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Introduction to Logicby Patrick Suppes
Synopses & ReviewsPublisher Comments:This wellorganized 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 indepth exploration of elementary intuitive set theory constitutes Part II, with separate chapters on sets, relations, and functions. The final section deals with the settheoretical 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. Book News Annotation:<:st>This is a reprint of Suppes' classic work of 1957, which is cited in
Annotation c. Book News, Inc., Portland, OR (booknews.com) Synopsis:Part I of this coherent, wellorganized text deals with formal principles of inference and definition. Part II explores elementary intuitive set theory, with separate chapters on sets, relations, and functions. Ideal for undergraduates. Synopsis: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. Synopsis:Coherent, wellorganized 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. Table of ContentsPREFACE
INTRODUCTION PART IPRINCIPLES OF INFERENCE AND DEFINITION 1. THE SENTENTIAL CONNECTIVES 1.1 Negation and Conjunction 1.2 Disjunction 1.3 Implication: Conditional Sentences 1.4 Equivalence: Biconditional Sentences 1.5 Grouping and Parentheses 1.6 Truth Tables and Tautologies 1.7 Tautological Implication and Equivalence 2. SENTENTIAL THEORY OF INFERENCE 2.1 Two Major Criteria of Inference and Sentential Interpretations 2.2 The Three Sentential Rules of Derivation 2.3 Some Useful Tautological Implications 2.4 Consistency of Premises and Indirect Proofs 3. SYMBOLIZING EVERYDAY LANGUAGE 3.1 Grammar and Logic 3.2 Terms 3.3 Predicates 3.4 Quantifiers 3.5 Bound and Free Variables 3.6 A Final Example 4. GENERAL THEORY OF INFERENCE 4.1 Inference Involving Only Universal Quantifiers 4.2 Interpretations and Validity 4.3 Restricted Inferences with Existential Quantifiers 4.4 Interchange of Quantifiers 4.5 General Inferences 4.6 Summary of Rules of Inference 5. FURTHER RULES OF INFERENCE 5.1 Logic of Identity 5.2 Theorems of Logic 5.3 Derived Rules of Inference 6. POSTSCRIPT ON USE AND MENTION 6.1 Names and Things Named 6.2 Problems of Sentential Variables 6.3 Juxtaposition of Names 7. TRANSITION FROM FORMAL TO INFORMAL PROOFS 7.1 General Considerations 7.2 Basic Number Axioms 7.3 Comparative Examples of Formal Derivations and Informal Proofs 7.4 Examples of Fallacious Informal Proofs 7.5 Further Examples of Informal Proofs 8. THEORY OF DEFINITION 8.1 Traditional Ideas 8.2 Criteria for Proper Definitions 8.3 Rules for Proper Definitions 8.4 Definitions Which are Identities 8.5 The Problem of Divison by Zero 8.6 Conditional Definitions 8.7 Five Approaches to Division by Zero 8.8 Padoa's Principle and Independence of Primitive Symbols PART IIELEMENTARY INTUITIVE SET THEORY 9. SETS 9.1 Introduction 9.2 Membership 9.3 Inclusion 9.4 The Empty Set 9.5 Operations on Sets 9.6 Domains of Individuals 9.7 Translating Everyday Language 9.8 Venn Diagrams 9.9 Elementary Principles About Operations on Sets 10. RELATIONS 10.1 Ordered Couples 10.2 Definition of Relations 10.3 Properties of Binary Relations 10.4 Equivalence Relations 10.5 Ordering Relations 10.6 Operations on Relations 11. FUNCTIONS 11.1 Definition 11.2 Operations on Functions 11.3 Church's Lambda Notation 12. SETTHEORETICAL FOUNDATIONS OF THE AXIOMATIC METHOD 12.1 Introduction 12.2 SetTheoretical Predicates and Axiomatizations of Theories 12.3 Ismorphism of Models for a Theory 12.4 Example: Profitability 12.5 Example: Mechanics INDEX What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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