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Deductive Logic
Warren Goldfarb
Walter Beverly Pearson Professor
of Modern Mathematics and Mathematical Logic
Harvard University
Hackett Publishing Company, Inc.
Indianapolis/Cambridge
CONTENTS
Preface
Introduction
xi
xiii
Part I: Truth-functional Logic
A. Analysis
§1 Statements
§2 Conjunction
§3 Negation
§4 Disjunction
§5 Grouping
§6 Truth-functions
§7 Conditional
§8 Logical Paraphrase
3
3
6
11
13
16
19
21
28
B. Logical Assessment
§9 Schemata and Interpretation
§10 Validity and Satisfiability
§11 Implication
§12 Use and Mention
§13 Equivalence
37
37
45
47
53
57
vu
CONTENTS
viii
C. Reflection
§14
§15
§16
§17
General Laws
Disjunctive Normal Form
Expressive Adequacy
Formal Systems
61
61
67
76
79
Part II: Monadic Quantification Theory
89
A. Analysis
91
§18
§19
§20
§21
§22
Monadic Predicates and Open Sentences
The Existential Quantifier
The Universal Quantifier
Further Notes on Paraphrase
Universe of Discourse
91
97
104
113
119
B. Logical Assessment
§23 Schemata and Interpretation
§24 Validity, Implication, and Equivalence
§25 Testing Monadic Schemata
123
123
129
133
C. Reflection
§26 Monadic Satisfiability
§27 General Laws
139
139
141
Part III: Polyadic Quantification Theory
147
A. Analysis
§28 Polyadic Predicates
§29 Paraphrase
149
149