Table Of ContentPraise for Meaning and Argument
"Meaning and Argument is especially strong on the subtleties of translating
natural language into formal language, as a necessary step in the clarification
of expression and the evaluation of arguments. The range of natural lan
guage constructions surveyed is broader and richer than in any competing
introductory logic text that I am aware of. As such, the book provides a solid
and attractive introduction to logic not only for philosophy students, but for
linguists as well."
Richard Larson, University Stony Brook
"I can thoroughly recommend Ernest Lepore's Meaning and Argument, par
ticularly for those seeking to teach or learn how to paraphrase into formal
symbolism, a much neglected aspect of logic. It contains a wealth of examples
and is informed throughout by a deep theoretical knowledge of contemporary
linguistics and philosophy of language."
Alan Weir, Queen's University Belfast
"Lepore's book is unusual for a beginning logic text in that it contains no
natural deduction proof system but rather concentrates on finding models and
countermodels by means of a semantic tableaux method. It is also unusual
in containing many translation examples that exemplify constructions that
linguists have found interesting in the last decades. In both of these ways the
book is well suited for use in educating philosophy students in the importance
of logic even when these students do not intend to go further in the study of
formal logic as a discipline."
Francis Jeffry Pelletier, University of Alberta
"Meaning and Argument is a beautiful display of both the power of first-order
logic and the complexity of natural language. The book focuses on the use of
logic to expose and remedy many difficulties with understanding a sentence's
exact meaning. Lepore's user-friendly style makes the book enjoyable for
beginning logic students, and his coverage of the details makes it useful for
advanced students and professionals. There is no logic textbook that comes
even remotely close to accomplishing what Meaning and Argument does."
Kent Johnson, University of California at Irvine
Meaning and Argument
An Introduction to
Logic Through Language
SECOND EDITION
Ernest Lepore
with Sam Cumming
(f)WILEY-BLACKWELL
A/ohn Wiley &. Sons, Ltd., Publication
This second edition first published 2009
© 2009 Ernest Lepore
Edition history: Blackwell Publishing Ltd (Ie, 2000);
Blackwell Publishing Ltd (revised, 2003)
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Library of Congress Cataloging-in-Publication Data
Lepore, Ernest, 1950-
Meaning and argument: an introduction to logic through
language I Ernest Lepore with Sam Cumming. - 2nd ed.
p. em.
Includes bibliographical references and index.
ISBN 97B-I-4051-9673-4 (pbk. : alk. paper)
1. Logic. 2. Language and logic. I. Cumming, Sam. II. Title.
BC108.L44 2009
16O-dc22
2009007419
A catalogue record for this book is available from the British Library.
Set in 10.5 on 13 point Minion by Graphicraft Limited, Hong Kong
Printed and bound in Singapore
01 2009
Contents
Preface to Second Edition xiii
Preface to Revised Edition xiv
Acknowledgments xv
Introduction 1
1 A Brief Introduction to Key Terms 5
1.1 Arguments 5
1.1.1 What is a Statement? 6
1.1.2 Premises and Conclusion 6
1.2 Putting Arguments into a Standard Format 7
1.3 Multiple Conclusions 9
1.4 Deductive Validity 10
1.5 Soundness 13
1.6 Missing Premises and Conclusions 13
2 Argument Forms and Propositional Logic 17
2.1 Formal Validity 17
2.2 Quotation Marks 19
2.3 Metalinguistic Variables 21
2.4 Non-formal Validity 23
2.5 The Need for Propositional Logic 24
