Meaning and Argument : An Introduction to Logic Through Language

by Lepore, Ernest; Cumming, Sam

• ISBN13: 9781405196734
• ISBN10: 1405196734
• Edition: 2nd
• Format: Paperback
• Copyright: 2009-08-24
• Publisher: Wiley-Blackwell

Summary

Meaning and Argument shifts introductory logic from the traditional emphasis on proofs to the symbolization of arguments. Another distinctive feature of this book is that it shows how the need for expressive power and for drawing distinctions forces formal language development. This revised edition includes expanded sections, additional exercises, and an updated bibliography. Updated and revised edition includes extended sections, additional exercises, and an updated bibliography. Distinctive approach in that this text is a philosophical, rather than mathematical introduction to logic. Concentrates on symbolization and does all the technical logic simply with truth tables and no derivations at all. Contains numerous exercises and a corresponding answer key. Extensive appendix which allows the reader to explore subjects that go beyond what is usually covered in an introductory logic course. Features accompanying website at www.meaningargument.com

Author Biography

Ernest Lepore is Director of the Center for Cognitive Science at Rutgers University. He is the author of numerous articles in philosophy of mind and is co-author (with Herman Cappelen) of Insensitive Semantics (Blackwell, 2004), co-author (with Jerry Fodor) of Holism (Blackwell, 1991). He is editor of Truth and Interpretation (Blackwell, 1989). He is co-editor (with Zenon Pylyshyn) of What is Cognitive Science? (Blackwell, 1999), and co-editor (with Robert Van Gulick) of John Searle and His Critics (Blackwell, 1992), as well as general editor of the series Philosophers and Their Critics, also published by Wiley-Blackwell.

Sam Cumming is Assistant Professor of Philosophy at University of California, Los Angeles.

