N:USERSRichardACAPC 2010 - The Role of Reasoning and … · The Role of Reasoning and Persuasion in the Legal Process Richard R. Orsinger [email protected] McCurley, Orsinger, McCurley,

The Role of Reasoning and Persuasionin the Legal Process

Richard R. [email protected]

http://www.orsinger.com

McCurley, Orsinger, McCurley,Nelson & Downing, L.L.P.

San Antonio Office:1717 Tower Life BuildingSan Antonio, Texas 78205

(210) 225-5567http://www.orsinger.com

and

Dallas Office:5950 Sherry Lane, Suite 800

Dallas, Texas 75225(214) 273-2400

24th Annual Advanced Civil Appellate Practice CourseSeptember 2-3, 2010Four Seasons Hotel

Austin, Texas

© 2010Richard R. OrsingerAll Rights Reserved

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Table of Contents

I. INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -1-II. USEFULNESS OF THE TOPIC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -1-III. THE IMPORTANCE OF INTUITION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -2-IV. THE COMMON LAW. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -3-V. LEGAL REASONING (OVERVIEW). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -7-

A. FORMAL LOGIC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -8-1. Deductive Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -8-2. Inductive Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -9-3. Reasoning With Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -9-4. Reasoning by Analogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -10-

B. INFORMAL LOGIC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -10-C. A RULE-ORIENTED APPROACH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -11-D. MODERN ARGUMENT THEORIES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -11-

VI. FORMAL LOGIC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -12-A. ARISTOTLE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -12-B. STATEMENTS, PROPOSITIONS, AND ARGUMENTS. . . . . . . . . . . . . . . -13-C. TRUTH, VALIDITY, AND SOUNDNESS. . . . . . . . . . . . . . . . . . . . . . . . . . . -13-

1. True and False. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -13-2. Valid and Invalid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -14-3. Sound and Unsound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -14-4. Application to Statements, Propositions, and Arguments. . . . . . . . . . -14-

VII. DEDUCTIVE LOGIC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -15-A. DEFINING CONCEPTS ESSENTIAL TO ARISTOTLE’S DEDUCTIVE

LOGIC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -16-1. Statements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -16-2. Affirmation, Denial, and Contradiction. . . . . . . . . . . . . . . . . . . . . . . . -16-3. All; None; and Some. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -16-4. Principles, Rules, and Symbols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -16-5. Three Fundamental Principles of Logic. . . . . . . . . . . . . . . . . . . . . . . . -17-

B. THE SYLLOGISM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -17-1. The Simple Syllogism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -17-2. Polysyllogism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -20-3. Enthymeme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -20-4. Sorites. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -21-5. When Premises are Inconsistent. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -22-6. The Hypothetical Syllogism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -23-

a. The Conditional Syllogism. . . . . . . . . . . . . . . . . . . . . . . . . . . . -23-b. The Conjunctive Syllogism. . . . . . . . . . . . . . . . . . . . . . . . . . . -23-c. The Disjunctive Syllogism. . . . . . . . . . . . . . . . . . . . . . . . . . . . -23-

7. Quantifiers and Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -23-8. The Rules of Opposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -24-9. Rules for Syllogisms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -25-10. Fallacies of Syllogistic Logic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -26-

a. The Fallacy of Four Terms. . . . . . . . . . . . . . . . . . . . . . . . . . . . -26-b. The Fallacy of the Undistributed Middle Term. . . . . . . . . . . . -26-

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c. The Fallacy of Illicit Process of the Major or Illicit Minor Term.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -27-

d. The Fallacy of Negative Premises. . . . . . . . . . . . . . . . . . . . . . -27-e. The Fallacy of Drawing Affirmative Conclusions From a Negative

Premise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -27-f. The Existential Fallacy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -27-g. Belief Bias. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -27-

11. Translating Natural Language Arguments to Syllogisms. . . . . . . . . . . -28-12. Viewing Legal Disputes as Syllogisms. . . . . . . . . . . . . . . . . . . . . . . . -28-

C. IMPLICATION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -28-1. The Validity and Soundness of Implications. . . . . . . . . . . . . . . . . . . . -29-2. The Five Forms of Conditional Propositions . . . . . . . . . . . . . . . . . . . . -29-3. The Material Implication. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -29-4. Modus Ponens (Affirming the Antecedent). . . . . . . . . . . . . . . . . . . . . -30-5. Modus Tollens (Denying the Consequent). . . . . . . . . . . . . . . . . . . . . . -30-6. “Not-P or Q.” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -31-7. Affirming the Consequent. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -31-8. Conditional Propositions Can Be Sorites. . . . . . . . . . . . . . . . . . . . . . . -31-9. Attacking a Conditional Proposition. . . . . . . . . . . . . . . . . . . . . . . . . . . -32-10. Disproving a Material Implication. . . . . . . . . . . . . . . . . . . . . . . . . . . . -32-11. Biconditional . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -32-12. Conjunctive Conditional Propositions. . . . . . . . . . . . . . . . . . . . . . . . . -32-13. Disjunctive Conditional Propositions. . . . . . . . . . . . . . . . . . . . . . . . . . -32-14. Other Conditionals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -33-

a. Indicative Conditionals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -33-b. Subjunctive Conditionals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . -33-c. Counterfactual Conditionals. . . . . . . . . . . . . . . . . . . . . . . . . . . -34-

15. The Dilemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -35-16. Degrees of Conditionals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -35-17. Disproving Other Conditionals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -36-18. Legal Presumptions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -36-

D. EULER CIRCLES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -36-E. TRUTH TABLES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -37-F. LOGICAL CONNECTORS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -39-

1. Logical Negation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -39-2. Logical Conjunction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -39-3. Logical Disjunction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -40-4. Material Implication. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -42-5. Material Equivalence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -43-6. Material Nonequivalence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -44-7. Alternative Denial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -44-8. Joint Denial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -44-

G. SYMBOLIC LOGIC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -45-H. TAUTOLOGIES AND SELF-CONTRADICTIONS. . . . . . . . . . . . . . . . . . . -45-I. AXIOMS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -46-J. CONSTRUCTING DEDUCTIVE ARGUMENTS IN PROPOSITIONAL

LOGIC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -46-

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1. Direct Deductive Arguments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -46-a. Rules of Inference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -46-b. Rules of Replacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -48-c. Logic Arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -49-

2. Conditional Proof. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -49-3. Indirect Proof. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -49-

K. FALLACIES OF DEDUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -49-1. The Fallacy of Affirming the Consequent. . . . . . . . . . . . . . . . . . . . . . -50-2. False Dichotomy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -51-3. Inconsistency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -51-4. Non Sequitur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -51-5. Slippery Slope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -51-6. Begging the Question. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -52-7. Circular Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -52-8. Changing the Premises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -52-

L. PARADOXES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -53-1. The Sorites Paradox. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -53-2. The Liar Paradox. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -53-3. Eubulides’s Paradox. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -54-4. Socrates’ Paradox. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -54-5. Smasandache Paradox. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -54-6. The Catalog Paradox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -54-7. The Omnipotent God Paradox. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -54-8. The Surprise Test Paradox. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -54-9. The Grandfather Paradox. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -55-10. The Envelope Paradox. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -55-11. Orsinger’s Paradox. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -56-12. A Famous Scientific Paradox. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -56-13. A Famous Political Paradox. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -56-14. Avoiding “All” or “None.” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -58-

M. THE IMPORTANCE OF RELEVANCE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . -58-N. THE PROBLEMS OF CONDITIONALS. . . . . . . . . . . . . . . . . . . . . . . . . . . . -59-

1. Problems with the Material Conditional. . . . . . . . . . . . . . . . . . . . . . . . -59-2. Problems With the Indicative Conditional. . . . . . . . . . . . . . . . . . . . . . -60-3. Problems With Subjunctive Conditionals. . . . . . . . . . . . . . . . . . . . . . . -60-4. Problems With Counterfactual Conditionals. . . . . . . . . . . . . . . . . . . . -61-

O. “SOME” and “ALL.” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -61-P. PROBABILITIES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -61-Q. TRANSLATING ENGLISH TO DEDUCTIVE LOGIC. . . . . . . . . . . . . . . . . -62-

1. Negation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -62-2. Logical Conjunction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -62-3. Logical Disjunction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -63-

a. Inclusive Disjunction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -63-b. Exclusive Disjunction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -63-

4. Implication. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -63-a. Material Conditional. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -64-b. Other Conditionals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -64-

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5. Premise Indicators/Conclusion Indicators . . . . . . . . . . . . . . . . . . . . . . -64-6. Identifying and Adding Suppressed Premises. . . . . . . . . . . . . . . . . . . -65-7. Examples of English-to-Logic Translations. . . . . . . . . . . . . . . . . . . . . -65-8. Hypothetical Arguments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -66-

R. LEGAL FORMALISM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -66-S. LEGAL EXAMPLES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -66-T. COGNITIVE STUDIES OF DEDUCTIVE REASONING. . . . . . . . . . . . . . . -67-U. REASONING EXPERIMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -68-

1. Tests of Conditional Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -68-a. The Wason Selection Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . -68-

VIII. INDUCTIVE LOGIC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -68-A. MODERN SCIENCE AS INDUCTIVE LOGIC. . . . . . . . . . . . . . . . . . . . . . . -69-B. JOHN STUART MILL ON INDUCTIVE LOGIC. . . . . . . . . . . . . . . . . . . . . -69-C. PRINCIPLES OF INDUCTIVE LOGIC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . -70-

1. Generalization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -70-2. Simple Induction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -71-3. Correlation and Causation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -71-4. Statistical Syllogism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -71-5. Statistical Prediction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -71-

D. COGNITIVE STUDIES OF INDUCTIVE REASONING. . . . . . . . . . . . . . . -71-E. GENERATING RULES TO RESOLVE LEGAL CASES. . . . . . . . . . . . . . . -71-F. FALLACIES OF INDUCTIVE REASONING. . . . . . . . . . . . . . . . . . . . . . . . -72-

1. Hasty Generalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -72-2. Fallacies of Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -72-3. Fallacy of Composition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -73-4. Fallacy of Division. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -73-5. Dicto Simpliciter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -73-6. Faulty Analogy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -73-7. False Cause. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -73-8. Suppressed Evidence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -74-9. Common Statistical Fallacies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -74-

a. Errors in Generating Statistics. . . . . . . . . . . . . . . . . . . . . . . . . -74-b. Errors in Interpreting Statistics. . . . . . . . . . . . . . . . . . . . . . . . . -75-c. Statistics in the Law. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -76-

10. Confusing Unexplained with Unexplainable. . . . . . . . . . . . . . . . . . . . -78-11. False Continuum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -78-

IX. ABDUCTIVE REASONING. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -78-X. REASONING IN UNCERTAINTY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -79-

A. THE BASIC RULES OF PROBABILITY. . . . . . . . . . . . . . . . . . . . . . . . . . . . -80-B. CONDITIONAL PROBABILITY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -80-

1. Where Probabilities Can Be Determined With Certainty. . . . . . . . . . . -80-a. Prior Probability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -80-b. The Monty Hall Dilemma. . . . . . . . . . . . . . . . . . . . . . . . . . . . . -80-c. Posterior Probability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -82-

2. Where Probabilities Cannot Be Determined With Certainty. . . . . . . . -82-C. BELIEF REVISION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -83-

XI. REASONING BY ANALOGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -83-

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XII. INFORMAL LOGIC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -85-XIII. THE SPECIAL LOGIC OF STATUTORY INTERPRETATION. . . . . . . . . . . . . . . . -86-

A. PHILOSOPHY OF INTERPRETING STATUTES. . . . . . . . . . . . . . . . . . . . . -86-1. Textualist Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -86-2. Intentionalist Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -87-3. Purposivist Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -87-

B. CANONS OF STATUTORY CONSTRUCTION. . . . . . . . . . . . . . . . . . . . . -88-1. Code Construction Act. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -88-2. Common Law Canons of Construction. . . . . . . . . . . . . . . . . . . . . . . . . -88-

XIV. RHETORIC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -89-A. APPEALS TO ETHOS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -90-B. APPEALS TO PATHOS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -91-C. APPEALS TO LOGOS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -91-

1. Syllogism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -91-2. Enthymeme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -91-3. Sorites. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -92-4. Inductive Inference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -92-5. Analogy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -92-6. Simile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -92-7. Metaphor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -92-8. Aetiologia. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -93-9. Anthypophora. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -93-10. Apophasis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -93-11. Contrarium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -93-12. Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -93-13. Epitrope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -93-14. Expeditio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -93-15. Proecthesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -93-16. Prosapodosis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -93-17. Paromologia. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -93-18. Dirimens Copulatio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -93-19. Commoratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -94-20. Hyperbole. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -94-21. Rhyming. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -94-22. Similiarities/Differences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -94-

D. THE FIVE CANONS OF RHETORIC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -94-1. Invention. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -94-2. Arrangement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -94-3. Style. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -94-4. Memory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -94-5. Delivery. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -95-

E. STRUCTURE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -95-1. Appellate Briefs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -95-2. Appellate Opinions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -95-3. The Courtroom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -95-

F. PUNCTUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -95-G. EMPHASIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -98-

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H. CITATION SIGNALS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -101-I. LEGALESE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -101-J. FIGURES OF SPEECH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -101-K. NARRATIVE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -102-L. CONTRAST. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -103-M. TYPES OF QUESTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -103-

1. Loaded Question. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -103-2. Leading Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -104-3. Rhetorical Question. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -104-4. Speaking Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -104-5. “Buttering Up” Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -104-6. A “Hook” Question. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -104-

N. TENSE, MOOD, AND VOICE OF VERBS. . . . . . . . . . . . . . . . . . . . . . . . . -104-1. Tense. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -104-2. Mood. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -104-3. Voice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -105-

O. KAIROS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -105-XV. FALLACIES OF ARGUMENTATION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -106-

1. Accident. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -106-2. Ambiguity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -106-3. Amphiboly. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -107-4. Appeal to Authority (ad Verecundiam). . . . . . . . . . . . . . . . . . . . . . . -107-5. Appeal to Belief. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -108-6. Appeal to Emotion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -108-7. Appeal to Fear (ad Baculum). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -108-8. Appeal to Flattery. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -108-9. Appeal to Novelty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -108-10. Appeal to Pity (ad Misericordiam). . . . . . . . . . . . . . . . . . . . . . . . . . . -108-11. Appeal to Ridicule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -108-12. Appeal to Tradition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -108-13. Argumentum ad Hominem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -108-14. Argumentum Ad Hominem Tu Quoque. . . . . . . . . . . . . . . . . . . . . . . -109-15. Argument From Fallacy (ad Logicano). . . . . . . . . . . . . . . . . . . . . . . -109-16. Argument from Ignorance (ad Ignorantiam). . . . . . . . . . . . . . . . . . . . -109-17. Argument From Popular Appeal (ad Populum) . . . . . . . . . . . . . . . . . -110-18. Argument to Moderation (ad Temperantiam). . . . . . . . . . . . . . . . . . . -110-19. Bandwagon Effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -110-20. Complex Question. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -110-21. Converse Accident . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -110-22. Equivocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -110-23. False Cause. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -110-24. False Dilemma. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -110-25. Genetic Fallacy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -111-26. Guilt by Association. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -111-27. Irrelevant Conclusion (Ignoratio Elenchi) . . . . . . . . . . . . . . . . . . . . . -111-28. Misapplied Burden of Proof. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -111-29. Misleading Vividness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -111-

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30. Moving the Goalposts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -111-31. No True Scotsman Fallacy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -111-32. Poisoning the Well. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -111-33. Questionable Cause. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -111-34. Special Pleading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -111-35. Red Herring. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -112-36. Relativist Fallacy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -112-37. Straw Man. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -112-

XVI. CATEGORIZING FALLACIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -112-A. ARISTOTLE’S FALLACIES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -112-B. FRANCIS BACON’S FALLACIES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -112-C. JOHN STUART MILL’S FALLACIES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . -113-D. A MODERN TAXONOMY OF FALLACIES. . . . . . . . . . . . . . . . . . . . . . . -114-

XVII. MODERN ARGUMENT THEORIES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -114-A. THE TOULMIN MODEL OF ARGUMENT. . . . . . . . . . . . . . . . . . . . . . . . -114-

1. Claims. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -114-2. Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -114-3. Warrants and Backing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -115-4. Rebuttals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -115-5. Comparison to Syllogism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -115-

B. DEFEASIBLE REASONING. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -115-C. ARGUMENTATION SCHEMES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -115-

XVIII. DEGREES OF CERTAINTY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -116-XIX. CATEGORIES VS. GRADATIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -116-

A. PHILOSOPHICAL PERSPECTIVE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -116-B. LOGICAL PERSPECTIVE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -117-C. LEGAL PERSPECTIVE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -117-

XX. VAGUENESS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -117-XXI. DISAMBIGUATION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -118-XXII. HEURISTICS AND COGNITIVE BIASES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -118-

A. HEURISTICS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -118-B. COGNITIVE BIASES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -119-

XXIII. USING LOGIC AND RHETORIC TO CONSTRUCT AND EVALUATE LEGALARGUMENTS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -120-

A. ADAPTING LOGIC CONCEPTS TO LEGAL ARGUMENTS. . . . . . . . . . -120-1. Use Syllogisms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -120-2. Use Enthymemes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -121-3. Use Conditional Propositions (Implication). . . . . . . . . . . . . . . . . . . . -121-4. Use Inductive Reasoning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -122-5. Use Analogical Reasoning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -122-6. Use Fallacies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -122-7. Indirect Argument. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -123-

B. USE OF AUTHORITIES TO SUPPORT A LEGAL ARGUMENT. . . . . . . -123-1. Invoking the Diety. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -124-2. Invoking a Higher Authority. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -124-3. Invoking the Founding Fathers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -124-

a. Lincoln’s Cooper Union Speech. . . . . . . . . . . . . . . . . . . . . . . -124-

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b. Lincoln’s Gettysburg Address. . . . . . . . . . . . . . . . . . . . . . . . -125-4. Self-Evident Propositions (Axioms). . . . . . . . . . . . . . . . . . . . . . . . . . -125-5. Affirmation by the Majority. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -125-6. The Hierarchy of Legal Authorities. . . . . . . . . . . . . . . . . . . . . . . . . . -126-7. Stare Decisis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -126-

a. Prior Appellate Decisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . -126-b. Holding, Dictum and Judicial Dictum. . . . . . . . . . . . . . . . . . -127-

8. Appeals to History. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -127-9. Policy Arguments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -127-10. Appeals to Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -127-

C. LEGAL “COMMONPLACES” TO USE IN LEGAL ARGUMENTS . . . . . . . . -128-1. Failure to Contest and Concession . . . . . . . . . . . . . . . . . . . . . . . . . . . -128-2. Acquiescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -128-3. Waiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -128-4. Action vs. Inaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -129-5. Mental State. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -129-

a. Culpability in Criminal Law . . . . . . . . . . . . . . . . . . . . . . . . . -129-b. Culpability in Tort Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -129-

6. Subjective Vs. Objective Points-of-View . . . . . . . . . . . . . . . . . . . . . -130-a. Negligence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -130-b. Gross Negligence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -131-c. Recusal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -131-

7. Legal Duty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -131-8. Causation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -132-9. Res Judicata Vs. Stare Decisis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -133-10. The Principle of Parsimony . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -133-11. Escaping a General Rule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -134-12. Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -135-13. Converting Limitations on Governmental Power to Rights of Individuals.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -135-

14. Using Supporting Rationales to Limit the Rule. . . . . . . . . . . . . . . . . -135-15. Appeal to Consistency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -136-16. Appeal to Fairness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -136-17. Appeal to Majority. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -136-18. Invoking Trends. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -136-

D. ADAPTING RHETORICAL CONCEPTS TO LEGAL ARGUMENTATION.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -137-

1. Reductio Ad Absurdum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -137-2. Using the Extreme to Reach the Middle. . . . . . . . . . . . . . . . . . . . . . . -137-

XXIV. REFRAMING. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -138-XXV. A SYNTHESIS OF THE CONCEPTS DISCUSSED IN THIS ARTICLE. . . . . . . . -138-

A. CONSTRUCTING ARGUMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -138-1. Preserve the Right to Argue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -138-2. Assemble the Facts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -138-3. Frame (or Reframe) the Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . -138-4. Determine Possible Then Preferable Arguments. . . . . . . . . . . . . . . . -139-5. Identify Commonplaces to Use in the Argument . . . . . . . . . . . . . . . -139-

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6. Select Rhetorical Tools. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -139-B. TESTING ARGUMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -140-C. PRESENTING ARGUMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -140-D. REFUTING YOUR OPPONENT’S ARGUMENTS . . . . . . . . . . . . . . . . . . -140-

XXVI. IMPORTANT DISTINCTIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -141-XXVII. GLOSSARY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -144-XXVIII. ENDNOTES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -148-

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The Role of Reasoning and Persuasion in theLegal Process

by

Richard R. OrsingerBoard Certified in Family Law& Civil Appellate Law by the

Texas Board of Legal Specialization

I. INTRODUCTION. The work of alawyer, as counselor and advocate, involvesreasoning and persuasion. Likewise, the workof a judge, in arriving at and articulatingdecisions, involves analysis and persuasion.This Article examines the logical part of legalreasoning and historically-recognizedtechniques of persuasion. The Article coversformal logic, informal logic, rhetoric, andselecting and applying legal rules. Theprinciples run from ancient Greece, throughthe Middle Ages, to today, as do theexamples.

An equally important topic is the psychologyof forming opinions and making judgments,which impacts both logic and rhetoric. Thepsychological and neuro-psychological studyof reasoning processes is examined briefly inthis Article.

Underlined terms appear in the Glossary at theend of the Article. Further explanations andcitations to supporting authority are inendnotes.1 Some endnotes also contain linksto follow if you want to explore a topicfurther.2 To avoid ambiguity, terms with aspecial meaning in Logic or Rhetoric arecapitalized, to distinguish their specialmeaning from the meaning accorded thoseterms in ordinary speech. By convention,writers on Logic put logical Propositions inquotation marks, and put the punctuationrequired for the surrounding sentence outsidethe quotation marks, so as not to confuse therules of sentence construction with the logical

concepts. That convention is followed in thisArticle.

II. USEFULNESS OF THE TOPIC. ThisArticle covers descriptions of logicalprocesses and argumentation techniques thatspan some 2,300 years. The reader mightreasonably ask, as to any one or even all ofthese topics: “What does this have to do withmy law practice, or my role as a judge?” Afterfour years of high school, at least four years ofcollege, three years of law school, and adecade or more of working in the legal field,we all have learned how to think logically andhow to speak or write in order to persuade.Much of what we know about logic andpersuasion was acquired implicitly, as a side-effect of studying or doing something else.Like knowing how to ride a bicycle or toswim, it is easier to do it than to explain howto do it.3 This Article has a differentperspective. In our jobs we reason and argue;in this Article we explore the ways we reasonand argue. Since the human brain has notchanged very much for at least the past 40,000years,4 many of the insights into the reasoningand argumentation process, achieved adecade, a century, and even two millenia ago,are as valid and applicable today as they werewhen they were first announced. In thisArticle these insights are sometimes placedinto a historical context, which puts a humanface on the abstract concepts, gives tributewhere it is due, and shows how enduring theseinsights really are. While many examples aretaken from the law, the reader must either

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enjoy or excuse periodic digressions intophilosophy, science, and history generally,since some of the most interesting examplesof logical thinking and rhetorical techniqueare in those domains.

Understanding the rules of Logic andprinciples of Rhetoric allows us to approachlegal problem-solving and persuasion in amore methodical and consistent way. It allowsus to construct good arguments, and identifybad arguments, more effectively. If yourpurpose is to transmit your thoughts throughcommunication into the minds of listeners,then knowing how people listen and think canhelp you do this.

Speaking of Logic, Gottfried Leibniz said:“This language will be the greatest instrumentof reason,” for “when there are disputesamong persons, we can simply say: let uscalculate, without further ado, and see who isright.”5 Logic’s strength is its weakness,however. Albert Einstein commented: “Logicwill get you from A to B. Imagination willtake you everywhere.” Perhaps later someonewill write an article on the role of imaginationin the legal process.

In the present discussion, Logic and Rhetoricare considered as they apply to legalreasoning and legal argumentation.Approaches to interpreting case law andinterpreting statutes have developed alongdifferent lines. Each are discussed separately.The general principles of reasoning andpersuasion are discussed.

III. THE IMPORTANCE OF INTUITION.Before we go deeply into Formal Logic andRhetoric, we should mention thepsychological theory that people have twodifferent ways of reasoning, eachfundamentally different from the other. Thisview is called the dual-process theory ofreasoning. According to this view, oneapproach to reasoning and decision-making is

based on logic and the other is based onintuition. As stated in a recent psychologicalpaper:

Traditionally, logical thinking andintuition have been viewed as rivalmodes of thought. The former isdeliberate, achieving accurate andjustifiable representations of the world,and the latter is ineffable, producingbest-guess answers to problems withoutany discernable effort.”6

Dividing man’s being into the rational and theemotional goes at least as far back asAristotle.7 The modern psychological viewthat there are two ways of assessing situationscan be traced back to William James in 1890and later Sigmund Freud in 1900. Jamescontrasted analytical deliberation with anexperiential-associative type of thinking.Freud contrasted a conscious and rationalapproach with an unconscious and associativeapproach.8 In 1994, Seymour Epsteindeveloped a theory that the personalityconsists of two parallel systems, one anonexperiential information processor that isrational, free of emotion, abstract, andanalytical, and the other that is an experientialinformation processor that is emotionallydriven, “encoding experiences in the form ofconcrete exemplars.”9 Epstein hypothesizedthat these two approaches developed inevolutionarily-distinct ways, and wereadapted to solve different types of problems.He believed that the rational facilitydeveloped more recently on the evolutionaryscale than the experiential-based one.10 Amore recent theory differentiates implicitreasoning from explicit reasoning. Implicitreasoning involves the creation of a set ofabstractions or inferences without a consciousawareness of the process. These abstractionsoccur unintentionally and are beyondconscious control. However, these processescan be developed and strengthened throughfrequent repetition so that they become

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“enduring, well defined, and stable throughrepeated use.”11 In contrast, explicit reasoninginvolves the use of abstractions and inferencesof which the mind is consciously aware, andthat are susceptible to conscious control. Theycan be reliably recalled from memory becausethey are stored in “working memory.”12

Currently there is a robust interest in the ideathat there are two ways of reasoning, oneintuitive and the other rational, which in theliterature have come to be called “System 1"(fast, intuitive, associative, pragmatic) and“System 2” (slow and rational, using morebrain capacity, subject to conscious control).This model of the process of assessing theworld (including arguments) suggests that theformal methods of Logic are important inargumentation, but that the less-logical ornon-logical components of persuasion that areaddressed through Rhetoric are also importantin argumentation.

IV. THE COMMON LAW. Since thisArticle operates against the background oflegal reasoning, it begins with thatbackground which is the Common Law. TheCommon Law has its roots in pre-historicBritain. As a result of successive invasions,the customs of the indigenous people ofBritain were intermixed with the practices ofthe Romans, the Picts, the Saxons, and theDanes, but there was never a formal exchangeof one system of laws for another.13 By thebeginning of the Eleventh Century, Englandhad three principal systems of law: the law ofthe ancient Britons, which prevailed in somemidland counties and west toward Wales; thelaw of the Saxons, in the south and west ofEngland; and Danish law, in the midlands andalong the eastern coast of the island.14 The lastSaxon king, Edward the Confessor, extractedfrom these separate systems a sketchy butuniform law for the entire Kingdom, and so itwas when William of Normandy establishedthe foothold for his invasion of England, atHastings in 1066.15

At the time of the Norman Conquest, whichbegan in 1066, the law of England was aloosely-integrated form of feudalism, basedprimarily on an hierarchy of mutual obligationbetween the common man and his local lord,between the local lord and his overlord, andbetween the overlord and the king. Upon thesuccess of his cross-Channel invasion ofEngland, William the Conqueror replaced theAnglo-Saxon overlords with his militarycohorts, while leaving the basic structure ofAnglo-Saxon feudalism in place. The pre-existing political structure of Anglo-SaxonEngland was so decentralized that asuccession of Normal kings struggled toimpose Norman ways across England withuneven effect. William I brought with him theFrench language, the Catholic church, and thevestiges of Roman Civil law. But the Englishcommon law “weathered the rude shock of theNorman Conquest,”16 and the foundation ofmodern English law was thus an amalgam ofpre-Norman institutions and France’s versionof Canon Law and Roman Civil Law. BecauseEngland was, as-it-were, on the periphery ofthe civilized world, even after the ConquestEnglish law developed independently fromthe law developing on the Continent ofEurope. Just like the English languagegenerally, English legal writing reflected amix of Anglo-Saxon, Latin and Frenchconcepts and terms. Additionally, post-Conquest England suffered from a successionof absentee-kings, dethronements, andinstitutional struggles as the kingsconsolidated power at the expense of thefeudal lords, all of which impaired thedevelopment of a uniform, top-down legalinfrastructure. To a greater extent thanelsewhere in Europe, in England the lawaccepted by the population developed fromthe bottom up, based on the rulings ofindividual judges in specific cases thateventually gained recognition as authoritativestatements of the law.