2.5.1 Symbolic Notation 25
2.6 The Type/Token Distinction 26
3 Conjunction 31
3.1 Logical Conjunction 31
vi Contents
3.2 Distinguishing Deductive from Non-deductive Aspects
of Conjunction 33
3.3 Phrasal Logical Conjunctions 34
3.4 Series Decompounding 34
3.5 Using 'Respectively' 35
3.6 Symbolizing Logical Conjunctions 35
4 Negation 42
4.1 Logical Negation 42
4.2 Some Other Negative Expressions 43
4.3 A Point about Methodology 45
4.4 A Point on Ambiguity 45
4.5 Symbolizing Logical Negations 45
4.6 Ambiguity and the Need for Groupers 46
4.7 Review of Symbols 47
4.8 Using 'Without' 48
4.9 Argument Forms Continued 48
4.10 Symbolizing Logical Negations Continued 51
5 Truth Tables 56
5.1 Well-formed Formulas 56
5.2 Scope 57
5.3 Main Connective 58
5.4 Truth Tables 59
5.4.1 Truth Table Analyses of Statements 61
5.4.2 Truth Table Analyses of Arguments 64
6 Disjunction 68
6.1 Logical Disjunction 68
6.2 Disjunction and Negation 69
6.3 Iterations and Groupers 71
6.4 Inclusive versus Exclusive 'Or' 73
6.5 Symbolizing Logical Disjunctions Continued 76
7 Conditionals 79
7.1 Conditionals with Constituent Statements 79
7.2 Conditionals without Constituent Statements 80
Contents vii
7.3 Logical Conditionals 80
7.4 Symbolizing Conditionals in PL 82
7.5 Necessary and Sufficient Conditions 82
7.6 Only If 84
7.7 Unless 86
7.8 Since, Because 88
7.9 Conditionals and Groupers 89
7.10 If and Only If 90
7.11 A Revised Grammar for Well-formedness in PL 91
7.12 Summarizing Truth Tables 99
7.12.1 Validity 99
7.12.2 Contradiction, Tautology, Contingency 102
7.12.3 Consistency 104
7.12.4 Logical Equivalence 105
8 Truth Trees 109
8.1 Reviewing Validity 109
8.2 Tree Trunks and Compound and Atomic Statements 110
8.3 Truth Tree Rules 111
8.3.1 Non-branching Rules 111
8.3.2 Branching Rules 112
8.4 Strategies 114
8.5 Truth Trees and Invalidity 117
8.6 Propositional Logic and Counter-examples (Counter-models) 121
8.7 Logical Properties and Relations Revisited 123
8.7.1 Consistency 123
8.7.2 Contradiction, Tautology, Contingency 124
8.7.3 Logical Equivalence 126
9 Property Predicate Logic 129
9.1 Limits of Propositional Logic 129
9.2 Singular Terms 130
9.3 Property Predicates 132
9.4 Quantifiers 134
9.4.1 Simple Existential Quantifier Statements 135
9.4.2 Symbolizing Simple Existential Statements 135
9.4.3 Simple Universal Quantifier Statements 137
9.4.4 Negations of Existentiais 138
viii Contents
9.5 Complex Predicates 139
9.6 Well-formedness in PPL 142
9.7 Quantifiers Modifying General Terms 145
9.7.1 Existential Quantifiers and General Terms 145
9.7.2 Universal Quantifiers and General Terms 147
10 Evaluating Arguments in Property Predicate Logic 155
10.1 Quantifiers and Scope 156
10.2 The Truth Tree Method Extended 157
ID.2.1 Quantifier Exchange Rule (QE) 157
10.2.2 Universal Quantifier Rule (UQ) 158
ID.2.3 Existential Quantifier Rule (EQ) 161
10.3 Super Strategy 164
10.4 Property Predicate Logic and Counter-examples
(Counter-models) 166
10.5 PPL Logical Equivalences and Non-equivalences 168
10.6 Other Logical Properties and Relations 170
ID.6.1 Consistency 170
ID.6.2 Logical Equivalence 170
ID.6.3 Contradiction, Logical Truth, Contingency 171
11 Property Predicate Logic Refinements 172
ILl Literal Meaning 172
11.2 'Any' as an Existential 173
11.3 Restrictive Relative Clauses 175
11.4 Pronouns Revisited 176
11.4.1 Deixis and Anaphora 176
11.4.2 Quantification and Anaphora 177
11.5 Only 180
11.6 Restrictive Words in English 182
11.7 Evaluating Symbolizations of English in
Logical Notation 185
12 Relational Predicate Logic 191
12.1 Limits of Property Predicate Logic 191
12.2 Convention 1: Number 193
