellent textbook; … Current students may have little interest in formal mathematics … the problem will solve itself when they all have a copy on their personal bookshelf." (Pieter Audenaert, Bulletin of the Belgian Mathematical Society, Vol. 12 (3), 2005)

Authors and Affiliations

  • Mathematisch Instituut, Rijksuniversiteit Utrecht, Utrecht, The Netherlands

    Dirk Dalen

About the author

Dirk van Dalen studied at the University of Amsterdam, where he obtained his PhD. He has taught since 1960 at Utrecht University, where he is full professor. He also taught at MIT and Oxford. His technical work is mostly in the area of intuitionistic mathematics and logic. He uses to call attention to the benefits and challenges of constructive methods. His current project is a biography of L.E.J. Brouwer and the editing of Brouwer's correspondence.

Bibliographic Information

  • Book Title: Logic and Structure

  • Authors: Dirk Dalen

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-3-662-08402-1

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1980

  • eBook ISBN: 978-3-662-08402-1Published: 09 March 2013

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: IX, 174

  • Number of Illustrations: 1 b/w illustrations

  • Additional Information: 4th ed., corrected 2nd printing.

  • Topics: Mathematical Logic and Foundations

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