Logic and Philosophy A Modern Introduction

by Tidman, Paul; Kahane, Howard

• ISBN13: 9780534561727
• ISBN10: 0534561721
• Format: Hardcover
• Copyright: 2002-11-15
• Publisher: Wadsworth Publishing

Summary

This text is designed for those who desire a comprehensive introduction to logic which is both rigorous and student friendly. Numerous, carefully graded exercise sets accompanied by crisp, clear exposition take the student from sentential logic through first order predicate logic with identity. The rules are carefully motivated and compared to other systems of rules for sentential and predicate logic. The text includes a solid range of additional material, including chapters devoted to Aristotelian logic, informal logic, inductive logic, and modal, epistemic, and deontic logics. Through all editions, the goal has been to make symbolic logic understandable for the typical student. Careful explanation and pedagogy make this the easiest text from which to learn symbolic logic.

Table of Contents

Preface	ix
Introduction	1	(16)
The Elements of an Argument	1	(4)
Deduction and Induction	5	(2)
Argument Forms	7	(1)
Truth and Validity	8	(3)
Soundness	11	(1)
Consistency	12	(1)
Consistency and Validity Compared	13	(1)
Contexts of Discovery and Justification	14	(1)
The Plan of This Book	15	(2)
Key Terms	16	(1)
Part One: Sentential Logic	17	(144)
Symbolizing in Sentential Logic	19	(30)
Atomic and Compound Sentences	19	(1)
Truth Functions	20	(1)
Conjunctions	20	(3)
Nontruth-Functional Connectives	23	(1)
Variables and Constants	24	(1)
Negations	25	(1)
Parentheses and Brackets	26	(2)
Disjunctions	28	(3)
``Not Both'' and ``Neither. . . Nor''	31	(2)
Material Conditionals	33	(2)
Material Biconditionals	35	(2)
``Only if'' and ``Unless''	37	(2)
Symbolizing Complex Sentences	39	(6)
Alternative Sentential Logic Symbols	45	(4)
Key Terms	47	(2)
Truth Tables	49	(30)
Computing Truth-Values	49	(5)
Tautologies, Contradictions, and Contingent Sentences	54	(5)
Logical Equivalences and Conditionals	59	(2)
Truth Table Test of Validity	61	(3)
Truth Table Test of Consistency	64	(1)
Validity and Consistency	65	(1)
The Short Truth Table Test for Invalidity	66	(5)
Substitution Instances	71	(5)
Truth Tables and Forms	76	(3)
Key Terms	78	(1)
Proofs	79	(36)
Argument Forms	79	(2)
Modus Ponens and Modus Tollens	81	(2)
Disjunctive Syllogism and Hypothetical Syllogism	83	(3)
Simplification and Conjunction	86	(1)
Addition and Constructive Dilemma	87	(3)
Principles of Strategy	90	(6)
Double Negation and DeMorgan's Theorem	96	(2)
Commutation, Association, and Distribution	98	(1)
Contraposition, Implication, and Exportation	99	(1)
Tautology and Equivalence	100	(4)
More Principles of Strategy	104	(3)
Common Errors in Problem Solving	107	(8)
Key Terms	114	(1)
Conditional and Indirect Proofs	115	(28)
Conditional Proofs	115	(9)
Indirect Proofs	124	(5)
Strategy Hints for Using CP and IP	129	(1)
Theorems	130	(1)
Proving Premises Inconsistent	131	(1)
Adding Valid Argument Forms	132	(2)
The Completeness and Soundness of Sentential Logic	134	(1)
Introduction and Elimination Rules	135	(4)
Material Implication and Valid Argument Forms	139	(4)
Key Terms	142	(1)
Sentential Logic Truth Trees	143	(18)
The Sentential Logic Truth Tree Method	143	(1)
The Truth Tree Rules	144	(8)
Details of Tree Construction	152	(5)
Rationale Behind the Tree Method	157	(2)
Putting Truth Trees to Work	159	(2)
Key Terms	160	(1)
Part Two: Predicate Logic	161	(148)
Predicate Logic Symbolization	163	(22)
Individuals and Properties	163	(4)
Quantifiers and Free Variables	167	(1)
Universal Quantifiers	168	(4)
Existential Quantifiers	172	(2)
Basic Predicate Logic Symbolizations	174	(1)
The Square of Opposition	175	(1)
Common Pitfalls in Symbolizing with Quantifiers	176	(3)