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Henry II, in the 1100's, succeeded in makinginroads into the legal authority of local lords,by adopting statutes that centralized theEnglish legal system through establishing a“permanent court of professional judges,” andby sending “itinerate judges throughout theland,” and by establishing new proceduressuch as writs that allowed the removal ofcourt actions from local courts to royalcourts.17 His efforts centralized the law andmade it uniform, and thus “Common” in thesense of shared throughout the realm.However, Henry II’s changes were more tothe structure of the legal system and not thecontent of the laws, so that the individualdecisions of judges still developed the lawincrementally.18 The common law of Englandevolved into a mixture of disconnected royaldecrees and enactments of Parliament (manymerely codifying existing common lawprinciples), court rulings recorded ininaccessible registers, local practices thatvaried widely, and settled customs developedby people as they went about their daily liveswithout the benefit of legal oversight.Periodically, a legal thinker would undertaketo organize and restate the law, as Sir ThomasLittleton did in 1481, with his three-volumework on real property rights, called TheTenures (written in Law French),19 and asEdward Coke later did with his four volumesof Institutes on the Lawes of England,published from 1628 to 1644.20 However,even treatises on the law that were written inEnglish were obtuse, dominated by proceduralconsiderations, and riddled with archaicFrench and Latin phrases, all of which servedas a barrier to the uninitiated. By theEighteenth Century, the works of Glanvil,21

Bracton,22 and Britton23 were out-of-date, andefforts to update them had merely engraftedlater developments on their outdatedconceptual frameworks.24 The legal writingsof Francis Bacon, while insightful, wereidiosyncratic and disjointed.25 Coke’s workwas rich in detail but lacking inorganization.26 Cowel’s Institutions was

written in Latin and patterned after the whollydissimilar laws of the Roman EmperorJustinian.27 Finch’s Discourse of Law wascomprehensive, with valuable examples, butby the mid-1700s had been made obsolete bychanges in property law and legal procedure.28

Another grouping of legal treatises, called“abridgements,” contained explanations, orone-sentence digests of case holdings, relatingto various legal principles that were listed inalphabetical order, making them useful asreference works for lawyers and judges, andstudents receiving instruction in the law at oneof the London’s Inns of Court or Inns ofChancery,29 but not to other persons interestedin the law. None of these works presented acohesive view of how the parts ofcontemporary English law fit together into awhole.

All of this changed in 1753, due to WilliamBlackstone, an unsuccessful barrister who hadbeen passed over as a candidate to fill anendowed professorship on civil law at OxfordUniversity, but who had enjoyed successes invarious administrative jobs and held afellowship at All Souls College, Oxford.30

After seven years of practicing law,Blackstone had concluded that he did not havethe gifts necessary to plead cases in court, andthat his strength was “the thinking theoreticalpart” of the law.31 He resolved to conduct aseries of lectures on English law, directed atUniversity students who intended to becomelawyers, as well as to interested members ofthe public.32 Blackstone “therefore made it ishis first Endeavor, to mark out a Plan of theLaws of ENGLAND, so comprehensive, as thatevery Title might be reduced under some orother of it’s general Heads, which the Studentmight afterwards pursue to any Degree ofMinuteness; and at the same time socontracted, that the Gentleman might withtolerable Application contemplate andunderstand the Whole.”33 When hispreparations were complete, Blackstoneadvertised that, in four lectures, he would “lay

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down a general and comprehensive plan of theLaws of England; to deduce their History; toenforce and illustrate their leading rules andfundamental Principles; and to compare themwith the Laws of Nature and other Nations;without entering into practical Niceties, or theminute Distinctions of particular Cases.”34

The registration fee for the four lectures wassix guineas.35

On June 23, 1753, in the dining hall at AllSouls College, Blackstone delivered his firstlecture, to great success. As his lecturescontinued, Blackstone realized--

That, in a Course of oral Lectures, on aScience entirely new, and sometimes alittle abstruse, it was not always easy forhis Audience so far to command theirAttention, as at once to apprehend boththe Method and Matter delivered: And,whenever, through Inattention in theHearers, or (too frequently) throughObscurity in the Reader, any Point ofImportance was forgot ten ormisunderstood, it became next toimpossible to gather up the broken Clue,without having some writ tenCompendium to which they might resortupon Occasion.36

Blackstone therefore issued in 1754 a syllabusof his lectures, called An Analysis of the Lawsof England, which amounted to a taxonomy ofEnglish law, drawn heavily from MatthewHale’s Analysis of the Law (1713).37 In 1756,Charles Viner, an Oxford-educated lawyerwho had authored a highly successfulalphabetically-arranged 23-volume GeneralAbridgment of Law and Equity,38 died andbequeathed £ 12,000 and the copyright to hisAbridgment to Oxford University, to endow achair on English Law (the first chair onEnglish law at any English university). Inview of the success of his private lectures,Blackstone secured the initial appointment tothat Chair on October 20, 1758. Blackstone

read his first Vinerian lecture on October 25,1758, entitled A Discourse on the Study of theLaw.39 In this 37-page lecture, Blackstone’sstated purpose was to “demonstrate the utilityof some general acquaintance with themunicipal law of the land, by pointing out itsparticular uses in all considerable situations oflife.”40 He compared the study of law in theuniversity setting favorably to the then-degraded circumstances of the Inns of Courtand Inns of Chancery, outlined the benefits“to the science of law itself” that could resultfrom University study, and concluded bystating his intent to follow the outline in hisAnalysis of the Laws of England in presentinga course of study whereby “gentlemen ofindependent estates and fortune,” who did notintend to become lawyers, could acquire asuitable knowledge of the law in a singleyear.41

As his Vinerian lectures continued, and boot-legged versions of his lectures began tocirculate and to be illicitly sold for profit,Blackstone compiled his lectures and writingson English law into a four-volume treatise,named COMMENTARIES ON THE LAWS OF

ENGLAND,42 that was published from 1769 toVolume I begins with a description ofBlackstone’s philosophical perspective on thenature of law in general, drawn heavily(without attribution) from the writings ofThomas Acquinas.43 Blackstone defined “law”as “a rule of action dictated by some superiorbeing.”44 The physical world is governed by“the law of nature,” such as the laws ofgravity, optics, and mechanics (expounded byIsaac Newton in the 1600s), that wereimposed by the supreme being when hecreated the universe and set things in motion.When applied to the affairs of man, the law ofnature reduces to this: the creator has “sointimately connected, so inseparablyinterwoven the laws of eternal justice with thehappiness of each individual” that one cannotbe attained without the other. Blackstoneasserted that what tends to man’s real

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happiness is part of the law of nature, andwhat is destructive of man’s real happiness“the law of nature forbids.”45 He continued:“This law of nature, being coeval withmankind, and dictated by God himself, is ofcourse superior in obligation to any other. It isbinding over all the globe in all countries, andat all times: no human laws are of anyvalidity, if contrary to this.”46 Blackstonewrote that the limitations of human reasonmake it difficult to discern how the law ofnature is applied to the affairs of man, so thecreator assisted in this discovery process bydivine revelation, reflected in the holyscriptures. Blackstone asserted that, upon thelaw of nature and the law of revelation,depend all human laws.47 From these twosources, he said, derive the law of nations, andthe laws of each particular nation.48

The law of a particular nation, whichBlackstone called “municipal law,” is a “ruleof civil conduct prescribed by the supremepower in the state.”49 Blackstone subdividedmunicipal law into constituent parts andprioritized them in a hierarchy from thegreatest to the least. He differentiatedcommon law from statutory law. Englishcommon law consists of general customs(observed everywhere), particular customs(observed in only parts of England), andparticular laws (observed only in certaincourts and jurisdictions).50 To be valid,particular customs must meet seven criteria.They must: originate beyond the memory ofman; be continuous; have been acquiesced in;be reasonable; be certain; be compulsory; andbe consistent.51 In passing, Blackstone statedrules of statutory construction52 and thedoctrine of stare decisis,53 with its exceptions.

Blackstone progressed to a discussion ofparticular municipal laws of England. Hedivided these into four categories: twocategories of rights and two categories ofwrongs. Book I includes the rights of persons,from the King on down to the common man.

Book I also discusses the relationships ofhusband and wife, master-servant, andguardian and ward. Book II discusses therights in things (property rights), primarily inland but including personal property. Book IIIdiscusses private wrongs (torts). Book IVdeals with public wrongs (primarily criminallaw).

Blackstone’s COMMENTARIES wereimmediately and immensely popular, goingthrough a number of printings in short period.The books sold well in America, too, with thefirst printing of 1,400 copies in 1771 sellingout quickly. After a period of time had passed,American law professors began to publishtheir own versions of the COMMENTARIES,with annotations and footnotes to theconstitutional, statutory, and case law of theirstates. The first was William & Mary LawProfessor St. George Tucker’s annotatedversion, called “Tucker’s Blackstone,”published in 1803, which reoriented the workfrom a monarchical to a constitutionalgovernment and tied it to the laws ofVirginia.54 THE COMMENTARIES had aprofound effect on American law,55 withBlackstone’s concept of natural law as a limiton the power of government findingexpression in the Declaration ofIndependence56 and the Federalist Papers.57

The COMMENTARIES were cited in ratificationconventions for the U.S. Constitution, as wellas in Chief Justice Marshall’s Opinion in thelandmark case of Marbury v. Madison.58

Blackstone’s concept of the balance ingovernmental power, which for him meant theKing versus Parliament versus the courts,found its expression in the checks andbalances of the U.S. government.Blackstone’s recognition of the writ of habeascorpus59 and the prohibition against ex postfacto laws60 garnered explicit mention in theU.S. Constitution. Of course, Blackstone didnot invent these concepts himself. But heorganized them into a logically-structuredwhole, and set them out in readable fashion, in

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a conveniently portable and affordable format.Unlike other forbears of the AmericanRevolution and government, such asRousseau, Montesquieu, and Locke,Blackstone merged philosophical principlesand legal doctrines into a kind of “appliedphilosophy of law” that penetrated thethinking of the men who created the post-colonial governments in America.

As the American frontier pushed westward,the COMMENTARIES moved with it, serving asa substitute for large, private law libraries thatwere non-existent in communities west of theAppalachian Mountains.61 Because theCOMMENTARIES could be read and understoodby persons with no background in the law,they became the favorite vehicle for self-studyby many Americans aspiring to becomelawyers without a lengthy apprenticeship,ranging from Patrick Henry to AbrahamLincoln.62

The view that the common law is a body ofprinciples, that can be discerned with carefulanalysis, was espoused not only byBlackstone but also by many that followedhim. It continues to be the way law is taught,and the way law is applied, through today.

V. LEGAL REASONING (OVERVIEW).Following the paradigm of scientific inquirydeveloped in the Sixteenth, Seventeenth, andEighteenth Centuries, it became acceptedamong legal thinkers in Nineteenth CenturyAmerica that legal reasoning was governed byan analytical process akin to the formaldeductive logic first elucidated by Aristotle,where rules of law were applied to specificfacts to arrive at the correct result. As notedabove, Blackstone’s COMMENTARIES

facilitated this approach, by assembling adisparate array of common law principles intoa compact and accessible format, whichbecame widely disseminated in the UnitedStates as a “body of law.” As societalinstitutions modernized, and a self-sufficient

agrarian economy was replaced with aneconomy based on manufacture, trade, andservices, new legal principles had to bedeveloped to accommodate these newactivities. Due to the federal nature of theUnited States of America, with each statebeing sovereign in its own geographicalregion, the common law developed indifferent states at different paces, without thecohesion that would have resulted from aunified legal system.

Beginning in 1870, when ProfessorChristopher Columbus Langdell introducedthe “case method” of study in his HarvardLaw School contracts class, the viewdeveloped that legal reasoning was more akinto inductive logic, where principles of lawcould be inductively discerned from analysisof the appellate court decisions of Englandand of various American states and theprinciples could then be applied to new casesin a deductive fashion.63 Prior to Langdell,American authors of legal treatises on, forexample, contract law used the “manualmethod,” which grouped cases aroundparticular factual components of situations,such as contracts with inkeepers, asdistinguished from contracts with “drunkards,spend thrifts, seamen, aliens, slaves, infants,married women, outlaws,” each of which wasdifferentiated from the others.64 Langdell, incontrast, thought that the “manual method”presented a small number of fundamentallegal doctrines under different guises thatwere no more than confusing repetitions ofeach other.65 Langdell suggested: “If thesedoctrines could be so classified and arrangedthat each should be found in its proper place,and no where else, they would cease to beformidable from their numbers.”66 WhereasWilliam Story’s 1844 treatise on contract lawcontains seventy-seven divisions andsubdivisions of contract law, Langdell greatlyreduced this number, and refocused contractlaw on basic principles such as offer,

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acceptance, consideration, and conditionalcontracts.67

The view that the common law consisted ofrules that must be understood and applied inan analytical fashion, came to be known as“legal formalism.” Legal formalism wascondemned by Oliver Wendell Holmes, Jr., inhis famous 1897 Harvard Law Review articleThe Path of the Law,68 which harbingered thechange in perception of the legal process fromthe application of a fixed body of rules (whatHolmes called a “brooding omnipresence inthe sky”)69 to the process of adapting existinglegal principles and inventing new ones inorder to reflect current practices in society.70

In 1906, Professor Roscoe Pound spoke outagainst what he called “mechanicaljurisprudence,” and argued that rules of lawshould be evaluated based on the socialinterests they served.71 In 1919, Yale lawprofessor Arthur L. Corbin wrote of thechanging nature of legal principles.72 In 1949,Chicago Law Professor Edward Levi, in hisbook, AN INTRODUCTION TO LEGAL

REASONING, rejected the idea that “the legalprocess is the application of known rules todiverse facts.”73 Instead, he said “[t]he basicpattern of legal reasoning is reasoning byexample. It is reasoning from case to case.”74

The writings of Justice Holmes, Dean Pound,Professor Corbin, Professor Levi, and others,paralleled the rise of the Legal Realismmovement of the first half of the TwentiethCentury, which disavowed the view of the lawas a system of abstract principles, andsuggested that the role of judges was toresolve legal disputes in a manner consistentwith contemporary practices and a modernsense of justice. This and other developmentsresulted in the replacement of the view thatLogic was the essential element of legalreasoning by the view that judicial decisionsshould be a benign and enlightened exerciseof political power.75 Since under this

“modern” view lawyers could arguedepartures from precedent with greatersuccess, the importance of policy, ingenuity,and persuasive techniques in the practice oflaw was greatly increased. Logic was notabandoned, but it was relegated to the statusof one of several tools the lawyer could use topersuade the decision-maker.

In recent times, an analytical method calledInformal Logic has developed outside of thelegal arena, as an alternative to the rigidstructure of formal logic. This Articlediscusses the principles of formal andinformal logic adapted to legal reasoning. Athird model for legal reasoning overhangs theentire Article, consider legal analysis as aprocess of determining and applying theappropriate legal rule to resolve a legaldispute. No single approach to legal reasoningcan claim to be sufficient, since these modelsare at best over-simplifications of a complexreality. Human reasoning has more aspectsthan any one approach can capture.

A. FORMAL LOGIC. Formal Logic hasbeen divided into two parts: Deductive Logicand Inductive Logic. To that some writershave added a third: reasoning by Analogy,although some say that reasoning by analogyis just a special instance of Inductive Logic.Since the work of Blaise Pascal and Pierre deFermat in the 1600s, Reasoning withProbabilities has become an important part ofLogic.

1. Deductive Logic. As expounded by theancient sage Aristotle, Deductive Logic is amethod of using known truths to arrive atabsolutely certain conclusions. Aristotle usedwhat is called Syllogisms to frame issues inthe form of formal propositions, where two

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overlapping Premises necessarily lead to aConclusion. Judges and lawyers seldomexplicitly frame legal issues as Syllogisms. Itcan be helpful, however, to put the issues of alegal problem into the form of Syllogisms, sothat the logical components of the legalproblem are more evident and can be morereadily evaluated.

In modern times, Deductive Logic is moreoften expressed as two ideas linked in aconditional relationship called Implication. Inthis approach, logical arguments take the form“P implies Q,” meaning that an Antecedent“P” is connected to a Consequent “Q” in sucha way that if “P” is proven to be true then itnecessarily follows that “Q” is true. Inaddition to this rule of inference, Logic alsoprovides a rule of refutation: if the Implicationthat “P implies Q” is Valid, then proving that“Q” is false establishes that “P” is false. Theforegoing rule of inference and rule ofrefutation are powerful tools in the reasoningprocess.

Implications abound in legal reasoning.Sometimes Implications are explicitly stated,as when jury instructions state evidentiarypresumptions by which the proof of one factallows or requires a certain conclusion.Sometimes Implications are implicit, like thesign in a convenience store that says “WeCard Everyone,” meaning that if you areunder 21 years of age then you may not buybeer. It can be very helpful to break a legalproblem down into its underlyingImplications, so that the Antecedents and theConsequents, and the relationships betweenthem, can be evaluated.

2. Inductive Logic. It is often said thatdeductive reasoning moves from the generalto the particular, while inductive reasoningmoves from the particular to the general. It isalso said that deductive reasoning draws aConclusion from things that are alreadyknown in the Premises, while inductive

reasoning draws a Conclusion aboutsomething that is not already known from thePremises. Inductive Logic operates byexamining multiple occurrences, usingcreativity or a “hunch” to propose anexplanatory or unifying underlying principlestated as a hypothesis, and then subjecting thehypothesis to testing to determine its validity.It is the accepted view that inductivereasoning cannot establish principles withlogical certainty, but only with probability,albeit sometimes with a high degree ofprobability. Since the 1800's, inductivereasoning is often expressed in terms ofprobability. Some probabilities can be arrivedat using probability theory, but others canonly be reached by statistical analysis of data.Probability theory and statistical analysis havecome to dominate discussions of InductiveLogic. Statistical data on the outcomes oflegal disputes is usually not captured, either atthe aggregate level or on a court-by-court orjudge-by-judge basis, despite the fact thatsuch information would be immensely helpfulin predicting outcomes of legal disputes.Statistical analysis has not yet been widelyapplied to legal decision-making and theextensive work describing inductive reasoningin terms of probability and statistics is not yetreadily applied to legal issues. But thefundamental approach of Inductive Logic canbe applied to legal reasoning, and it is thisaspect of Inductive Logic that is addressed inthis Article.

3. Reasoning With Probabilities. Reasoningwith Probabilities has replaced the old Logicin those areas of concern where the mattersbeing considered cannot be determined withcertainty, but can be quantified (i.e., expressedin numbers) and subjected to mathematicalprocesses. Deductive Logic assumes thatPropositions are either True or False, based onPremises that are either self-evident or can beproved to a certainty. This Logic did not workwell with Premises that are partly true andpartly false, or Propositions that are

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sometimes True and sometimes False. If aPremise that is partly true and partly false canbe restated in narrower terms, to include onlythe “trues” and none of the “falses,” then theold Logic could still be used. However, insome situations advancing knowledgerequired that the revised Premise exclude somany exceptions that it lost its utility insupporting Propositions. The same processwas applied to Propositions that weresometimes True and sometimes False. If theProposition could be narrowed in scope toinclude only certainties, the old Logic couldstill be used. But there were instances whereno amount of narrowing could reach a placewhere the Proposition was always either Trueor False. In situations where the Propositionwas unavoidably sometimes True andsometimes False, then the old Logic could notbe applied. When probability theory wasdeveloped in the 1600s, the mathematiciansstepped forward to quantify uncertainties, andthe logicians followed in the 1800s and 1900swith logical systems that could handleprobabilities as well as certainties. Thisopened Logic up to the potential of deducingprobable Conclusions from possible Premises,and gave the methods of reasoning developedunder the old Logic a role in a wider ranges ofsituations, ranging from predicting the mostlikely position of an electron to predicting thelikely choice a person would make in a givensituation. Probabilities have their applicationin law, as when a psychiatrist testifies to thelikelihood of future dangerousness in a capitalmurder case, or when the Supreme Court isevaluating the constitutionality of continueddetention of a person convicted of a sexualcrime after he has completed the term of hiscriminal incarceration. In this Article, thebasics of Reasoning with Probabilities arediscussed, but extensive discussion is left tothe mathematically-minded.

4. Reasoning by Analogy. Reasoning byAnalogy is an analytical process that attemptsto associate a new item with a familiar item

that has already been classified, or attempts toassociate a new problem with a familiarproblem that has already been solved. If thesimilarities between the new and the old arejudged sufficient, then the classification orrule used for the old item or problem isapplied to the new one. This process isapplied whether it is a nuclear physicistconsidering a new subatomic particle createdwith a particle accelerator, or a zoologistclassifying a new insect discovered in the rainforest, or an astronomer classifying a newgalaxy discovered with a more powerfultelescope. Reasoning by Analogy is also usedwhenever a legal dispute does not clearly fallunder an existing rule of law, so that the judgemust compare the new case to various oldercases until s/he finds the closest fit, and usesthe rule from the old case to resolve the newone. Reasoning by Analogy also occurs whena judge is called upon to interpret a vague orambiguous statutory provision, which mayrequire her or him to compare the statute inquestion to other statutes in search of aconsistent meaning.

B. INFORMAL LOGIC. Informal Logicstarted in the 1960s as an effort to make Logicmore relevant to the kinds of arguments thatoccur in ordinary conversation. The goal is todevelop a logic that can be applied toeveryday reasoning. While the focus is still onestablishing premises that lead to aconclusion, there is no requirement (like thereis in Deductive Logic) that premises beabsolutely true before a sound argument canbe made. Informal Logic is willing to acceptthe possibility that an illogical argument maybe a useful starting place on the road toward abetter argument. Additionally, since exactnessand logical necessity are not a requirement forInformal Logic, people can make acceptablearguments that are based on approximationsand likelihoods. Informal Logic findsexamples of acceptable arguments in themedia, in political speech, in advertising, and

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not just in the rigidly structured hypotheticalexamples typically used in formal Logic.

C. A RULE-ORIENTED APPROACH.Deductive reasoning, inductive reasoning, andreasoning by analogy, come together in legalreasoning. Legal reasoning can be seen as alogical process in which problems areresolved by (i) determining the correct legalrule to apply, and then (ii) applying that ruleto resolve the dispute at hand. The rule-centered approach has two phases, “ruleselection” and “rule application.”

Rule selection requires the lawyer or judge todiscern which of the great welter of legalprinciples would best be applied to resolve alegal problem. A lawyer’s or judge’sawareness of these rules could come from lawschool, or from prior experience in thepractice of law, or from research in theparticular case, or from the arguments ofopposing counsel. Broad knowledge of thelaw, and broad experience with the law, andgood research skills, and creativity, and goodadvocacy, all play a part in the rule selectionprocess.

The rule-application process is more tightlyconnected to the facts of the specific case. Ifthe facts are in dispute, then rule-applicationgets into non-logical considerations likewhether a witness’s memory is accurate,whether a witness is lying, whether asignature is genuine, and the like. In thisdomain, human emotions, and the techniquesof comedy and drama and entertainment andpersuasion, compete with and can evenoutweigh logic. Where the rule finally appliedin the case requires the trial judge to exercisediscretion, then even when the law and thefacts are determined there is still the issue ofhow the judge might be persuaded to exercisethat discretion. In the realm of rule-application, natural-born persuaders contrastwith those who have studied the art ofpersuasion, and persons who act on intuition

contrast with those who act based on theirstudy of human psychology.

Having just neatly divided the legal reasoningprocess into two phases, it is necessary to saythat the process of rule-determination is notreally divorced from the process of rule-application. The nature of the dispute andfacts of the case are used to narrow the rangeof rules that might be selected to resolve thedispute. In some instances, anticipating how alegal rule will affect the outcome of a case caninfluence or even determine what rule isselected, so that anticipation of the rule-application process becomes part of the rule-selection process. Likewise, anticipating whatrule will be applied when a dispute winds upin court can influence how individuals act asthe underlying dispute is developing longbefore the dispute makes its way to acourtroom. In that instance, rule-determination can influence what the factswill be when the rule application processeventually occurs. So in actuality rule-determination and rule-application can beinteractive and interdependent. This Article,however, will treat the simpler case where therule-determination precedes and is notinfluenced by rule-application.

This rule-oriented approach to legal reasoningis taken up in more detail later in this Article,after formal logic and informal logic havebeen explored.

In a broad sense, Logic was developed as away to help people think and speak moreeffectively. The principles were derived froma study of successful reasoning techniques,used in philosophical discourse and persua-sive speaking. Thus, from the beginning Logicwas tied to the way people communicate, andthis tie persists to this day.

D. MODERN ARGUMENT THEORIES.Modern argument theories have recentlydeveloped to describe how arguments are

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presented in daily life. An important aspect tothe new approach is to view arguments as“defeasible,” meaning that they are subject tobeing refuted or abandoned as more data orevidence are received. In this light, defeasiblearguments are provisional, and make no claimto conclusive force as does Deductive Logic,or even to the strength of many examples orreliance on statistics and probabilities as inInductive Logic. Modern argument theoryfollows the premises-conclusion orantecedent-consequent forms of Logic, butwith no guarantees as to the ultimate truth ofthe Premises or the Conclusion. In this view,an Implication may be seen as a workinghypothesis, treated as reliable unless and untilsomething better comes along. The idea ofDefeasible Arguments is a useful construct inareas, such as the law, where there are rules oflaw that have exceptions, and where the appli-cability of a rule or exception depends onevidence for and against that must be weigh-ed. In such areas, some facts give rise togeneral rule that is presumptively appliedunless and until additional facts give moresupport to an exception to the rule or to analternate rule.

VI. FORMAL LOGIC. As Logic was bornof the intellectual analysis of the way peoplecommunicate, Logic eventually settled on theform of the reasoning process, and not thecontent of what was said. Thus, Logic con-cerns “Valid” and “Invalid” methods of rea-soning. Logic emphasizes the relationshipbetween two or more concepts, as opposed tothe relationship between concepts and reality(which would be philosophy or science), orthe relationship between concepts and audi-ences (which would be rhetoric or the arts.)76

This Article focuses on Propositional Logic,which is a system for using Logic Operatorsto connect Statements together into logicalPropositions, and to connect simple Proposi-tions together into more complex Proposi-tions, and to construct logical proofs using the

tools of Logic Argument. Propositional Logicapproximates the way people talk and reasonabout matters that arise in daily lives andbusiness.

A. ARISTOTLE. Aristotle of Stagira,Macedonia, lived from 384 B.C. to 322 B.C.His writings are the earliest comprehensivestudy of Logic that has survived to today,perhaps because--as Aristotle himselfclaimed--his were the first descriptivewritings on the subject. Aristotle was astudent of the philosopher Plato and a tutor ofthe conqueror Alexander the Great ofMacedonia. Aristotle wrote on most subjectsof interest to the ancient mind. Aristotle’swriting on Logic appear in six differentbooks: CATEGORIES, ON INTERPRETATION,PRIOR ANALYTICS, POSTERIOR ANALYTICS,TOPICS, and ON SOPHISTICAL REFUTATIONS,collectively called THE ORGANON. Thinkersand writers of western Europe’s Middle Agesseized on Aristotle’s works as a foundationfor their analysis of Logic, and Aristotle’sideas have remained foundational in the studyof Logic. Aristotle’s writing on Logicemphas i zed deduc t ive r ea son ing(sullogismos), but in his writings on sciencediscussed inductive reasoning (epagôgê).Aristotle characterized the two types of Logicin this way:

All instruction given or received by wayof argument proceeds from pre-existentknowledge. This becomes evident upon asurvey of all the species of suchinstruction. The mathematical sciencesand all other speculative disciplines areacquired in this way, and so are the twoforms of dialectical reasoning, syllogisticand inductive; for each of these lattermake use of old knowledge to impartnew, the syllogism assuming an audiencethat accepts its premisses, inductionexhibiting the universal as implicit in theclearly known particular. Again, thepersuasion exerted by rhetorical

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arguments is in principle the same, sincethey use either example, a kind ofinduction, or enthymeme, a form ofsyllogism.77

Aristotle thus ties together deductive logic,Inductive Logic, and Rhetoric. These threetopics are examined in this Article.

B. STATEMENTS, PROPOSITIONS,AND ARGUMENTS. Some of the termsused in Logic are words that have meanings inordinary usage, but also have specialmeanings in Logic that are different from theordinary meanings of the same words. This istrue for the terms “Statement,” “Proposition,”and “Argument” which are used throughoutthis Article. In this Article, the word“Statement” is used to describe a sentence, orpart of a sentence, that is used in a logicalProposition and can be said to be true or false,measured against the real world. The word“Proposition” refers to: (i) a Statement thathas been subjected to a Logic operation; (ii)two or more Statements that have beenlogically linked using a Logic Operator; or(iii) two or more logical Propositions thathave been linked using one or more LogicOperators into a Compound Proposition (i.e.,a Proposition consisting of simplerPropositions). The word “Argument” refers toa series of Statements or Propositions thathave been linked together to prove or disprovea contention in accordance with the rules ofLogic.

Example: “A”, “B”, and “C” are individualStatements, each of which can be true or false(with reference to the real world). “A And B”is an example of a Proposition, where twoStatements are logically connected by theLogic Operator “And”. The Proposition “AAnd B” is logically “True” or “False”depending on the individual truth or falsity of“A” and of “B”. “A and B together imply C”is an example of a compound Proposition,where two Statements, that have been joined

together in a Conjunctive Proposition (to wit:“A And B”), are logically linked to anotherStatement in a more complex Propositioncalled an Implication. Here the resultingcompound Proposition is that, “if A is trueand B is true, then C must be true.” Anexample of an Argument would be a series ofLogic steps that demonstrate that, if “A” and“B” imply “C”, and if “C” is false, then either“A” is false or “B” is false, or both are false.

C. T R U T H , V A L I D I T Y , A N DSOUNDNESS. In Logic, we deal withtruth/Truth (in both a factual and a Logicsense), Validity, and Soundness.

1. True and False. Propositional Logic,which is the focus of this Article, is“bivalent,” meaning that Statements,Propositions, and Arguments, must either befactually true (or logically True) or factuallyfalse (or logically False), not both and notneither. This is a consequence of Aristotle’sLaw of Excluded Middle, discussed in SectionVIII.A.5. Logic systems that are not bivalenthave been devised that avoid some problemsthat arise from bivalence, but they do noteasily correlate to normal speech and are notcovered in this Article.

When the terms “true” and “false” are appliedto Statements, they mean that the Statementaccurately reflects the real world, or it doesnot. When the terms "True" and "False" areapplied to a Logic Proposition or LogicArgument, they (confusingly) mean that theProposition or Argument is "logically True""or "logically False," according to the rules ofLogic (which may differ from the way that thereal world operates). To avoid confusionbetween the real world “true and false” andLogic’s “True and False,” when "true" and"false" are used in the ordinary sense (i.e.,accurate in reality or not), they are in lowercase, and when they are used in the Logicsense they are capitalized.

