Goldrei - Propositional_and_predicate_calculus.pdf - Rhetoric discourse and writing - michalszasz121

Propositional and Predicate Calculus: A Model

of Argument

Derek Goldrei

Propositional and

Predicate Calculus

A Model of Argument

123

Derek Goldrei, MA, MSc

Open University

Milton Keynes

Mathematics Subject Classiﬁ cation (2000): 03B05, 03B10,03C07

British Library Cataloguing in Publication Data

Goldrei, Derek

Propositional and predicate calculus: a model of argument

1. Propositional calculus 2. Predicate calculus

I.Title

511.3

ISBN 1852339217

Library of Congress Cataloging-in-Publication Data

Goldrei, Derek.

Propositional and predicate calculus: a model of argument/Derek Goldrei.

p.cm.

Includes bibliographical references and index.

ISBN 1-85233-921-7 (acid-free paper)

1. Propositional calculus. 2. Predicate calculus. I. Title.

QA9.3.G65 2005

511.3--dc22

2005040219

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as

permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced,

stored or transmitted, in any form or by any means, with the prior permission in writing of the

publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued

by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be

sent to the publishers.

ISBN-10: 1-85233-921-7

ISBN-13: 978-1-85233-921-0

Springer Science+Business Media

springeronline.com

The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of

a speciﬁ c statement, that such names are exempt from the relevant laws and regulations and therefore

free for general use.

The publisher makes no representation, express or implied, with regard to the accuracy of the

information contained in this book and cannot accept any legal responsibility or liability for any errors

or omissions that may be made.

Typesetting: Camera-ready by author

Printed in the United States of America

12/3830-543210 Printed on acid-free paper SPIN 11345978

PREFACE

How to Use This Book

This book is intended to be used by you for independent study, with no other

reading or lectures etc., much along the lines of standard Open University

materials. There are plenty of exercises within the text which we would rec-

ommend you to attempt at that stage of your work. Almost all are intended

to be reasonably straightforward on the basis of what’s come before and many

are accompanied by solutions – it’s worth reading these solutions as they of-

ten contain further teaching, but do try the exercises ﬁrst without peeking,

to help you to engage with the material. Those exercises without solutions

might well be very suitable for any tutor to whom you have access to use as

the basis for any continuous assessment of this material, to help you check

that you are making reasonable progress. But beware! Some of the exercises

pose questions for which there is not always a clear-cut answer: these are

intended to provoke debate! In addition there are further exercises located at The book is also peppered with

notes in the margins, like this!

They consist of comments meant to

be on the fringe of the main text,

rather than the core of the

teaching, for instance reminders

about ideas from earlier in the

book or particularly subjective

opinions of the author.

If you would like any further reading in logic textbooks, there are plenty of

good books available which use essentially the same system, for instance those

by Enderton [12], Hamilton [18], Mendelson [25] and Cori and Lascar [7].

this book. My enthusiasm for the subject was fuelled by Robin Gandy, Paul

Bacsich, Jane Bridge, Angus Macintyre and Harold Simmons, when I stud-

ied at the Universities of Oxford and Aberdeen. Anything worthwhile I have

successfully learnt about teaching stems from my colleagues at the Open Uni-

versity and the network of mathematicians throughout the UK who support

the Open University by working as Associate Lecturers, external assessors and

examiners. They have taught me so much. It has been particularly stimu-

lating writing this book alongside producing the Open University’s course on

Mathematical Logic (with a very diﬀerent angle on the subject) with Alan

Pears, Alan Slomson, Alex Wilkie, Mary Jones, Roger Lowry, Jeﬀ Paris and

Frances Williams. And it is a privilege to be part of a university which puts

so much care and eﬀort into its teaching and the support of its students. The

practicalities of producing this book owe much to my publishers, Stephanie

Harding and Karen Borthwick at Springer; and to my colleagues at the Open

University who have done so much to provide me with a robust and attrac-

tive L a T E X system: Alison Cadle, David Clover, Jonathan Fine, Bob Margolis

and Chris Rowley. And thanks to Springer, I have received much invaluable

advice on content from their copy-editor Stuart Gale and their anonymous,

the end of most sections. These vary from further routine practice to rather

hard problems: it’s well worth reading through these exercises, even if you

don’t attempt them, as they often give an idea of some important ideas or

results not in the earlier text. Again your tutor, if you have one, can guide

you through these.

Acknowledgments

I would like to thank all those who have in some way helped me to write Plainly the blame for any errors

and inadequacies of this book lies

entirely with me. But perhaps at

some deep and subtle level, the

fault lies with everyone else!

Preface

very collegial, reviewers. I would also like to thank Michael Goldrei for his

work on the cover design.

Perhaps the main inspiration for writing the book is the enthusiasm and talent

for mathematical logic displayed by my old students at the Open University

and at the University of Oxford, especially those of Somerville, St. Hugh’s and

Mansﬁeld Colleges. In particular I’d like to thank the following for their com-

ments on parts of the book: Dimitris Azanias, David Blower, Duncan Blythe,

Rosa Clements, Rhodri Davies, David Elston, Michael Hopley, Gerrard Jones,

Eleni Kanellopoulou, Jakob Macke, Zelin Ozturk, Nicholas Thapen, Matt

Towers, Chris Wall, Garth Wilkinson, Rufus Willett and especially Margaret

Thomas.

This book is dedicated to all those whose arguments win me over, especially

Jennie, Michael, Judith and Irena.

Goldrei - Propositional_and_predicate_calculus.pdf

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika: