Elements of Deductive Inference : An Introduction to Symbolic Logic

by Bessie,Joseph

• ISBN13: 9780534551216
• ISBN10: 0534551211
• Edition: CD
• Format: Hardcover
• Copyright: 1999-08-02
• Publisher: Wadsworth Publishing

Summary

The text covers elementary logic, from statement logic through relational logic with identity and function symbols. The authors acquaint students with formal techniques at a level appropriate for undergraduates, but extends far enough and deep enough into the subject that it is suitable for a brief first-year graduate course. The text covers full and brief truth tables, and presents the method of truth (consistency) trees and natural deduction for the whole of elementary logic. The text's organization allows instructors to cover just statement logic, or statement logic combined with various extensions into predicate logic: monadic logic with or without identity, or the preceding plus relational logic with or without identity and with or without function symbols. At each stage, the instructor may elect to pursue truth trees and/or natural deduction. A final chapter provides a perspective for further study and applications of logic. The text may be used with or without the accompanying software.

Table of Contents

Preface	ix
Introduction	1	(27)
Logic and Argument	1	(11)
Deduction and Induction	12	(8)
Statements, Propositions, and Context	20	(4)
Use and Mention	24	(4)
Statement Logic I: A New Language	28	(43)
Introduction	28	(3)
Truth-Functionally Simple and Truth-Functionally Compound Statements	31	(5)
Symbolizing Simple and Compound Statements	36	(17)
Symbolizing More Complex Statements and Arguments	53	(12)
Spelling It Out Formally	65	(6)
Statement Logic II: Semantic Methods	71	(84)
Introduction	71	(1)
Truth Tables	72	(14)
Formalized Semantics for SL	86	(6)
Truth-Functional Validity and Tautologousness	92	(10)
Further Semantic Properties and Relationships	102	(7)
Truth-Functional Consistency	109	(4)
The Material Conditional Revisited	113	(2)
Brief Truth Tables	115	(10)
Truth Trees	125	(13)
Using Truth Trees to Test for Other Semantic Properties	138	(9)
The Adequacy of the Tree Method	147	(8)
Statement Logic III: Syntactic Methods	155	(45)
Introduction	155	(5)
Whole-Line Inference Rules for DSL	160	(6)
Replacement Rules for DSL	166	(7)
Conditional Proof and Reductio ad Absurdum	173	(11)
Proof Strategy	184	(2)
Proving Tautologousness and Other Semantic Properties	186	(3)
The Adequacy of the Natural Deduction System DSL	189	(6)
Additional Inference Rules	195	(2)
A Second Look at the Truth Table for the Material Conditional	197	(3)
Predicate Logic I: Syntax and Semantics	200	(65)
Introduction	200	(1)
Informal Introduction to the Language of Predicate Logic	201	(6)
Syntax for L	207	(9)
Formal Semantics I: Interpretations	216	(11)
Formal Semantics II: Truth under an Interpretation	227	(12)
Symbolizing English I: Monadic Logic and Categorial Forms	239	(14)
Symbolizing English II: Polyadic Logic and Nested Quantifiers	253	(6)
Semantic Properties and Relationships for L	259	(3)
Classifying Logical Relations	262	(3)
Predicate Logic II: Semantic Methods	265	(39)
Introduction	265	(1)
Truth Trees for L	266	(14)
Reading Interpretations from Finished Open Branches	280	(5)
The Problem of Infinite Trees	285	(7)
The Adequacy of the Tree Method for Lm and L	292	(6)
Soundness, Completeness, and Undecidability	298	(6)
Predicate Logic III: Syntactic Methods	304	(24)
Introduction	304	(1)
The Rules UI, EG, and Q	304	(6)
The Rules UG, R, PA-EI, and EI	310	(13)
The Adequacy of DL	323	(5)
Extensions to L: Identity and Functions	328	(55)
Introduction	328	(1)
Syntax and Semantics for L	329	(2)
Symbolization in L=, I: `At Least', `At Most', and `Exactly'	331	(6)
Symbolization in L=, II: Identity and Polyadic Predicates	337	(7)
Truth Trees for L=	344	(11)
Natural Deduction in L=	355	(7)
Functions	362	(1)
Syntax and Semantics for L*	362	(6)
Symbolization in L*	368	(8)
Truth Trees in L*	376	(3)
Natural Deduction in L*	379	(4)
Some Applications, Limitations, and Extensions of L*	383	(43)
Introduction	383	(1)
Definite Descriptions and Ontological Commitment	384	(7)
Axiom Systems for Arithmetic	391	(5)
The Incompleteness of Arithmetic	396	(4)
Applications of Axiomatic Theories to the Philosophy of Science	400	(3)
Higher-Order Logic	403	(2)
Modal Logic	405	(7)
Strict and Counterfactual Conditionals	412	(3)
General Intensional Logic	415	(2)
Deontic Logic	417	(1)
Free Logic	418	(3)
Many-Valued Logic	421	(5)
Appendix One: Additional Reading in Logic	426	(3)
Appendix Two: Solutions to Selected Exercises	429	(44)
Index	473