“mortal” means it does matter what “all” means.īorogoves are mimsy whenever it is brillig. The inference is justified by the form of the sentences rather than by empiricalįacts about mortality. The validity of inferring the third sentence (the conclusion) from the first two (the assumptions) does not depend The real-life objects are certain “logically correct” deductions. The selection of the properties of the original object to be Model meets its intended purpose will depend largely on In some ways (which you call essential) and unlike it in others (which you call irrelevant). And then you build an object that is like the original Then you select some features of this original object to be represented in the model,įor example its shape, and others to be ignored, for example How are models constructed? You begin with a real-life Model for situations involving chance and uncertainty. In much the same way that modern probability theory is a Other branches of mathematics it has grown beyond Or at least that was true originally as with Ymbolic logic is a mathematical model of deductive I would be pleased to receiveĬomments and corrections from the users of this book. I cheerfully acknowledge my debt to my teachers, a category in which I includeĪlso those who have been my colleagues or students. Unusually challenging exercises are marked with an asterisk. If the exercise bears aīoldface numeral, then the results of that exercise are used in the exposition in the Lectures and have a precise version in the book rather than to have the situationĮxercises are given at the end of nearly all the sections. I prefer to give an informal account of these subjects in Induction and recursion are given a more extensive discussion (in Section 1.4) The later chapters (Chapter 3 and 4) tend to be moreĭemanding of the reader than are the earlier chapters. Some examples drawn from abstract algebra. Numbers completely (at the cost of losing some theorems). The amount of set theory employed for example it is possible to avoid cardinal
Instead intended for reference if and when the need arises. One should not begin the book by studying this chapter it is There is the inevitable use of basic set theory. There are no specific prerequisitesĪside from a willingness to function at a certain level of abstraction and rigor. Has some experience in mathematical reasoning. The book is intended for the reader who has not studied logic previously, but who Term, the material of Chapter 3 (on undecidability) can be more adequately covered. Glimpse of undecidability, as in Section 3.0. The extra time afforded by a semester would permit some The material on models of first-order theories (Section 2.6). Their relationship to the reader’s other mathematical work.Īs a text, the book can be used in courses anywhere fromĪ quarter to a year in length. The objectives are to present the important conceptsĪnd theorems of logic and to explain their significance and The book is intended to serve as a textbook for an introductory mathematics course in logic at the junior-senior Some material on finite models has been incorporated into Issues of computability are taken more seriously. In recent years, and some of that influence is reflected in thisĮdition. Third, theoretical computer science has influenced logic Optional paths the instructor - or the independent reader. Or her course, the organization has been made more flexible.įootnotes at the beginning of many of the sections indicate Second, for the instructor who wants to fit the book to his In the mainĭevelopment, I have tried not to take for granted information or insights that might be unavailable to a junior-level
Numerous “local” changes, there are three “global” ways inįirst, I have attempted to make the material more accessible to the typical undergraduate student. Is directed toward the reader with some mathematical background and interests. His book, like the first edition, presents the basicĬoncepts and results of logic: the topics are proofs, International Standard Book Number: 0-12-238452-0 Library of Congress Catalog Card Number: 00-110670 Harcourt Place, 32 Jamestown Road, London NW1 7BY, UKĢ00 Wheeler Road, Burlington, Massachusetts 01803, USA Permissions Department, Harcourt, Inc., 6277 Sea Harbor Drive, Orlando, Floridaĥ25 B Street, Suite 1900, San Diego, California 92101-4495, USA Requests for permission to make copies of any part of the work should be mailed to: Information storage and retrieval system, without permission in writing from the Means, electronic or mechanical, including photocopy, recording, or any No part of this publication may be reproduced or transmitted in any form or by any A Harcourt Science and Technology Company