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The Proposition that “All A is B” is True ifand only if every “A” is a “B”. Otherwise it isFalse. The Proposition that "some A is B" isTrue if and only if at least one “A” is a “B”.The former Proposition (“All B”) can berefuted by finding a single counter-example ofan “A” that is not a “B”. The latterProposition (“Some B”) can be refuted onlyby considering every possible instance of “A”and “B”, if that is even possible. Viewed fromthe standpoint of making a persuasiveargument, the former type of Proposition(“all”) is easier to refute than the latter(“some”), and should be avoided if possible.

2. Valid and Invalid. Propositions andArguments can be Valid or Invalid. AllPropositions and Arguments start with aPremise, or several Premises, and passthrough one or more reasoned steps thatconform to the rules of Logic, to reach aConclusion. A Proposition or Argument isValid only if, in every conceivable instance,when the Premise is true the Conclusion istrue. It therefore follows that, if there is asingle instance where the Premise is true andthe Conclusion is false, then the Propositionor Argument is logically Invalid. Thus, if aProposition asserts “if P then Q", theProposition is Valid if and only if every time“P” is true “Q” is also true. (This bivalentapproach does not apply when the connectionbetween “P” and “Q” is only probable;accordingly, probable relationships arediscussed separately, later in this Article).

3. Sound and Unsound. Propositions andArguments can be Sound or Unsound. AProposition or Argument is Sound when (i) itis logically Valid, and (ii) the Premise (orAntecedent) is true. If a Proposition orArgument contains a Premise that is false (i.e.,pigs have wings), then the Proposition orArgument is Unsound and the truth of itsConclusion is not certain. A Proposition orArgument can be logically Valid even when itis Unsound. This is because Logic is an inter-

nally-consistent system of principles and rulesthat requires certain Statements to relate toother statements in particular ways. Whilelogical relationships often agree with ourconception of reality, accord with reality isnot required for Logic to work, and sometimesthe principles of Logic lead to Conclusionsthat are not in accord with reality. Thus, tosome extent Logic is independent from thereal world. This may seem like a deficiency,but this also allows us to use Logic todistinguish good from bad reasoning, evenwhen we are not certain of the truth of thePremise (or Antecedent).

4. Appl icat ion to Statements ,Propositions, and Arguments. A Statementis an assertion about the way the world is or isnot, or the way it might be, or the way itmight have been. A Statement is true if itaccurately reflects reality, and false if it doesnot.78

A simple Proposition is logically True orFalse, depending on the truth or falsity of theStatements contained in the Proposition.79 ACompound Proposition is True or False,depending on the Truth or Falsity of thesimple Propositions contained in theCompound Proposition.

An Argument is Valid or Invalid, dependingwhether each step of the Argument complieswith the principles and rules of Logic.Deductive and Inductive reasoning oftenproceed from one or more Premises, througha series of logical steps, to a Conclusion. Thisreasoning process is said to be Valid if andonly if, in every conceivable circumstance,when the Premises are true, the Conclusion isalso true. If there is a single instance wherethe Premises are true and the Conclusion isfalse, then the reasoning process is Invalid.The reasoning process is said to be Sound if itis logically Valid and all of its Premises aretrue. Although in real life disputes aresometimes won with an argument that is

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Invalid or Unsound, having the ability tomake an argument that is Valid and Sound, orspot an argument that is Invalid or Unsound,can be an advantage in some situations.

Here is an example of a Proposition,containing two Premises and a Conclusion,that is both Valid and Sound: “Four-leggedanimals can walk; pigs have four legs;therefore, pigs can walk”. The Proposition isValid because, in all instances, when the twoPremises are true the Conclusion is true. TheProposition is Sound because its two Premisesare true. If one or more of the Premises of aValid Proposition are false, then theProposition is Unsound. Here is an example ofa Proposition that is Valid but Unsound:“Creatures with wings can fly; pigs havewings; therefore, pigs can fly”. ThisProposition is Valid, but it is also Unsound,because the second Premise is false (pigsdon’t have wings).80 If someone were to makethe same statement in normal conversation, itwould likely be a conditional statement in thesubjunctive mood81: “if pigs had wings, theycould fly,” or stated more formally, “if pigswere to have wings, then they would be ableto fly.” In normal English speech and writing,a conditional statement and the subjunctivemood are typically used when the speakerknows that the Antecedent is false, or isunsure of the truth of the Antecedent, orwishes to defer an assessment of the truth ofthe Antecedent until after the Argument hasbeen completed. The issue of Validity andSoundness becomes more complex when theProposition involves Premises that are knownto be untrue, as when a person speculates onhow history might have been different ifsomething that did happen had not, or ifsomething that did not happen had happened.Example: “if Napoleon had not invadedRussia, he would have died the Emperor ofFrance.” See Section VII.C.14.c.

Whether a Proposition is Sound or Unsounddepends upon whether the Premises are true

or false, not upon whether the Conclusion istrue or false. An Invalid Proposition can havea Conclusion that is true, just as an UnsoundProposition can have a Conclusion that is true.When it comes to the truth of Conclusions,Deductive Logic only guarantees that ValidPropositions with true Premises have trueConclusions, nothing more. Many logicalPropositions simply assume that the Premiseis true, and concern themselves with theConclusion that follows from that assumption.Thus, logical analysis can be applied toPremises whose truth is unknown. Where aProposition is logically Valid, if an assumedPremise leads to a Conclusion that we knowto be false, then Logic says that the Premisemust be false.82 If we change the focus of thisreasoning process from a Conclusion that isfalse to a Conclusion that is undesirable, thenwe have a rule of reason that guides our dailylives: if we don’t want a certain result, thenwe avoid the action that leads to that result.

VII. DEDUCTIVE LOGIC. DeductiveLogic is a system of reasoning orargumentation, in which rules of Logic areused to show that the truth of one thing (called“the Premise” or “the Antecedent”)establishes the truth of another thing (called“the Conclusion” or “the Consequent”).Deductive Logic Propositions can bedeclarative or conditional. A declarativeProposition arrives at a Conclusion based ontwo (or more) Premises that are asserted to betrue. Example: “the fact that grass is greenindicates that grass contains chlorophyll”. Thetwo Premises in this Proposition (one explicitand one implicit) are that (i) “grass is green”and that (ii) “green plants containchlorophyll”. A Conditional Proposition takesthe form: “if a certain thing is true, thensomething else necessarily follows.”Example: “If you shout ‘fire’ in a crowdedtheater, then you will start a stampede for theexits and people will be hurt.”83

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In Aristotle’s own words, translated intoEnglish:

A deduction is speech (logos) in which,certain things having been supposed,something different from those supposedresults of necessity because of their beingso. (PRIOR ANALYTICS, I.2 246 18-20).

This formulation has become the essence ofDeductive Logic. Aristotle’s “thing supposed”is today called “the Premise” (or“Antecedent” in a Conditional Statement) andwhat results of necessity is called “theConclusion” (or “Consequent” in aConditional Statement).

A. DEFINING CONCEPTS ESSENTIALTO ARISTOTLE’S DEDUCTIVELOGIC.

1. Statements. In Aristotle’s view,Deductive Logic is composed of Statements,in the form of declarative sentences with asubject and a predicate, where the subjecteither affirms or denies what is stated in thepredicate. For Aristotle, each Statementrelates a single subject to a single predicate.Accordingly, unlike modern logicians,Aristotle did not see Logical Conjunction (“AAnd B”) or Logical Disjunction (“A Or B”) aslogical Propositions.84 In a Statement, thegrammatical subject and predicate eachcontain a “Term.” A Term can be either“Particular” or “Universal.” A particular Termis a specific person, like the philosopherSocrates, or a particular animal, like Buce-phalus (Alexander the Great’s horse), or aparticular thing, like the Parthenon. AUniversal term is an abstraction like “man,” or“horse,” or “temple.” To Aristotle, the subjectof a Statement can be either Particular orUniversal, but the predicate can only beUniversal.85

2. A f f i r m a t i o n , D e n i a l , a n dContradiction. An affirmation asserts that

something is true. Aristotle believed thatevery affirmation corresponds to one denial,where the denial denies what the affirmationaffirms. An affirmation that is logically pairedwith its corresponding denial constitutes a“Contradiction.” To Aristotle, one member ofa Contradiction is true and the other is false.Example: to say that a particular thing is both“A” and “not-A” is a Contradiction. ToAristotle, either “A” is true and “not-A” isfalse, or else “A” is false and “not-A” is true.“A” and “not-A” cannot both be true or bothbe false. In this context, “A” and “not-A” aresaid to be “mutually exclusive.” See the Lawof Contradiction, discussed in SectionVIII.A.5.

3. All; None; and Some. The Quantifiers“All,” “None,” and “Some” play an importantpart in Aristotle’s logic, and even more so inthe version of modern formal Logic that arosefrom the writings of Gottlob Frege in the lateNineteenth Century. You can assert that “all Ais B,” or “no A is B,” or “some A is B,” or“some A is not B”. The Propositions “All A isB” and “no A is B” are Universal assertions,and these two Universals are Contradictory.“Some A is B” is a Particular assertion whichis Contradictory to the universal assertion “NoA is B”. Where the subject of an assertion isUniversal (all A is B), it can be deniedUniversally (no A is B) or in the Particular(some A is not B). These concepts arediscussed in greater detail in Section VII.B.8.,relating to the Rules of Opposition.

4. Principles, Rules, and Symbols. Just asmathematics has principles, rules, andsymbols, that allow us to make calculationseasily with confidence in the result, so Logichas principles and rules and symbols thatallow us to reason easily and with confidencethat the Conclusions we draw from ourPremises are correct. However, in manyinstances natural language sentencesoccurring in normal conversation or in legalarguments are not stated in strictly logical

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terms. Sometimes an illogical argument isobviously illogical on its face. At other timesit is necessary to translate a natural languagestatement or argument into the structure andlanguage of Logic in order to more easily seehow the principles and rules of Logic can beapplied. The most efficient way to convertnatural language arguments into Logic is bysubstituting variables (such as A, B, C, P, Q,etc.) for the assertions in a natural languageargument, and substituting Logic symbols forthe verbal connections between assertions,and then organizing the natural languageargument into one or more of the forms ofLogic Argument that are familiar and whoseproperties are well-known. This process oftranslation makes it much easier to tellwhether the natural language argument isValid and Sound.

5. Three Fundamental Principles ofLogic. Aristotle suggested three fundamentalprinciples of Logic (also known as “Rules ofThought”): the Law of Identity; the Law ofContradiction; and the Law of the ExcludedMiddle.

The Law of Identity provides that a thing isthe same as itself. This can be stated: “A isA”.86

The Law of Contradiction provides that athing cannot be both itself and not itself.Aristotle said: “it will not be possible to beand not to be the same thing.”87 Stateddifferently, a thing cannot be both “A” and“not-A” at the same moment.88 Aristotle statedit three ways: (i) “It is impossible that thesame thing belong and not belong to the samething at the same time and in the samerespect;” “no one can believe that the samething can (at the same time) be and not be;”and “the most certain of all basic principles isthat contradictory propositions are not truesimultaneously.” It has been said that inWestern Philosophy, the principle of non-contradiction is deemed essential to all

thought, as it asserts the incompatibilitybetween truth and falsity, which is the basisfor all intellectual distinctions about theworld.

The Law of the Excluded Middle, providesthat something is either one kind of thing or itis not that kind of thing--there is no thirdalternative. Stated differently, something iseither “A” or it is “not-A”.89 Leibniz wrote it:“Every judgment is either true or false.”

B. THE SYLLOGISM.90 Aristotle’sstructure for Deductive Logic, which latercame to be called the Syllogism, consists oftwo Statements, called “Premises,” which leadby logical necessity to a third Statement,called the “Conclusion.” Since Aristotle’sapproach to organizing his thoughts about theworld was to put things into categories, hisSyllogisms involved including things in, orexcluding them from, categories. This form ofSyllogism is therefore called the “CategoricalSyllogism.”

There are four forms of Syllogism: (i) thesimple Syllogism; (ii) the HypotheticalSyllogism; (iii) the Disjunctive Syllogism;and (iv) the Dilemma.

1. The Simple Syllogism. The form ofSyllogism that Aristotle discussed in his bookON INTERPRETATION is made up of declarativesentences, where the Term (which may beParticular or Universal) expressed in thesubject of each sentence is included in orexcluded from the Universal categoryexpressed in the predicate of that sentence.The Term presented in the subject of adeclarative sentence is connected by “is” or“is not” to the Term in the predicate of thesentence. The classic example of this form ofSyllogism, coined in the Middle Ages andused ever since, is:

All men are mortal.Socrates is a man.

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Therefore, Socrates is mortal.

In the foregoing example, the first sentence isthe “Major Premise;” the second sentence isthe “Minor Premise;” and the third sentence isthe “Conclusion.” This 1-2-3 sequence iscalled the “Standard Order.” The order of thesentences can be switched around withoutaffecting the Validity of the Syllogism. Thestructure of the Syllogism works like this: theMajor Premise presents general categories,general alternatives, or general conditions,while the Minor Premise addresses aparticular instance of the Major Premise. Ifthe Major and Minor Premises are true, thenthe Conclusion necessarily follows.91

Conversely, if the Conclusion is false, theneither the Major Premise or the MinorPremise, or both, are false.92

The rules of Syllogism require that the MajorPremise and Conclusion share a commonTerm, called the “Major Term,” in theforegoing example “mortal.” Likewise, theMinor Premise and the Conclusion must sharea Term, called the “Minor Term,” in theforegoing example “Socrates.” The MajorPremise and Minor Premise must share aTerm that does not appear in the Conclusion.This Term is called the “Middle Term,” in theforegoing example “men/man.” The MiddleTerm is what links the Minor Premise to theMajor Premise. Unless the Major Premise andthe Minor Premise are linked by the MiddleTerm, the deductive nature of the Syllogismfails, and the Conclusion does not deductivelyfollow from the two Premises.

The Socrates example includes the ParticularTerm (Socrates) in a Universal category(men), which in turn is included in aUniversal category (mortal). One could saythat the individual “Socrates” belongs to thecategory of “men,” and the category of “men”belongs to the category of “mortal”; therefore,Socrates belongs to the category of “mortal”.

The following Syllogism excludes theParticular from a Universal category:

All mammals have hair.This specimen has no hair.Therefore, the specimen is not a mammal.

The following is a Syllogism, with partsidentified (this Syllogism includes a Particularin one of two mutually exclusive Universalcategories, which results in the Particularbeing excluded from the other UniversalCategory):

Major Premise: Cats are not dogs.Minor Premise: Felix is a cat.Conclusion: Therefore, Felix is not a dog.

The Major Term is “dog.” The Minor Term is“Felix.” The Middle Term is “cat.” The MajorPremise could have been stated “No cats aredogs” without changing the Conclusion.

Here is another Syllogism:

All swans are white.This bird is black.Therefore, this bird is not a swan.

The Middle Term is “white” (where “black” istaken to mean “not white”). This “swan”Syllogism is logically Valid, but it was provedto be Unsound (for Western Europeans) in1679, when a Dutch explorer found blackswans on the Swan River in Australia. Thisdiscovery disproved the Major Premise of theSyllogism. After the discovery of blackswans, the Syllogism was Unsound, but it wasnonetheless still logically Valid. TheSyllogism could be thought of as Conditional:“if all swans are white, then this black bird isnot a swan”. The Dutch explorer disprovedthe Antecedent of the Conditional Proposition,but he did not prove the ConditionalProposition to be logically Invalid. The term“black swan” has now come to signify asituation once believed to be impossible, that

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nevertheless has actually occurred. TheConditional Proposition had to be restated:“Since most swans are white, this black bird isprobably not a swan”.

The following Syllogism is logically Valid,even though the Major and Minor Premisesare untrue:

Unicorns have four legs.This animal is a unicorn.Therefore, this animal has four legs.

Because at least one (in this case, both) of thePremises is false, the foregoing Syllogism isUnsound.

Here are more examples of Syllogisms:

Toyotas are not safe to drive.This car is a Toyota.Therefore, this car is not safe to drive.

2 x 2 = 4.2 x 4 = 8.Therefore, 2 x (2 x 2) = 8.

In the foregoing Syllogism; the Major Term is“2 x 2;” the Minor Term is “8”, and theMiddle Term is “4”. More examples ofSyllogisms:

A is to the left of B.B is to the left of C.Therefore, A is to the left of C.

Paris is not in England.Jean is in Paris.Therefore, Jean is not in England.

Take the following Syllogism:

Presidents must be born in the USA.Barak Hussein Obama is President.Therefore, Obama was born in the USA.

The foregoing Syllogism is logically Validand Sound, but whether the Conclusion is trueis a matter of controversy.93 See “Begging theQuestion” discussed in Section VII.K.6.

The following Syllogism is invalid:

Toyotas are not safe to drive.This car is a Ford Explorer.Therefore, this car is safe to drive.

The Major Term is “safe to drive,” whichappears in the Major Premise (in negativeform) and appears in the Conclusion (inaffirmative form). The Minor Term is “thiscar”, which appears in the Minor Premise andthe Conclusion. The Middle Term is . . . thereis no Middle Term, because the Middle Termmust appear in the Major Premise and MinorPremise but not in the Conclusion. Whatshould be the Middle Term is “Toyotas” in theMajor Premise and “Ford Explorer” in theMinor Premise, but since the terms are not thesame, there is no Middle Term that connectsthe two Premises, so the Syllogism is Invalid.See the “Fallacy of Four Terms,” discussed inSection VII.B.10.a. The fact that theSyllogism has failed does not tell us whetherthe Conclusion is true or false. As you mayhave heard, some juries have found that FordExplorers are not safe to drive, at least withFirestone tires. If these juries are right, thenthe Conclusion is true--not because of thefailed Syllogism, but rather because ofexternal fact.

Here is another invalid Syllogism:

Things that honk are cars.This goose honks.Therefore, this goose is a car.

Although, the foregoing Syllogism appears tohave the word “honk” as a Middle Term, inactuality it does not. Although the MajorPremise and the Minor Premise both use thesame word “honk,” they use the same word in

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different senses (i.e., a car’s honk and agoose’s honk are different kinds of honks).The foregoing Syllogism is another exampleof the Fallacy of Four Terms. See SectionVII.B.10.a. The Fallacy arises because ofAmbiguity, which occurs when a word orphrase has two or more meanings. See SectionXV.2. When a person uses the Middle Termin one sense in the Major Premise and anothersense in the Minor Premise of a syllogisticargument, this use of Ambiguity is called“Equivocation.” See Section XV.22.

Another Invalid Syllogism:

All Country and Western singers wearcowboy hats.

That fella is wearing a cowboy hat.Therefore, that fella is a Country and

Western singer.

This is Invalid reasoning. Cattle ranchers alsowear cowboy hats, and that fella could be acattle rancher who can’t sing. This is anexample of the “Fallacy of the UndistributedMiddle Term.” See Section VII.B.10.b. Hereis another example that reflects the Fallacy ofthe Undistributed Middle Term:

All kangaroos are marsupials.This animal is a marsupial.Therefore, this animal is a kangaroo.

This is Invalid reasoning. Wombats are alsomarsupials, and the animal in question couldbe a wombat and not a kangaroo.

As noted before, the primary focus of Logic ison the relationship between the Premise andthe Conclusion, and only incidentally on thetruth of the Premise or the Conclusion. Givingexamples of Syllogisms that use real worldconcepts makes it unfortunately too easy toconfuse the Validity of a Syllogism with thetruth of the Statements made in the Syllogism.To avoid this problem, Aristotle substitutedsymbols for words, and thereby introduced to

the world the concept of “variables,” whichone writer called Aristotle’s most enduringcontribution to the history of thought. Usingvariables, a simple categorical Syllogism isexpressed: “All A is B; all B is C; therefore,all A is C”. Discussing logical Propositionsusing variables allows the reader to look pastthe truth of the statements in the Propositionand to focus instead on the logicalrelationships between the Statements.

In PRIOR ANALYTICS, Aristotle identifiedthree types of syllogistic Propositions: (i) Abelongs to B; (ii) A is predicated of B; and(iii) A is said of B.94 “A belongs to B” when Ais an item that fits within the category B. “A ispredicated of B” when A appears in thepredicate of a sentence in which B is thesubject. “A is said of B” when A and B aresubcategories of a larger category, butsubcategory B is smaller and belongs tosubcategory A.95 There are many othercomplexities to Aristotle’s explanation ofSyllogisms which interested readers may wishto explore.

2. Polysyllogism. Deductive reasoning caninvolve one Syllogism, or a series of linkedSyllogisms. A series of linked Syllogisms iscalled a Polysyllogism. In a Polysyllogism,the Conclusion of the preceding Syllogism isthe Major Premise of the next Syllogism.Example:

(1) All A is B.(2) All B is C.(3) Therefore, all A is C.(4) All A is C.(5) All C is D.(6) Therefore, all A is D.

3. Enthymeme. In speaking or writing,people often state arguments in the form of aSyllogism, while omitting one of the twoPremises, or the Conclusion. Such anincomplete Syllogism is called an“Enthymeme”. Example:

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1. All arguments missing a premise areenthymemes.

2. Therefore, this argument is an enthy-meme.96

Since an Enthymeme can be a Syllogism thatis missing either the Major Premise, the MinorPremise, or the Conclusion, to see the logic ofsuch an Enthymeme it is sometimes necessaryto “expand” the Enthymeme into a Syllogismby supplying the missing part(s). Expandingthe Enthymeme allows the Proposition to bemore easily evaluated using the rules ofSyllogisms. This can be an important exercisebecause, when one of the parts of a Syllogismis implicit, the asserted Proposition is morereadily assumed to be Valid when it is not, orthe possibility that a Conclusion is Unsound ismore likely to be overlooked. Rules forexpanding Enthymemes are discussed inSection VII.B.11.

Enthymemes have another feature thatdistinguishes them from Syllogisms:Enthymemes do not have to arrive atConclusions that are certain; they may arriveat Conclusions that are possible or probable.A Logic Proposition that has a Major Premise,Minor Premise, and Conclusion, but theConclusion is only possible or probable ratherthan certain, is an Enthymeme.

Aristotle wrote that Enthymemes arefrequently used in public speaking, and hecovered the topic in detail in his book onRHETORIC. See Section XIV.C.2. Manybelieve that Aristotle used the wordEnthymemes differently in the RHETORIC.

4. Sorites. A SORITES is a chain ofincomplete syllogisms in which the predicateof each Premise forms the subject of the nextuntil the end, when the Conclusion is linked tothe subject of the first Premise. A Soritesomits all Conclusions except for the last one.

An example:

For want of a nail the shoe was lost.For want of a shoe the horse was lost.For want of a horse the rider was lost.For want of a rider the battle was lost.For want of a battle the kingdom waslost.And all for the want of a horseshoe nail.

Sorites are of two types: ARISTOTELIAN SO-RITES and GLOCLENIAN SORITIES. In anAristotelian Sorites, the first Proposition is theMinor Premise of its Syllogism and theremaining Propositions are Major Premiseswhich lead to the Conclusion. In a GloclenianSorities, the first Proposition is the MajorPremise of its Syllogism and the rest of thePropositions are Minor Premises which leadto the Conclusion.

Example of Aristotelian Sorites:

A is BAll B is CAll C is DTherefore, A is D.

Example of a Gloclenian Sorites:

All A is BB is CC is DTherefore, A is D.

Another example of a Sorites:

Julius Caesar was a great conqueror.Through conquest, Caesar acquired wea-

lth and glory.Caesar’s wealth and glory increased his

popularity.Caesar’s popularity increased his

political power.Caesar’s increased political power

threatened the aristocracy.Therefore, aristocrats killed Caesar.

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Charles L. Dodgson (a/k/a Lewis Carroll, ofALICE IN WONDERLAND fame) was alogician.97 In 1896, Dodgson developed asystem to determine the validity of highlycomplicated arguments that take the form ofSorites.98 He listed some playful examples ofSorites with the Conclusions omitted, a few ofwhich are set out below. In case you want toplay along with Lewis Carroll, the Conclusionfor each Sorites is contained in an end note.

(1) Babies are illogical; (2) Nobody is despised who can manage a

crocodile; (3) Illogical persons are despised.99

(1) My saucepans are the only things I havethat are made of tin;

(2) I find all your presents very useful; (3) None of my saucepans are of the slightest

use.100

(1) No potatoes of mine, that are new, havebeen boiled;

(2) All my potatoes in this dish are fit to eat;(3) No unboiled potatoes of mine are fit to

eat.101

(1) Every one who is sane can do Logic; (2) No lunatics are fit to serve on a jury; (3) None of your sons can do Logic.102

(1) No birds, except ostriches, are 9 feethigh;

(2) There are no birds in this aviary thatbelong to any one but me;

(3) No ostrich lives on mince-pies; (4) I have no birds less than 9 feet high.103

(1) When I work a Logic-example withoutgrumbling, you may be sure it is one thatI can understand;

(2) These Sorites are not arranged in regularorder, like the examples I am used to;

(3) No easy example ever makes my headache;

(4) I can't understand examples that are notarranged in regular order, like those I amused to;

(5) I never grumble at an example, unless itgives me a headache.104

(1) Every idea of mine, that cannot beexpressed as a Syllogism, is reallyridiculous;

(2) None of my ideas about Bath-buns areworth writing down;

(3) No idea of mine, that fails to come true,can be expressed as a Syllogism;

(4) I never have any really ridiculous idea,that I do not at once refer to my solicitor;

(5) My dreams are all about Bath-buns; (6) I never refer any idea of mine to my

solicitor, unless it is worth writingdown.105

5. When Premises are Inconsistent. InFormal Logic, a Proposition, with one or morePremises leading to a Conclusion, is Valid ifand only if there is no possible situation inwhich all Premises are true and theConclusion is false. Where two or more of thePremises of an Argument are inconsistent, itis impossible for all of the Premises to be true.An Argument with inconsistent Premises cannever be Invalid because there are nosituations in which all of the Premises are trueand the Conclusion is false.

Example: “All A is B; no A is B; therefore,the Tower of Piza does not lean”. ThisProposition is logically Valid, because the twoPremises are a Contradiction, meaning thatthere is no instance in which all of thePremises are true and the Conclusion false.This example demonstrates a larger principle:a Proposition with inconsistent Premises isalways logically Valid, no matter what theConclusion may be. Thus, inconsistentPremises validly imply all Conclusions, orstated differently: anything can be inferredfrom a Contradiction. This situation is calledthe “Principle of Explosion.” When Premises

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are contradictory (meaning that one of thePremises must be false so that the propositionby necessity is Unsound), the rules of Logicvalidate Conclusions that do not help us tounderstand the world. Unsound Propositionsdo not tell us whether the Conclusion is trueor false.

6. The Hypothetical Syllogism. In anHypothetical Syllogism, the first Premisepresents a choice which must be resolved bythe second Premise in order to reach theConclusion. There are three kinds ofHypothetical Syllogisms: Conditional;Conjunctive; and Disjunctive.

a. The Conditional Syllogism. AConditional Syllogism takes the form: “if Pimplies Q and Q implies R, then P implies R”.

b. The Conjunctive Syllogism. AConjunctive Syllogism contains a compoundMajor Premise in the form of a ConjunctiveProposition that is denied. The Minor Premiseof the Syllogism then either affirms or deniesone of the conjunctive terms. Example:

A and Not-A cannot both be true.Not-A is true.Therefore, A must be false.

c. The Disjunctive Syllogism. The MajorPremise of a Disjunctive Syllogism presentstwo or more alternatives from which tochoose, only one of which can be true. (Thisis the Exclusive Disjunctive, discussed inSection VII.F.3). The Minor Premise theneither chooses one of the alternatives, orrejects all alternatives except one. Example:

A or B. A or B.A. or B.Therefore, not-B. Therefore, not-A.

In the foregoing example, “A” and “B” mustbe mutually exclusive or the Disjunctive

Syllogism is Unsound (i.e., it has a falsePremise). Another example:

A or B or C or D.Not-A.Not-B.Not-C.Therefore, D.

The foregoing example shows proof by“process of elimination.” Another example:

Either it is night or it is day.It is not night.Therefore, it is day.106

The foregoing Syllogism raises the problem ofgradations (i.e., when does night becomeday?) See Section XIX.

Enthymemes may be disjunctive.

7. Quantifiers and Distribution.Quantifiers are Logic Operators that signifyquantity, or degree, or extent, in connectionwith categorical Propositions. TypicalQuantifiers are “all,” “every,” “some,” and“no.” The phrase from the Declaration ofIndependence, “all men are created equal,”contains the Quantifier “all.” George Orwell’s1945 book ANIMAL FARM says: ”All animalsare equal but some animals are more equalthan others.” This sentence contains twoQuantifiers: “all” and “some.” (It alsoexemplifies Equivocation, discussed inSection XV.22.) The sentence “no trueScotsman would do such a thing” contains theQuantifier “no.” “No true Scotsman” is arecognized Fallacy. See Section XV.31.

The most common forms of categoricalPropositions using Quantifiers are designatedA, E, I and O. In the following listing, “S”stands for the subject of the Proposition and“P” stands for the predicate.

A = All S is P.

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E = No S is P.I = Some S is P.O = Some S is not P.

When a Categorical Proposition is in one ofthe foregoing forms it is said to be in“Standard Form.”

The first three of the foregoing Propositionsare subject to Conversion, in which a newProposition is stated having as its subject theoriginal predicate and having as its predicatethe original subject. The following tablereflects the Conversion:

Original ConverseA All S is P Some P is SE No S is P No P is SI Some S is P Some P is SO Some S is not P N/A

In the A-type Proposition, the Converse isonly implied. In the E- and I-type Propositionsthe Converse is Logically Equivalent to theoriginal. See Section VII.F.5 for a discussionof Logical Equivalence.