Table of Contents

Preface to Second Edition	p. xiii
Preface to Revised Edition	p. xiv
Acknowledgments	p. xv
Introduction	p. 1
A Brief Introduction to Key Terms	p. 5
Arguments	p. 5
What is a Statement?	p. 6
Premises and Conclusion	p. 6
Putting Arguments into a Standard Format	p. 7
Multiple Conclusions	p. 9
Deductive Validity	p. 10
Soundness	p. 13
Missing Premises and Conclusions	p. 13
Argument Forms and Propositional Logic	p. 17
Formal Validity	p. 17
Quotation Marks	p. 19
Metalinguistic Variables	p. 21
Non-formal Validity	p. 23
The Need for Propositional Logic	p. 24
Symbolic Notation	p. 25
The Type/Token Distinction	p. 26
Conjunction	p. 31
Logical Conjunction	p. 31
Distinguishing Deductive from Non-deductive Aspects of Conjunction	p. 33
Phrasal Logical Conjunctions	p. 34
Series Decompounding	p. 34
Using 'Respectively'	p. 35
Symbolizing Logical Conjunctions	p. 35
Negation	p. 42
Logical Negation	p. 42
Some Other Negative Expressions	p. 43
A Point about Methodology	p. 45
A Point on Ambiguity	p. 45
Symbolizing Logical Negations	p. 45
Ambiguity and the Need for Groupers	p. 46
Review of Symbols	p. 47
Using 'Without'	p. 48
Argument Forms Continued	p. 48
Symbolizing Logical Negations Continued	p. 51
Truth Tables	p. 56
Well-formed Formulas	p. 56
Scope	p. 57
Main Connective	p. 58
Truth Tables	p. 59
Truth Table Analyses of Statements	p. 61
Truth Table Analyses of Arguments	p. 64
Disjunction	p. 68
Logical Disjunction	p. 68
Disjunction and Negation	p. 69
Iterations and Groupers	p. 71
Inclusive versus Exclusive 'Or'	p. 73
Symbolizing Logical Disjunctions Continued	p. 76
Conditionals	p. 79
Conditionals with Constituent Statements	p. 79
Conditionals without Constituent Statements	p. 80
Logical Conditionals	p. 80
Symbolizing Conditionals in PL	p. 82
Necessary and Sufficient Conditions	p. 82
Only If	p. 84
Unless	p. 86
Since, Because	p. 88
Conditionals and Groupers	p. 89
If and Only If	p. 90
A Revised Grammar for Well-formedness in PL	p. 91
Summarizing Truth Tables	p. 99
Validity	p. 99
Contradiction, Tautology, Contingency	p. 102
Consistency	p. 104
Logical Equivalence	p. 105
Truth Trees	p. 109
Reviewing Validity	p. 109
Tree Trunks and Compound and Atomic Statements	p. 110
Truth Tree Rules	p. 111
Non-branching Rules	p. 111
Branching Rules	p. 112
Strategies	p. 114
Truth Trees and Invalidity	p. 117
Propositional Logic and Counter-examples (Counter-models)	p. 121
Logical Properties and Relations Revisited	p. 123
Consistency	p. 123
Contradiction, Tautology, Contingency	p. 124
Logical Equivalence	p. 126
Property Predicate Logic	p. 129
Limits of Propositional Logic	p. 129
Singular Terms	p. 130
Property Predicates	p. 132
Quantifiers	p. 134
Simple Existential Quantifier Statements	p. 135
Symbolizing Simple Existential Statements	p. 135
Simple Universal Quantifier Statements	p. 137
Negations of Existentials	p. 138
Complex Predicates	p. 139
Well-formedness in PPL	p. 142
Quantifiers Modifying General Terms	p. 145
Existential Quantifiers and General Terms	p. 145
Universal Quantifiers and General Terms	p. 147
Evaluating Arguments in Property Predicate Logic	p. 155
Quantifiers and Scope	p. 156
The Truth Tree Method Extended	p. 157
Quantifier Exchange Rule (QE)	p. 157
Universal Quantifier Rule (UQ)	p. 158
Existential Quantifier Rule (EQ)	p. 161
Super Strategy	p. 164
Property Predicate Logic and Counter-examples (Counter-models)	p. 166
PPL Logical Equivalences and Non-equivalences	p. 168
Other Logical Properties and Relations	p. 170
Consistency	p. 170
Logical Equivalence	p. 170
Contradiction, Logical Truth, Contingency	p. 171
Property Predicate Logic Refinements	p. 172
Literal Meaning	p. 172
'Any' as an Existential	p. 173
Restrictive Relative Clauses	p. 175
Pronouns Revisited	p. 176
Deixis and Anaphora	p. 176
Quantification and Anaphora	p. 177
Only	p. 180
Restrictive Words in English	p. 182
Evaluating Symbolizations of English in Logical Notation	p. 185
Relational Predicate Logic	p. 191
Limits of Property Predicate Logic	p. 191
Convention 1: Number	p. 193
Convention 2: Order	p. 194
Convention 3: Active/Passive Voice	p. 195
Convention 4: Single quantifiers	p. 197
Variables	p. 199
Convention 5: Variables and Quantifiers	p. 200
Convention 6: Variables and Property Predicates	p. 200
