The Many Worlds of Logic

by Herrick, Paul William; Herrick, Paul

• ISBN13: 9780155071650
• ISBN10: 0155071653
• Edition: 2nd
• Format: Hardcover
• Copyright: 1999-07-01
• Publisher: Oxford

Summary

With clear explanations and many examples drawn right out of day-to-day life, Paul Herrick untangles the complexities of logical theory in The Many Worlds of Logic. This new edition adds new chapters on informal logic and critical thinking. It also breaks out longer chapters from the previousedition into shorter, more focused chapters. Herrick has added many new explanations and examples; in each chapter, he covers the fundamentals completely before moving on to more challenging areas.Features* Difficult terms are highlighted and explained carefully * End-of-chapter glossaries help students remember important terms * Hundreds of examples demonstrate the application of concepts * Hundreds of exercises help students learn logic by actually doing it * Truth-trees in an appendix help students go beyond the basics

Table of Contents

To the Instructor	v	(2)
To the Student	vii	(2)
Acknowledgments	ix
CHAPTER 1 FUNDAMENTALS	1	(28)
Recognizing Arguments	2	(1)
Some Typical Conclusion Indicators	3	(1)
Some Typical Premise Indicators	3	(2)
Distinguishing Sentences and Statements	5	(1)
Two General Categories of Argument: Deductive and Inductive Arguments	6	(2)
Deductive and Inductive Indicator Words	8	(1)
Evaluating Inductive Arguments: The Strong, the Weak, and the Inductively Sound	9	(2)
Evaluating Deductive Arguments: The Valid, the Invalid, and the Deductively Sound	11	(2)
Deciding Whether an Argument is Valid or Invalid	13	(7)
Consistency and Inconsistency	20	(1)
Implication	21	(1)
Logical Equivalence	21	(1)
Necessity	22	(1)
Ideals	23	(1)
Appendix: Some Logical Puzzles	24	(1)
Glossary	25	(4)
PART I TRUTH-FUNCTIONAL LOGIC	29	(192)
CHAPTER 2 INTRODUCTORY TRUTH-FUNCTIONAL LOGIC	31	(16)
Simple and Compound Sentences, Sentence Operators, and the Conjunction	32	(3)
Negation	35	(2)
Disjunction	37	(2)
Truth-Functions and Truth-Functional Compound Sentences	39	(1)
Conditional Sentences	40	(2)
Biconditional Sentences	42	(4)
Glossary	46	(1)
CHAPTER 3 TRANSLATING ENGLISH INTO LOGICAL SYMBOLS	47	(19)
Symbolizing Sentences Containing More than One Operator	48	(3)
Throwing the Tilde into the Mix	51	(1)
From And to Or and Back Again-With a Few Nots Thrown In	52	(3)
Some General Hints on Symbolizing	55	(2)
Translating Conditionals and Biconditionals	57	(2)
Symbolizing Necessary and Sufficient Conditions	59	(6)
Glossary	65	(1)
CHAPTER 4 OUR NEW LANGUAGE GETS A NAME AND A FORMAL SYNTAX	66	(11)
The Language TL	66	(3)
How to Calculate the Truth-Value of the Whole from the Values of the Parts	69	(5)
Glossary	74	(3)
CHAPTER 5 TRUTH-TABLE ANALYSIS	77	(24)
Constructing a Truth-Table for a Formula	78	(1)
Eight-Row Tables	79	(2)
How to Make Your Own Tautology Detector Using Just Paper and Pencil	81	(1)
How to Make an Inexpensive Contradiction Detector For Home or Office	82	(1)
The Contingency Detector: Don't Leave Home without It	83	(2)
Testing an Argument for Validity	85	(7)
Showing an Argument Invalid with a Partial Truth-Table	92	(5)
Testing a Pair of Sentences For Equivalences	97	(2)
Glossary	99	(2)
CHAPTER 6 THE CONCEPT OF LOGICAL FORM	101	(17)
Sentence Forms	101	(4)
Argument Forms	105	(1)
The Disjunctive Syllogism Form	105	(1)
The Modus Ponens Form	106	(1)
The Modus Tollens Form	107	(1)
The Hypothetical Syllogism Form	108	(1)
Valid Argument Forms	108	(2)
Invalid Argument Forms	110	(2)
Concluding Comments	112	(2)
Appendix: Contradictory and Tautological Sentence Forms	114	(2)
Glossary	116	(2)
CHAPTER 7 TRUTH-FUNCTIONAL NATURAL DEDUCTION	118	(22)