In recent times, what was traditionally called“categories” have come to be called “sets,”which are groupings of objects (which may bereal things, or may be purely conceptualthings like numbers or mathematicalfunctions). A set has “members.” Members ofa set are distinguished from non-members ofthat set by virtue of their membership in theset. The non-members of the set belong toanother set, which is the set of things that donot belong to the first set. The set of non-members is called the “Complement” of theoriginal set. In the A-form in foregoinglisting, the set of all S is a sub-set of the set ofall P. In the E-form, no member of set S aremembers of set P. In the I-form, somemembers of set S are members of set P. In theO-form, some members of set S are notmembers of set P.

Quantifiers also involve the concept of“distribution.” A Term in a Syllogism isDistributed if it extends to all or none of themembers of the category or class to which itrelates. The Term is Undistributed if it appliesonly to some of the members. Thus, thesubject of the A- and E-type Propositions areDistributed, while the subject in the I- and O-type Propositions are Undistributed. ThePredicate is distributed in the E and O forms,but not the A and I forms. The following tabledemonstrates:

Type DistributionA = All S is P S= Yes P= NoE = No S is P S= Yes P= YesI = Some S is P S= No P= NoO = Some S is not P S= No P= Yes

8. The Rules of Opposition. The A, E, I, O,and U forms discussed in the previous Sectionalso arise in connection with the concept ofOpposition. The conventional view ofstatements in Opposition to each other datesback to Aristotle. Aristotle envisionedcategorical statements to have different formsof Opposition. Here are the Quantifiers, andtheir status in terms of Opposition:107

A = All S is P Universal AffirmativeE = No S is P Universal NegativeI = Some S is P Particular AffirmativeO = Some S is not P Particular Negative108

A medieval theorist named Boethius, placedthese terms into a Square of Opposition:

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The Square of Opposition indicates that A andE are Contradictories; that is to say, “All S isP” is the Contradictory of “Some S is not P”and vice-versa. The Square of Opposition alsoindicates that I and E are Contradictories; thatis to say, “Some S is P” is the Contradictoryof “No S is P” and vice-versa. The Squarealso indicates that A is a Contrary of E; that isto say, “All S is P” is Contrary to “No S is P”and vice-versa. And the Square indicates thatI is a Subcontrary to O; that is to say, “SomeS is P” is the Subcontrary of “Some S is notP” and vice versa. The Square also indicatesthat A is a Subaltern of I; that is to say, “All Sis P” is a Subaltern of “Some S is P” and viceversa. The Square indicates that E is aSubaltern of O; that is to say, “No S is P” isthe Subaltern of “Some S is not P”, and viceversa.109

The Square may help in distinguishingContradictories, Contraries, Subcontraries,and Subalterns, which are defined as follows:

Contradictories–two Propositions areContradictory if and only if they cannot bothbe true and cannot both be false.Contraries–two Propositions are Contraries ifand only if they cannot both be tru but canboth be false.Subcontraries–two Propositions are Subcon-traries if and only if they cannot both be falsebut can both be true.Subalterns–two Propositions are Subalterns ifand only if, when one Subaltern is true thenthe other Subaltern must be true, and whenone Subaltern is false then the other Subalternmust be false.110

9. Rules for Syllogisms. There are six rulesfor syllogisms that must be observed for theSyllogism to be in proper form. A Syllogismthat violates such a rule is a Fallacy.Syllogistic Fallacies are discussed in SectionVII.B.10.

Rule No. 1: A Syllogism contains threeTerms, no more and no less. Aristotle wrote:“[I]t has been shown that the positing of onething--be it one term or one premiss--neverinvolves a necessary consequent: twopremisses constitute the first and smallestfoundation for drawing a conclusion at all andtherefore a fortiori for the demonstrativesyllogism of science.”111 For a Syllogism towork, it must contain a Major Term (thatconnects the Major Premise to theConclusion), a Minor Term (that connects theMinor Premise to the Conclusion), and theMiddle Term (that connects the MajorPremise to the Minor Premise). If there areonly two Terms, then a Syllogism cannot beconstructed.

A Syllogism with four Terms occurs whenwhat is supposed to be the Middle Terminstead consists of two different words, whichmeans that the two Premises are notconnected by a shared Term. Example: “Allmen are mortal; Socrates is a Greek”. Becausethere are four Terms instead of three in thetwo Premises, the Premises are not connectedand no Conclusion can be reached. See the“Fallacy of Four Terms” in SectionVII.B.10.a. Four Terms also can occur whenthe same word appears as the Middle Term ineach Premise, but the Middle Term’s meaningin the Major Premise is different from theMiddle Term’s meaning in the Minor Premise.This problem is called Ambiguity, andsometimes Equivocation.

Rule No. 2: The Middle Term must bedistributed (“Universal”) in one or both ofthe Premises. A Term is “distributed” when itdescribes the entire class to which is applies.“All” or “No” are words indicatingdistribution. For a Syllogism to work, theMiddle Term must be distributed in either theMajor Premise or in the Minor Premise.Example: “All men are mortal; Socrates is aman; therefore, Socrates is mortal”. Here theMiddle Term “man/men” is distributed in the

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Major Premise, because “all men” isdistributed, or Universal. The Middle Term isnot distributed in the Minor Premise becausethe reference is to an individual man namedSocrates. If the Major Premise said “some,”“many,” or “most” men, and the MinorPremise were limited to one man, then theMiddle Term would not be distributed ineither Premise and the Syllogism would notwork. Example: “Some men are mortal;Socrates is a man.” You cannot conclude fromthe foregoing Syllogism that Socrates ismortal, because the Middle Term (man/men)is not distributed in either Premise, and thetwo Premises do not indicate whether Socratesis within the portion of men who are mortal. Asecond example: “All A is B; some B is C”.You cannot conclude from these two Premiseswith an Undistributed Middle Term, that “allA is C” or even that “some A is C”.

Rule No. 3: Each Distributed Term in theConclusion must be Distributed in one of thePremises. For a Syllogism to be Valid, theConclusion cannot contain a distributed Termthat is derived from a non-distributed Term inthe Premises. Example: “Some A is B; all B isC; therefore, all A is C”. The foregoingSyllogism is invalid because the Major Term(“A”) in the Conclusion is Distributed whilethe Major Term in the Premises is notDistributed.

Rule No. 4: A Syllogism cannot contain twonegative Premises. A Syllogism that containstwo negative Premises cannot ensure that theCategories in the two Premises overlap, sothere is no linkage between the two Premisesthat can guarantee that the Conclusionnecessary follows. Example: “No A is B; no Bis C”. You cannot conclude from theforegoing Premises whether or not any “A” is“C”. Second example: “No B is C; all A is B;therefore, no A is C”. The foregoingSyllogism, with only one negative Premise, isvalid. Fourth example: “Either X or Y, but notboth; not X; therefore, Y”. The foregoing

Syllogism is Valid, because only one Premiseis negative.

Rule No. 5: If either Premise is negative, thenthe Conclusion must be negative. Rule 5 saysthat if a Premise excludes something from acategory, the Conclusion also must excludesomething from a category. Example: “All Ais B; no B is C; therefore, no A is C”.

Rule No. 6: If both Premises are Distributed,the Conclusion must be Distributed. If theMajor Term is Distributed, and the MinorTerm is Distributed, then the subject of theConclusion must be Distributed. Examples ofValid Syllogisms: “All A is B; all B is C;therefore, all A is C”. “All A is B; no B is C;therefore, no A is C”.

10. Fallacies of Syllogistic Logic. Aristotlesuggested several Fallacies related to theSyllogism of Deductive Logic. Subsequentwriters have added more to the list.

a. The Fallacy of Four Terms. Alegitimate Syllogism has three Terms: theMajor Term; the Minor Term; and the MiddleTerm. The Fallacy of Four Terms occurswhen the Syllogism has four Terms, whichoccurs because the Term in the Major Premisethat is supposed to be the Middle Term doesnot match the Term in the Minor Premise thatis supposed to be the Middle Term. Peopleseldom use different words for the MiddleTerm, since it is so evidently wrong. TheFallacy usually results from using same wordas the Middle Term in both Premises, butwhere the meaning or sense of the word isdifferent as used in each Premise. Thisproblem arises from Ambiguity. When doneintentionally, the defect is called“Equivocation.”

b. The Fallacy of the UndistributedMiddle Term. The Fallacy of theUndistributed Middle Term occurs when theMiddle Term is not distributed in either the

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Major Premise or the Minor Premise, so itnever refers to all members of the categoriesit describes. A Term is Distributed when itapplies to all members of the class to which itrefers. Examples:

All Z is BY is BTherefore, Y is Z

All arguments with undistributed middleterms are bad arguments. This is a bad argument. Therefore, this argument has anundistributed middle.112

The Fallacy of the Undistributed Middle wasmentioned in Hicks v. State, 241 S.W.3d 543,546 (Tex. Crim. App. 2007):

The Legislature has clearly provided thestandard for establishing when an actorhas assumed “care, custody, or control”of a disabled individual under subsection(b)(2). This standard is clearly andunambiguously set out in subsection (d).Although “possession” in Section1.07(a)(39) is defined as “care, custody,or control,” the court of appealsincorrectly assumed that “care, custody,or control” under Section 22.04(b)(2)means “possession.” This is like saying,“I am a mammal, a dog is a mammal;therefore, I am a dog.” This is the fallacyof the undistributed middle.18 (Somefootnotes omitted)

FN18. Douglas Lind, Logic and LegalReasoning 130-31 (The National JudicialCollege 2001).

c. The Fallacy of Illicit Process of theMajor or Illicit Minor Term. Where aConclusion contains a Distributed term that isnot Distributed in its related Premise, it iscalled an “Illicit Process.” The Illicit Processof the Major term occurs when the Major

Term is Undistributed in the Major Premisebut is Distributed in the Conclusion. Example:

All A is BNo C is ATherefore, no C is B.

An illicit minor term occurs when the MinorTerm is Undistributed in the Minor Premisebut Distributed in the Conclusion. Example:

All A is B.All A is C.Therefore, all C is B.

All dogs are canines.All dogs are mammals.Therefore, all mammals are canines.

d. The Fallacy of Negative Premises. Therules of Syllogisms permit only one of thePremises to be negative. The Fallacy ofNegative Premises occurs when both theMajor Premise and the Minor Premise arenegative, in which case there is no connectionbetween the Major and the Minor Premisesthat can support a Conclusion. Example: “NoA is B. No B is C.” From these Premises, youcannot tell whether all A’s are B’s.

e. The Fallacy of Drawing AffirmativeConclusions From a Negative Premise.Where a Syllogism contains a negativePremise, it cannot have an affirmativeConclusion. To do so is a Fallacy.

f. The Existential Fallacy. The ExistentialFallacy occurs when a Standard FormSyllogism has two Universal Premises and aparticular Conclusion. Example:

All P are Q. All X are P. Therefore, some X are Q.

g. Belief Bias. Modern psychologists haveidentified a bias in evaluating Syllogisms.

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Called “Belief Bias,” it reflects the tendencyto base the assessment of the validity of aSyllogism on the believability of its content.113

Where belief and logic agree, logical accuracygoes up; where belief and logic disagree,logical accuracy goes down.

11. Translating Natural LanguageArguments to Syllogisms. As noted above, itis often helpful in evaluating the logic of anatural language argument to translate theargument into a Syllogism to more easily spotany syllogistic errors. The first step intranslating an English language argument intoa Syllogism is to locate the Conclusion. TheTerm in the subject of the Conclusion is theMinor Term (shared between the MinorPremise and the Conclusion). The Term in thepredicate of the Conclusion is the Major Term(shared between the Major Premise and theConclusion). The second step is to put theSyllogism in Standard Order, with thePremise containing the Major Term first, andthe Premise containing the Minor Termsecond. The Middle Term will be the Termshared by the Major Premise and the MinorPremise. If the natural language argument isan Enthymeme, then part or all of one of itsPremises may be unstated. In that event, itwill have to be constructed from the Termsthat are not allocated to the Premise that isexplicitly stated. Once the Major and MinorTerms and Middle Term are identified, thePremises can be put into Standard Form (A, E,I, O). See Section VII.B.7. Havingconstructed the three parts of the Syllogism,and putting them in Standard Order andStandard Form, check to see if any of the rulespertaining to Syllogism have been violated(see Section VII.B.9), and if the Syllogismexpresses a Syllogistic Fallacy (the Fallacy ofFour Terms, the Fallacy of the UndistributedMiddle, etc.). (See Section VII.B.10). If theSyllogism passes this test, then the Syllogismcan be visualized using Euler Circles to testits Validity. (See Section VII.D.).

12. Viewing Legal Disputes as Syllogisms.A legal dispute often can be framed as a ruleof law that operates as the Major Premise, andan adjudicative fact in the case that operatesas the Minor Premise, leading to a Conclusionthat suggests the outcome of the case. In somecases the dispute is over which rule of law toapply; in others, whether the facts come with-in the rule.114

C. IMPLICATION. “Implication” is a keycomponent of Deductive Logic. Implication isalso a key component to the way people thinkand talk about the world. Much confusionarises from the fact that, in Logic,“implication” means that one thingnecessarily establishes another thing, while innatural language “implication” sometimesmeans that but also sometimes means than onething may establish another thing. If we saythat “X” is an event or condition, everydayreasoning is concerned not just with thingsthat follow with certainty from X but alsowith things that probably follow from X orpossibly follow from X.

Much modern writing on Logic is taken upwith discussions about one thing implyinganother thing. Such propositions are calledHypothetical Propositions, to be distinguishedfrom the Categorical Propositions discussedabove in connection with Syllogisms.Hypothetical Propositions, sometimes called“Conditional Propositions” or “Conditionals,”express a relation between Terms, where thetruth of one Term is dependent upon the truthof another Term. The Term that depends onthe other Term is called the “Consequent.”The Term on which the Consequent dependsis called the “Antecedent.” In a ConditionalProposition, the Antecedent is oftensymbolized as “P” and the Consequent isoften symbolized as “Q”. An Implication isoften stated: “P implies Q”, or “if P then Q”,or “P, therefore Q”.

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To express the classical Syllogism in terms ofa Conditional Statement, one would say that,if the Major Premise is true and if the MinorPremise is true, then the Conclusion must betrue. The Major Premise and the MinorPremise taken together thus become theAntecedent “P”, and the Conclusion becomesthe Consequent “Q”. Stated differently, aSyllogism, expressed as a Conditional, wouldtake the form “if A and B are true, then C istrue.” Example: “If all men are mortal andSocrates is a man, then Socrates is mortal”.

There are fundamental rules aboutImplication. One rule is that the fact that “P”is false does not, of itself, establish that “Q” isfalse. Example: “If it is raining, then thesidewalk is wet; it is not raining; therefore, thesidewalk must be dry.” This is Invalid logic,since even if the sidewalk is not wet fromrain, it could be wet for other reasons, forexample if the woman next door was wateringher roses.

Another rule of Implication is that the fact that“P” implies “Q” does not establish that “Q”implies “P.” Example: “If it is raining, thatmeans that the sidewalk is wet”. However, thefact that the sidewalk is wet does notnecessarily mean that it is raining. It could bethat that neighbor again.

Another rule is that, if “P” implies “Q”, thenproving that “Q” is not true means that “P” isalso not true, or that “not-Q implies not-P”.Example: “If it is raining, then the sidewalk iswet; the sidewalk is not wet; therefore it is notraining”.

An Implication can either affirm the Term inthe predicate of the sentence, or negate thatTerm. In other words, an Implication cansuggest that “P implies Q” or that “P impliesnot-Q”.

1. The Validity and Soundness ofImplications. An Implication is Valid if and

only if the Conclusion necessarily followsfrom the Premise. Stated differently, like otherDeductive Logic, Logic Propositions, anImplication (a Proposition in which anAntecedent implies a Consequent) is Valid ifand only if there is no situation where theAntecedent is true and the Consequent isfalse. Even one counter-example establishesthat the Implication is Invalid. An Implicationis Sound whenever the Implication is logicallyValid and the Antecedent is true.

Implications sometimes take the form of alogical Argument, which starts with aPremise(s), then moves through a series ofdeductive steps, and culminates in aConclusion. Such a Deductive Argument isValid when the truth of the Premise(s)guarantees the truth of the Conclusion in allinstances. A Deductive Argument is Soundonly when it is logically Valid and allPremises are true.

2. The Five Forms of ConditionalPropositions. The following variations ofLogic Propositions exist for ConditionalPropositions.

Implication If P then QInverse If not P, then not QConverse If Q then PContrapositive If not Q, then not PContradiction If P, then not Q

3. The Material Implication. In FormalLogic, the expression of an Implication iscalled “Material Implication” or the “MaterialConditional.” The Material Conditional is aspecial form of Conditional Proposition thathas a Truth Table (see Section VII.E.) andconforms to the rules of Logic. The SymbolicLogic expression for the Material Conditionalis “P e Q ” or “P Y Q”. The Logic symbol“e”, also called the horseshoe, indicates theMaterial Conditional, as does the symbol “Y”.In Logic, the Proposition “if P is true then Qis true” is the same as “if P then Q” which is

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the same as “P implies Q” which is the sameas “P e Q” which is the same as “P Y Q”.Material Implication is reflexive (“P e P”),and transitive (“if P e Q, and Q e R, then P eR”). Material Implication represents only aportion of the many types of implication thatoccur in the natural language we use ineveryday life. In this Article, the single-arrowsymbol “6” is used to signify an Implicationthat is not a Material Conditional. Naturallanguage conditionals have many subtlequalities and ramifications that cannotadequately be captured by the MaterialConditional. See Section VII.C.14.

4. Modus Ponens (Affirming theAntecedent). Modus ponendo ponens (inEnglish, “the way that affirms by affirming”)is a particular form of ConditionalProposition. Modus Ponens is central toLogic, to reasoning, and to language. ModusPonens is a rule of inference that takes theform: “if P is true, then Q is true; P is shownto be true; therefore Q must be true”. Stateddifferently:

(1) P implies Q.(2) P.(3) Therefore, Q.

The foregoing Proposition, state symbolically,is: “P e Q; P ˆ Q”, where “e” signifiesMaterial Implication and “ˆ” signifies“therefore”.

In English, the “if” portion of the ConditionalProposition is the “subject term” of thesentence; the “then” portion of the Propositionis the “predicate term”; and the verb (alwayssome form of “to be”) connecting the subjectto the predicate is called the “Copula”(because it couples the subject and thepredicate). Modus Ponens is also calledAffirming the Antecedent. A Propositionpresented in Modus Ponens form is“deductive.” The Proposition has twoPremises: the first is that the Implication “P 6

Q” is true, and the second is that “P” is true.In Modus Ponens, given the truth of those twoPremises, it necessarily follows that theConclusion “Q” is true.

5. Modus Tollens (Denying theConsequent). Modus tollendo tollens (inEnglish, “the way that denies by denying”) isanother form of Conditional Proposition.Modus Tollens is the contra positiveinference, called “Denying the Consequent,”where proving that the Consequent is falseestablishes that the Antecedent is also false. Ittakes the form: “If P is true, then Q is true; Qis shown to be false; therefore, P is false”.Stated differently:

(1) P implies Q.(2) Not Q.(3) Therefore, not P.

Stated symbolically: “P e Q; ¬ Q; ˆ ¬ P”,where the logic symbol” ¬” stand forNegation and the logic symbol “ˆ” stands forthe English word “therefore.” This inferenceis also called the Law of Contraposition.Example: “If it rains, then the sidewalk willbe wet; the sidewalk is dry; therefore, it hasnot rained”. The Modus Tollens form can beconstructed by taking the negative of theConsequent and making it the Antecedent ofthe Conditional, and making the negative ofthe Antecedent into the Consequent of a newConditional. Modus Tollens applies equally toMaterial Conditionals and to other kinds ofConditionals.

Note that Modus Tollens does not disprovethe Validity of the Implication relationship.Rather, it assumes that the Implicationrelationship is Valid, and instead Negates theAntecedent whenever the Consequent is false.Attacking the Implication itself is requiresproof that the Consequent if false when theAntecedent is true.

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Modus Tollens was proposed by philosopherof science Karl Popper as the engine ofscientific advancement. Popper theorized thata scientific theory lasts only until it isfalsified, at which time it must be replacedwith a new theory. Popper went so far as tosuggest that theories that could not besubjected to falsification were not scientific.This concept ended up as one criteria for thevalidity of scientific opinion in the Daubertcase.115

6. “Not-P or Q.” From the Law of theExcluded Middle, we know that “Q” is eithertrue or false; that is, either “Q or not-Q”.Modus Ponens indicates that when “P” is true,“Q” is true. One way of saying that “Q istrue” is “Q”. Thus, when “P” is true thenModus Ponens can be shortened from “P e Q”to “Q”. Modus Tollens indicates that when“Q” is false, “P” is false. Thus, when “Q” isfalse, Modus Tollens can be shortened to“not-P”. Thus, Modus Ponens and ModusTollens taken together leave you with onlytwo outcomes: “Q or Not-P.” Therefore, “PeQ” is logically Equivalent to “Q or not-P”.By convention, logicians reverse the order bysaying “not-P or Q”. Because “Pe Q” and“not P or Q” are logical Equivalents, they canbe substituted for one another in DeductiveLogic Proofs. The Paradoxes of the MaterialConditional (see Section VII.N.1) could beeliminated by describing “P e Q” as “P isfalse or Q is true.”

7. Affirming the Consequent. As notedabove, in the Proposition “P implies Q”, theAntecedent is “P” and the Consequent is “Q”.A rule of Logic says that the fact that “Pimplies Q” does not mean “Q implies P”.Examples of a logically Invalid ConditionalProposition:

(1) P implies Q.(2) Q.(3) Therefore, P.

This logically Invalid deduction is called the“Fallacy of Affirming the Consequent.” In theforegoing example, the Consequent “Q” hasbeen proven, or affirmed. Affirming “Q” doesnot, however, affirm “P”. This is because, inour example, the only logic-based relationshipbetween “P” and “Q” we are given is that “Pimplies Q”. This is not enough information tosay whether “Q implies P”. “Q” may imply“P”, or it may not. We simply cannot say, ifall we know is that “P implies Q”.

Note, for the Implication “P implies Q”, that(i) affirming the Antecedent affirms theConsequent, (ii) denying the Antecedent doesnot affirm or disprove the Consequent, (iii)affirming the Consequent does not affirm theAntecedent, and (iv) denying the Consequentdisproves the Antecedent. If you deny theAntecedent, then the Proposition is Unsoundand therefore Invalid.

8. Conditional Propositions Can BeSorites. Conditional propositions can bestated as sorites. In this case, the Consequentof the preceding Syllogism is the Antecedentof the next.

Example:

If A then B.If B, then C.If C, then D.If D, then E.Therefore, if A, then E.

The example restated:

P implies Q.Q implies R.R implies S.S implies T.P.Therefore, T.

Stated in symbolic form:

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P e Q e R e S e T; P; ˆ T.

The foregoing example is called “ChainReasoning.”

9. Attacking a Conditional Proposition.There are three ways to attack the Conclusionof the Implication that “P implies Q”: (i)disproving “P”; (ii) disproving “Q”; or (iii)proving that the Implication is Invalid. Thefirst attack establishes that the Implication isUnsound, but it does not establish whether“Q” is true or false, nor does it prove that theImplication is Invalid. It merely establishesthat the Implication does not apply to the factsin question.116 The second attack negates theConsequent (which under Modus Tollenswould negate the Antecedent) but does notprove that the Implication is Invalid. The thirdattack disproves the asserted implicationrelation between “P” and “Q”, but it doesn’testablish whether “P” or “Q” are true orfalse.117

10. Disproving a Material Implication.Given the Material Implication that “P e Q”,there is a distinction between disproving “P”or disproving “Q” and disproving the MaterialImplication relation itself. From theperspective of Logic, the Material Conditional“P e Q” is only False when “P” is true and“Q” is false. In all other situations, “P e Q” isTrue. Thus, a Material Implication can beproved Invalid only by showing an instancewhere “P” is true and “Q” is false.

One consequence of this principle is that aMaterial Implication is True when “P” isfalse, regardless of whether “Q” is true orfalse. This is because, when “P” is false, therecan be no instance where “P” is true and “Q”is false. Thus, the Material Conditional isTrue whenever “Q” is true, even if “P” isfalse, or “P” is completely unrelated to “Q”.These oddities about the Material Conditionalgive rise to difficult conceptual issues, called

Paradoxes of the Material Conditional,discussed in Section VII.N.1.

11. Biconditional. It is possible for “P” toimply “Q” and for “Q” to imply “P”. Thissituation is called “Biconditional”, and isrepresented by the double-arrow symbol “]”.In natural language, the Biconditional issometimes stated as “if and only if.” TheBiconditional logical Operator reflects that theAntecedent implies the Consequent while atthe same time the Consequent implies theAntecedent. Looked at differently, theBiconditional is two linked ConditionalPropositions that are both true: “P e Q” and“Q e P”. Other Logic-based names forBiconditional are Equivalence and Identity.The symbol for Equivalence or Identity is“/”. Logical Equivalence or Identity meansthat, from a logical perspective, the TruthValues of the Antecedent and the Consequentare the same (either both true or both false),which means that the Truth Tables areidentical, and that, in logical Arguments, theterms on either side of the Biconditional areinterchangeable, and can be substituted onefor the other in Logic proofs.

12. Conjunctive Conditional Propositions.A Conjunctive Proposition is a ConditionalProposition that relates two or moreAntecedents, joined conjunctively, to aConsequent. The Conditional Proposition “ifA and B, then C”.

13. Disjunctive Conditional Propositions.A Disjunctive Proposition is a ConditionalProposition that relates two or moreAntecedents, joined disjunctively, to aConsequent. The Conditional Proposition “ifeither A or B or both, then C”, is an instanceof the Inclusive Disjunctive Conditional. (SeeSection VII.F.3 for discussion of InclusiveDisjunction). The Conditional Proposition “ifeither A or B, but not both, then C” is aninstance of the Exclusive Disjunctive

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Conditional. (See Section VII.F.3 fordiscussion of Exclusive Disjunction).

The Inclusive Disjunctive Conditional “eitherA or B, or both, implies C”, can be attacked intwo ways: (i) disproving both “A” and “B”;and (ii) disproving the Implicationrelationship. Attack (i) proves the Propositionto be Unsound; attack (ii) proves theProposition to be Invalid. An ExclusiveDisjunctive Conditional “either A or B, butnot both, implies C” can be Invalidated threeways: (i) disproving both “A” and “B”; (ii)showing that C is true when both “A” and “B”are true; or (iii) disproving the Implicationrelationship. Attack (i) proves the Propositionto be Unsound; attacks (ii) and (iii) prove theProposition to be Invalid.

14. Other Conditionals. The MaterialConditional (“P e Q”) is only one of manytypes of Conditional Propositions. It is aTruth-Value-based conception, which is Falsewhen “P” is true and “Q” is false, but is Truein all other instances. Treating the MaterialConditional as True--when the Antecedent isfalse--makes little sense in terms of the waypeople normally use conditional statements inregular speech. In regular speech, most peoplelink P to Q in a Conditional only when P andQ are “relevant,” meaning that P and Q mightreasonably be connected. This sense ofrelevancy has given rise to a form of logiccalled Relevancy Logic, which adds to thelogical calculus an additional parameter thatreflects a relevancy requirement. Also, inregular speech if a Conditional is asserted, andit is shown that the Antecedent is false, thenormal reaction is to treat the ConditionalProposition as Invalid or the Conclusion asfalse, with no thought given to the fact that theProposition is really Unsound and that nothingcan be determined about the truth ofConclusion.

Examples of other conditionals are IndicativeConditionals, Subjunctive Conditionals,

Counterfactual Conditionals, and the MaterialBiconditional.

a. Indicative Conditionals. “IndicativeConditional” is the name applied to “if . . .then” statements that are (usually) in thepresent tense and indicative mood, such as wefrequently find in normal conversation. AnIndicative Conditional is usually used whenthe speaker believes that the Consequent ishighly likely or even certain to follow fromthe Antecedent. Example: “if I drive drunk Iwill go to jail.” Or, “if you don’t finish yourhomework then you can’t watch television.”More generally: “if A is true, then B is true”.

The following is an Indicative Conditionalstated in the past tense.

#1: If Booth did not kill Lincoln, thensomeone else did.

Fictional works, despite the fact that they areimaginary, are normally written in the presenttense, indicative mood, with specific instancesof past and future tenses, and the subjunctivemood. This makes the story seem more “real,”and is less cumbersome than if the subjunctivemood were used throughout.

b. Subjunctive Conditionals. SubjunctiveConditionals are “if . . . then” statements thatare in the subjunctive mood rather than theindicative mood. Subjunctive conditionals areused when the truth of the Antecedent isuncertain, when the Antecedent is known tobe untrue, and when the Antecedent is a futureevent. The subjunctive mood is also used witha true Antecedent when the likelihood that theConsequent follows from the Antecedent isquestionable. Examples:

#2: If my husband got off work at 5pm today,then he will have picked up the drycleaning.

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#3: If I hadn’t had to work late today, then Iwould have picked up the dry cleaning.

#4: If I were to use my knight to capture hisbishop, and he were to take my knightwith his queen, I could move my rook toput his king in check, and he would haveto move his queen to block the check,which would allow me to capture hisqueen with my rook. Even if his kingwere to capture my rook, I would comeout ahead in the exchange of pieces.

#5: Under the principle of Mutual AssuredDestruction, if the USSR were to launchICBMs at the USA, then the USA wouldlaunch ICBM’s at the USSR, resulting inboth countries being utterly destroyed,and vice-versa. Therefore, neithercountry will launch ICBMs.

Example #5 stated with logic symbols wouldbe as follows. The Logic Operator “and” issymbolized by “v”. The Logic Operator “or”is symbolized by “w”. The subscript “L”signi-fies that the country launches ICBMs (USAL

w USSRL). The subscript “D” signifies that thecountry is utterly destroyed (USAD w USSRD).

(1) USSRL 6 USAD.(2) USSRL 6 USAL.(3) USAL 6 USSRD.(4) USSRL.(5) ˆ USAD v USSRD.

