Introduction to Logic

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

ISBN: 9780486406879 | 0486406873
Cover: Paperback
Copyright: 1/26/1999

Rent

(Recommended)

$17.71

Term

Due

Price

Semester

Dec 13

$18.63

Quarter

Aug 16

$17.71

Short Term

Jul 5

$16.77

*This item is part of an exclusive publisher rental program and requires an additional convenience fee. This fee will be reflected in the shopping cart.
Buy New

In Stock Usually Ships in 24-48 Hours

$20.96
eBook

Available Instantly

Online: 1825 Days

Downloadable: Lifetime Access

$21.32

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.

Preface	p. iii
Introduction	p. xi
Principles of Inference and Definition
The Sentential Connectives	p. 3
Negation and Conjunction	p. 3
Disjunction	p. 5
Implication: Conditional Sentences	p. 6
Equivalence: Biconditional Sentences	p. 9
Grouping and Parentheses	p. 10
Truth Tables and Tautologies	p. 11
Tautological Implication and Equivalence	p. 15
Sentential Theory of Inference	p. 20
Two Major Criteria of Inference and Sentential Interpretations	p. 20
The Three Sentential Rules of Derivation	p. 25
Some Useful Tautological Implications	p. 32
Consistency of Premises and Indirect Proofs	p. 36
Symbolizing Everyday Language	p. 43
Grammar and Logic	p. 43
Terms	p. 43
Predicates	p. 45
Quantifiers	p. 47
Bound and Free Variables	p. 52
A Final Example	p. 55
General Theory of Inference	p. 58
Inference Involving Only Universal Quantifiers	p. 58
Interpretations and Validity	p. 64
Restricted Inferences with Existential Quantifiers	p. 80
Interchange of Quantifiers	p. 87
General Inferences	p. 89
Summary of Rules of Inference	p. 98
Further Rules of Inference	p. 101
Logic of Identity	p. 101
Theorems of Logic	p. 108
Derived Rules of Inference	p. 113
Postscript on Use and Mention	p. 121
Names and Things Named	p. 121
Problems of Sentential Variables	p. 123
Juxtaposition of Names	p. 125
Transition From Formal to Informal Proofs	p. 128
General Considerations	p. 128
Basic Number Axioms	p. 129
Comparative Examples of Formal Derivations and Informal Proofs	p. 131
Examples of Fallacious Informal Proofs	p. 138
Further Examples of Informal Proofs	p. 142
Theory of Definition	p. 151
Traditional Ideas	p. 151
Criteria for Proper Definitions	p. 152
Rules for Proper Definitions	p. 155
Definitions Which are Identities	p. 161
The Problem of Division by Zero	p. 163
Conditional Definitions	p. 165
Five Approaches to Division by Zero	p. 166
Padoa's Principle and Independence of Primitive Symbols	p. 169
Elementary Intuitive Set Theory
Sets	p. 177
Introduction	p. 177
Membership	p. 177
Inclusion	p. 181
The Empty Set	p. 184
Operations on Sets	p. 184
Domains of Individuals	p. 187
Translating Everyday Language	p. 189
Venn Diagrams	p. 195
Elementary Principles About Operations on Sets	p. 202
Relations	p. 208
Ordered Couples	p. 208
Definition of Relations	p. 210
Properties of Binary Relations	p. 213
Equivalence Relations	p. 218
Ordering Relations	p. 220
Operations on Relations	p. 225
Functions	p. 229
Definition	p. 229
Operations on Functions	p. 234
Church's Lambda Notation	p. 242
Set-Theoretical Foundations of the Axiomatic Method	p. 246
Introduction	p. 246
Set-Theoretical Predicates and Axiomatizations of Theories	p. 249
Isomorphism of Models for a Theory	p. 260
Example: Probability	p. 274
Example: Mechanics	p. 291
Index	p. 307
Table of Contents provided by Syndetics. All Rights Reserved.

Please wait while the item is added to your bag...

FREE SHIPPING

Amazon no longer offers textbook rentals. We do!

Introduction to Logic

Summary

Table of Contents

Supplemental Materials