The Disjunctive Syllogism Rule	119	(2)
The Modus Ponens Rule	121	(1)
The Modus Tollens Rule	122	(2)
The Hypothetical Syllogism Rule	124	(1)
Proving that a Conclusion Validly Follows	125	(3)
The System TD	128	(1)
Proofs	128	(11)
Glossary	139	(1)
CHAPTER 8 FOUR MORE INFERENCE RULES	140	(20)
The Simplification Rule	140	(1)
The Conjunction Rule	141	(2)
The Addition Rule	143	(1)
The Constructive Dilemma Rule	144	(2)
Some Unsolicited Advice on Learning to Construct Proofs	146	(1)
Proof Strategies	147	(4)
Some Additional Suggestions Concerning Strategy	151	(6)
Appendix: Some Common Deduction Errors	157	(3)
CHAPTER 9 INDIRECT PROOFS AND CONDITIONAL PROOFS	160	(23)
The Indirect Proof Rule	162	(6)
The Conditional Proof Rule	168	(7)
Nested Proofs	175	(3)
Proving Sentences Tautological	178	(3)
The Law of Noncontradiction	181	(1)
Glossary	182	(1)
CHAPTER 10 REPLACEMENT RULES	183	(27)
The Commutative Rule	184	(1)
The Associative Rule	185	(1)
The Double Negation Rule	186	(1)
DeMorgan's Rule	187	(3)
The Distribution Rule	190	(7)
Five More Replacement Rules	197	(1)
The Transposition Rule	197	(1)
The Implication Rule	197	(1)
The Exportation Rule	198	(1)
The Tautology Rule	199	(1)
The Equivalence Rule	200	(1)
Are Replacement Rules Worth the Bother?	201	(8)
Glossary	209	(1)
CHAPTER 11 INDIRECT AND CONDITIONAL PROOFS WITH REPLACEMENT RULES	210	(11)
Indirect Proofs with Replacement Rules	210	(4)
Conditional Proof with Replacement Rules	214	(2)
Proving Tautologies	216	(3)
Glossary	219	(2)
PART II TWO INFORMAL TOPICS	221	(54)
CHAPTER 12 DEFINITION	223	(19)
The Purposes of Definition	224	(2)
Five Types of Definition	226	(4)
Two Types of Meaning	230	(3)
Constructing a Definition: Techniques	233	(4)
Rules For Intensional Definitions	237	(2)
Glossary	239	(3)
CHAPTER 13 INFORMAL FALLACIES	242	(33)
Fallacies of No Evidence	243	(12)
Fallacies of Little Evidence	255	(8)
Fallacies of Language	263	(7)
Glossary	270	(1)
A Summary of the Fallacies	271	(4)
PART III ARISTOTELIAN CATEGORICAL LOGIC	275	(60)
CHAPTER 14 THE LOGIC OF CATEGORICAL STATEMENTS	277	(26)
Categorical Sentences	278	(2)
Quality and Quantity	280	(1)
The Traditional Square of Opposition	281	(6)
Translating English Sentences into Standard Categorical Forms	287	(7)
Equivalence Rules for Aristotelian Logic	294	(3)
Dropping the Assumption of Existential Import	297	(2)
The Modern Square of Opposition	299	(1)
Glossary	300	(3)
CHAPTER 15 CATEGORICAL SYLLOGISMS	303	(32)
Logical Form	303	(3)
Venn Diagrams	306	(2)
Testing a Categorical Syllogism for Validity with Venn Diagrams	308	(2)
Diagramming Aristotelian Categorical Syllogisms	310	(5)
Diagramming from the Boolean Standpoint	315	(5)
The Sorites	320	(2)
Testing a Sorites with Venn Diagrams	322	(3)
Enthememes	325	(2)
Refutation by Logical Analogy	327	(2)
Appendix: Rules for Evaluating Categorical Syllogisms	329	(6)
PART IV MODERN QUANTIFICATIONAL LOGIC	335	(106)
CHAPTER 16 QUANTIFICATIONAL LOGIC I: THE LANGUAGE QL	337	(28)
Two Types of Sentences	338	(4)
General Sentences	342	(6)
A Syntax for our New Language	348	(1)
The Vocabulary of QL	348	(1)
Symbolizing General Sencences	349	(1)
Categorical Sentences	349	(5)
The Old "Quantifier Switch" Trick	354	(2)
Switching Quantifiers on Categoricals	356	(2)
Symbolizing Complicated General Sentences	358	(2)
Denying Existence	360	(1)
The Only Way to Go	360	(2)
What is a Cat-Dog?	362	(2)
Glossary	364	(1)
CHAPTER 17 THE LANGUAGE OF QUANTIFICATIONAL LOGIC II: RELATIONS	365	(21)
Sentences with a Quantifier-Dyadic Predicate Combo	366	(1)
Any and Every	367	(1)
Reflexive Sentences	368	(1)
Sentences with Overlapping Quantifiers	369	(3)