This logical Argument indicates that if theUSSR were to launch ICBMs, then the USAwould be destroyed. However, if the USSRwere to launch ICMBs, then the USA wouldalso launch ICBMs in the moments before itwas destroyed. If the USA were to launchICBMs, then the USSR would be destroyed.Therefore, if the USSR were to launchICBMs, then it would bring about its owndestruction. Since no country wants to destroyitself, the USSR will not launch ICBMs. Thesame goes for the USA. The principle may not

work where the persons in possession of anuclear device do not think and act rationally,or cannot be identified as belonging to a statethat can be annihilated in response to anuclear explosion.

Where the Implication relationship is taken torepresent causation, it is easy to see thatpeople deal with subjunctive conditionalsconstantly in their daily lives, in decidingwhether to do a particular thing or not do thatthing, in order to bring about or avoid a futureevent or future condition. Logic can help thattype of task. Example: If I do X, then Y willoccur. I do not want Y to occur, so I do not doX. Unfortunately, refraining from doing Xdoes not guarantee that Y will not occur, if Yhas other possible causes. Such thinking isDenying the Antecedent, which is a logicalfallacy. Y can only be avoided if you know allof the Antecedents of Y and negate all ofthem. However, in the special case where weknow that Y will occur if and only if X occurs,then by avoiding X we can avoid Y. This is anexample of the Biconditional.

The subjunctive mood is used whendiscussing how things might have beendifferent if some event in the past had or hadnot occurred. (If Booth had not killedLincoln). The subjunctive mood is also usedin describing the future when the future is notcertain. (If Congress were to raise theminimum wage, it would increaseunemployment among the marginallyemployed). The subjunctive mood can also beused for the present, where the Antecedent ofthe Conditional Proposition is contrary to fact.Example: The commuter driving home fromwork sees a sign that says: “if you lived in thissubdivision, you would be home by now.”

c. Counterfactual Conditionals. Anothertype of conditional statement is the“counterfactual Conditional.” A counterfactu-al Conditional is a Conditional has anAntecedent that the speaker knows is contrary

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to fact. Example: "if p were to happen the qwould be the case," or "if p were to havehappened then q would have happened". Thespeaker usually uses the subjunctive mood,but sometimes counterfactual Conditionals arestated in the indicative mood ("step on a crackand break your mother's back").

Subjunctive conditionals are also used whenthe Antecedent is an event or condition in thepast that contravenes history. (If Napoleonhad not invaded Russia). Example:

#6: If Booth had not killed Lincoln, thensomeone else would have.

Conditional #1 and Conditional #5 are worldsapart. Conditional #1 expresses certainty (i.e.,it is 100% certain that someone killedLincoln), while Conditional #6 deals with aworld that might have been (noone knows forsure that someone other than Booth wouldhave tried or been able to kill Lincoln).Another example:

#7: If Hinckley had succeeded in killingReagan, the Berlin Wall would bestanding today.

#8: If the Confederacy had won the CivilWar, America would now be a voluntaryunion like Canada, united but with a rightto withdraw from the union.

U.S. Philosopher David Lewis has suggestedthat counterfactual Conditionals be evaluatedas true or false according to whether theConsequent is true in the ‘most similar’possible worlds to ours for which “p” is true.

Counterfactual Conditionals are an essentialpart of some liability claims. Example: If thedecedent had not been killed in the refineryexplosion, he would have earned X dollarsduring his working life. Another example: Ifthe supplier hadn't breached his contract, the

business would have had a net profit of Ydollars.

15. The Dilemma. In Logic, a Dilemma is aProposition in which two options lead to thesame Conclusion. A Dilemma is symbolizedas follows:

A or BA P CB P CTherefore, C

A Dilemma in ordinary speech has a differentmeaning. It usually means the necessity ofchoosing between two or more options, eachof which leads to a different but nonethelessdisagreeable outcome.

A dilemma was depicted in CATCH-22. “InJoseph Heller's novel of this title, Americanpilots in the second World War learned thatthey could not avoid flying bombing missionsunless they were crazy; to be relieved fromduty, they had to request a reprieve. The‘catch-22' was that the very act of seeking toavoid hazardous combat duty demonstrated apilot's sanity, thereby ensuring a denial of therequest.”118

16. Degrees of Conditionals. Conditionalstatements are sometimes categorized as zero,first, second, and third conditionals. Zeroconditionals are always true when the Antece-dent is true. Example: “If you heat water to210E, it will boil.” With a “first conditional,”the Antecedent must occur for the Consequentto be possible. Example: “If you unlock thedoor, I can come inside.” A “secondconditional” involves an imaginary presentAntecedent and an unlikely futureConsequent. Example: “If I had $200,000, Iwould buy a Maserati,” or “if I buy a ticket Imight win the lottery.” A “third conditional”describes a past that did not happen and aConsequent that is imaginary. Example:“When Strom Thurmond ran for President, we

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voted for him. We’re proud of it. And if therest of the country had followed our lead, wewouldn’t have had all these problems over theyears, either.”119

17. Disproving Other Conditionals. AConditional Proposition (or Implication) “P 6Q” (which is not the Material Conditional)can be disproved by finding a counterexample where “P” is true and “Q” is false.This is particularly so when the Implication ismeant to suggest that P causes Q. The historyof science is filled with examples ofobservations of natural phenomena and theconduct of contrived experiments designed todemonstrate or disprove claims of causation,which is a form of Implication.

The Premise of a Conditional Proposition canbe disapproved in two ways: by proving that“P” is false, or by proving that “Q” is false.The latter method is an instance of ModusTollens.

It is necessary to distinguish disproving theConditional Proposition from Denying theAntecedent or Denying the Consequent. Todisprove the Conditional Proposition, youmust show that, in at least one instance, theAntecedent is true when Consequent is false.Denying the Antecedent establishes that “P”is not true, and that the Proposition istherefore Unsound. Denying the Consequentestablishes that Q is not true and that thereforethe Antecedent “P” is not true. Denying theConsequent is discussed in Section VII.C.5.

18. Legal Presumptions. Some legalpresumptions are “structural,” meaning thatthey assign the burden of persuasion in a courtcase. Examples include the presumption ofinnocence in a criminal case,120 and thepresumption of community property in amarital property dispute.121

Apart from structural presumptions like these,there are a host of other legal presumptions

that indicate that proof of a particular factpermits or requires the fact finder to draw acertain conclusion. In this Article, suchpresumptions are called “particular” presump-tions. Particular presumptions are a form ofindicative conditional statement, P 6 Q. Someparticular presumptions are rebuttable, andsome are not. In some instances, two or morepresumptions can collide, and it is necessaryto determine which of the opposingpresumptions will prevail.

D. EULER CIRCLES. One clearest way tovisualize a logical proposition is to use adiagram called an “Euler Circle,” originatedin 1768 by Leonhard Euler, a Swissmathematician. In an Euler Circle, aclassification is represented by a circle.122 Allinstances of that classification fall within thatcircle. The proposition that “All A is B” isdepicted:

In the foregoing Euler Circle, since all As areBs, the circle of all As is totally inside thecircle of all Bs. The foregoing diagram alsodepicts the conditional proposition that “Aimplies B” (A e B) and that “not-B impliesnot-A” (¬ B e ¬ A). The foregoing diagramalso indicates that some B is A.

If only “some A is B”, then the Euler Circle isthis:

In the foregoing Euler Circle, some As fallwithin the circle of Bs, but some As falloutside the circle of Bs. The portion of As thatare Bs falls within the area where the twocircles overlap, marked in the foregoing Euler

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Circle with the “+” sign. The foregoing EulerCircle also indicates both that some As are Bsand that some Bs are As.

If “no A is B,” then the circle of As does notoverlap the circle of Bs:

The foregoing Euler Circle also reflects that“no B is A”. The proposition that “no A is B”and the proposition that “no B is A” arelogically Equivalent.

If all As are Bs and all Bs are As, then thecircle of As is coterminous with the circle ofBs:

The foregoing Euler Circle reflects LogicalEquivalence (A / B) or the Biconditional (Aø B)

The following Syllogism reflects the Fallacyof the Undistributed Middle:

(1) All politicians are pompous.(2) John Doe is pompous.(3) Therefore, John Doe is a politician.

The reasoning is fallacious, because John Doecould be pompous even if he is not apolitician, say if, for example, he is a lawprofessor.123 Expressed as an Euler Circle(where Politicians are “PL”, Pompous is“PM”, and John Doe is “JD”):

If Circle PL is the universe of all politicians,and Circle PM is the universe of pompouspersons, and Circle JD is John Doe, then tosay that all PL is PM (i.e., all politicians arepompous) means that the Circle PL is insideCircle PM. But as the Euler Circle shows,there are members of Circle PM that are notmembers of Circle PL. So it cannot be saidthat because the person is within Circle PM heis therefore within Circle PL.

Euler Circles can be used to visualize anumber of different propositions. Forexample, Euler Circles can be constructed fora lawsuit to recover damages, where “L” isliability, “C” is causation, “D” is damages:

The plaintiff recovers a judgment only in thearea with a “+,” where liability, causation, anddamages, coincide.

E. TRUTH TABLES. Truth Tables weredeveloped as an effective way to visualizewhether a logical proposition is True or Falsefor every Truth Value of each component ofthe Proposition.

A Truth Table consists of all possiblecombinations of Truth Values of a Statementor Proposition. The Truth Table for theStatement “P” is:

A Truth Table for the two Statements “P” and“Q” is:

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The following Truth Table pertains to theLogic Operator “Logical Conjunction.”Logical Conjunction is signified by the word“and”; it operates like the conjunction “and”in standard English. When two Statements ina logical Proposition are joined by an “and,”the Proposition is True if and only if bothStatements are true. The logic symbol forConjunction is “v”.

In the following Truth Tables, “P” and “Q”are Statements; “P v Q” is a Proposition; “T”means “true; ” and “F” means “false.”

The Truth Table for Logical Conjunctionreads like this:(1st row) if P is true and Q is true, then P v Q

is true.(2nd row) if P is true and Q is false, then P v Q

is false.(3rd row) if P is false and Q is true, then P v Q

is false.(4th row) if P is false and Q is false, then P v

Q is false.

Note that in a Truth Table there is a columnfor each Statement of the Proposition, and acolumn for the Proposition itself. The columnunder the Proposition indicates whether the

Proposition is logically True or Falsedepending on the Truth Values of eachStatement. Every possible combination ofTrue and False, for all Statements that makeup the Proposition, are recorded in the TruthTable.

If there are more than two Statements in aProposition, then the Truth Table widens andlengthens. (The number of columns is 6 andthe number of rows is 26, or two to the nthpower, where “n” is the number of statementsin the proposition. For three statements joinedconjunctively, the Truth Table looks like this:

In law, the burden of persuasion requires theparty asserting a proposition to prove the“truth” of the proposition. In a simple lawsuitto recover damages, the plaintiff must proveliability (L) and causation (C) and damages(D), to win a money judgment. This is aspecific application of the general proposition“P v Q v R”. Here is the Truth Table for asimple damage suit, where “J” is a judgmentfor the plaintiff:

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F. LOGICAL CONNECTORS. Thebranch of Logic that focuses on the role ofLogical Connectors is called PropositionalLogic. Logical Connectors connect two ormore Statements (or elements) in a logicalProposition. Logical Connectors include: not;and; or; equivalent; nonequivalent; implies;NAND; NOR; NOT; XNOR; and XOR (moreprecisely, “not” is a Logical Operator, not aLogical Connector). The Logical Connectorsare discussed below.124

1. Logical Negation. In Logic, Negationmeans the opposite of the term, Statement orProposition that is being Negated. Forexample, the Negation of “P” is “¬ P”, wherethe symbol “¬” means “not.” Negation issimilar to the word “not” in normal language,or a prefix (like “un”) that reverses themeaning of the word or concept. As a LogicalOperator, Negation applies to the firstmeaningful proposition to the right of theNegation sign. As a consequence, if the intentis to negate a compound Proposition, it isnecessary to put the compound Proposition inparenthesis. Otherwise the negative operatorwould apply only to the first element of theCompound Proposition. Example: compare “¬P and Q” to “¬ (P and Q)”. The firstproposition is True when “P” is false and “Q”is true. The second proposition is True wheneither “P” or “Q” is false, or both, are false.

See the discussion of Conjunction in the nextsection.

The Truth Table for Negation is:

The Truth Table for Negation reads like this:(1st row) If P is true, then ¬ P is false.(2nd row) If P is false, then ¬ P is true.Under the Law of Contradiction, “P” and “¬P” cannot both be true or both be false.

The Euler Circle for Negation is:

Everything that is “P” is inside the P-Circle;everything that is “not-P” is outside the P-Circle.

2. Logical Conjunction. In formal Logic,as well as in grammar, two Statements joinedby the word “And” are “Conjunctive.” TheLogic Connector symbol for “And” is “v”, anupside-down V. A Proposition consisting oftwo terms connected by an “And” Connectoris logically True only if both terms are true. Ifthree, four, or more Statements areconjunctively joined into one Proposition, theProposition is logically True if and only if allStatements in the Proposition are true. TheTruth Table for Conjunction is set out inSection VII.E. above. The Euler Circle for theConjunction of two terms is:

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The Proposition “A and B” is true only for thearea where the two circles overlap, markedwith a “+.”

(The following list uses logical Connectors,which are discussed in greater detail later inthis Section.) Conjunction has the followinglogical properties (where “w” signifiesLogical Disjunction, and “/” signifies“Logically Equivalent”).

Associative: A v (B v C) / (A v B) v C

Commutative: A v B / B v A

Distributive: A v (B w C) / (A v B) w(A v C)

Idempotent:125 A v A / A

“Truth-preserving” means that when allvariables in a Proposition are true, theProposition is True.

“Falsehood-preserving” means that when allvariables in a Proposition are false, theProposition is False.

“A and B” is a common “search term” onWestlaw and Lexis. It returns legal authoritiesthat contain both terms. Conjunction is apowerful way to narrow a computer-basedsearch. The foregoing Euler Circle reflectsthat “A and B” is a subset of all A’s and allB’s.

The Logic Operator “And” is similar to butnot the same as the English conjunction“and.” In natural English, the word “and”sometimes connotes sequence, as in “I atebreakfast and went to work.” The English“and” also sometimes implies a division of thewhole into parts, as in “police cars are blackand white,” meaning not that the car is allblack and at the same time all white, butrather that part of the police car is black and

part is white. The English “and” sometimesjoins two or more terms in the subject orpredicate of a sentence, like “Jack and Jillwent up the hill.” There are other examples ofEnglish usage that differ from the logicalOperator.

3. Logical Disjunction. Logical “Disjunc-tion” is a logical Operator analogous to theEnglish word “or.” A Proposition consistingof two Statements connected by the Operator“Or” is “Disjunctive.” There are two types ofDisjunction: Inclusive and Exclusive.Inclusive Disjunction permits the Proposition“A Or B” to be True if either A is true or B istrue, or both are true. Stated in naturallanguage, a logical Proposition consisting oftwo Statements joined by an “inclusive or”Connector is True if either or both Statementsare true. If three or more Statements arejoined by Inclusive Disjunction, theProposition is True if any one or more of theStatements is true. The Inclusive DisjunctiveProposition is False if and only if allStatements in the Proposition are false.Logical Propositions can be joinedDisjunctively, with the same effect. A realworld example of the Inclusive Disjunctionoccurs in a cafeteria, where you can havegreen beans, mashed potatoes, black eyedpeas, french fries, or another vegetable.Selection of one does not preclude selectionof another. The Logic symbol for InclusiveDisjunction is “w” and is written “OR.”

The other instance of disjunction is the“Exclusive Disjunction.” The “exclusive or”allows the Disjunctive Proposition “A Or B”to be True if either A is true or B is true, butnot both. If three or more Statements arejoined by the Exclusive Disjunction, theProposition is True if and only if one, andonly one, of the Statements is true. If morethan one Statement is true, or if all Statementsin the Proposition are false, then theProposition is False. A real world example ofExclusive Disjunction is: you can be either in

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Dallas or Houston at 10:00 a.m. tomorrow,but not both. The Logic Operator symbol forExclusive Disjunction is “x” and is written“XOR.” A mathematical example ofExclusive Disjunction: an integer is either oddor even. Often a sentence in English doesn’t tell youwhether the Inclusive Disjunction or theExclusive Disjunction is intended. In naturallanguage sentences, we can usually rely oncontext or common sense to tell us which typeof disjunction is intended. However, Logicdoes not rely on context or common sense.Logic requires that you specify the form of“or” you are using in a disjunctiveproposition.

Disjunction has the following logicalproperties:

Associative: A w (B w C) / (A w B) w C

Commutative:126 A w B / B w A

Distributive: A w (B v C) / (A w B) v(A w C)

Av (B w C) / (A v B) w (Av C)

Idempotent:127 A w A / A

Truth-preserving: meaning that when allvariables in a Proposition are true, theProposition is True.

Falsehood-preserving: meaning that whenall variables in a Proposition are false, theProposition is False.

The Truth Table for two statements joined byInclusive Disjunction is:

The Inclusive Disjunction Truth Tableindicates:(1st Row) When “P” is true and “Q” is true,

then the Proposition “P w Q” is True.(2nd Row) When “P” is true and “Q” is false,

then the Proposition “P w Q” is True.(3rd Row) When “P” is false and “Q” is true,

then the Proposition “P w Q” is True.(4th Row) When “P” is false and “Q” is false,

then the Proposition “P w Q” is False.

Examples of Inclusive Disjunction:

A 17-year old female is an adult if (i) she ismarried,128 or (ii) she has had her disabilitiesof minority removed by a court, or (iii) orboth.

The Truth Table for two statements joined byExclusive Disjunction is:

The Exclusive Disjunction Truth Tableindicates:(1st Row) When both P and Q are true, then

the proposition “P x Q” is false.(2nd Row) When P is true and Q is false, then

the proposition “P x Q” is true.

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(3rd Row) When P is false and Q is true, thenthe proposition “P x Q” is true.

(4th Row) When both P and Q are false, thenthe proposition “P x Q” is false.

Examples of Exclusive Disjunction:

• A “true-false” test.• A multiple choice test.• Game show host: “Do you want what’s

behind Door No. 1, Door No 2, or DoorNo. 3?”

• Aristotle’s Law of Excluded Middle:“Either A is B or A is not B”. Expressedsymbolically: (A = B) x (A … B).

• A real number is either odd or even.• Either God exists or God does not exist.• President Bush: “Either you are with us,

or you are with the terrorists.”• A person is an American citizen if (i) she

was born in America, or (ii) she has been“naturalized” by a federal judge.

Disjunctive propositions involving theExclusive Disjunction, would take thefollowing form:

1. P x Q.2. P.3. ˆ ¬ Q.

The foregoing Argument expressed in Englishis: either P is true or Q is true, but not both; Pis true; therefore, Q is false.

Or:1. P x Q.2. ¬ P.3. ˆ ¬ Q.

The foregoing Argument, expressed inEnglish is: either P is true, or Q is true, but notboth; P is false; therefore, Q is true.

The following Euler Circle depicts bothInclusive Disjunction and Exclusive Disjunc-tion:

The Inclusive Disjunction is true foreverything that is inside either the P-Circle orthe Q-Circle or both. The ExclusiveDisjunction is true for everything that iswithin the parts of P-Circle or the Q-Circlethat do not overlap (i.e., excluding the areawith a + sign).

4. Material Implication. MaterialImplication, discussed in Section VII.C.3above, has the following Truth Table:

If “P e Q” is True, and P is true, then Q mustbe true. If P is true and Q is false, then “P eQ” is False. The first row of the foregoingTruth Table exemplifies Modus Ponens (i.e.,if P is true then Q must be true). The fourthrow of the foregoing Truth Table exemplifiesModus Tollens (i.e., if “P e Q” is True, and Qis false, then P must also be false.) Note that,for the Material Conditional, if P is false then“P e Q” is True, regardless of whether Q istrue or false. This leads to the problem ofExplosion, discussed in Section VII.B.5.

The Truth Table reflects an important aspectof the Material Conditional: the MaterialConditional is False only when P is true and Qis false. In all other instances, the MaterialConditional is True. The fact that the MaterialConditional is True whenever P is true,regardless of whether Q is true or false,creates conceptual problems when dealing

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with “real world” Conditionals and limits theusefulness of the Material Conditional as away to express natural language Conditionals.See Section VII.N.

The Euler Circle for all kinds of implicationlooks like this:

The foregoing Euler Circle reflects that allinstances of P are also instances of Q, whichallows us to say that P implies Q. However, Qmay include instances that are not P, showingthat Q does not necessarily imply P. If Q isNegated, then P is also Negated, because allinstances of ¬ Q lie outside of the Q-circle,while all instance of P lie within the Q-circle.From a categorical perspective, the foregoingEuler Circle reflects that all P’s are Q’s, whilesome Q’s are P’s. Stated in terms ofImplication: “P implies Q”; “Q sometimesimplies P”;” not-Q implies not-P”; “not-Psometimes implies not-Q”.

Aristotle’s simple declaratory Syllogism canbe expressed in Propositional Logic: (P v Q)e R, where P is the Major Premise, Q is theMinor Premise, and R is the Conclusion.When the Major Premise (P) is true, and theMinor Premise (Q) is true, then theConclusion (R) necessarily is true.

5. Material Equivalence. “MaterialEquivalence” is a logical Operator thatsignifies that two terms are true together orfalse together. Material Equivalence isdifferent from equality, because equals are thesame while Material Equivalents merely havethe same Truth Values for every Truth Valueof Terms that make up the Proposition (i.e.,either both are true or both are false). BothStatements and Propositions, as used in thisArticle (see Section VI.B.), can be MaterialEquivalents.

Symbolically, Material Equivalence issignified by “/” or “:.” This logical Operatoris also called Biconditional. The Proposition“A / B” is True when A and B are both trueor are both false. The Proposition A / B isFalse when A is true and B is false, and whenA is false and B is true. The Truth Table forMaterial Equivalence is:

Here are some Material Equivalents expressedin symbolic Logic:

(1) ¬ (P v Q) / ¬ P w ¬ Q. This means that theNegation of the Conjunctive Proposition “PAnd Q” is Materially Equivalent to theDisjunctive Proposition “not-P or not-Q.” Putdifferently, the statement “P And Q” is Falseif either “P” is false or “Q” is false. SeeAlternative Denial, at Section VII.F.7.

(2) ¬ (P w Q) / ¬ P v ¬ Q. This means thatNegation of the Disjunctive Proposition “P OrQ” is “not-P And not-Q.” Put differently, thestatement “P Or Q” is False when both P andQ are false.

(3) P e Q / ¬ Q e ¬ R. This means that theMaterial Conditional Proposition “P impliesQ” is Materially Equivalent to the MaterialConditional Proposition “Not - Q implies not -P”. This is Modus Tollens.

(4) P e Q / ¬ P w Q. This means that theMaterial Conditional Proposition “P impliesQ” is Materially Equivalent to “¬ P w Q”, andindicates that either “P” is false or “Q” is true.This is because when “P” is true then “Q” isalso true (Modus Ponens), but when Q is false

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then P is also false (Modus Tollens). SeeSection VII.C.4&5.

(5) Some S is P / Some P is S. This isConversion. No S is P / No P is S. This isConversion.

The Euler Circle for Material Equivalence is:

In the foregoing Euler Circle, the A-circle andthe B-circle are coterminous, meaning that allA’s are B’s and all B’s are A’s.

6. Material Nonequivalence. “MaterialNonequivalence” is a logical Operator thatsignifies that two terms always have oppositeTruth Values. Terms with opposite TruthValues are called “Contradictories.”

Symbolically, Material Nonequivalence issignified by “†”. The Proposition “A † B” isTrue where A and B have opposite TruthValues, so that when A is true then B is false,and when A is false then B is true. TheProposition “A † B” is False when A and Bare both true, and when A and B are bothfalse. The Truth Table for MaterialNonequivalence is:

Here are some Material Nonequivalents(1) A † ¬ A(2) (P e Q) † (P e ¬ Q)

The Euler Circle for nonequivalence is:

In the foregoing Euler Circle, the A-Circleand the B-Circle do not overlap, meaning thatno A’s are B’s which means that no B’s areA’s.

7. Alternative Denial. In PropositionalLogic, “Alternative Denial” means that theProposition “A And B” is False when either“A” is false or “B” is false, or both are false.In Propositional Logic “Alternative Denial” isexpressed “¬ A w ¬ B.” In Symbolic Logic,Alternative Denial is depicted “A * B”. Theverbal Connector for Alternative Denial is“NAND.”

The Euler Circle for Alternative Denial is allarea outside the overlap of the A-Circle withthe B-Circle (marked with a + sign):

8. Joint Denial. In Propositional Logic,Joint Denial means that the Proposition “AAnd B” is False only when both A and B arefalse. In English the phrase used to indicateJoint Denial is “neither A nor B.” InPropositional Logic, Joint Denial is depicted“¬ A v ¬ B”. In Symbolic Logic, Joint Denialis depicted “A 9 B”. The verbal indicator forJoint Denial is “A NOR B”. The Truth Tablefor Joint Denial is:

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The Euler Circle for Joint Denial is everythingoutside of both circles:

G. SYMBOLIC LOGIC. Symbolic Logicuses symbols to signify the Logic Operatorsused in Propositions and Arguments. It issimilar to mathematics in the sense that thereare special symbols that can be used inprocesses that follow rigid rules. Once thesesymbols and rules have been learned,allowing Logic operations to be expressedwithout words, it is much easier to bothexpress and understand the way Logic works.

Symbolic logic is divided into PropositionalLogic and Predicate Logic. PropositionalLogic uses symbols to stand for LogicPropositions and Logic Connectors.Propositional logic only considers whether aproposition is true or false. Predicate logic isan extension of Propositional Logic that usesvariables that can be quantified.

Here are some logical Propositions expressedin Symbolic Logic:

(i) Modus Ponens: P e Q; P; ˆQ(ii) Modus Tollens: P e Q; ¬ Q; ˆ ¬ P(iii) The Law of Identity: A / A -or- A ] A(iv) The Law of Contradiction:

A † ¬ A -or- ¬ (P v ¬ Q)(v) The Law of the Excluded Middle: A w ¬

A(vi) Material Implication: P e Q / ¬ P w Q

H. TAUTOLOGIES AND SELF-CONTRADICTIONS. The ancient Greeksdefined Tautology as a logical statement thatsays that a thing is the same as itself. Anexample of a mathematical tautology wouldbe 2 = 2 or (x + 4) = (4 + x). In Logic this iscalled the Law of Identity. In terms ofpractical utility, a Tautology tells you nothing

that you don’t already know. However, ifsomeone proposes that A and B are different,and you demonstrate that A and B are thesame, you have refuted the proposition, whichmay prompt the proponent to move in a newdirection.

In Propositional Logic, a Tautology is alogical Proposition or formula that is alwaystrue, regardless of whether the individualterms of the Proposition are true or false. Anexample is Aristotle’s Law of the ExcludedMiddle, which can be expressed in symbols as“A x ¬ A”, and in words as “either A or not-A, but not both”, meaning that a particularthing is either itself or it is not itself, but itcannot be both. The Truth Table for “A x ¬A”(either A or not-A but not both) is:

Note that the T-T-F and F-F-F rows areomitted because under the Law ofContradiction, A and ¬A cannot have thesame Truth Value–that is, they cannot both beTrue or both be False.

Here are more Tautologies:

(A v B) w (¬A) w (¬B)Law of Contraposition: (A e B) ] (¬B e ¬A)

Indirect proof known as Reductio adAbsurdum: ((¬A e B) v (¬A e ¬B)) e A

A Self-Contradiction is a logical Propositionthat is always False regardless of whether theterms of the Proposition are True or False.The Proposition “A And Not-A”, (A v ¬A) isa Self-Contradiction because, under allconditions, something cannot be both A andnot-A. The Truth Table for the Proposition “Av ¬ A” is:

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A Proposition that is neither a Tautology nora Self-Contradiction is called a “Contingent”Proposition. It is True for some Truth Valuesof its Terms but not others.

A definition is a Tautology, but definitions arenonetheless useful in that they describe anunknown word using words that are known, orpermit a longer phrase or more complicateddescription to be represented by a single wordor shorter phrase.

I. AXIOMS. An “Axiom, ” also called a“Postulate,” is a statement regarded as beingself-evidently true without proof.129 Manylogical Arguments start with an Axiom inorder to avoid an infinite regression in searchof a starting assumption.130 Success in using aself-evident assumption, as the first step in aline of reasoning, depends upon theaudience’s agreeing with the Axiom.

One familiar Axiom is Rene Descartes’assertion: “Cogito ergo sum,” (I think;therefore, I am). In pursuing his “Method” ofanalysis, Descartes had challenged theassumptions underlying all of his beliefs andarrived at a bedrock belief that he could notdoubt without creating a logical paradox:Descartes could doubt everything except thathe could not doubt the existence of hisconsciousness that was doing the doubting.He took this as his starting point for buildinga new view of the world.

The American Declaration of Independencebegins with several Axioms:

We hold these truths to be self-evident:that all men are created equal, that theyare endowed by their Creator with certainUnalienable Rights, that among these are

Life, Liberty, and the pursuit ofHappiness.”

J. CONSTRUCTING DEDUCTIVEARGUMENTS IN PROPOSITIONAL LO-GIC. This subsection of the Article discussesconstructing deductive arguments expressedin Propositional Logic.

1. Direct Deductive Arguments. ADeductive Logic Argument is a step-by-stepproof that one or more Premises lead to aparticular Conclusion. The process ofconnecting the Premises to the Conclusion isdone using “Rules of Inference” and “Rules ofReplacement.” In a Direct DeductiveArgument, every step of the proof is either aPremise, or a Rule of Inference, or a Rule ofReplacement, or a Conclusion.131

a. Rules of Inference. Here are some Rulesof Inference that allow you to move from onestep of an Argument to a subsequent step, ina deductive fashion:132

(1) Syllogism

(A e B) v (B e C) e (A e C)

The fact that A implies B and B implies Cmeans that A implies C.

