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 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.
Author(s): Mark Zegarelli
Series: For Dummies
Edition: 1
Publisher: Wiley
Logic For Dummies
About the Author
Dedication
Author’s Acknowledgments
Contents at a Glance
Table of Contents
Introduction
About This Book
Conventions Used in This Book
What You’re Not to Read
Foolish Assumptions
How This Book Is Organized
Icons Used in This Book
Where to Go from Here
Part I: Overview of Logic
Chapter 1: What Is This Thing Called Logic?
Getting a Logical Perspective
Building Logical Arguments
Making Logical Conclusions Simple with the Laws of Thought
Combining Logic and Math
Chapter 2: Logical Developments from Aristotle to the Computer
Classical Logic — from Aristotle to the Enlightenment
Modern Logic — the 17th, 18th, and 19th Centuries
Logic in the 20th Century and Beyond
Chapter 3: Just for the Sake of Argument
Defining Logic
Studying Examples of Arguments
What Logic Isn’t
Whose Logic Is It, Anyway?
Part II: Formal Sentential Logic (SL)
Chapter 4: Formal Affairs
Observing the Formalities of Sentential Logic
The Five SL Operators
How SL Is Like Simple Arithmetic
Lost in Translation
Chapter 5: The Value of Evaluation
Value Is the Bottom Line
Making a Statement
Eight Forms of SL Statements
Evaluation Revisited
Chapter 6: Turning the Tables: Evaluating Statements with Truth Tables
Putting It All on the Table: The Joy of Brute Force
Baby’s First Truth Table
Putting Truth Tables to Work
Putting the Pieces Together
Chapter 7: Taking the Easy Way Out: Creating Quick Tables
Dumping the Truth Table for a New Friend: The Quick Table
Outlining the Quick Table Process
Planning Your Strategy
Working Smarter (Not Harder) with Quick Tables
Chapter 8: Truth Grows on Trees
Understanding How Truth Trees Work
Showing Consistency or Inconsistency
Testing for Validity or Invalidity
Separating Tautologies, Contradictions, and Contingent Statements
Checking for Semantic Equivalence or Inequivalence
Part III: Proofs, Syntax, and Semantics in SL
Chapter 9: What Have You Got to Prove?
Bridging the Premise-Conclusion Divide
Using Eight Implication Rules in SL
Chapter 10: Equal Opportunities: Putting Equivalence Rules to Work
Distinguishing Implications and Equivalences
Discovering the Ten Valid Equivalences
Chapter 11: Big Assumptions with Conditional and Indirect Proofs
Conditioning Your Premises with Conditional Proof
Thinking Indirectly: Proving Arguments with Indirect Proof
Combining Conditional and Indirect Proofs
Chapter 12: Putting It All Together: Strategic Moves to Polish Off Any Proof
Easy Proofs: Taking a Gut Approach
Moderate Proofs: Knowing When to Use Conditional Proof
Difficult Proofs: Knowing What to Do When the Going Gets Tough
Chapter 13: One for All and All for One
Making Do with the Five SL Operators
Downsizing — A True Story
Chapter 14: Syntactical Maneuvers and Semantic Considerations
Are You WFF Us or Against Us?
Comparing SL to Boolean Algebra
Part IV: Quantifier Logic (QL)
Chapter 15: Expressing Quantity with Quality: Introducing Quantifier Logic
Taking a Quick Look at Quantifier Logic
Expressing Quantity with Two New Operators
Picking out Statements and Statement Forms
Chapter 16: QL Translations
Translating the Four Basic Forms of Categorical Statements
Discovering Alternative Translations of Basic Forms
Identifying Statements in Disguise
Chapter 17: Proving Arguments with QL
Applying SL Rules in QL
Transforming Statements with Quantifier Negation (QN)
Exploring the Four Quantifier Rules
Chapter 18: Good Relations and Positive Identities
Relating to Relations
Identifying with Identities
Chapter 19: Planting a Quantity of Trees
Applying Your Truth Tree Knowledge to QL
Non-Terminating Trees
Part V: Modern Developments in Logic
Chapter 20: Computer Logic
The Early Versions of Computers
The Modern Age of Computers
Chapter 21: Sporting Propositions: Non-Classical Logic
Opening Up to the Possibility
Getting into a New Modality
Taking Logic to a Higher Order
Moving Beyond Consistency
Making a Quantum Leap
Chapter 22: Paradox and Axiomatic Systems
Grounding Logic in Set Theory
Discovering the Axiomatic System for SL
Proving Consistency and Completeness
Gödel’s Incompleteness Theorem
Pondering the Meaning of It All
Part VI: The Part of Tens
Chapter 23: Ten Quotes about Logic
Chapter 24: Ten Big Names in Logic
Aristotle (384–322 BC)
Gottfried Leibniz (1646–1716)
George Boole (1815–1864)
Lewis Carroll (1832–1898)
Georg Cantor (1845–1918)
Gottlob Frege (1848–1925)
Bertrand Russell (1872–1970)
David Hilbert (1862–1943)
Kurt Gödel (1906–1978)
Alan Turing (1912–1954)
Chapter 25: Ten Tips for Passing a Logic Exam
Breathe
Start by Glancing over the Whole Exam
Warm up with an Easy Problem First
Fill in Truth Tables Column by Column
If You Get Stuck, Jot Down Everything
If You REALLY Get Stuck, Move On
If Time Is Short, Finish the Tedious Stuff
Check Your Work
Admit Your Mistakes
Stay Until the Bitter End
Index
