Introduction to Logic

ISBN-10: 0486406873

ISBN-13: 9780486406879

Edition: Unabridged 

Authors: Patrick Suppes

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Description:

Coherent, well-organized text familiarizes readers with complete theory of logical inference and its applications to math and the empirical sciences. Part I deals with formal principles of inference and definition. Part II explores elementary intuitive set theory, with separate chapters on sets, relations, and functions. Last section introduces numerous examples of axiomatically formulated theories.
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Book details

List price: $19.95
Publisher: Dover Publications, Incorporated
Publication date: 1/28/1999
Binding: Paperback
Pages: 336
Size: 5.50" wide x 8.75" long x 0.75" tall
Weight: 0.748
Language: English

Preface
Introduction
Principles of Inference and Definition
The Sentential Connectives
Negation and Conjunction
Disjunction
Implication: Conditional Sentences
Equivalence: Biconditional Sentences
Grouping and Parentheses
Truth Tables and Tautologies
Tautological Implication and Equivalence
Sentential Theory of Inference
Two Major Criteria of Inference and Sentential Interpretations
The Three Sentential Rules of Derivation
Some Useful Tautological Implications
Consistency of Premises and Indirect Proofs
Symbolizing Everyday Language
Grammar and Logic
Terms
Predicates
Quantifiers
Bound and Free Variables
A Final Example
General Theory of Inference
Inference Involving Only Universal Quantifiers
Interpretations and Validity
Restricted Inferences with Existential Quantifiers
Interchange of Quantifiers
General Inferences
Summary of Rules of Inference
Further Rules of Inference
Logic of Identity
Theorems of Logic
Derived Rules of Inference
Postscript on Use and Mention
Names and Things Named
Problems of Sentential Variables
Juxtaposition of Names
Transition From Formal to Informal Proofs
General Considerations
Basic Number Axioms
Comparative Examples of Formal Derivations and Informal Proofs
Examples of Fallacious Informal Proofs
Further Examples of Informal Proofs
Theory of Definition
Traditional Ideas
Criteria for Proper Definitions
Rules for Proper Definitions
Definitions Which are Identities
The Problem of Division by Zero
Conditional Definitions
Five Approaches to Division by Zero
Padoa's Principle and Independence of Primitive Symbols
Elementary Intuitive Set Theory
Sets
Introduction
Membership
Inclusion
The Empty Set
Operations on Sets
Domains of Individuals
Translating Everyday Language
Venn Diagrams
Elementary Principles About Operations on Sets
Relations
Ordered Couples
Definition of Relations
Properties of Binary Relations
Equivalence Relations
Ordering Relations
Operations on Relations
Functions
Definition
Operations on Functions
Church's Lambda Notation
Set-Theoretical Foundations of the Axiomatic Method
Introduction
Set-Theoretical Predicates and Axiomatizations of Theories
Isomorphism of Models for a Theory
Example: Probability
Example: Mechanics
Index
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