(2) Modus Ponens

P e QPˆ Q

If P implies Q, and if P is true then Q is alsotrue. In different words, given a MaterialImplication, if we know the Antecedent thenwe know the Consequent, under the rule ofModus Ponens.

(3) Modus Tollens

P e Q

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¬ Qˆ ¬ P

If P implies Q, and Q is not true, then P is nottrue.

(4) Proof by Cases

((A w B) v (A e C) v (B e C)) e C

If “A implies C” and “B implies C”, then C istrue if either A or B (or both) is true.

(5) Exclusive Disjunctive Syllogism

A w B A w B¬ A or ¬ Bˆ B ˆ A

(First iteration). If the Proposition “A Or B” isTrue, and A is not true, then B must be true.(Second iteration). If the Proposition “A OrB” is True, and B is not true, then A must betrue.

(6) Disjunction Introduction (Addition)

A Bˆ A w B or ˆ A w B

(First iteration). If A is true, then theProposition “A Or B” is true. (Seconditeration). If B is true, then the Proposition “AOr B” is True. This follows from the fact thata Disjunctive Proposition is True if any Termin the Proposition is true.

(7) Simplification

A v B A v Bˆ A or ˆ B

(First iteration). If the Proposition “A And B”is True, then A is true. (Second iteration). Ifthe Proposition “A And B” is True, then B istrue. Stated differently, if a conjunction ofterms is True, then each term must be true.

(8) Conjunction Introduction

ABˆ A v B

If A is true and B is true, then the Proposition“A And B” is True.

(9) Conjunction Elimination

A v B A v Bˆ A or ˆ B

(First iteration). If the Proposition “A And B”is True, then A is true. (Second iteration). Ifthe Proposition “A And B” is True, then B istrue.

(10) Hypothetical Syllogism (ChainReasoning)

P e QQ e Rˆ P e R

If P implies Q and Q implies R, then P impliesR.

(11) Constructive Dilemma

(A e B) v (C e D)A w Cˆ B w D

If A implies B and C implies D, and either Ais true or C is true, then either B is true or D istrue.

(12) Absorption

A e Bˆ A e ( A v B)

If the Proposition “A implies B” is True, andA is true, then A and B are both true.

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(13) Conversion (A-Type)

All S is P e Some P is S

If all instances of S are also instances of P,then some instances of P are also instances ofS.

b. Rules of Replacement. Rules ofReplacement allow you to substitute Terms inan Argument, where the Terms are MateriallyEquivalent. Here are some Rules ofReplacement.133

(1) Double Negation (or “NegationElimination”)

¬ ¬ A / A

Not “not-A” is A.

(2) Commutativity

A v B / B v A

The Proposition “A or B” is LogicallyEquivalent to the Proposition “B or A”.

(3) Associativity

(A v B) v C / A v ( B v C)

The Complex Proposition of “A and B”coupled with “C” is Logically Equivalent tothe Compound Proposition os “A” coupledwith “B and C”.

(4) Tautology

A / (A w A)

“A” is Logically Equivalent to “A or A”. Theproposition is always true no matter what “A”is.

(5) DeMorgan’s Law

¬(A v B) / (¬A w ¬B)¬(A w B) / (¬A v ¬B)

The Negation of the Proposition “A and B” isLogically Equivalent to the Proposition “Not-A or Not-B”. DeMorgan’s Law also holds forthe Negation of the Proposition “A or B”,which is Logically Equivalent to “Not-A andNot-B”.

(6) Transposition (or “Contraposition”)

A e B / ¬ B e ¬ A

The Material Implication “A implies B” isLogically Equivalent to the MaterialImplication “not-B implies not-A”. This isModus Tollens.

(7) Material Implication

A e B / ¬ A w B

The Material Implication “A implies B” isLogically Equivalent to the Proposition “not-A or B”. See Section VII.C.6.

(8) Exportation

A e (B e C) / (A v B) e C

The Proposition that “A implies that B impliesC” is Logically Equivalent to the Propositionthat “if A and B are both true, then C is true”.

(9) Distribution

A v (B w C) / (A v B) w (A v C)A w (B v C) / (A w B) v (A w C)

(First iteration). Saying that A is true andeither B or C is true is Logically Equivalent tosaying that “A and B” is True or “A and C” isTrue. (Second iteration). Saying that “either Ais true or B and C are true” is Logically Equi-valent to saying that the Proposition “A or B”and “A or C” are both True.

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(10) Material Equivalence

A ] B / A e B v B e AA ] B / (A v B)A ] B / (¬ A v ¬ B)

(First iteration). The Proposition “A if andonly if B” is Logically Equivalent to theCompound Proposition “A implies B and Bimplies A”. (Second iteration). TheProposition “A if and only if B” is LogicallyEquivalent to the Proposition “A and B”.(Third Iteration). The Proposition “A if andonly if B” is Logically Equivalent to theProposition “not-A and not-B”.

(11) Conversion (E- and I-Type)

No S is P / No P is SSome S is P / Some P is S

(First iteration). The Proposition “no S is P”has as its Converse134 the LogicallyEquivalent Proposition “no P is S”. (Seconditeration). The Proposition “some S is P” hasas its Converse the Logically EquivalentProposition “some P is S”.

c. Logic Arguments. Here are two proofsof Logical Equivalence for the MaterialImplication.

Proof that (P e Q) / ¬ P v Q

(1) (P e Q) Assumed Valid(2) ¬ (P v ¬ Q) Follows from the

Validity of (1)(3) ¬ P v ¬ ¬ Q D i s t r i b u t i v e

Property(4) ¬ P v Q Eliminate Double

Negation

Proof of the Contrapositive, that (P e Q) / (¬Q e ¬ P)

(1) P e Q Assumed Valid

(2) ¬ (P v ¬ Q) Follows from the Validityof (1)

(3) ¬ (¬ Q v P) Commutative Property(4) ¬ ¬ Q v ¬ P Distributive Property(5) Q v ¬ P Eliminate Double Negation(6) ¬ (Q e P) F o l l o w s f r o m M a t e r i a l

Implication(7) ¬ Q e ¬ P Distributive Property

2. Conditional Proof. Conditional proof isproving the Validity of a ConditionalProposition. A Conditional Proof takes theform of asserting a Conditional Proposition,then through argument proving that theAntecedent necessarily leads to theConsequent. A Conditional Proof need notshow that the Antecedent is true, only that thetruth of the Antecedent guarantees the truth ofthe Consequent. The proof takes the form:

1. P 6 Q2. [intervening arguments]3. Therefore, P 6 Q.

Note that the Conditional Proposition “P 6 Q”can be proved regardless of whether “P” isproved to be true or “Q” is proved to be true.

3. Indirect Proof. An Indirect Proofestablishes that the Premise of an Argument istrue by assuming the Negation of the Premiseand showing that this assumption leads to alogical Contradiction.135 The rules of Logicsay that if a Premise (or hypotheticalassumption) leads to a logical Contradiction,then the Premise (or assumption) is proved tobe wrong. Indirect Proof is expressed inSymbolic Logic as “((¬A e B) v (¬A e ¬B))e A”, which says that “if not-A implies B andnot-A implies not-B, then A”. Indirect Proofis a form of Argument known as “Reductio adAbsurdum” (reduction to absurdity)

K. FALLACIES OF DEDUCTION. Afallacy is specious reasoning that appears tobe valid.136 An example is the popularmathematical deductive fallacy that purports

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to prove that 1 = 2. The fallacy occurs becauseone easily-overlooked step in the proofinvolves a division by zero, which is notallowed by the mathematical system incommon use.137 The Syllogistic Fallaciesdiscussed in Section VII.B.10 are Fallacies ofDeduction. They are joined by the followingDeductive Fallacies.

1. The Fallacy of Affirming theConsequent. Affirming the Consequent is alogical fallacy that occurs when someoneconcludes that, because “P” implies “Q”,therefore “Q” implies “P”. The term“Affirming the Consequent” comes from thefact that “the Consequent” in the conditionalclause, which is “Q”, has been “affirmed,” orproven to be true. This Fallacy is also knownas Converse Error.

(1) If P, then Q. (1) P implies Q.(2) Q. or (2) Q.(3) Therefore, P. (3) Therefore, P.

We can put the discussion into the context ofcause and effect. Where there are severalpossible causes of a particular effect, theexistence of that effect cannot itself establishwhich cause is involved. However, knowingthe list of causes of a particular effectcertainly can be useful in focusing efforts todetermine which cause is involved. If amedical condition is known to result fromcertain causes, then the physician knowswhich causes to rule out or confirm until theparticular cause is determines.

The case of E.I. du Pont de Nemours & Co. v.Robinson, 923 S.W.2d 549 (Tex. 1995),exemplifies the fallacy of Affirming theConsequent. In this case, the Robinsons sueddu Pont, alleging that an adulterant containedin du Pont’s Benlate fungicide, that waspurchased by the Robinsons and applied totheir pecan trees, caused the trees to havechlorosis, a yellowing of the leaves. Id. at 559.The Robinsons’ expert studied their trees and

concluded that the chlorosis resulted from SUherbicides that had inadvertentlycontaminated the Benlate. The expert claimedthat the fact that SU herbicides causedchlorosis had been established by analysis hehad conducted prior to being hired in the case.The Robinsons’ expert “did not conduct anysoil or tissue testing, did not research relevantweather conditions, and did not test any of theBenlate used by the Robinsons, even thoughthey had one opened box of the fungicideremaining.” Id. at 551. To put the Robinsons’expert’s analysis into syllogistic form: (1) SUherbicides cause chlorosis; (2) the Robinsons’trees exhibited chlorosis; (3) therefore theBenlate the Robinsons applied to their treeswas contaminated with SU herbicides. Hisreasoning took the form:

(1) P implies Q.(2) Q.(3) Therefore, P.

This is Aristotle’s fallacy of Affirming theConsequent. Since there are several causes ofchlorosis, the existence of chlorosis in and ofitself does not establish the particular cause inthis particular instance. Additional empericalefforts are required to rule out all otherpossible causes or to positively confirm onecause. It can also be said that the Robinsons’expert committed the Inductive fallacy of PostHoc Ergo Propter Hoc, (see Section VIII.F.7),since he reasoned that because chlorosisfollowed application of the Benlate, ittherefore must have been caused byapplication of the Benlate. At best the expert’sprior work established SU herbicide as onepossible cause of chlorosis, but in the case athand the expert did not make the effort toempirically rule out other possible causes ofchlorosis, and most importantly he did notempirically confirm his conclusion ofcontamination by chemically analyzing theRobinsons’ partially unused Benlate to see ifit contained SU herbicide

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Although Affirming the Consequent is alogical fallacy, it can still be a helpful tool inproblem-solving. Example: A patient entersthe clinic with a body temperature of 100degrees Farenheit. Possible causes include:recent physical exertion; a recent hot bath; anelevated temperature that is normal for thepatient; a microbial infection; a viralinfection. The physician must determine thecause in order to determine the best medicalresponse. The physician can narrow thepossible causes of the fever by questioning thepatient about recent physical exertions or arecent bath, or looking at the patient’s chart ofprior temperature readings. Even after rulingout these causes, the physician must stillchoose between a bacterial and a viralinfection. If it is flu season and a member ofthe patient’s household has recently beenconfirmed to have flu, the physician mayconclude that it is probable that the elevatedtemperature results from the flu virus. Anantibiotic would therefore be useless and thebest advice is to go home, rest, and drinkplenty of liquids. This assumption can beconclusively determined by laboratoryanalysis of a saliva culture.

2. False Dichotomy. A False Dichotomyreduces a set of possibilities down to a setnumber (2, 3, or more). The Propositionforces a choice between the statedalternatives, when there are in fact more thanthe listed choices.

3. Inconsistency. Inconsistency occurswhen a set of standards is applied to oneargument but not to another argument thatshould be evaluated on the same basis.

4. Non Sequitur. A Non Sequitur is anargument in which the Conclusion does notfollow by necessity from the Premises.

5. Slippery Slope. A “slippery slope”argument attempts to refute a proposition byclaiming that acceptance of the Proposition

will lead to a series of developments thatresult in an undesirable outcome.138 To avoidthe undesirable outcome, it is argued that thefirst step should be rejected. Stated insymbolic terms, a slippery slope argumenttakes the form of Modus Tollens:

A 6 B, B 6 C, C 6 D, D 6 E; ¬ E; ˆ ¬ A.

Slippery slope arguments are fallaciouswhenever the proponent fails to establish thateach step of the claimed sequence of eventsnecessarily will occur. Not all slippery slopearguments are fallacious. For example,German theologian Martin Niemöller, whocriticized Hitler and was arrested, butsurvived Sachsenhausen and Dachau,famously said:

"THEY CAME FIRST for the Communists,and I didn't speak up because I wasn't aCommunist.THEN THEY CAME for the trade unionists,and I didn't speak up because I wasn't a tradeunionist.THEN THEY CAME for the Jews, and Ididn't speak up because I wasn't a Jew.THEN THEY CAME for me and by that timeno one was left to speak up . . . .”

The implication is that, to avoid their comingfor you, you should stand up for the firstgroup they come to take away.

Another slippery slope argument waspowerfully stated by Justice Robert Jackson,in West Virginia State Board of Education v.Barnette, 319 U.S. 624, 640-41 (1943), theJehovah’s Witness children flag salute case,handed down during World War II, shortlyafter American and British soldiers pushed theGerman and Italian armies out of North Africabut before the Allies invasion of Sicily:

National unity as an end which officialsmay foster by persuasion and example isnot in question. The problem is whether

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under our Constitution compulsion ashere employed is a permissible means forits achievement.

Struggles to coerce uniformity ofsentiment in support of some end thoughtessential to their time and country havebeen waged by many good as well as byevil men. Nationalism is a relativelyrecent phenomenon but at other times andplaces the ends have been racial orterritorial security, support of a dynastyor regime, and particular plans for savingsouls. As first and moderate methods toattain unity have failed, those bent on itsaccomplishment must resort to ane v e r - i n c r e a s i n g s e v e r i t y . A sgovernmental pressure toward unitybecomes greater, so strife becomes morebitter as to whose unity it shall be.Probably no deeper division of ourpeople could proceed from anyprovocation than from finding itnecessary to choose what doctrine andwhose program public educationalofficials shall compel youth to unite inembracing. Ultimate futility of suchattempts to compel coherence is thelesson of every such effort from theRoman drive to stamp out Christianity asa disturber of its pagan unity, theInquisition, as a means to religious anddynastic unity, the Siberian exiles as ameans to Russian unity, down to the fastfailing efforts of our present totalitarianenemies. Those who begin coerciveelimination of dissent soon findthemselves exterminating dissenters.Compulsory unification of opinionachieves only the unanimity of thegraveyard.

It seems trite but necessary to say that theFirst Amendment to our Constitution wasdesigned to avoid these ends by avoidingthese beginnings.

Slippery slope arguments have been studied inthe legal literature.139

6. Begging the Question. “Begging theQuestion,” also called “Circular Reasoning,”is an argument in which the propositionassumes the truth of what it purports to prove.Stated differently, it is a proposition thatstates the conclusion (sometimes in differentwords) as support for the conclusion. In PriorAnalytics, Book II, xvi, Aristotle wrote that--

begging the question is proving what isnot self-evident by means of itself...either because predicates which areidentical belong to the same subject, orbecause the same predicate belongs tosubjects which are identical.

Example:

Q. Why do you keep snapping yourfingers?

A. To keep away elephants.Q. But there are no elephants around

here.A. That’s because I’m snapping my

fingers.

7. Circular Reasoning. See “Begging theQuestion.”

8. Changing the Premises. The Fallacy ofChanging the Premises occurs when, in thefirst part of an argument a premise is assumedor proved, and in the second part of theargument another premise is substituted thatresembles the first closely enough to bemistaken for it. This can occur when apremise is originally asserted with aqualification, but in the process of making theargument the qualification is forgotten. It canalso occur when an unstated limitation orcondition is necessary to the truth of theproposition, but is forgotten when thatproposition is employed as a premise.140

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L. PARADOXES. The term “paradox” hasbeen variously defined as: (i) a statement orexpression so surprisingly self-contradictoryas to provoke us into seeking another sense orcontext in which it would be true; (ii) aseemingly-self-contradictory statement madeto arrest attention and provoke fresh thought;(iii) a valid Logic argument that lead to acontradiction. The root of the word is Greekwords meaning “conflicting withexpectation.” When the paradoxical idea iscombined into one term, it is called an“oxymoron.” An “epigram” is a short, witty,and often paradoxical statement, like themany Oscar Wilde is remembered for.Paradoxes can arise that are internal to Logic.But paradoxes can also arise from a Soundargument that leads to a Conclusion we knowto be false. From a practical perspective,paradoxes are anomolies of language orthought that reflect some problem with theway we are thinking about something.Paradoxes are a small but important part ofthe history of thinking.

1. The Sorites Paradox. The SoritesParadox, attributed to Eubulides of Miletes (apupil of Euclid and teacher of Demosthenes),occurs when the premise of a logic-basedargument is sufficiently vague as to “allowsfor a range of borderline cases in which thetruth-value of propositions containing thepredicate” cannot be determined.141 The name“sorites” derives from the ancient Greek wordfor “heap.” In its historically original form,the Paradox of the Heap is:

A grain of sand is not a heap. (Premise 1)Add to it another grain of sand and it is stillnot a heap. (Premise 2)Therefore, adding a grain of sand does notmake a heap. (Conclusion)

Take two grains of sand, and add a third. It isstill not a heap. Continue the process toinfinity and you still have no heap. And yet at

a certain point, we know that we have enoughsand to make a heap. Thus, the paradox.

The Sorites can be done by subtraction:

1,000,000 grains of sand is a heap (Premise 1)Remove one grain of and it is still a heap.(Premise 2)Therefore, removing a grain of sand does noteliminate a heap. (Conclusion)

The process can be repeated until there is nomore sand left, and still it is a heap. Thus, theparadox.

Stated in modern terms: “Would you describea single grain of wheat as a heap? No. Wouldyou describe two grains of wheat as a heap?No. … You must admit the presence of a heapsooner or later, so where do you draw theline?”142

You can resolve the nomenclature problem bydefining a dividing line, for example that 1million grains of sand constitutes a heap. Butyou would have a hard time justifying why 1million grains of sand is a heap, but 999,999is not. The same problem is presented whenconsidering how many hairs to take from anhirsute man before he is bald. In someinstances, a disputant will retreat to gradationsin order to avoid a difficulty arising from amore categorical statement of a proposition.

2. The Liar Paradox. Epimenedes was apoet in ancient Crete who believed that Zeuswas immortal, contrary to the view thenprevailing in Crete. Epimenedes wrote:

They fashioned a tomb for thee, Oholy and high one.The Cretans, always liars, evil beasts,idle bellies!But thou art not dead: thou livest andabidest forever,For in thee we live and move and haveour being.

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This sentiment was picked up by the ApostlePaul, who wrote in his Epistle to Titus143:“One of themselves, even a prophet of theirown, said, the Cretians are always liars, evilbeasts, slow bellies. This witness is true.”HOLY BIBLE Titus 1:12-13. If Cretans arealways liars, then when a Cretan tells you thatCretans are always liars, he must be lying. SoEpimenedes’ statement that “Cretans arealways liars” must itself be a lie, which meansthat at least one Cretan must be truthful. Butthat conclusion negates the original assertionthat Cretans are always liars. So the assertionnegates itself. This form of self-contradictionis called “the Liar Parodox.”144 The paradoxcould be avoided by moderating the assertionfrom “always” to “usually,” withoutsubstantially weakening the point being made.

3. Eubulides’s Paradox. The Liar Paradoxhas been streamlined to the assertion: “thisstatement is false.” If the statement is true,then by its own terms it must be false.However, if the statement is false, then by itsown terms the statement must be true. Astatement that falsifies itself is sometimescalled a “Pragmatic Paradox.”

4. Socrates’ Paradox. Plato wrote thatSocrates said: “One thing I know is that Iknow nothing.” This statement attributed byPlato to Socrates cleverly refutes the skeptics’claim that it is impossible to know anything.The skeptics’ assertion, that nothing can beknown, itself tacitly asserts certain knowledgeof one thing (i.e., that nothing in knowable).Thus, assuming as a premise that nothing canbe known leads to a self-contradiction. This isa form of Indirect Proof: since the Premisethat nothing can known leads to a logicalcontradiction, the Premise is disproved, whichValidates the opposite of the Premise, andconfirms the idea that something is knowable.The statement also demonstrates that aparadox can be a dramatic and effectiverhetorical technique.

As an historical aside, Rene Descartes’ Axiom“I think; therefore I am”, can be viewed inlight of Socrates’ Paradox. Descartes pursuedhis famous “Method” of reasoning, ofchallenging each of his beliefs by identifyingits underlying assumptions and challengingtheir underlying assumptions, et cetera.Descartes pulled out of an infinite regressionwhen he reached the point of challenging hisown existence. To use Socrates’s style, theone thing Descartes could not doubt was thefact that he was doubting. He thereforeconcluded that the mental consciousnessdoing the doubting must exist. From that hestarted building a new world view thatbequeathed us the philosophical doctrine ofdualism, as well as analytic geometry, amongother things.

5. Smasandache Paradox. Given “A” assome attribute, if everything is “A”, then “¬A” must be “A”. This violates the postulate atthe foundation of Aristotle’s system of logic,the Law of Contradiction, which says that “A† ¬ A”.

6. The Catalog Paradox. A library iscompiling a bibliographic catalog of all (andonly those) catalogs which do not listthemselves. Should the library list its owncatalog?

7. The Omnipotent God Paradox. If Godis all-powerful, can God make a weight tooheavy for even God to lift?

8. The Surprise Test Paradox. In theSurprise Test Paradox, a classroom teacherannounces that she will give a surprise testnext week.

(1) If the test is not given by Thursday, thenthe class knows it will be on Friday, and thereis no surprise. Therefore, to be a surprise thetest must be given before Friday.

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(2) If the test is not given by Wednesday, thenit must be given on Thursday or Friday. Butunder (1) we know it can’t be Friday or itwould not be a surprise test. So the test mustbe given on Thursday, which would be nosurprise at the end of the day on Wednesday.So the test must be given before Thursday.

(3) If the test is not given by Tuesday, then itmust be given on Wednesday, Thursday, orFriday, but under (1) and (2) we know thatgiving the test on Thursday or Friday wouldnot be a surprise. Therefore, the test must begiven on Wednesday, which as of the end ofTuesday would not be a surprise.

(4) From (1) through (3) we know that a testgiven on Wednesday or Thursday or Fridaywould not be a surprise, which leaves onlyMonday or Tuesday. If the test is not given onMonday, then it can only be given onTuesday, so by the end of the day Monday atest given on Tuesday would be no surprise.

(5) Propositions (1) through (4) show that atest given on Tuesday, Wednesday, Thursday,or Friday would not be a surprise, leavingMonday as the only possible day to give theSurprise Test. But once we know that the testmust be given on Monday, then a test onMonday would be no surprise.

(6) Therefore, the teacher cannot give asurprise test next week if the fact that the testwill be given is announced in advanced.

9. The Grandfather Paradox. The“Grandfather Paradox” is the name given tothe idea that, with time travel, it would bepossible to go back in time to keep yourgrandfather from meeting your grandmother,so that you would never have been born.Variations of this idea are found in the plotsof short stories, books, and movies (TheTerminator, Back to the Future). This paradoxhas been used as proof that travelingbackward in time is not possible, and has even

spawned speculation among physicists aboutparallel universes, and the like.145

10. The Envelope Paradox. The two-envelopes Paradox, an adaptation of aproblem posed by a mathematician in 1953, isas follows:

You are presented with twoindistinguishable envelopes containingsome money. You are further informedthat one of the envelopes contains twiceas much money as the other. You mayselect any one of the envelopes and youwill receive the money in the selectedenvelope. When you have selected one ofthe envelopes at random but not yetopened it, you get the opportunity to takethe other envelope instead. Should youswitch to the other envelope?146

The paradox is understood in this way:(1) Call the amount of money in the envelopeyou selected “A”.(2) The probability that A is the lesser amountis 0.5; the probability it is larger is the same.(3 Therefore, the other envelope containseither A/2 or it is 2A.(4) If A is the lesser, then the other envelopecontains 2A. If A is the larger, the otherenvelope contains A/2.(5) The probabilities of the other envelope are0.5 of A/2 and 0.5 of 2A.(6) The expected value in the other envelopeis shown by the following formula:

½ @ (A/2) + ½ @ 2A = 1/4 @ A + A = 5/4 @A.(7) Since the expected value in the otherenvelope is 5/4A, which is more than A, youshould switch envelopes.(8) However, once you acquire the otherenvelope, the same reasoning process wouldlead you to swap again. This goes oninfinitely.

Another way to look at the problem is using“expected values.” In the following formula

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E(A) is the expected value in Envelope A;E(B) is the expected value in Envelope B; Xis the lesser amount of money in the twoenvelopes:

E(A) = E(B) = 0.5 @ X + 2 @ X = 1.5 @ X.

Since the expected value of A and B is equal,there is no reason to switch the envelopes.147

11. Orsinger’s Paradox. A more legally-oriented paradox, hereby dubbed “Orsinger’sParadox,” is the following: “All rules haveexceptions.” If true, then this rule must haveexceptions. An exception to this rule would bea rule that has no exceptions. If even one rulehas no exceptions, then to say that all ruleshave exceptions negates itself.

12. A Famous Scientific Paradox. A famousparadox occurred in the scientificunderstanding of the speed of light in avacuum. “Velocity” is measured by thechange in position of a moving object over aninterval in time. The formula is V = Δd ÷ Δt,stated in words as “velocity equals the changein distance divided by the change in time.”Galileo Galilei had suggested that theperception of motion was relative to theobserver. So, standing on the earth it appearsthat the sun moves around the earth, butrelative to a stationary position in space itappears that the earth moves around the sun.Take the example of a passenger on a movingtrain, and an observer on an embankment nextto the train track. If a train is moving at 40mph, and the conductor on the train began towalk from the back to the front of the train at2 mph, the passenger on the train would seethe conductor walking at 2 mph toward thefront of the train. However, the observer onthe embankment next to the train would seethe conductor moving at 42 mph in thedirection the train is traveling. Likewise, if theconductor began to walk from the front to theback of the train at 2 mph, a passenger wouldsee the conductor moving rearward at 2 mph,

while an observer on the embankment wouldsee the conductor moving backwards at 38mph in the direction the train is traveling. Thisexample reflects the additive nature of thevelocity of someone moving on a movingplatform relative to a fixed observer. Theperspective of the observer on theembankment can be generalized to anobserver who is watching everything movefrom a stationary location in space. In 1887,Albert Michelson and Edward Morley emitteda light beam that they split into two beamstraveling at a 90< right angle to each other.They were able to make a precise-enoughmeasure of the velocity of the light beams todetermine that the speed of light was the sameregardless of the direction in which it wasemitted. Since the earth was a “platform”moving at a high speed through the æther ofspace when the light beam was emitted, thefact that the two light beams exhibited noeffect from the earth’s motion through theæther created a paradox, in conflict with theprevailing understanding of motion throughthe æther of space. This paradox left scientistsin a quandary until June 30, 1905, whenAlbert Einstein published his paper on specialrelativity, which reasserted Gallileo’s beliefthat the perception of motion is relative to theobserver. But Einstein went further, theorizingthat, if the velocity of light in a vacuum isfixed, then at speeds approaching the speed oflight either the change in distance or thechange in time must be relative to theobserver. He concluded that both space andtime are relative. This insight eliminated theparadox by refuting the belief in absolutestationary space that was filled with æther(i.e., there is no “embankment” in space). Italso refuted the view that the rate at whichtime passes is fixed. And it made Einsteinjustifiably famous.

13. A Famous Political Paradox. On April27, 1861, President Abraham Lincolnsuspended the writ of habeas corpus “at anypoint on or in the vicinity of any military line,

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which is now used or which shall be usedbetween the City of Philadelphia and the Cityof Washington.” On September 24, 1862, heexpanded the geographical scope of thesuspension to include the entire country. As aresult, Union military officers arrested andheld thousands of citizens in loyal statesincommunicado without civilian arrestwarrant, grand jury indictment, or trial, forcriticizing the war effort. Lincoln was assailedfor violating his oath of office by violating theHabeas Corpus Clause of the U.S.Constitution. Lincoln’s action was subjectedto methodical and cogent criticism by ChiefJustice Roger Taney in his Opinion in Exparte Merryman, 17 F. Cas. 144, 151-152(C.D. Md. 1861), which stated that Lincolnhad usurped a power reserved to Congress,and violated the Fourth, Fifth and SixthAmendments. Lincoln sent a Message toCongress in Special Session on July 4, 1861,which set out his response to these and otherattacks. Lincoln argued that he had impliedpower as Chief Executive to suspend the writof habeas corpus in an emergency. Inparticular, he countered the claim that he hadviolated the Habeas Corpus Clause byarguing, among other things, that the criticismwas paradoxical. Here’s what he wrote:

Soon after the first call for militia it wasconsidered a duty to authorize thecommanding general in proper casesaccording to his discretion, to suspendthe privilege of the writ of habeas corpus,or in other words to arrest and detain,without resort to the ordinary processesand forms of law, such individuals as hemight deem dangerous to the publicsafety. This authority has purposely beenexercised but very sparingly.Nevertheless the legality and propriety ofwhat has been done under it arequestioned and the attention of thecountry has been called to the propositionthat one who is sworn to "take care thatthe laws be faithfully executed" should

not himself violate them. Of course someconsideration was given to the questionsof power and propriety before this matterwas acted upon. The whole of the lawswhich were required to be faithfullyexecuted were being resisted and failingof execution in nearly one-third of theStates. Must they be allowed to finallyfail of execution, even had it beenperfectly clear that by the use of themeans necessary to their execution somesingle law, made in such extremetenderness of the citizen's liberty thatpractically it relieves more of the guiltythan of the innocent, should to a verylimited extent be violated? To state thequestion more directly, are all the lawsbut one to go unexecuted and theGovernment itself go to pieces lest thatone be violated? Even in such a casewould not the official oath be broken ifthe Government should be overthrown,when it was believed that disregardingthe single law would tend to preserve it?

