Logic and Philosophy A Modern Introduction

by Hausman, Alan; Kahane, Howard; Tidman, Paul

• ISBN13: 9780495128441
• ISBN10: 0495128449
• Edition: 10th
• Format: Paperback
• Copyright: 2006-06-05
• Publisher: Wadsworth Publishing

Summary

This text is designed for those instructors who desire a comprehensive introduction to formal logic that is both rigorous and accessible to students encountering the subject for the first time. Numerous, carefully crafted exercise sets accompanied by clear, crisp exposition give students a firm grasp of basic concepts and take the student from sentential logic through first-order predicate logic, the theory of descriptions, and identity. As the title suggests, this is a book devoted not merely to logic; students will encounter an extraordinary amount of philosophy as well. Upon completing the first two parts of the text, a student will be well prepared for advanced courses in analytic philosophy. The last part deals with supplemental matters-informal fallacies, modal logic, and inductive logic, among others.

Table of Contents

Preface	xi
Introduction	1	(18)
The Elements of an Argument	1	(4)
Deduction and Induction	5	(2)
Deductive Argument Forms	7	(1)
Truth and Validity	8	(3)
Soundness	11	(1)
Consistency	12	(1)
Consistency and Validity Compared	13	(2)
Contexts of Discovery and Justification	15	(1)
The Plan of This Book	15	(4)
Key Terms	16	(3)
Part One: Sentential Logic	19	(144)
Symbolizing in Sentential Logic	21	(34)
Atomic and Compound Sentences	22	(1)
Truth-Functions	23	(1)
Conjunctions	23	(4)
Non--Truth-Functional Connectives	27	(1)
Variables and Constants	27	(2)
Negations	29	(1)
Parentheses and Brackets	30	(1)
Use and Mention	31	(1)
Disjunctions	32	(3)
``Not Both'' and ``Neither . . . Nor''	35	(2)
Material Conditionals	37	(3)
Material Biconditionals	40	(2)
``Only If'' and ``Unless''	42	(1)
Symbolizing Complex Sentences	43	(7)
Alternative Sentential Logic Symbols	50	(5)
Key Terms	52	(3)
Truth Tables	55	(33)
Computing Truth-Values	55	(5)
Logical Form	60	(5)
Tautologies, Contradictions, and Contingent Sentences	65	(6)
Logical Equivalences	71	(1)
Truth Table Test of Validity	72	(3)
Truth Table Test of Consistency	75	(1)
Validity and Consistency	76	(2)
The Short Truth Table Test for Invalidity	78	(4)
The Short Truth Table Test for Consistency	82	(1)
A Method of Justification for the Truth Tables	83	(5)
Key Terms	87	(1)
Proofs	88	(37)
Argument Forms	88	(2)
The Method of Proof: Modus Ponens and Modus Tollens	90	(3)
Disjunctive Syllogism and Hypothetical Syllogism	93	(2)
Simplification and Conjunction	95	(1)
Addition and Constructive Dilemma	96	(3)
Principles of Strategy	99	(6)
Double Negation and DeMorgan's Theorem	105	(3)
Commutation, Association, and Distribution	108	(1)
Contraposition, Implication, and Exportation	109	(1)
Tautology and Equivalence	109	(4)
More Principles of Strategy	113	(4)
Common Errors in Problem Solving	117	(8)
Key Terms	124	(1)
Conditional and Indirect Proofs	125	(25)
Conditional Proofs	125	(9)
Indirect Proofs	134	(5)
Strategy Hints for Using CP and IP	139	(1)
Zero-Premise Deductions	140	(1)
Proving Premises Inconsistent	141	(2)
Adding Valid Argument Forms	143	(1)
The Completeness and Soundness of Sentential Logic	144	(1)
Introduction and Elimination Rules	145	(5)
Key Terms	149	(1)
Sentential Logic Truth Trees	150	(13)
The Sentential Logic Truth Tree Method	150	(1)
The Truth Tree Rules	151	(2)
Details of Tree Construction	153	(6)
Normal Forms and Trees	159	(1)
Constructing Tree Rules for Any Function	160	(3)
Key Terms	162	(1)
Part Two: Predicate Logic	163	(192)
Predicate Logic Symbolization	165	(24)
Individuals and Properties	165	(4)
Quantifiers and Free Variables	169	(1)
Universal Quantifiers	170	(5)
Existential Quantifiers	175	(1)
Basic Predicate Logic Symbolizations	176	(2)
The Square of Opposition	178	(1)
Common Pitfalls in Symbolizing with Quantifiers	178	(3)
Expansions	181	(3)
Symbolizing ``Only,'' ``None but,'' and ``Unless''	184	(5)
