Logic and Structure

1. Front Matter

   Pages I-X

   PDF

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. Intuitionistic Logic

   • Dirk van Dalen

   Pages 165-199

8. Appendix

   • Dirk van Dalen

   Pages 200-202

9. Bibliography

   • Dirk van Dalen

   Pages 203-203

10. Gothic Alphabet

    • Dirk van Dalen

    Pages 204-204

11. Back Matter

    Pages 205-210

    PDF

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.

• Goedel's theorem
• basic model theory
• computability theory
• first-order logic with natural deduction
• intuitionistic logic and semantics
• model theory
• normalisation of first-order logic
• predicate logic
• proof
• proof theory
• recursive functions
• second order logic
• set theory

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)

• Mathematisch instituut, Rijksuniversiteit Utrecht, TA Utrecht, The Netherlands

  Dirk Dalen

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.

Policies and ethics