Introduction to Logic

By: PATRICK SUPPES

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Paperback | 26 January 1999

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336 Pages

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20.9 x 13.6 x 1.91

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This well-organised book was designed to introduce students to a way of thinking that encourages precision and accuracy. As the text for a course in modern logic, it familiarizes readers with a complete theory of logical inference and its specific applications to mathematics and the empirical sciences. Part I deals with formal principles of inference and definition, including a detailed attempt to relate the formal theory of inference to the standard informal proofs common throughout mathematics. An in-depth exploration of elementary intuitive set theory constitutes Part II, with separate chapters on sets, relations, and functions. The final section deals with the set-theoretical foundations of the axiomatic method and contains, in both the discussion and exercises, numerous examples of axiomatically formulated theories. Topics range from the theory of groups and the algebra of the real numbers to elementary probability theory, classical particle mechanics, and the theory of measurement of sensation intensities. Ideally suited for undergraduate courses, this text requires no background in mathematics or philosophy.

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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.

Introduction to Logic

At a Glance

Paperback

Shipping

How to return your order

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