Logic: An Introduction to Elementary Logic

289 Pages·2001·3 MB·English

by  Wilfrid Hodges

PENGUIN BOOKS
Logic
Wilfrid Hodges was born in 1941 and educated at New College, Oxford (1959–
65), where he received a first degree not only in Literae Humaniores but also in
Theology. In 1970 he was awarded a doctorate for a thesis in Logic. He was a
lecturer in Philosophy and later in Mathematics at Bedford College, University
of London. He has held visiting appointments in the philosophy department of
the University of California, Los Angeles, and the mathematics department of
the University of Colorado at Boulder. He is now a Professor of Mathematics at
Queen Mary and Westfield College, University of London.
Among his publications are the chapter on Elementary Predicate Logic in the
Handbook of Philosophical Logic (vol. 1, 1983), three textbooks in model
theory, and papers on the mathematics, history and psychology of logic in
various journals and proceedings. He has given several public lectures on topics
in logic, mathematics and music. He has held editorial positions on five logic
journals, and he has been President of the British Logic Colloquium and the
European Association for Logic, Language and Information.
WILFRID HODGES
Logic
Second Edition
PENGUIN BOOKS
PENGUIN BOOKS
Published by the Penguin Group Penguin Books Ltd, 80 Strand, London WC2R 0RL, England Penguin
Putnam Inc., 375 Hudson Street, New York, New York 10014, USA Penguin Books Australia Ltd, 250
Camberwell Road, Camberwell, Victoria 3124, Australia Penguin Books Canada Ltd, 10 Alcorn Avenue,
Toronto, Ontario, Canada M4V 3B2
Penguin Books India (P) Ltd, 11 Community Centre, Panchsheel Park, New Delhi – 110 017, India Penguin
Books (NZ) Ltd, Cnr Rosedale and Airborne Roads, Albany, Auckland, New Zealand Penguin Books
(South Africa) (Pty) Ltd, 24 Sturdee Avenue. Rosebank 2196, South Africa Penguin Books Ltd, Registered
Offices: 80 Strand, London WC2R 0RL, England www.penguin.com
First published in Pelican Books 1977
Reprinted in Penguin Books 1991
Second Edition published 2001
7
Copyright © Wilfrid Hodges, 1977, 2001
All rights reserved
Except in the United States of America, this book is sold subject to the condition that it shall not, by way of
trade or otherwise, be lent, re-sold, hired out, or otherwise circulated without the publisher’s prior consent
in any form of binding or cover other than that in which it is published and without a similar condition
including this condition being imposed on the subsequent purchaser ISBN:978-0-14-192684-1
Contents
Acknowledgements
Introduction
Consistency
1. Consistent Sets of Beliefs
Expressing Beliefs in Sentences
2. Beliefs and Words
3. Declarative Sentences
4. Ambiguity
When is a Sentence True?
5. Truth and References
6. Borderline Cases and Bizarre Situations
7. Misleading Statements
8. Possible Situations and Meanings
Testing for Consistency and Validity
9. Consistent Sets of Short Sentences
10. The Tableau Technique
11. Arguments
How Are Complex Sentences Built Up?
12. Phrase-classes
13. Phrase-markers
14. Scope
15. Context-free Grammars
Logical Analysis
16. Sentence-functors and Truth-functors
17. Some Basic Truth-functors
18. Special Problems with ‘→’ and ‘∧’
19. Analysis of Complex Sentences
Sentence Tableaux
20. Sentence Tableaux
21. Interpretations
Propositional Calculus
22. A Formal Language
23. Truth-tables
24. Properties of Semantic Entailment
25. Formal Tableaux
Designators and Identity
26. Designators and Predicates
27. Purely Referential Occurrences
28. Two Policies on Reference
29. Identity
Relations
30. Satisfaction
31. Binary Relations
32. Same, at least and more
33. Equivalence Relations
Quantifiers
34. Quantification
35. All and some
36. Quantifier Rules
Predicate Logic
37. Logical Scope
38. Analyses Using Identity
39. Predicate Interpretations
40. Predicate Tableaux
41. Formalization Again
Horizons of Logic
42. Likelihood
43. Intension
44. Semantics
Answers to Exercises
Tableau Rules
A Note on Notation
Further Reading
Index
Acknowledgements
Nothing in this book is original, except perhaps by mistake. It is meant as an
introduction to a well-established field of ideas; I only added a pattern and some
examples. For discussions on various drafts of parts of the book, and related
topics, I have many people to thank: chiefly David Wiggins, David K. Lewis,
Ted Honderich, my wife Helen, and six generations of undergraduates
specializing in various subjects at Bedford College. I thank Mariamne
Luddington for her cheerful illustrations.
Permission to reproduce material in this book is acknowledged to the
following sources: To Pan Books Ltd for permission to quote in section 4 from
Denys Parsons’s collection of newspaper howlers, Funny Amusing and Funny
Amazing, published in 1969.
To Harcourt Brace Jovanovich, Inc., and to Faber & Faber Ltd, for four lines
from T. S. Eliot’s ‘Burnt Norton’, from Four Quartets.
To the Oxford University Press for lines from ‘Spelt from Sibyl’s Leaves’ by
Gerard Manley Hopkins, from the fourth edition (1967) of The Poems of Gerard
Manley Hopkins, edited by W. H. Gardner and N. H. Mackenzie, published by
arrangement with the Society of Jesus.
To the Controller of Her Majesty’s Stationery Office for an extract from
paragraph 46 of Corporal Punishment, cmnd 1213, published in I960, Crown
copyright.
The extract from the Authorized Version of the Holy Bible – which is
copyright – is used with permission.
Wilfrid Hodges Bedford College March 1976
Introduction
This book was written for people who want to learn some elementary logic,
regardless of whether they are taking a course in it.
The book is written as a conversation between you (the reader) and me (the
author). To keep the conversation from being too one-sided, I put in fairly
frequent exercises. You are strongly urged to try to answer these as you reach
them. Correct answers are given at the end of the book.
If you have a phobia of symbols, you should leave out the seven sections
marked ‘+’ in the text. These cover the branch of logic known as Formal Logic;
they contain the worst of the mathematics.
English words and phrases which are being discussed are usually printed
bold; most of these are listed in the index. A word is printed in quotes ‘ ’ when
we are chiefly interested in the way it occurs in some phrase.
For the second edition I rewrote sections 41 and 44 and added a few new
exercises. I also corrected some typos and stupidities (and I thank the kind
people who pointed these out). My special thanks to Jamal Ouhalla and Trevor
Toube for helping me with linguistics and with chemical terminology
respectively.
Wilfrid Hodges
Queen Mary
University of London
August 2000