"What Are You Talking About?" The Universe of Discourse	372	(2)
Dean Martin, Universal Love, and a Summary of Logic Relations	374	(2)
To Be or Not To Be: The Logic of Identity	376	(2)
The Identity Sign	378	(4)
Appendix: Properties of Relations	382	(3)
Glossary	385	(1)
CHAPTER 18 PROOFS WITH MONADIC PRRDICATES	386	(20)
The Universal Instantiation Rule	386	(3)
Existential Generalization	389	(1)
Existential Instantiation	390	(3)
Memories of Geometry Class: Universal Generalization	393	(7)
One New Replacement Rule: Quantifier Exchange	400	(4)
Naming Our System	404	(1)
Glossary	405	(1)
CHAPTER 19 INTERPRETATIONS, INVALIDITY, AND SEMANTICS	406	(12)
Interpretations of Multiply Quantified Sentences	408	(1)
Using Interpretations to Show Invalidity	409	(5)
Semantics	414	(1)
The Monadic Predicate Test	414	(3)
Glossary	417	(1)
CHAPTER 20 CONDITIONAL AND INDIRECT QUANTIFIER PROOFS	418	(9)
Adding Truth-Functional Replacement Rules to the Mix	420	(3)
Putting QD on a Diet: A Reduced Set of Quantifier Rules	423	(1)
Proving Logical Truths	424	(3)
CHAPTER 21 PROOFS WITH OVERLAPPING QUANTIFIERS	427	(6)
Properties of Relations	430	(3)
CHAPTER 22 PROOFS WITH IDENTITY	433	(8)
Properties of the Identity Relation	436	(3)
Glossary	439	(2)
PART V MODAL LOGIC	441	(68)
CHAPTER 23 INTRODUCTORY MODAL LOGIC	443	(35)
To Shave or Not to Shave: That Is the Question	443	(1)
Five Modal Properties	444	(1)
Possible Truths, Possible Falsehoods, Contingencies	445	(1)
Necessary Truths	446	(2)
Necessary Falsehoods	448	(1)
Putting Statements into Symbols	448	(7)
Translating English Sentences into Modal Symbols	455	(2)
A Name and Syntax for our Modal Language	457	(1)
The Vocabulary for ML	457	(1)
The Grammar for ML	457	(2)
Linking Modal Operators	459	(1)
"It Ain't Necessarily So," Or, Trading a Diamond for a Box and a Box for a Diamond	460	(2)
Modal Operators Need Scope, Too	462	(2)
Modal Relations	464	(5)
Scopes of the Dyadic Modal Operators	469	(1)
Symbolizing with Dyadic Operators	470	(2)
Modal Operators Are Not Truth-Functional	472	(1)
Appendix: There's Nothing New under the Sun	473	(3)
Glossary	476	(2)
CHAPTER 24 MODAL LOGIC: METHODS OF PROOF	478	(31)
Five Modal Principles	478	(2)
Six Inference Rules	480	(4)
The Possibility to Necessity Rule	484	(3)
The Necessitation Rule	487	(4)
Four Modal Replacement Rules	491	(3)
Validity in S5	494	(5)
Proving Theorems of S5	499	(1)
Another Inference Rule: The Tautology Necessitation Rule	500	(2)
Appendix 1: Putting an S5 Formula on a Diet: S5 Reduction	502	(3)
Appendix 2: The Modal Fallacy	505	(3)
Glossary	508	(1)
PART VI INDUCTION	509	(60)
CHAPTER 25 INDUCTIVE REASONING	511	(24)
Analogical Reasoning	512	(1)
Evaluating Analogical Arguments	513	(5)
Analogies as Models	518	(4)
Enumerative Induction	522	(3)
Statistical Inductive Generalization	525	(6)
Inference to the Best Explanation	531	(1)
What Makes One Explanation Better than Another?	532	(2)
Glossary	534	(1)
CHAPTER 26 SCIENTIFIC REASONING	535	(34)
Scientific Reasoning	536	(1)
Comments on the Steps	536	(2)
Confirming and Disconfirming Scientific Hypotheses	538	(3)
The Confirmation of a Scientific Hypothesis	541	(3)
The Disconfirmation of a Scientific Hypothesis	544	(3)
The Fact of the Cross	547	(1)
What Makes One Hypothesis Better than Another?	548	(1)
Case Studies	549	(4)
Cause and Effect and Mill's Methods	553	(1)
Cause and Effect	554	(1)
Mill's Method of Agreement	555	(3)
Mill's Method of Difference	558	(2)
The Joint Method of Agreement and Difference	560	(1)
Mill's Method of Residues	561	(1)
Mill's Method of Concomitant Variation	561	(5)
Glossary	566	(3)
APPENDIX 1 TRUTH-TREES	569	(23)
APPENDIX 2 TRUTH	592	(7)
Answers to Selected Exercises	599	(70)
Index	669