Key Terms	187	(2)
Predicate Logic Semantics	189	(9)
Interpretations in Predicate Logic	189	(2)
Proving Invalidity	191	(3)
Using Expansions to Prove Invalidity	194	(1)
Consistency in Predicate Logic	195	(1)
Validity and Inconsistency in Predicate Logic	196	(2)
Key Terms	197	(1)
Predicate Logic Proofs	198	(24)
Proving Validity	198	(1)
The Four Quantifier Rules	199	(6)
The Five Main Restrictions	205	(5)
Precise Formulation of the Four Quantifier Rules	210	(2)
Mastering the Four Quantifier Rules	212	(4)
Quantifier Negation (QN)	216	(6)
Key Terms	221	(1)
Relational Predicate Logic	222	(32)
Relational Predicates	222	(3)
Symbolizations Containing Overlapping Quantifiers	225	(1)
Expansions and Overlapping Quantifiers	225	(5)
Places and Times	230	(1)
Symbolizing ``Someone,'' ``Somewhere,'' ``Sometime,'' and So On	231	(5)
Invalidity and Consistency in Relational Predicate Logic	236	(1)
Relational Predicate Logic Proofs	237	(7)
Strategy for Relational Predicate Logic Proofs	244	(3)
Theorems and Inconsistency in Predicate Logic	247	(3)
Predicate Logic Metatheory	250	(1)
A Simpler Set of Quantifier Rules	250	(4)
Rationale Behind the Precise Formulation of the Four Quantifier Rules	254	(15)
Cases Involving the Five Major Restrictions	254	(3)
One-to-One Correspondence Matters	257	(4)
Accidentally Bound Variables and Miscellaneous Cases	261	(4)
Predicate Logic Proofs with Flagged Constants	265	(4)
Predicate Logic Truth Trees	269	(14)
Introductory Remarks	269	(1)
General Features of the Method	270	(1)
Specific Examples of the Method	270	(5)
Some Advantages of the Trees	275	(1)
Example of an Invalid Argument with at Least One Open Path	275	(1)
Metatheoretic Results	276	(4)
Strategy and Accounting	280	(3)
Key Terms	282	(1)
Identity and Philosophical Problems of Symbolic Logic	283	(33)
Identity	283	(6)
Definite Descriptions	289	(2)
Properties of Relations	291	(3)
Higher-Order Logics	294	(2)
Limitations of Predicate Logic	296	(4)
Philosophical Problems	300	(7)
Logical Paradoxes	307	(9)
Key Terms	314	(2)
Syllogistic Logic	316	(39)
Categorical Propositions	316	(3)
Existential Import	319	(1)
The Square of Opposition	320	(3)
Conversion, Obversion, Contraposition	323	(3)
Syllogistic Logic---Not Assuming Existential Import	326	(3)
Venn Diagrams	329	(2)
Syllogisms	331	(2)
Determining Syllogism Validity	333	(1)
Venn Diagram Proofs of Validity or Invalidity	334	(5)
Five Rules for Determining Validity or Invalidity	339	(3)
Syllogistics Extended	342	(3)
Enthymemes	345	(1)
Sorites	346	(2)
Technical Restrictions and Limitations; Modern Logic and Syllogistic Logic Compared	348	(7)
Key Terms	352	(3)
Part Three: Other Systems of Logic	355	(86)
Informal Fallacies	357	(19)
The Nature of Fallacy	357	(2)
Fallacy Classification	359	(17)
Key Terms	375	(1)
Inductive Logic	376	(35)
A Mistaken View of Induction and Deduction	376	(2)
Kinds of Inductive Arguments	378	(10)
Cause and Effect	388	(3)
Mill's Methods	391	(7)
Inductive Probability	398	(1)
The Probability Calculus	399	(2)
Bayes' Theorem	401	(2)
Induction Is Unjustified---The Old Riddle of Induction	403	(3)
Not All Instances of Theories Confirm Them---The New Riddle of Induction	406	(5)
Key Terms	409	(2)
Axiom Systems	411	(14)
The Nature of an Axiom System	411	(1)
Interpreted and Uninterpreted Systems	412	(1)
Properties of Axiom Systems	413	(3)
Outline of an Axiom System for Sentential Logic	416	(5)
Axiom Systems for Predicate Logic	421	(1)
Other Kinds of Axiom Systems	422	(1)
Objections to Axiom Systems	423	(2)
Key Terms	423	(2)
Alternative Logics	425	(16)
Modal Logic	425	(1)
Strict Implication	426	(2)
Modal Axioms	428	(1)
Modal Theorems	429	(1)
Modal Paradoxes	430	(1)
A Philosophical Problem	430	(1)
Modal Predicate Logic	431	(2)
Epistemic Logic: The Logic of Knowledge and Belief	433	(2)
Epistemic Theorems	435	(2)
Deontic Logic	437	(1)
Problems with Deontic Systems	438	(3)
Key Terms	440	(1)
Answers to Even-Numbered Exercise Items	441	(64)
Bibliography	505	(4)
Special Symbols	509	(2)
Index	511