First Course in Mathematical Logic

by Patrick Suppes, Shirley Hill

Overview

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.

Product Details

ISBN-13:	9780486422596
Publisher:	Dover Publications
Publication date:	06/17/2010
Series:	Dover Books on Mathematics
Edition description:	Reprint
Pages:	288
Product dimensions:	5.50(w) x 8.50(h) x (d)

Table of Contents

1. Symbolizing Sentences
1.1 Sentences
1.2 Sentential Connectives
1.3 The Form of Molecular Sentences
1.4 Symbolizing Sentences
1.5 The Sentential Connectives and Their Symbols—Or; Not; If . . . then . . .
1.6 Grouping and Parentheses. The Negation of a Molecular Sentence
1.7 Elimination of Some Parentheses
1.8 Summary
2. Logical Inference
2.1 Introduction
2.2 Rules of Inference and Proof
Modus Ponendo Ponens
Proofs
Two-Step Proofs
Double Negation
Modus Tollendo Tollens
More on Negation
Adjunction and Simplification
Disjunctions as Premises
Modus Tollendo Ponens
2.3 Sentential Derivation
2.4 More About Parentheses
2.5 Further Rules of Inference
Law of Addition
Law of Hypothetica Syllogism
Law of Disjunctive Syllogism
Law of Disjunctive Simplification
Commutative Laws
De Morgan's Laws
2.6 Biconditional Sentences
2.7 Summary of Rules of Inference. Table of Rules of Inference
3. Truth and Validity
3.1 Introduction
3.2 Truth Value and Truth-Functional Connectives
Conjunction
Negation
Disjunction
Conditional Sentences
Equivalence: Biconditional Sentences
3.3 Diagrams of Truth Value
3.4 Invalid Conclusions
3.5 Conditional Proof
3.6 Consistency
3.7 Indirect Proof
3.8Summary
4. Truth Tables
4.1 Truth Tables
4.2 Tautologies
4.3 Tautological Implication and Tautological Equivalence
4.4 Summary
5. Terms, Predicates, and Universal Quantifiers
5.1 Introduction
5.2 Terms
5.3 Predicates
5.4 Common Nouns as Predicates
5.5 Atomic Formulas and Variables
5.6 Universal Quantifiers
5.7 Two Standard Forms
6. Universal Specification and Laws of Identity
6.1 One Quantifier
6.2 Two or More Quantifiers
6.3 Logic of Identity
6.4 Truths of Logic
7. A Simple Mathematical System: Axioms for Addition
7.1 Commutative Axiom
7.2 Associative Axiom
7.3 Axiom for Zero
7.4 Axiom for Negative Numbers
8. Universal Generalization
8.1 Theorems with Variables
8.2 Theorems with Universal Quantifiers
Index

Editorial Reviews

Some 40 years after its original publication (Blaisdell Publishing Co., 1964), this reprint makes available Suppes' and Hill's (both, Stanford U.) text, which aims to provide an accessible and clear presentation of mathematical logic for high school and elementary college mathematics classrooms. Coverage includes the sentential theory of inference, inference with universal quantifiers, and applications of the theory of inference developed to the elementary theory of communicative groups. Annotation c. Book News, Inc., Portland, OR