logic and structure.pdf - Dirk van Dalen Logic and...

This preview shows page 1 - 6 out of 275 pages.

Background image
Background image
Dirk van DalenLogicand StructureFourth EditionABC
Dirk van DalenDepartment of PhilosophyUtrecht UniversityHeidelberglaan 8P.O. Box 801263508 TC UtrechtThe Netherlands[email protected]Corrected 2nd printing 2008ISBN 978-3-540-20879-2Library of Congress Control Number: 2008929906Mathematics Subject Classification (2000): 03-01 (textbook); 03B15, 03F05, 03C07c 2004, 1994, 1983, 1980 Springer-Verlag Berlin HeidelbergThis work is subject to copyright. All rights are reserved, whether the whole or part of the materialis concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broad-casting, reproduction on microfilm or in any other way, and storage in data banks. Duplication ofthis publication or parts thereof is permitted only under the provisions of the German Copyright Lawof September 9, 1965, in its current version, and permission for use must always be obtained fromSpringer. Violations are liable to prosecution under the German Copyright Law.The use of general descriptive names, registered names, trademarks, etc. in this publication does notimply, even in the absence of a specific statement, that such names are exempt from the relevant pro-tective laws and regulations and therefore free for general use.Cover design: Erich Kirchner, HeidelbergPrinted on acid-free paper9 8 7 6 5 4 3 2 1springer.com
PrefaceLogic appears in a ‘sacred’ and in a ‘profane’ form; the sacred form is domi-nant in proof theory, the profane form in model theory. The phenomenon isnot unfamiliar, one observes this dichotomy also in other areas, e.g. set the-ory and recursion theory. Some early catastrophies, such as the discovery ofthe set theoretical paradoxes (Cantor, Russell), or the definability paradoxes(Richard, Berry), make us treat a subject for some time with the utmostawe and diffidence. Sooner or later, however, people start to treat the mat-ter in a more free and easy way. Being raised in the ‘sacred’ tradition, myfirst encounter with the profane tradition was something like a culture shock.Hartley Rogers introduced me to a more relaxed world of logic by his exampleof teaching recursion theory to mathematicians as if it were just an ordinarycourse in, say, linear algebra or algebraic topology. In the course of time I havecome to accept this viewpoint as the didactically sound one: before going intoesoteric niceties one should develop a certain feeling for the subject and ob-tain a reasonable amount of plain working knowledge. For this reason thisintroductory text sets out in the profane vein and tends towards the sacredonly at the end.The present book has developed out of courses given at the mathematicsdepartment of Utrecht University. The experience drawn from these coursesand the reaction of the participants suggested strongly that one should notpractice and teach logic in isolation. As soon as possible examples from every-day mathematics should be introduced; indeed, first-order logic finds a richfield of applications in the study of groups, rings, partially ordered sets, etc.

Upload your study docs or become a

Course Hero member to access this document

Upload your study docs or become a

Course Hero member to access this document

End of preview. Want to read all 275 pages?

Upload your study docs or become a

Course Hero member to access this document

Term
Summer
Professor
Stat
Tags
Logic, The Land, First order logic, Snow,

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture