Logic For Dummies

A straightforward guide to logic concepts Logic concepts are more mainstream than you may realize. There's logic every place you look and in almost everything you do, from deciding which shirt to buy to asking your boss for a raise, and even to watching television, where themes of such shows as CSI and Numbers incorporate a variety of logistical studies. Logic For Dummies explains a vast array of logical concepts and processes in easy-to-understand language that make everything clear to you, whether you're a college student of a student of life. You'll find out about: Formal Logic Syllogisms Constructing proofs and refutations Propositional and predicate logic Modal and fuzzy logic Symbolic logic Deductive and inductive reasoning L ogic For Dummies tracks an introductory logic course at the college level. Concrete, real-world examples help you understand each concept you encounter, while fully worked out proofs and fun logic problems encourage you students to apply what you've learned. Logic For Dummies 3 About the Author 5 Dedication 7 Author’s Acknowledgments 7 Contents at a Glance 9 Table of Contents 11 Introduction 21 About This Book 21 Conventions Used in This Book 22 What You’re Not to Read 23 Foolish Assumptions 23 How This Book Is Organized 23 Icons Used in This Book 26 Where to Go from Here 26 Part I: Overview of Logic 27 Chapter 1: What Is This Thing Called Logic? 29 Getting a Logical Perspective 29 Building Logical Arguments 33 Making Logical Conclusions Simple with the Laws of Thought 35 Combining Logic and Math 37 Chapter 2: Logical Developments from Aristotle to the Computer 39 Classical Logic — from Aristotle to the Enlightenment 40 Modern Logic — the 17th, 18th, and 19th Centuries 45 Logic in the 20th Century and Beyond 49 Chapter 3: Just for the Sake of Argument 53 Defining Logic 53 Studying Examples of Arguments 57 What Logic Isn’t 59 Whose Logic Is It, Anyway? 66 Part II: Formal Sentential Logic (SL) 69 Chapter 4: Formal Affairs 71 Observing the Formalities of Sentential Logic 71 The Five SL Operators 73 How SL Is Like Simple Arithmetic 83 Lost in Translation 85 Chapter 5: The Value of Evaluation 93 Value Is the Bottom Line 94 Making a Statement 97 Eight Forms of SL Statements 102 Evaluation Revisited 103 Chapter 6: Turning the Tables: Evaluating Statements with Truth Tables 105 Putting It All on the Table: The Joy of Brute Force 106 Baby’s First Truth Table 107 Putting Truth Tables to Work 113 Putting the Pieces Together 120 Chapter 7: Taking the Easy Way Out: Creating Quick Tables 127 Dumping the Truth Table for a New Friend: The Quick Table 128 Outlining the Quick Table Process 129 Planning Your Strategy 133 Working Smarter (Not Harder) with Quick Tables 136 Chapter 8: Truth Grows on Trees 145 Understanding How Truth Trees Work 145 Showing Consistency or Inconsistency 148 Testing for Validity or Invalidity 151 Separating Tautologies, Contradictions, and Contingent Statements 154 Checking for Semantic Equivalence or Inequivalence 160 Part III: Proofs, Syntax, and Semantics in SL 165 Chapter 9: What Have You Got to Prove? 167 Bridging the Premise-Conclusion Divide 168 Using Eight Implication Rules in SL 169 Chapter 10: Equal Opportunities: Putting Equivalence Rules to Work 181 Distinguishing Implications and Equivalences 182 Discovering the Ten Valid Equivalences 183 Chapter 11: Big Assumptions with Conditional and Indirect Proofs 195 Conditioning Your Premises with Conditional Proof 196 Thinking Indirectly: Proving Arguments with Indirect Proof 201 Combining Conditional and Indirect Proofs 204 Chapter 12: Putting It All Together: Strategic Moves to Polish Off Any Proof 207 Easy Proofs: Taking a Gut Approach 208 Moderate Proofs: Knowing When to Use Conditional Proof 211 Difficult Proofs: Knowing What to Do When the Going Gets Tough 215 Chapter 13: One for All and All for One 225 Making Do with the Five SL Operators 226 Downsizing — A True Story 228 Chapter 14: Syntactical Maneuvers and Semantic Considerations 233 Are You WFF Us or Against Us? 234 Comparing SL to Boolean Algebra 237 Part IV: Quantifier Logic (QL) 243 Chapter 15: Expressing Quantity with Quality: Introducing Quantifier Logic 245 Taking a Quick Look at Quantifier Logic 246 Expressing Quantity with Two New Operators 251 Picking out Statements and Statement Forms 255 Chapter 16: QL Translations 259 Translating the Four Basic Forms of Categorical Statements 259 Discovering Alternative Translations of Basic Forms 264 Identifying Statements in Disguise 267 Chapter 17: Proving Arguments with QL 271 Applying SL Rules in QL 272 Transforming Statements with Quantifier Negation (QN) 276 Exploring the Four Quantifier Rules 279 Chapter 18: Good Relations and Positive Identities 295 Relating to Relations 296 Identifying with Identities 303 Chapter 19: Planting a Quantity of Trees 307 Applying Your Truth Tree Knowledge to QL 307 Non-Terminating Trees 315 Part V: Modern Developments in Logic 319 Chapter 20: Computer Logic 321 The Early Versions of Computers 322 The Modern Age of Computers 324 Chapter 21: Sporting Propositions: Non-Classical Logic 329 Opening Up to the Possibility 330 Getting into a New Modality 335 Taking Logic to a Higher Order 337 Moving Beyond Consistency 338 Making a Quantum Leap 340 Chapter 22: Paradox and Axiomatic Systems 343 Grounding Logic in Set Theory 343 Discovering the Axiomatic System for SL 347 Proving Consistency and Completeness 348 Gödel’s Incompleteness Theorem 350 Pondering the Meaning of It All 352 Part VI: The Part of Tens 353 Chapter 23: Ten Quotes about Logic 355 Chapter 24: Ten Big Names in Logic 357 Aristotle (384–322 BC) 357 Gottfried Leibniz (1646–1716) 357 George Boole (1815–1864) 358 Lewis Carroll (1832–1898) 358 Georg Cantor (1845–1918) 358 Gottlob Frege (1848–1925) 359 Bertrand Russell (1872–1970) 359 David Hilbert (1862–1943) 359 Kurt Gödel (1906–1978) 360 Alan Turing (1912–1954) 360 Chapter 25: Ten Tips for Passing a Logic Exam 361 Breathe 361 Start by Glancing over the Whole Exam 361 Warm up with an Easy Problem First 362 Fill in Truth Tables Column by Column 362 If You Get Stuck, Jot Down Everything 362 If You REALLY Get Stuck, Move On 362 If Time Is Short, Finish the Tedious Stuff 363 Check Your Work 363 Admit Your Mistakes 363 Stay Until the Bitter End 364 Index 365

Logic concepts are more mainstream than you may realize. There’s logic every place you look and in almost everything you do, from deciding which shirt to buy to asking your boss for a raise, and even to watching television, where themes of such shows as CSI and Numbers incorporate a variety of logistical studies. Logic For Dummies explains a vast array of logical concepts and processes in easy-to-understand language that make everything clear to you, whether you’re a college student of a student of life. You’ll find out about:

• Formal Logic
• Syllogisms
• Constructing proofs and refutations
• Propositional and predicate logic
• Modal and fuzzy logic
• Symbolic logic
• Deductive and inductive reasoning

Logic For Dummies tracks an introductory logic course at the college level. Concrete, real-world examples help you understand each concept you encounter, while fully worked out proofs and fun logic problems encourage you students to apply what you’ve learned.