One of the criticisms Lincoln faced was theargument that the structure of the Constitutionand the few historical precedents (involvingPresidents Washington and Jefferson)suggested that only Congress could suspendthe Writ. It is interesting to note that Lincolnused pronouns and the passive voice in a waythat depersonalized his actions and de-emphasized the fact that, in suspending theWrit, he acted alone, as Chief Executive. Theargument was mooted when Congress ratifiedLincoln’s actions. At any rate, the paradoxLincoln proposed was that treating this oneconstitutional rule as inviolate would lead tothe loss of the entire Constitution, theinviolate rule included. The only way out ofthe paradox was to ignore this one rule(which, he offered in mitigation, mainlybenefitted guilty persons anyway). The fallacyin Lincoln’s argument was that the estimated30,000 people whose constitutional rightswere abrogated were not in the one-third of

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the former states that had repudiated theConstitution, but rather in the two-thirds ofthe states where the Constitution, includingthe Habeas Corpus Clause, continued to be therule of law. Thus, the people in rebellion werenot arrested, while the people arrested werenot in rebellion.148 Lincoln’s argument was aNon Sequitur. Logical considerations aside,Lincoln in essence allowed local militarycommanders around the Union to sequesterand thus silence non-rebelling citizens whopeacefully criticized Lincoln’s policy of usingmilitary force to overturn secession. The issuewas ultimately determined after Lincoln’sdeath, in Ex parte Milligan, 71 U.S. 2, 127(1866) (1866 WL 9434), where a 5-to-4majority of the Supreme Court agreed that therights ensured by the Bill of Rights could notbe abrogated, even in times of insurrection orwar, in geographical areas where the civilgovernment and civil justice system werefunctioning normally.

14. Avoiding “All” or “None.” The “LiarParadox” shows that some propositions refutethemselves. This self-refuting quality canusually be eliminated by switching “all” to“most” or switching “all” to “some.” Thisswitch avoids self-refutation. This is a specialapplication of a larger rule, that you shouldavoid stating propositions in absolute terms,where possible. An absolute assertion can berefuted with one counter-example, whereas anassertion using “nearly all” or “most” cannotbe refuted without considering all possibleinstances. Just as people say “never saynever,” you should almost never say “all” and“none.”

M. THE IMPORTANCE OF RELE-VANCE. For deductive reasoning to be usefulit is important that the Premises (orAntecedents) be relevant to the Conclusion (orConsequent). The validity of a Proposition orLogic Argument is measured by a single test,no matter what the Premises and Conclusionmight be: a Proposition or Argument is Valid

if it is impossible for its Premises all to be trueand the Conclusion to be false.149 Thefollowing Proposition is Valid:

(1) The number 4 is an even number.(2) What is black is not white.(3) Therefore, the earth circles the sun.

Since it is impossible for (3) to be false when(1) and (2) are true, the foregoing Propositionis Valid. Furthermore, because the Premisesare true and the Logic is Valid, theProposition is Sound. But the Premises haveno relevance to each other or to theConclusion. This example is extreme, sincethe lack of relevance is obvious. However,many Propositions are stated where the Termsappear to be relevant but are not. Sincerelevance is a subjective assessment, in anargument stated in natural language thecorrectness of the argument can depend onrelevance, which often is “in the eye of thebeholder.”

Relevance can also be a problem where thetwo Premises are inconsistent (i.e., so that itwould be logically impossible for bothPremises to be true at the same time).150 Sinceit can never be the case that both InconsistentPremises can be true, then it will neverhappen that both Premises are true and thisConclusion false. By definition, then, aProposition with inconsistent Premises isalways Valid, no matter what the Conclusionmay be. Example:

(1) Black is white.(2) White is black.(3) Therefore, yellow is blue.

This deductive Proposition is Valid, but weknow that it makes no sense. In Logic, thisProposition is Unsound (i.e., one or more ofthe Premises are false). An UnsoundProposition gives no assurance that theConclusion is true. While Soundness alerts usto a problem when Premises are false, a

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relevance requirement protects againstPremises that are true but not sufficientlyrelated to the issue at hand to result in areliable Conclusion.

Some logicians have developed systems ofLogic that include an additional parameterindicating the degree of relevance between theparts of a Proposition or Argument. Suchsystems do not involve certainty of theoutcome that is required for bivalentDeductive Logic, and are therefore part ofInductive Logic (see Section VII.).

N. T H E P R O B L E M S O FCONDITIONALS. “Conditionals” arestatements involving logical Implication. Innatural language, a Conditional Proposition isreflected by clauses like “if . . . then,” or “Qbecause of P.” The normal way to discussconditionals in Logic is to use phrases like “Pimplies Q,” or “P implies not-Q,” or “not-Pimplies Q,” or “not-P implies not-Q.”

Conditionals can be difficult to deal with,because a Proposition has a Truth Value basedon the truth or falsity of the Antecedent andthe Consequent. Additionally, either theAntecedent or Consequent or both can be acomplicated logical Proposition, includinganother Conditional Proposition.151

1. Problems with the MaterialConditional. In Formal Logic, the propositionthat “P implies Q” is depicted “ P e Q” or “PY Q”, and is called the Material Conditional.From the standpoint of Logic, the MaterialConditional is considered to be False when Pis true and Q is false, but True in all otherinstances. That means that, in Formal Logic,when P is false then the proposition “P e Q”is True, regardless of whether Q is true orfalse. The Truth Table for the MaterialConditional is:

There are two recognized Paradoxes ofMaterial Implication. The first it that,whenever the Antecedent is false, the MaterialImplication is True, regardless of whether theConsequent is true or false.

The idea that the Material Conditional is Truewhenever the Antecedent is false (3rd & 4th

Rows) reflects a departure of Logic from theway we intuitively perceive the world. Forexample, let P stand for the assertion “it issnowing in the Sahara Desert.” Let Q standfor the proposition that “Martians landed onthe White House lawn”. Remember that, withthe Material Conditional, “P e Q” is truewhenever P is false, even if Q is false (4th

Row). It is logically Valid to say that the factit is snowing in the Sahara implies thatMartians have landed in the nation’s capital.If such assertions are logically Valid, then theMaterial Implication is of little practical use inordinary discourse in instances where theAntecedent is false.

The foregoing problem has been identified asa lack of relevance between the Antecedentand the Consequent, which some thinkershave tried to eliminate by developing arelevancy requirement in assessingConditionals.

The second Paradox of Material Implication isthat the 1st Row and 3rd Row of the TruthTable for the Material Conditional, takentogether, indicate that P e Q and that ¬P e Q.Since Aristotle’s Law of the Excluded Middleestablishes that everything is either P or not-P,then “P v ¬ P” includes everything. If both P

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and ¬ P imply Q then, when Q is true,everything Materially Implies Q.

Consider the following proof: if P is false,then, based on Aristotle’s Law of theExcluded Middle, ¬ P must be true. Using theTruth Table for the Material Conditional,substituting ¬ P in the 3rd Row, where P isfalse, results in the logically-Equivalentproposition “¬ P e Q” being True.Substituting ¬ P for P, when P is false, andsubstituting ¬ Q for Q, when Q is false (4th

Row), results in the proposition “¬ P e ¬ Q”being True (4th Row). Thus, the 3rd and 4th

Rows together indicate that (¬ P e Q) v (¬ Pe ¬ Q). This is logically Equivalent to ¬ P e(Q v ¬ Q). Since (Q v ¬ Q) includeseverything, ¬ P, when used in the MaterialConditional, implies everything. Thus, theMaterial Conditional with a false Antecedentcannot be used to differentiate anything fromanything else, which makes it useless, exceptas a topic of endless discussion amongphilosophy graduate students.

These problems result from the fact thatFormal Logic operates in the abstract, whilewhat “makes sense” to us involves ourlanguage, our experience, our habits, and ofcourse the real world. We are again led to therecognition that what is logically Valid maynot be Sound.

Consider the Material Conditional “P e P”. Ifthe Premise is true, then the Consequent istrue, and the Material Conditional is bothValid and Sound, but it is a Tautology.Consider the Material Conditional “P e ¬ P”.If the Premise is true, then the Consequent isfalse, which makes the Material ConditionalInvalid and therefore Unsound. If theAntecedent is false, then the Consequent istrue, which makes the Material ConditionalValid but Unsound.

2. Problems With the IndicativeConditional. An indicative Conditional uses

a verb (the Copula) that is in the indicativemood. The indicative mood conveys a strongbelief that the Consequent follows from theAntecedent. Example: “If Mary is late, thatmeans that she got caught in traffic.” Anindicative Conditional may be “truthpreserving” (if the Terms are true then theentire Proposition is True), or may not,depending on how it is used.

The indicative mood reveals less informationthan a subjunctive Conditional, according to apaper coauthored by British psychologist RuthM.J. Byrne, which gave two examples:152

If John wore a seatbelt then his injurieswere slight. (Example 1)If John had worn a seatbelt then hisinjuries would have been slight.(Example 2)

Example 1 is an indicative Conditional whileExample 2 is a subjunctive Conditional.Byrne believes that Example 1 does notsuggest whether John wore a seatbelt, whileExample 2 suggests he did not. This suggeststhat the mood of the verb contained in aConditional can affect the way it will beinterpreted.

3. Problems With SubjunctiveConditionals. A subjunctive Conditional is aConditional stated in the subjunctive mood.The subjunctive mood is used in English tosuggest that the things described are not true,or might not be true. In her paper mentionedabove, Byrne asserts that “[u]nless thecontent, context, or general knowledgesuggests the contrary, conditionals in thesubjunctive mood, such as Example 2, conveyinformation about the truth status of theirantecedents and consequents, unlikeconditionals in the indicative mood, such asExample 1.”153 Some philosophers haveattempted to evaluate subjunctiveConditionals in terms of “possible worlds”that could exist. They distinguish between

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propositions that are true (true in the realworld), false (untrue in the real world),possible (true in at least one possible world),contingently true or false (true in somepossible worlds and false in others), necessary(true in all possible worlds), and impossible(false in all possible worlds).

4. Problems With CounterfactualConditionals. Some counterfactualConditionals can be said to be correct orincorrect. For example:

If Jean were at the Louvre, he would bein North America. (Example 3)If Jean were at Chichen Itza, he would bein North America. (Example 4)

Example 3 is always wrong, and Example 4 isalways right, no matter where Jean might be.

Other counterfactual Conditionals cannot besaid to be correct or incorrect, such as: “IfNapoleon had not invaded Russia, he wouldhave died the Emperor of France.” There is noway to know, even absent the War of 1812,whether England could have persuaded andpaid Austria and Russia to invade France andwhether such an invasion, if attempted, wouldhave been successful. Or as Napoleon aged,he could have suffered dementia, becomementally incompetent, and been removed bya coup d’etat prior to his death.

Reasoning from counterfactual Conditionalsrequires the reasoner to imagine a Premisethat the reasoner knows is not true. Somepsychologists suggest that reasoning fromcounterfactuals requires reasoning proceduresthat are an extension of the reasoning used fornormal Conditionals.154 One difficulty ofcounterfactual Conditionals is to evaluatepossible worlds that might have resulted hadthe counterfactual Conditional occurred. Froma Truth Value perspective, counterfactualConditionals are always True because theAntecedent is false. See Section VII.N.1 & 4.

O. “SOME” and “ALL.” Lincoln’s famousstatement, “you can fool some of the peopleall of the time, and all of the people some ofthe time, but you can’t fool all of the peopleall of the time,” can be expressedsymbolically (“F” is a situation in which thepeople are fooled, “P” is people, and “T” istime): F(›P, œT), (œP, ›T), ¬F(œP, œT). SeeSection VII.B.7. A separate point is that it issometimes considerably more difficult toprove, and thus easier to refute, Propositionsthat use “all” as opposed to “some.” The LiarParadox mentioned above can be eliminatedby using the quantifier “some” instead of“all”: “Some Cretians are liars.” Most “all”statements can be rewritten as “some”statements and still accomplish the necessarypurpose.

P. PROBABILITIES. From a practicalperspective, if we know that the Proposition“P implies Q” is Valid, then when P is true Qmust therefore be true. This is the rule ofModus Ponens. And if “P implies Q” is Valid,and Q is untrue, then we know that P must beuntrue. This is the rule of Modus Tollens. Butwhat if the Validity of the Proposition “Pimplies Q” is not a given, but instead is ahypothesis that needs to be proven. We mightbe able to deductively Validate theImplication “P implies Q” by constructing alogical Argument using Propositions that havebeen proven Valid, or Axioms (i.e., Premisesthat are assumed to be true), to prove that theProposition “P implies Q” is Valid. Wherethis is not possible, then we can only hope toprove that “P implies Q” by makingobservations or conducting experiments to seewhether any, and eventually every, instance ofP is accompanied by an instance of Q. If everyinstance of P is accompanied by an instance ofQ, then the Proposition “P implies Q” isValid. If we find a single instance where Qdoes not accompany P, then we have shownthat the proposition “P implies Q” is Invalid.

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What if P sometimes implies Q, but notalways? This forces us into a less certaindomain, where the best we can do is ascertainthe likelihood that P implies Q. We thus movefrom the domain of certainty (and DeductiveLogic) to the domain of probability (andInductive Logic). After many observations, ormany experiments, the statistician may beable to say, for example, that P implies Q 80%of the time. Stated differently, there is an 80%probability that P implies Q.

Some of the choices we face in our livesinvolve certainties, where a particular action(or inaction) will always lead to a certainresult. For example, if you don’t buy a lotteryticket, your chances of winning the lottery arezero (but if you do buy a lottery ticket, yourodds of winning the Texas Lotto lottery arearound 1-in-26 million). But many of thechoices we face do not lead with certainty toa particular result. Sometimes we may becontemplating a choice where scientists orstatisticians have calculated the probability ofdifferent outcomes. More often in life andbusiness we are faced with choices where theprobability of various outcomes has neverbeen determined. Then we fall back ongeneralities, saying for example that a certainoutcome is highly likely, or more likely thannot, or unlikely.

The burden of persuasion in a trial can beviewed in this light. Where the burden ofpersuasion is a preponderance of the evidence,the question for the jury is whether aproposition is more likely than not (statedlegally, supported by the “greater weight ofcredible evidence”). Where the burden ofpersuasion is clear and convincing evidence,the question for the jury is whether aproposition is highly likely (stated legally,where the jury has “a firm belief orconviction” that the proposition is true).Where the burden of proof is beyond areasonable doubt, the question for the jury iswhether all reasonable explanations other than

guilt have been eliminated (there is no“official” definition of reasonable doubt).

Logical Propositions involving probabilitiesare the domain of Inductive Logic. SeeSection X.

Q. TRANSLATING ENGLISH TODEDUCTIVE LOGIC. In many instances,logical propositions embedded in Englishsentences are so obvious that the deductivevalidity or invalidity of the argument isreadily apparent. In other instances, the logicunderlying an argument is not evident, andwhether the logic is valid or invalid is moredifficult to discern. It is therefore sometimeshelpful to translate English languagearguments into the language of Logic, to makethe logical propositions underlying theargument more evident. Here are sometechniques to make this translation fromnatural language to easier.

1. Negation. The word “not,” ingrammatical usage, indicates that thestatement immediately following the “not” isfalse (or does not apply). English words thatcorrelate to Logical Negation include “not,”“neither . . . nor,” “never,” “none,” “isn’t,”and “cannot be.” Negation in English can alsobe indicated by prefixes such as “un-,” as in“untimely,” “unjustified,” etc. In FormalLogic, which is bivalent and thereforerecognizes that a statement has only twovalues (True or False), Negation converts theTruth Value of a Logical Statement or LogicProposition from True to False or from Falseto True. For example, in the ExclusiveDisjunction “either A or B, but not both,”“not-A” is logically Equivalent to “B”, and“not-B” is logically Equivalent to “A”. Thisreasoning is Valid only if “A” and “B” arecollectively exhaustive.

2. Logical Conjunction. The word “and” is,in grammatical usage, a conjunction that joinstwo words, phrases, or sentences. The word

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“and” often translates to the Logic Connector“And,” symbolized as “v”. Other words thatoften translate to Logical Conjunction are“but,” “moreover,” “however,” “although,”and “even though.” Examples:

• It was a dark and dark v stormy v night stormy night• A day late and day late v dollar short a dollar short• Be on time and on time v ready to go ready to go

Not all English language usages of the word“and” translate to Logical Conjunction. Inthese instances, the English languagestatement has no assignable Truth Values.Examples:

• Two and two equals four.• Isaac and Ishmael were half-brothers.• Dr. and Mrs. Marcus Welby.• Proctor and Gamble.

Example of Logical Conjunction in Law: Tex.R. App. P. 33.1 provides:

(a) In General. As a prerequisite topresenting a complaint for appellatereview, the record must show that:

(1) the complaint was made to the trialcourt by a timely request, objection, ormotion that:

(A) stated the grounds for the rulingthat the complaining party soughtfrom the trial court with sufficientspecificity to make the trial courtaware of the complaint, unless thespecific grounds were apparent fromthe context; and (B) complied with the requirementsof the Texas Rules of Civil orCriminal Evidence or the TexasRules of Civil or AppellateProcedure; and

(2) the trial court:

(A) ruled on the request, objection, ormotion, either expressly or implicitly;or (B) refused to rule on the request,objection, or motion, and thecomplaining party objected to therefusal. [Emphasis added].

Considering TRAP 33.1 to be a LogicProposition that is either True or False,subparts (1) and (2) are conjunctively joined,meaning that both must be true for TRAP33.1(a) to be True. Sub-subparts (1)(A) and(1)(B) are conjunctively joined, meaning thatboth must be true for subpart (1) to be True.However, sub-subparts (2)(A) and (2)(B) aredisjunctively joined, meaning that subpart 2 isTrue if either (2)(A) or (2)(B) is true. Thedisjunction in question is an ExclusiveDisjunction, as explained below.

3. Logical Disjunction. The word “or,”when used grammatically, often signalsLogical Disjunction. Logical Disjunction canbe either Inclusive or Exclusive.

a. Inclusive Disjunction. InclusiveDisjunction is specified by the phrase “either.. . or . . . , or both.” Often in natural languagesentences, the reader must use the context ofthe argument or surrounding circumstances toascertain whether the Inclusive Disjunction issuggested.

b. Exclusive Disjunction. ExclusiveDisjunction is specified by the phrase “either.. . or . . . , but not both.” Often in naturallanguage sentences, the reader must use thecontext of the argument or surroundingcircumstances to ascertain whether theExclusive Disjunction is suggested.

4. Implication. Some implications stated inEnglish language sentences can be translatedinto Truth-Functional, Bivalent Logic, and

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some cannot. When they can, they translateinto the Material Conditional. See SectionVII.C.3. The Material Conditional issometimes not useful in analyzing Englishlanguage statements because of the Paradoxesof the Material Conditional. See SectionVII.N.1.

a. Material Conditional. The MaterialConditional describes a logical propositionsuch that when the Antecedent is true theConsequent must also be true (ModusPonens). The Material Conditional alsoindicates that, when the Consequent is false,the Antecedent must therefore be false(Modus Tollens).

In Natural Language In Logic

(1) If you heat water to 210E e boil210E F, it will boil (Modus Ponens)

(2) Water boils at 210E F 210E e boil(Modus Ponens)

(3) You must heat water 210E e boilto 210E F for it to boil (Modus Ponens)

(4) Water will not boil at 210E e boilless than 210E F (Modus Tollens)

(5) If it is raining, then rain e wet walkthe sidewalk will be wet (Modus Ponens)

(6) If the sidewalk is dry, rain e wet walkthen it is not raining (Modus Tollens)

Note that the Modus Tollens of “rain e wetwalk” is the Logic Equivalent of the ModusPonens of “dry walk e not rain”.

b. Other Conditionals. Implication can beexpressed in the English language in manyways that do not translate to the MaterialConditional. For example, the statement “Ifyou finish your homework in time, you canwatch your favorite television program” has

no Truth Value. Most speakers tacitly requirea degree of relevance between the Antecedentand the Consequent before they make aconditional statement.

Conditional statements may not reflectimplication at all. The phrase “B only if A”signifies that A is a necessary condition for Bto occur. For example, Texas Probate Code§ 694K says the following:

694K. Attorney Retained on Ward'sBehalf

(a) A ward may retain an attorney for aproceeding involving the completerestoration of the ward's capacity ormodification of the ward's guardianship.

(b) The court may order thatcompensation for services provided by anattorney retained under this section bepaid from funds in the ward's estate onlyif the court finds that the attorney had agood-faith belief that the ward had thecapacity necessary to retain the attorney'sservices.

This means that before a court cancompensate a retained attorney from a ward’sestate, the court must first find that theattorney had a good faith belief that the wardwas competent. In other words, the award offees is contingent on the good faith belief.However, but the court is not required toaward fees, just because good faith beliefexisted.

5. Premise Indicators/ConclusionIndicators. In translating natural languagearguments into logic, it is important toidentify the premises and the conclusions.Words that indicate a premise include “if,”“since,” “for,” “because,” “given that,” “forthe reason that,” “seeing that,” “based on thefact that,” “on account of,” and “in light of thefact that”. Conclusion indicators include

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“therefore,” “thus,” “hence,” “consequently,”“so we conclude,” “so,” “it follows that,”“accordingly,” “implies that,” “it is likelythat,” and “then” where paired with an “if”.155

Words that signify a conditional statementinclude “if,” “only if,” “given that,” “providedthat,” “supporting that,” “implies,” “even if,”and “in case.”

6. Identifying and Adding SuppressedPremises. While arguments are readily madewith suppressed premises, in evaluating anargument it is necessary to locate thesesuppressed premises and to make themexplicit.

7. Examples of English-to-LogicTranslations. In the following examples, thePremise or Antecedent is marked by a [1] andthe Conclusion or Consequent by a [2]:

<[2] “Opportunity is missed by most peoplebecause [1] it is dressed in overalls and lookslike work,” Thomas A. Edison. Edison issaying that success results from hard workand not luck.

<“‘I have always been fond of the WestAfrican proverb: [1] ‘Speak softly and carry abig stick; [2] you will go far.’” TheodoreRoosevelt

<[2] The sidewalk is wet, so [1] it must haverained last night.

<[1] You should finish high school [2] so youcan get a better job.

<[1] If I don’t set the alarm clock, [2] I won’tget to work on time.

<[1] Given that Luna failed to attack eachindependent ground listed in Stripes's motionfor summary judgment, [2] she cannot prevailon appeal.

<[1] The State has not met its burden toestablish that the letter is untrustworthy. Seeid. (“The party opposing the admission of thereport has the burden of proving the report'suntrustworthiness.”); Moss, 933 F.2d at1307-08. We therefore conclude that [2] thetrial court did not err in overruling the State'shearsay objection to the letter.

<Even though [1] the trial judge erred byoverruling Pearson's motion to modify basedon its failure to meet the requirements ofsection 156.401, we nevertheless concludethat [2] the trial court did not err by overrulingthe motion.

< Here, the trial court concluded that the leasewas ambiguous as to whom the tenant was;the court determined that the tenant was either“Paul Avenell, Individually and DBA K & SContracting” or “K & S Contracting, Inc.”However, [1] we see nothing in the contract toindicate that Avenell entered into the leaseagreement on behalf of “K & S Contracting,Inc.” Instead, each time his name is includedin the contract, it is associated with “K & SContracting.” . . . Thus, we conclude that [2]the lease is unambiguous and that K & SContracting is the tenant.

< In sum, although we disagree with the trialcourt's legal conclusion that the lease isambiguous, we agree [2] that Avenell,individually, is liable under the lease. [Thequoted excerpt reflects that the Premiseadopted by the trial court was false, but thetrial court’s Conclusion was nonethelesscorrect for a different reason].

< Because [1] we have concluded that the trialcourt did not err in refusing to grant acontinuance, we further conclude that [2] thetrial court did not err in refusing to grantappellant a new trial based on evidence thatappellant was harmed by the denial of hismotions for continuance.

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< In his fourth issue, Turner contends that theevidence was legally insufficient to supporthis conviction because the State failed toprove that he was a primary actor to theoffense.FN2 Turner's entire argument on thispoint is based upon the premise that [1] thejury charge did not authorize the jury toconvict him under the law of parties. . . .Contrary to his arguments on appeal, the jurycharge also authorized the jury to convictTurner of capital murder or felony murder ona conspiracy theory, as contemplated bySection 7.02(b) of the Penal Code. Asdiscussed below, [2] the evidence wassufficient to convict Turner of capital murderunder this theory of responsibility.

< [1] Based on this statute, the Rizzos arguethat the rollback taxes must have beenassessed due to Ancira's change in use of theproperty, as they were assessed for yearsduring which Ancira owned the land. Thisargument, however, rests on a faulty premise.The fact that the tax code lays out the properprocedures for a certain task does notguarantee that the procedures were followedin any given case. Accordingly, [2] the factthat the tax code indicates that rollback taxesshould only be assessed due to a change in useof property does not compel the conclusionthat, in this case, the taxes were assessed forthat reason. The Rizzos' arguments on appealconsequently lack merit.

8. Hypothetical Arguments. Hypotheticalarguments make a temporary assumption forpurposes of the argument in order to show theconclusion that would follow from theassumption. It is not necessary that theassumption be true. In fact, in an IndirectProof you assume a hypothesis with thepurpose of showing that it is false because itleads to a contradition.

R. LEGAL FORMALISM. Legalformalism describes a view that the lawconsists of rules, and that cases consist of

facts, and that all legal disputes can beresolved by applying the correct rule to thefacts. This approach to legal problem-solvinglends itself to the Syllogism of DeductiveLogic, where the legal rule is the MajorPremise, the facts of the case the MinorPremise, and the legal result is the Conclusionthat necessarily follows.156 Cut-and-driedcases may fit into this mold, where theapplicable rule of law is clear and the onlyquestion is whether the facts of the case fallwithin the rule. More complex cases, oftencalled “hard cases,” do not easily fit withinthis mold. When there is no clearly-applicablerule of law, the rule to be applied may have tobe arrived at using Inductive Logic (seeSection VIII) or Reasoning by Analogy (seeSection XI).

S. LEGAL EXAMPLES. Some courtdecisions reflect deductive reasoning, wherethe Major Premise is a legal principle, theMinor Premise a new case that is held to comewithin the scope of that legal principle,leading to the result.

Take, as an example, the rules fordisqualification of a Texas judge. The groundsfor disqualification are set out in TexasConstitution art. V, § 1, and in Tex. R. Civ. P.18(b)(1). If the judge is related to a partywithin the third degree of affinity orconsanguinity, s/he is disqualified. It is clearwhat law applies and it is clear how that lawapplies. The only question is whether the factsof the case fall within the scope of the rule. Ifso, then the judge is disqualified. If not, thenthe judge is not disqualified.

A more complicated example involves theenforceability of premarital agreements underTexas law. Under Texas Family Code Section4.006, a premarital agreement is enforceableunless the party opposing enforcementestablishes the defenses of lack ofvoluntariness or unconscionability. In a TruthTable, the premarital agreement is enforceable

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unless “not voluntary” (¬V) is found to betrue, or “unconscionability” is found to betrue. In the following Truth Table, theheadings are constructed to reflect theproposition that the party opposingenforcement must prove in order to defeat theagreement (involuntary is “not-V”,unconscionable is “U”, and enforceable is“E”):

Defenses to Enforcement of Premarital Agreement:

Voluntariness and Unconscionability

The Truth Table for enforceability of apremarital agreement reads like this:

(1st row) If “not voluntary” is true and“unconscionable” is true, thenthe agreement is unenforceable.

(2nd row) If “not voluntary” is true and“unconscionable” is false, thenthe agreement is unenforceable.

(3rd row) If “not voluntary” is false and“unconscionable” is true, thenthe agreement is unenforceable.

(4th row) If “not voluntary” is false and“unconscionable” is false, thenthe agreement is enforceable.

The unconscionability defense is complicated.Even if the premarital agreement isunconscionable, it is nonetheless enforceableunless the party opposing enforcement provesthat, before the agreement was signed: (i) s/hewas not provided a fair and reasonabledisclosure of property or financial obligationsof the other party. (ii) s/he did not expresslywaive, in writing, such disclosure; and (iii)s/he did not have, or reasonably could not

have had, adequate knowledge of the propertyand financial obligations of the other party.Tex. Fam. Code § 4.006(a)(2). Stated insymbolic logic, where q = unconscionable, r =disclosure, s = waiver, and t = knowledge, tosucceed with an unconscionability defense theparty opposing enforcement must prove:

q v ¬ r v ¬ s v ¬ t.

Here is the Truth Table reflecting theunconscionability defense:

Truth Table for the Unconsionability defense to enforcement of premarital agreement

T. COGNITIVE STUDIES OFDEDUCTIVE REASONING. Cognitivescientists have studied the way people engagein deductive thinking, through Syllogisms,Conditionals and in other ways. Thesescientists have attempted to correlate thedifficulty of certain mental processes withobjective measures such as reading times,answer times, and percentage of correctanswers. Some psychologists believe thatpersons untrained in Logic use mental rules ina process to derive Conclusions fromPremises. Other psychologists reject that idea,saying that logical propositions are valid orinvalid based on form, while natural languagesentences are judged by many persons to betrue or false based on content.157 One schoolof thinking is that persons solve logicproblems by constructing “mental models” of

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the problem, then quickly checking to see ifthe conclusion holds true in all instances (andis thus “necessary”), or most instances (and isthus “probable”), or at least one instance (andis thus “possible”), or no instances (makingthe Proposition “Invalid”). Invalidity can bemodeled as a search for a counter-example,and if none is found then the Syllogism isdeemed valid; if a counter example is found,then the Syllogism is deemed Invalid.158

U. REASONING EXPERIMENTS. Thetypical reasoning experiment provides theparticipant with a Premise and asks him/her toa produce or evaluate a Conclusion that wouldfollow from the Premise. The psychologistlimits the non-logical content of the problem,in order to avoid interference from generalknowledge.159

1. Tests of Conditional Reasoning. Thetypical reasoning experiment provides theparticipant with a Premise and asks him/her toproduce or evaluate a Conclusion thatnecessarily follows from the Premise. Thepsychologist limits the non-logical content ofthe problem, in order to avoid interferencefrom general knowledge.160 In general terms,most people, when given the indicativeConditional in Modus Ponens form that “Pimplies Q,” and given the Premise “P”, arriveat the Conclusion “Q”. Only half of the peoplearrive at the Modus Tollens result, that theIndicative Conditional “P implies Q,” togetherwith the Premise “not-Q”, leads to theConclusion “not-P”.

a. The Wason Selection Task. A famoustest of deductive reasoning was devised byPeter C. Wason in 1966, called the “WasonSelection Task.” In this task, the examinee isshown four cards, one with the number 3,another with the number 8, another purely red,and the last purely brown. The examinee wasasked, “Which card(s) should you turn over totest the truth of the proposition that if a card

shows an even number on its face, then itsopposite face is red?”