General Comments about Variables	p. 201
Relational Predicate Logic with Nested Quantifiers	p. 207
Multiply General Statements	p. 209
Universal Quantifier Procedure	p. 212
Existential Quantifier Procedure	p. 213
Double Binding Variables	p. 213
Kicking Out	p. 216
Systematic and Analytic Procedures	p. 217
A Grammar for Well-formedness in RPL	p. 218
Nested Quantifiers, Variables, and Scope	p. 220
Order and Scope Refinements	p. 221
The Order and Scope Procedure	p. 224
Summary of the Overall Procedure for Symbolizing English Statements with Nested Quantifiers into RPL	p. 226
Extending the Truth Tree Method to RPL	p. 229
RPL Arguments without Quantifiers	p. 229
RPL Arguments without Nested Quantifiers	p. 230
RPL Arguments with Nested Quantifiers	p. 232
Choosing Singular Terms to Instantiate	p. 233
Infinite Truth Trees for RPL Arguments	p. 234
Summary of Truth Tree Strategies	p. 236
Relational Predicate Logic and Counter-Examples (Counter-models)	p. 239
Negation, Only, and Restrictive Relative Clauses	p. 244
Negation	p. 244
'Only' as a Quantifier	p. 246
Restrictive Relative Clauses	p. 249
The Quantificational Restrictive Relative Clause Procedure	p. 250
Quantifiers and Anaphora	p. 252
Repair Algorithm	p. 254
Anaphora and Restrictive Relative Clauses	p. 257
Anaphora Across Sentences	p. 262
Quantification in English	p. 265
Relational Predicate Logic with Identity	p. 268
Limits of Relational Predicate Logic	p. 268
Extending the Truth Tree Method to RPL=	p. 270
Identity-out Rule	p. 270
Identity-in Rule	p. 271
Sameness and Distinctness in English	p. 273
'Only' Again	p. 273
Words of Distinction: Except, But, Other (than), Besides, Else	p. 274
Numerical Adjectives	p. 276
At Least n	p. 276
At Most n (No More than n)	p. 279
Exactly n	p. 281
Counting Pairs	p. 283
Combinatorics (optional)	p. 283
Definite Descriptions	p. 284
The Definite Description Quantifier Procedure	p. 288
Definite Descriptions as Anaphors	p. 289
Plural Definite Descriptions	p. 289
Verbs and their Modifiers	p. 294
Prepositional Phrases	p. 294
The Event Approach	p. 296
Indirect Support of the Event Approach	p. 298
Fixing Referents and Binding Anaphoric Pronouns	p. 298
Quantification over Events	p. 299
Conversational Inferences and Events	p. 300
Methodological Reflections	p. 300
Adverbial Modification	p. 301
Problems with the Event Approach	p. 304
	p. 308
Conjunction	p. 308
Prepositional Phrases	p. 308
Conversational Inferences and Deductive Validity	p. 309
Relative Clauses	p. 311
Negation and Disjunction	p. 314
Modalities and Negation	p. 314
Conversational Inferences	p. 315
Conditionals	p. 315
Explication of the Material Conditional Truth Table	p. 315
Paradoxes of implication	p. 317
Conditionals and conversational inferences	p. 318
Paradoxes of implication revisited	p. 320
'If's and 'Then's without Conditionality	p. 320
Property Predicate Logic	p. 321
Only	p. 321
Conversational Inferences	p. 321
Existential import	p. 321
Scalar inferences	p. 323
More on Literal Meaning	p. 324
Adjectival Modification and Predication	p. 325
A Non-standard Quantifier - Most	p. 328
Relational Predicate Logic	p. 329
Passive Voice: Another Argument for Variables	p. 329
Passive voice for nested quantifier procedure	p. 332
Properties of Relations	p. 333
Symmetry, asymmetry, non-symmetry	p. 333
Transitivity, intransitivity, non-transitivity	p. 334
Total reflexivity, reflexivity, irreflexivity, and non-reflexivity	p. 334
Relational Predicate Logic with Identity	p. 337
'Only' and Existential Import	p. 337
Descriptions and Anaphora	p. 338
Plural Anaphora	p. 339
Plural definite descriptions as anaphors	p. 343
Singular indefinite antecedents of Plural pronouns	p. 344
Partitives	p. 345
Existence	p. 346
Intensionality	p. 347
Properties of the Identity Relationship	p. 348
The Superlative	p. 348
Identity and Predicative Adjectives	p. 349
Verbs and their Modifiers	p. 350
Infinitives and Gerunds	p. 350
Reference to Events	p. 352
The Logic of perceptual Verbs	p. 353
	p. 356
	p. 356
	p. 357
	p. 358
	p. 361
	p. 363
	p. 364
	p. 366
	p. 373
	p. 378
	p. 381
	p. 389
	p. 391
	p. 392
	p. 394
	p. 398
	p. 402
	p. 408
	p. 409
Logical Symbols	p. 411
Index	p. 412
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