Expansions	179	(2)
Symbolizing ``Only'', ``None but'', and ``Unless''	181	(4)
Key Terms	184	(1)
Predicate Logic Semantics	185	(10)
Interpretations in Predicate Logic	185	(1)
Proving Invalidity	186	(3)
Using Expansions to Prove Invalidity	189	(2)
Consistency in Predicate Logic	191	(1)
Validity and Inconsistency in Predicate Logic	192	(3)
Key Terms	193	(2)
Predicate Logic Proofs	195	(24)
Proving Validity	195	(1)
The Four Quantifier Rules	196	(6)
The Five Main Restrictions	202	(4)
Precise Formulation of the Four Quantifier Rules	206	(2)
Mastering the Four Quantifier Rules	208	(5)
Quantifier Negation (QN)	213	(6)
Key Terms	217	(2)
Relational Predicate Logic	219	(32)
Relational Predicates	219	(2)
Symbolizations Containing Overlapping Quantifiers	221	(1)
Expansions and Overlapping Quantifiers	222	(4)
Places and Times	226	(1)
Symbolizing ``Someone'', ``Somewhere'', ``Sometime'', and ``So On''	227	(5)
Invalidity and Consistency in Relational Predicate Logic	232	(1)
Relational Predicate Logic Proofs	233	(7)
Strategy for Relational Predicate Logic Proofs	240	(3)
Theorems and Inconsistency in Predicate Logic	243	(3)
Predicate Logic Metatheory	246	(1)
A Simpler Set of Quantifier Rules	246	(5)
Rationale Behind the Precise Formulation of the Four Quantifier Rules	251	(16)
Cases Involving the Five Major Restrictions	251	(3)
One-to-One Correspondence Matters	254	(4)
Accidentally Bound Variables and Miscellaneous Cases	258	(5)
Predicate Logic Proofs with Flagged Constants	263	(4)
Predicate Logic Truth Trees	267	(8)
The Predicate Logic Truth Tree Method	267	(5)
Infinite Trees	272	(3)
Identity and Philosophical Problems of Symbolic Logic	275	(34)
Identity	275	(6)
Definite Descriptions	281	(2)
Properties of Relations	283	(3)
Higher-Order Logics	286	(2)
Limitations of Predicate Logic	288	(3)
Philosophical Problems	291	(8)
Logical Paradoxes	299	(10)
Key Terms	306	(3)
Part Three: Other Systems of Logic	309	(126)
Syllogistic Logic	311	(38)
Categorical Propositions	311	(3)
Existential Import	314	(1)
The Square of Opposition	315	(3)
Conversion, Obversion, Contraposition	318	(3)
Syllogistic Logic---Not Assuming Existential Import	321	(2)
Venn Diagrams	323	(3)
Syllogisms	326	(2)
Determining Syllogism Validity	328	(1)
Venn Diagram Proofs of Validity or Invalidity	328	(6)
Five Rules for Determining Validity or Invalidity	334	(3)
Syllogistics Extended	337	(3)
Enthymemes	340	(1)
Sorites	341	(2)
Technical Restrictions and Limitations	343	(6)
Key Terms	347	(2)
Informal Fallacies	349	(20)
The Nature of Fallacy	349	(2)
Fallacy Classification	351	(18)
Key Terms	367	(2)
Inductive Logic	369	(36)
A Mistaken View of Induction and Deduction	369	(2)
Kinds of Inductive Arguments	371	(10)
Cause and Effect	381	(3)
Mill's Methods	384	(7)
Inductive Probability	391	(1)
The Probability Calculus	392	(2)
Bayes' Theorem	394	(2)
Induction Is Unjustified---The Old Riddle of Induction	396	(3)
Not All Instances of Theories Confirm Them---The New Riddle of Induction	399	(6)
Key Terms	402	(3)
Axiom Systems	405	(14)
The Nature of an Axiom System	405	(1)
Interpreted and Uninterpreted Systems	406	(1)
Properties of Axiom Systems	407	(3)
Outline of an Axiom System for Sentential Logic	410	(5)
Axiom Systems for Predicate Logic	415	(1)
Other Kinds of Axiom Systems	416	(3)
Key Terms	418	(1)
Alternative Logics	419	(16)
Modal Logic	419	(1)
Strict Implication	420	(2)
Modal Axioms	422	(1)
Modal Theorems	423	(1)
Modal Paradoxes	424	(1)
A Philosophical Problem	424	(1)
Modal Predicate Logic	425	(2)
Epistemic Logic: The Logic of Knowledge and Belief	427	(2)
Epistemic Theorems	429	(2)
Deontic Logic	431	(1)
Problems with Deontic Systems	432	(3)
Key Terms	434	(1)
Answers to Even-Numbered Exercise Items	435	(64)
Bibliography	499	(4)
Special Symbols	503	(2)
Index	505