Deductive Logic

This text provides a straightforward, lively but rigorous, introduction to truth-functional and predicate logic, complete with lucid examples and incisive exercises, for which Warren Goldfarb is renowned.

Preface

xi

Introduction

xiii

Part I: Truth-functional Logic

1

(88)

A. Analysis

3

(34)

1 Statements

3

(3)

2 Conjunction

6

(5)

3 Negation

11

(2)

4 Disjunction

13

(3)

5 Grouping

16

(3)

6 Truth-functions

19

(2)

7 Conditional

21

(7)

8 Logical Paraphrase

28

(9)

B. Logical Assessment

37

(24)

9 Schemata and Interpretation

37

(8)

10 Validity and Satisfiability

45

(2)

11 Implication

47

(6)

12 Use and Mention

53

(4)

13 Equivalence

57

(4)

C. Reflection

61

(28)

14 General Laws

61

(6)

15 Disjunctive Normal Form

67

(9)

16 Expressive Adequacy

76

(3)

17 Formal Systems

79

(10)

Part II: Monadic Quantification Theory

89

(58)

A. Analysis

91

(32)

18 Monadic Predicates and Open Sentences

91

(6)

19 The Existential Quantifier

97

(7)

20 The Universal Quantifier

104

(9)

21 Further Notes on Paraphrase

113

(6)

22 Universe of Discourse

119

(4)

B. Logical Assessment

123

(16)

23 Schemata and Interpretation

123

(6)

24 Validity, Implication, and Equivalence

129

(4)

25 Testing Monadic Schemata

133

(6)

C. Reflection

139

(8)

26 Monadic Satisfiability

139

(2)

27 General Laws

141

(6)

Part III: Polyadic Quantification Theory

147

(84)

A. Analysis

149

(18)

28 Polyadic Predicates

149

(8)

29 Paraphrase

157

(10)

B. Logical Assessment

167

(32)

30 Schemata and Interpretation

167

(8)

31 Validity, Implication, and Equivalence

175

(4)

32 Instances

179

(2)

33 Deduction

181

(7)

34 Deduction Extended

188

(11)

C. Reflection

199

(32)

35 Soundness

199

(7)

36 Other Laws

206

(3)

37 Prenex Form

209

(7)

38 Completeness

216

(9)

39 Further Consequences

225

(2)

40 Decidability

227

(4)

Part IV: Identity and Names

231

(22)

41 Identity

233

(7)

42 Inference with Names

240

(3)

43 Descriptions

243

(4)

44 Elimination of Descriptions

247

(6)

Exercises

253

(36)

Index

289

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Summary

Table of Contents

Supplemental Materials