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First Course in Mathematical Logic

By: PATRICK SUPPES

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Paperback | 17 June 2010

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Paperback
288 Pages

Dimensions(cm)
20.9 x 13.6 x 2.54

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In modern mathematics, both the theory of proof and the derivation of theorems from axioms bear an unquestioned importance. The necessary skills behind these methods, however, are frequently underdeveloped. This book counters that neglect with a rigorous introduction that is simple enough in presentation and context to permit relatively easy comprehension. It comprises the sentential theory of inference, inference with universal quantifiers, and applications of the theory of inference developed to the elementary theory of commutative groups. Throughout the book, the authors emphasize the pervasive and important problem of translating English sentences into logical or mathematical symbolism. Their clear and coherent style of writing ensures that this work may be used by students in a wide range of ages and abilities.

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You Can Find This Book In

Non-Fiction Mathematics Mathematical Foundation Mathematical Logic

Preface	p. v
Symbolizing Sentences	p. 1
Sentences	p. 1
Sentential Connectives	p. 2
The Form of Molecular Sentences	p. 5
Symbolizing Sentences	p. 9
The Sentential Connectives and Their Symbols	p. 12
Or	p. 14
Not	p. 16
If ... then ...	p. 19
Grouping and Parentheses	p. 21
The Negation of a Molecular Sentence	p. 29
Elimination of Some Parentheses	p. 33
Summary	p. 35
Logical Inference	p. 43
Introduction	p. 43
Rules of Inference and Proof	p. 44
Modus Ponendo Ponens	p. 44
Proofs	p. 48
Two-Step Proofs	p. 49
Double Negation	p. 52
Modus Tollendo Tollens	p. 54
More on Negation	p. 58
Adjunction and Simplification	p. 61
Disjunctions as Premises	p. 64
Modus Tollendo Ponens	p. 65
Sentential Derivation	p. 69
More About Parentheses	p. 77
Further Rules of Inference	p. 79
Law of Addition	p. 80
Law of Hypothetical Syllogism	p. 83
Law of Disjunctive Syllogism	p. 88
Law of Disjunctive Simplification	p. 92
Commutative Laws	p. 95
De Morgan's Laws	p. 98
Biconditional Sentences	p. 103
Summary of Rules of Inference	p. 107
Table of Rules of Inference	p. 108
Truth and Validity	p. 110
Introduction	p. 110
Truth Value and Truth-Functional Connectives	p. 111
Conjunction	p. 111
Negation	p. 112
Disjunction	p. 113
Conditional Sentences	p. 114
Equivalence: Biconditional Sentences	p. 117
Diagrams of Truth Value	p. 118
Invalid Conclusions	p. 122
Conditional Proof	p. 129
Consistency	p. 138
Indirect Proof	p. 146
Summary	p. 152
Truth Tables	p. 161
Truth Tables	p. 161
Tautologies	p. 169
Tautological Implication and Tautological Equivalence	p. 171
Summary	p. 176
Terms, Predicates, and Universal Quantifiers	p. 180
Introduction	p. 180
Terms	p. 183
Predicates	p. 185
Common Nouns as Predicates	p. 187
Atomic Formulas and Variables	p. 191
Universal Quantifiers	p. 197
Two Standard Forms	p. 205
Universal Specification and Laws of Identity	p. 211
One Quantifier	p. 211
Two or More Quantifiers	p. 223
Logic of Identity	p. 230
Truths of Logic	p. 236
A Simple Mathematical System: Axioms for Addition	p. 241
Commutative Axiom	p. 241
Associative Axiom	p. 245
Axiom for Zero	p. 255
Axiom for Negative Numbers	p. 258
Universal Generalization	p. 263
Theorems with Variables	p. 263
Theorems with Universal Quantifiers	p. 267
Index	p. 273
Table of Contents provided by Syndetics. All Rights Reserved.

First Course in Mathematical Logic

At a Glance

Paperback

Shipping

How to return your order

Defective items

You Can Find This Book In

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