The answer to the Wason Selection Task is atthis endnote.161 In Wason’s study, less thanten percent of the people got the right answer.The experiment suggests that in solvingproblems people use something other thananalytic processes. Some say they use “rulesof thumb” or short-cut ways of evaluatingproblems--which psychologists call“heuristics.”162 Other say that peopledetermine the validity of a deductiveproposition by creating “mental models” ofthe problem, then running through theoutcomes to see whether a counter-exampleoccurs. If not, the problem is deemed valid.163

Subsequent studies suggest that people nottrained in Logic assess the validity of aSyllogism based on the believability of itscontent. For example, an experimentpublished in 1983 found that most participantssaw that the following Syllogism wasincorrect: “No police dogs are vicious; somehighly trained dogs are vicious; thereforesome police dogs are not highly trained.”164

VIII. INDUCTIVE LOGIC. In addition todescribing reasoning by deduction, Aristotlealso wrote about induction (epagôgê). In hiswritings on Logic, Aristotle says little morethan that induction is reasoning from theparticular to the general. In his writings onscience, however, Aristotle describesinduction as a process in which an observerevaluates many specific instances and drawsfrom them underlying principles that connectthese specific instances in a necessary way.This has become an idealized view of thescientific process, in which the scientistobjectively makes many observations, then

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uses intuitive processes to abstract from allthese instances some underlying principle thatexplains how or why they occur. Thisprinciple is then published as a hypothesis,which is subjected to analysis and testing byother scientists. More generally, people useinductive reasoning every time they use whatthey already know to deal with novelsituations.165

The hallmark of Inductive Logic is that theconclusion does not necessarily follow fromthe premises. An Inductive inference orArgument is “strong” if it is improbable thatthe Conclusion is false when the Premises aretrue. In many instances, it is possible toestimate the likelihood that the Conclusionfollows from the Premises using probabilitytheory. Thus, probabilities play an importantrole in Inductive Logic. Probabilities cansometimes be generated using the principlesof statistical analysis. Statistics can be used toextrapolate from a few instances to allinstances. Statistics can be used to predictfuture outcomes or conditions based on pastor present circumstances. Generatingconclusions using probabilities and statisticscan thus be evaluated using the principles ofInductive Logic.

A. MODERN SCIENCE AS INDUCTIVELOGIC. The philosophy of science has gonethrough many stages. The current view ofmodern science, seeded with the writings ofFrancis Bacon (1561-1626) and theobservational work and philosophical writingsof Galileo Galilei (1564-1642), is a process ofgathering observations about nature andnatural phenomena, and drawing from theseobservations certain underlying principles thatare posed as hypotheses that are thereaftertested for validity, and are adjusted orabandoned as further efforts confirm ordiscredit the hypotheses. The process ofdrawing underlying principles from manyexamples is Inductive Logic.

The Inductive Logic component of modernscience is epitomized by the work of GalileoGalilei, who drew on his own carefulobservations of physical phenomena topropose theories about the way the worldworks. Galileo’s measurements regarding thespeed of balls rolling down an inclined planeled him to propose that falling objects ofdifferent weights all gain speed at the samerate of acceleration. Using a telescope that hedeveloped, Galileo discovered that Jupiter hadthree moons, and that Venus went throughphases like the moon. Both observationsdestroyed the central tenet of the geocentricview of the universe, that all celestial objectsmoved around the earth which remained still.In a similar manner, Keppler determined hisThree Laws of Planetary Motion fromastronomical data collected by Tycho Brahe,and Newton developed his explanation ofoptics from careful observation of theproperties of light. Einstein deduced, inModus Tollens fashion, that experimentalevidence, showing that the speed of light wasinvariable in a vacuum, refuted the traditionalassumptions that space and time wereinvariable, and he inductively generated hisTheories of Special and General Relativity asa result.

B. JOHN STUART MILL ONINDUCTIVE LOGIC. John Stuart Mill’s1843 book, A SYSTEM OF LOGIC, contains animportant analysis of Inductive Logic. Millbelieved that all knowledge derived fromexperience, and that the rules of mathematicsand rules of Logic were drawn by humansfrom their interactions with the world. In fact,Mill saw Deductive Logic as deriving fromInductive Logic, in that the Premises assertedin Deductive Logic were themselves anextrapolation of general principles drawnfrom many individual experiences. Forexample, the Premise “All men are mortal”can be asserted as a Premises derived fromour experience that, in every case we haveseen so far, all human beings eventually die.

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Mill described Inductive Logic in thesewords:

Induction, then, is that operation of themind, by which we infer that what weknow to be true in a particular case orcases, will be true in all cases whichresemble the former in certain assignablerespects. In other words, Induction is theprocess by which we conclude that whatis true of certain individuals of a class istrue of the whole class, or that what istrue at certain times will be true in similarcircumstances at all times.166

Mill’s approach to inductive reasoning is mostreadily applied to scientific inquiry about theworld, which is not surprising given Mill’sthesis that the methods of logical analysis arethemselves a product of our observationsabout the way the world works. Mill’sinductive techniques are thus adapted to thedevelopment of hypotheses about the cause ofevents or phenomena in the natural world,which can be validated or invalidated byobservations of natural phenomena, or moreeffectively by conducting experiments inwhich possible causal agents are isolated andthen varied to see how they affect the result.Mill extended his theories to purely socialquestions such as morality, but Mill believedthat the only “social science” that was trulysusceptible to this type of verification waspsychology, where concrete rules of humanbehavior could be identified and tested toestablish validity.

Unfortunately, Mill did not apply his thinkingto jurisprudence, so we are left to our owndevices in applying his model of inductivereasoning to the legal process. Nevertheless,it is apparent that the inductive processoutlined with great specificity by Mill doesdescribe some aspects of legal analysis.Applying Mill’s insight to the common law,all principles of law, described by Blackstoneas deriving from Natural Law, are inductive

conclusions drawn from a multiplicity of courtrulings that in turn were originally drawnfrom the way people naturally acted in variouscircumstances. When no existing rule of lawfits the case, and a new rule must be ab-stracted from a variety of possible rules thatmight be extended to the case at hand,Inductive Logic comes into play. In thatrespect, it is probably fortunate that courts oflast resort are inclined to allow extensions ofthe law to develop at the intermediateappellate court level before these “supreme”courts foreclose more exploration bypronouncing the law and thus precludingfurther inquiry about what the law should be.

C. PRINCIPLES OF INDUCTIVE LO-GIC. Since Inductive Logic starts withPremises and ends with a Conclusion,inductive arguments have features that existfor Deductive Logic, except for the certaintyin outcome. Looked at syllogistically,Inductive Logic involves inferring the truth ofthe Major Premise of a Syllogism of whichthe Minor Premise is assumed to be true andthe Conclusion is proved to be true.167

1. Generalization. A key aspect ofInductive Logic is generalization. There aretwo types of generalization: AnecdotalGeneralization and Statistical Generalization.Anecdotal Generalization proceeds fromanecdotes, which are informal accounts ofevents that cannot be investigated using thescientific method. Anecdotal evidence is notnecessarily typical, so the risk is great thatsomeone will make an unwarrantedassumption that the anecdote is representativeof the general case. This is called the Fallacyof Hasty Generalization (see SectionVIII.F.1). A Statistical Generalization is ageneralization that attributes to a larger groupa property that exists in a representativesample of the target population, typicallyexpressed as a percentage.168

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2. Simple Induction. Simple inductioninvolves inferring generalized knowledgefrom example observations. Stated differently,induction is deriving a general rule frombackground knowledge and observations.Example:

Socrates is a man.Socrates is mortal.Therefore, I hypothesize that all men aremortal.

If induction is used to generate a hypothesis,and that hypothesis is confirmed as true, it canbecome a Premise to use in Deductive Logic(like “all men are mortal”).

3. Correlation and Causation. Animportant part of Inductive Logic is toidentify causes, whether of events, orconditions, or diseases, or anything else. Amajor problem in Inductive Logic is thinkingthat things that correlate have a causalrelationship. Consequently, a dictum hasdeveloped that “correlation does not implycausation,” meaning that correlation maysuggest a causal relationship but it does notprove it. Two things may correlate becausethey are both responding to a third cause.

4. Statistical Syllogism. A statisticalSyllogism is a Syllogism that does not assertthe Conclusion with certainty. A statisticalSyllogism reasons from a generalization thatis for the most part true in a particular case.This contrasts with Induction, which reasonsfrom particular cases to generalizations.Statistical Syllogisms may use qualifyingwords like "most", "frequently", "almostnever", "rarely", etc., or may have a statisticalgeneralization as one or both of theirpremises. A statistical syllogism has the form:“This is an A and the probability of an Abeing a B is high, so this is probably also aB.” 169

5. Statistical Prediction. Statisticalprediction is predicting outcomes based onbroad statistics and not on individualassessment of a specific situation. Americanpsychologist Paul Meel long championed theidea that the course of mental illness could bebetter predicted using general statistics thanclinical evaluation of the individual patient.

D. COGNITIVE STUDIES OFINDUCTIVE REASONING. Psychologistshave been studying the way people engage ininductive reasoning. Interesting conclusionsare developing from these studies. In oneexperiment, examiners were asked to rate anargument that a drug was safe, based onclinical trials that showed no negative side-effects. The examinees rated the conclusionbased on one drug study to be weaker than thesame conclusion based on 50 clinical trials.170

Neuro-scientists have begin to study thephysical manifestations of different types oflogical thinking using brain imaging tools likethe functional MRI. The process is called“neuro-imaging.”171 Studies are showing thatperforming different types of tasks usinginductive logic involves different parts of thebrain. It is possible that eventually sciencewill help rhetoricians to refine their theoriesor develop new ones based on a more accurateunderstanding of the way the brain works.

E. GENERATING RULES TO RE-SOLVE LEGAL CASES. In many legaldisputes, the law to be applied is notcontested. The only issue is how the legal ruleapplies to the facts of the case. However, insome instances there is a dispute as to whichrule of law applies to a case. This occurs whenthe facts make a case uniquely different fromearlier cases or when, in a developing area ofthe law, the controlling legal principles havenot yet been firmly established. In thatsituation, it is necessary for a judge or lawyerto use legal reasoning to determine the rule oflaw to be applied. The first and most frequent

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approach is to look at prior cases involvingsimilar issues and argue for or againstapplying the rule of law of an earlier case tothe current case, based on similarities anddistinctions between the two cases. If there areno prior cases that are sufficiently similar tocopy, then the second approach is to look atprior cases in other areas of the law, to see ifan underlying rule of law can be discernedthat could be used to resolve the case at hand.If the comparison is to be made to rules of lawin other areas (rather than specific cases), thenthe goal is to see if these different rules can beunified as expressions of a more fundamentalunderlying principle of law that can beapplied to the current case. If this is notpossible, then as a third alternative thelawyers and judges must fall back on generalprinciples of law, to fashion from them aparticular application that can be applied tothe case at hand.

The first method mentioned above has beenidentified as “reasoning by analogy.” Millconsidered reasoning by analogy to be a formof inductive reasoning. Others have arguedthat reasoning by analogy goes from thespecific to the specific, rather than from thespecific to the general, and thus is not reallyinductive. In this Article, Reasoning byAnalogy is discussed separately, in SectionXI.

The second approach described above is aform of Inductive Logic epitomized by theAmerican Law Institute’s process ofdeveloping its Restatements of the Law,which gathered and organized court decisionsfrom many jurisdictions, and synthesizedthem into general rules of law. Where thesynthesis is among existing rules of law, onesuch inductive effort was aptly described inthe British case of Heaven v. Pender, (1883)11 Q.B.D. 503 (1883): “The logic of inductivereasoning requires that where two majorpropositions lead to exactly similar minorpremises there must be a more remote and

larger premise which embraces both of themajor propositions.”

The third approach is a blend of inductive anddeductive reasoning, in that inductivereasoning is needed to canvass generalprinciples to find likely candidates for the ruleto be applied in the case, but the decision ofwhich principles, or combination of generalprinciples, to apply may be based on familiardeductive techniques like Modus Ponens,Modus Tollens, Reductio ad Absurdum, andthe like.

F. FALLACIES OF INDUCTIVEREASONING. There are recurrent dangers ininductive reasoning that have been identifiedas fallacies.

1. Hasty Generalization. HastyGeneralization is inferring a conclusion aboutan entire class of things based on knowledgeof an inadequate number of class members.Stated differently, a hasty generalization is anunwarranted conclusion that a sample of apopulation is representative of the entirepopulation, so that qualities of the samplesuggest identical qualities of the generalpopulation. This fallacy is also called the“Law of Small Numbers.”

2. Fallacies of Distribution. The Fallacy ofDistribution is a logical fallacy that resultsfrom ignoring the difference between thedistributive sense of a term (referring to eachmember of a class) and the collective sense ofthat term (referring to the class as a whole).This can be either the Fallacy of Compositionof the Fallacy of Division. Some writersassociate this fallacy with what is called the“Representativeness Hueristic,” which refersto the common inclination to assess theprobability of something unfamiliar bycomparing it to the probability of a familiarbut different proposition.

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3. Fallacy of Composition. The Fallacy ofComposition occurs when you infer thatsomething that is true of a part is also true ofthe whole. The Fallacy of Composition issimilar to Hasty Generalization, in that hastygeneralization is the error of attributing thequalities of a small portion of a group to theentire group. Another Fallacy of Compositionis the Fallacy of Anecdotal Evidence, whichuses a few examples to counter a claim basedon solid evidence.

4. Fallacy of Division. The Fallacy ofDivision occurs when you assume that what istrue of the whole is also true of a part of thewhole.

5. Dicto Simpliciter. The Fallacy of DictoSimpliciter occurs when an acceptableexception is ignored or eliminated. There aretwo forms: Accident (ignoring an acceptableexception) and Converse Accident(eliminating or simplifying an acceptableexception).

6. Faulty Analogy. The Fallacy of FaultyAnalogy occurs when one assumes thatbecause two things being compared aresimilar in some known respects, that they aretherefore similar in other unknown respects.Faulty analogy is analogical reasoning whoseinductive probability is low because thesimilarities relied upon to draw the connectionbetween the Source and Target are tenuous ornot relevant to the comparison. FaultyAnalogy can be the basis for humorous quips.“Ancient Rome declined because it had aSenate; now what's going to happen to us withboth a Senate and a House?” --Will Rogers.

7. False Cause. The False Cause Fallacyoccurs when an argument attributes a causallinkage between events or conditions whenthe link has not been proved.

The Fallacy of False Cause involves theerroneous attribution of a causal relationship.

The Fallacy can take several forms. It canoccur when a cause is confused with an effect(Non Causa Pro Causa).

Another example is the Fallacy of Ignoring aCommon Cause. The fallacy occurs when it iswrongly believed that A causes B or B causesA, when in reality both A and B are caused byan independent cause, which is C.172

Another example is the Post Hoc Ergo PropterHoc Fallacy. The “Post Hoc” Fallacy isinferring that, because A precedes B, A mustcause B.

The Post Hoc Fallacy was addressed inGuevara v. Ferrer, 247 S.W.3d 662, 667-68(Tex. 2007), where the issue was whether theplaintiff had established, in the absence ofexpert testimony, that medical expenses ofover $1 million were caused by an automobileaccident. The Court said:

Daubert and Robinson require trialjudges to scrutinize evidence forreliability. Robinson, 923 S.W.2d at 554.Most federal courts that have consideredthe issue after Daubert have concludedthat temporal proximity alone does notmeet standards of scientific reliability anddoes not, by itself, support an inferenceof medical causation. See, e.g., McClainv. Metabolife Int'l, Inc., 401 F.3d 1233,1243 (11th Cir.2005) (concluding that atemporal relationship does not, by itself,establish causation, and rejecting “thefalse inference that a temporalre la t ionship proves a causalrelationship”); Rolen v. Hansen BeverageCo., 193 Fed. Appx. 468, 473 (6th Cir.2006); . . . ; see also Roche v. LincolnProp. Co., 278 F.Supp.2d 744, 764 (E.D.Va. 2003) (“An opinion based primarily,if not solely, on temporal proximity doesnot meet Daubert standards.”); In reBreast Implant Litig., 11 F.Supp.2d 1217,1238-39 (D. Colo. 1998) (“[A] temporal

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relationship by itself, provides noevidence of causation.... The fact of atemporal relationship establishes nothingexcept a relationship in time. Proof of atemporal relationship merely suggests thepossibility of a causal connection anddoes not assist Plaintiffs in provingmedical causation.”); Schmaltz v. Norfolk& W. Ry., 878 F.Supp. 1119, 1122 (D.Ill.1995) (“It is well settled that a causationopinion based solely on a temporalrelationship is not derived from thescientific method and is thereforeinsufficient to satisfy the requirements of[Rule] 702.”). One federal court noted theimportance of focusing on scientificreliability to ensure “that decision makerswill not be misled by the post hoc ergopropter hoc fallacy--the fallacy ofassuming that simply because abiological injury occurred after a spill, itmust have been caused by the spill.”Ohio v. U.S. Dep't of the Interior, 880F.2d 432, 473 (D.C.Cir. 1989). This isnot to say that evidence of temporalproximity, that is, closeness in time,between an event and subsequentlymanifested physical conditions isirrelevant to the causation issue.Evidence of an event followed closely bymanifestation of or treatment forconditions which did not appear beforethe event raises suspicion that the eventat issue caused the conditions. Butsuspicion has not been and is not legallysufficient to support a finding of legalcausation. When evidence is so weak asto do no more than create a surmise orsuspicion of the matter to be proved, theevidence is “no more than a scintilla and,in legal effect, is no evidence.” FordMotor Co. v. Ridgway, 135 S.W.3d 598,601 (Tex.2004). Nevertheless, whencombined with other causation evidence,evidence that conditions exhibitedthemselves or were diagnosed shortlyafter an event may be probative in

determining causation. See, e.g., Westber-ry v. Gislaved Gummi AB, 178 F.3d 257,265 (4th Cir.1999) . . . .

Undoubtedly, the causal connectionbetween some events and conditions of abasic nature (and treatment for suchconditions) are within a layperson'sgeneral experience and common sense.This conclusion accords with humanexperience, our prior cases, and the lawin other states where courts have heldthat causation as to certain types of pain,bone fractures, and similar basicconditions following an automobilecollision can be within the commonexperience of lay jurors. . . . thus,non-expert evidence alone is sufficient tosupport a finding of causation in limitedcircumstances where both the occurrenceand conditions complained of are suchthat the general experience and commonsense of lay persons are sufficient toevaluate the conditions and whether theywere probably caused by the occurrence.. . . [Footnotes omitted]

8. Suppressed Evidence. The Fallacy ofSuppressed Evidence occurs when a personomits relevant data. The Fallacy is hard todetect since it is difficult to detect omitteddata.

9. Common Statistical Fallacies. There area number of misconceptions that can ariseabout statistical evidence. Some relate toflaws in the selection of the statistical sample,or the failure to screen out extraneous factorsthat might influence results. Others relate tothe drawing of Invalid or Unsoundconclusions from the statistical data.

a. Errors in Generating Statistics.

(1) Sampling Bias. Sampling Bias occurswhen the person who is selecting examples toanalyze unknowingly assembles a group of

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examples that is not representative of theentire group of cases. Sampling Bias canintroduce unrecognized factors in the studythat invalidate the conclusions derived fromthe results of the study. In Inductive Logic,Sampling Bias is a form of Fallacy ofComposition, or assuming that a part isrepresentative of the whole. This is also calledthe Fallacy of Biased Sample. Drawingsamples at random is a way to avoid thisFallacy.

b. Errors in Interpreting Statistics.

(1) Fallacy of Small Sample. The Fallacy ofthe Small Sample occurs when the sample sizeis too small to justify the conclusion drawn.This is a form of the inductive Fallacy ofHasty Generalization.

(2) Base Rate Fallacy. The Base Rate is theprior probability of an event or condition,determined before new information isacquired. The Base Rate Fallacy (Ignoring theBase Rate) occurs when the ConditionalProbability of a hypothesis (H) given someevidence (E) is assessed without taking intoaccount the "base rate" or "prior probability"of H and the total probability of evidence E.The Fallacy is also expressed as the erroneousassumption that “p(x*y) = p(y*x).173

(3) Ignoring Regression to the Mean.“Regression to the mean” is the tendency ofan event that is extreme to be followed by anevent much closer to the mean.

(4) Conjunction Fallacy. The ConjunctionFallacy is a belief that the likelihood of twoevents occurring together is greater than thelikelihood of either event occurring alone. Inactuality, the probability of two eventsoccurring together can never exceed theprobability of the least likely event occurringalone. In a famous psychological studypublished in 1983, participants were toldabout a woman named Linda. “As a student,

she was deeply concerned with issues ofdiscrimination and social justice, andparticipated in anti-nuclear demonstrations.”Participants were then asked to rank eightstatements (e.g., “Linda is active in thefeminist movement,” “Linda is a bank teller,”“Linda is a bank teller and is active in thefeminist movement”), based on probability. Ifreasoning correctly, the participant wouldknow that the probability of a conjunction oftwo outcomes cannot exceed the probabilityof each outcome standing alone. Eightypercent of the participants found it more likelythat Linda was both a feminist and a bankteller than that she was a feminist alone or abank teller alone.174 The psychologists gavethe test to Stanford undergraduates, graduatestudents in psychology, and doctoralcandidates in the decision science program,and found that 85-89% of the participantscommitted the Conjunction Fallacy.175 Effortsto improve scores with additional explanationdid not greatly improve scores.176

(5) Gambler’s Fallacy. Given a series ofidentical events (a “streak”) and the necessityto make a choice as to the next outcome,people must make one of three possibleinductions: (1) that the streak is irrelevant, (2)that the streak will continue, or (3) that thestreak will stop.”177 Those who opt for option(1), expect the next outcome to be unaffectedby the past outcomes. For them, theprobability of the next outcome is the baserate probability calculated before the firstoutcome. Option (2) is sometimes called the“Hot Hand” phenomenon, based on apsychological study of persons watchingbasketball. Psychologists noted that basketballfans believe it more likely that a streak of abaskets will contine while a streak of misseswill come to an end.178 Option (3) is called theGambler’s Fallacy, based on the notedproclivity of gamblers to keep on betting evenwhen they have been losing. While the odds atthe outset of ten losing hands in a row is low,after the ninth hand the odds of a losing hand

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are the same as after the eighth hand or beforethe first hand. It has been suggested that theGambler’s Fallacy arises from therepresentativeness heuristic leading people tobelieve in a “law of small numbers.” Peopleexpect a sequence of events to berepresentative of overall probability, and thatan unlikely streak of one type of outcomesmust quickly end and be evened out by otherevents. That principle, however, would notreadily explain the Hot Hand phenomenon.Another explanation would be that peoplewho opt for (2) or (3) do not believe that theoutcomes are random. When events are not infact random, then following streaks may yieldbetter outcomes than disregarding streaks.179

This points up the fact that the Fallacy is onlyfallacious when applied to random events.

(6) Texas Sharpshooter Fallacy. The TexasSharpshooter Fallacy describes a shooter whoshoots the side of a barn and then draws thetarget around the place where the bullets hit.The Fallacy is an effect of the “clusteringillusion,” or the belief that random events thatoccur in clusters are not really random.

c. Statistics in the Law. The role ofstatistics in the legal process is not well-understood by judges, lawyers, witnesses, andjurors. In 2007, Jonathan Koehler, a professorat the University of Texas School of Business,published on the internet a preliminary draftof an article discussing nine statisticalfallacies.180

(1) Misconception #1: The Importance ofStatistics in Litigation. The firstmisconception addressed by ProfessorKoehler is the view that jurors overweightstatistical evidence, a view espoused byHarvard Law Professor Lawrence Tribe in his1971 law review article, L. Tribe, Trial byMathematics: Precision and Ritual in theLegal Process, 84 HAR. L. REV. 1329 (1971).Psychological studies show just theopposite.181

2. Misconception #2: Small Samples AreNot Informative. People wonder how asurvey of 1,000 people can accuratelyrepresent millions of Americans. Thereliability of a survey (called “the margin oferror”) is unrelated to the size of thepopulation that the survey seeks to describe.The more important consideration is theextent to which members of the sample wereselected at random from the population ofinterest.182

3. Misconception #3: The Significance of“Statistically Significant.” Sample size playsa central role in determining whether adifference is statistically significant. Largesample sizes are more likely to yieldstatistically significant differences. Butsample size plays no role at all in determiningwhether a difference is practically significant.Statistical significance is reflected as a “p-value.” The p-value identifies the probabilitythat a disparity as large (or larger) than thatobserved in the study would occur withrandom chance. Professor Koehler wrote:

Statistical novices also mistakenlyassume that statistically significantdifferences are practically important andthat statistically insignificant differencesare practically unimportant. However, itis important to distinguish between thesetwo types of significance. Sample sizeplays a central role in determining whe-ther a difference is statisticallysignificant. Large sample sizes are morelikely to yield statistically significantdifferences. But sample size plays no roleat all in determining whether a differenceis practically significant.183

(4) Misconception #4: Correlation ImpliesCausation. In truth, correlation does notimply causation. Just because two variablesare correlated or associated with one another,does not mean that one of the variables causedthe other. The correlation could result from an

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unrecognized third variable. Nonetheless,people rely on correlation as a primaryindicator of causality, and people sometimesequate degree of correlation with degree ofcausal strength. One way to combat thismisconception is to identify the third variable,and push it aggressively as a possible cause.184

(5) Misconception #5: Base Rates Don’tMatter. One of the most prevalentmisconceptions is that backgroundprobabilities (called “base rates”) areirrelevant for specific judgments. ProfessorKoehler wrote

Though base rate evidence sometimes“feels” different from other types ofevidence, it is no more or less inherentlyprobative than individuating or directevidence. An 80 percent probability ofguilt based entirely on a base rate carrieswith it the same 20 percent chance of afalse conviction as an 80 percentprobability of guilt based on, say, thesomewhat unreliable testimony of aneyewitness.

Appellate courts have, on occasion, rejectedbase rate statistics as not being sufficientlytied to the specific case to be helpful to thefact finder.185

(6) Misconception #6: A Small MatchProbability Implies Source Identification.Forensic evidence does not match one thing toanother with certainty; it is probabilisticevidence, comparing the probability that thematch would occur at random given theunderlying population. Professor Koehlernotes:

[I]f the match is rarer than the number ofpeople on earth (e.g., 1 in 10 billion),there couldn’t be a second person whomatches as well, right? Wrong. Theprobability that at least one other personin a population of 6.5 billion will match

a set of genetic markers that occurs justone time in 10 billion is about 48%.186

(7) Misconception #7: The MatchProbability Identifies the Chance ofInnocence. Forensic experts will presentevidence that requires statistical analysisbefore the significance of the evidence can beunderstood. Taking for example evidence of aDNA match with blood at a crime scene,testimony will be introduced regarding thefrequency in which the genetic profile occursin the population, which is the probability offinding a match with a person who is not thesource of the evidence. Professor Koehlerpoints out that jurors are more interested inknowing how likely it is that the accused isthe person who left the blood stains.187

(8) Misconception #8: Error Rates: Nice toHave But Not Essential. In some instancesthe statistical evidence (particularly DNAmatches) has a very small match probabilitywhile the chance of a mismatch (i.e., the errorrate) is much larger. When this happens, thenthe importance of the statistical evidence iscontrolled by the chance of an error.Nonetheless, appellate courts have beenunwilling to overturn convictions for failure toadmit error rates.188

(9) Misconception #9: Non-Unique Match-es Are Worthless. Non-unique matchevidence is statistical evidence that is able toreduce the group of potential individuals to asmall group but not an individual. This leadsto an argument, termed “the Defense AttorneyFallacy,” that twenty males (or whatever thecount may be) might be the perpitrator. Thisargument fails to distinguish betweenprobative evidence and conclusive evidence.Non-unique evidence is very probative if theinclusion group is small compared to theexclusion group, and the addition of thestatistical evidence to other evidence of guiltcan substantially increase the likelihood ofguilt.189

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10. Confusing Unexplained withUnexplainable. The Fallacy of Confusing theUnexplained with the Unexplainable occurswhen there is no apparent explanation ofsomething using known principles, and it istherefore concluded that the explanation isunknowable.

11. False Continuum. The Fallacy of FalseContinuum is the idea that, because there is noclear demarcation between two things, thatthose things therefore cannot be distinguished.

IX. ABDUCTIVE REASONING. Abduc-tive Reasoning was suggested by Americanphilosopher, logician, mathematician,psychologist, scientist and thinker190 CharlesSanders Peirce in 1883 to describe the waypeople generate hypotheses explainingapparent correlations between certain eventsor conditions. Peirce was not convinced thatdeductive and inductive logic togethercaptured the essence of man's apprehendingthe world. Peirce believed the human mind,being a product of the world, "naturally thinkssomewhat after nature's pattern," and thatpeople "often derive from observation strongintimations of truth, without being able tospecify what were the circumstances we hadobserved which conveyed thoseintimations.”191 Based on psychologicalstudies of human perception, Peirce believedthat perceiving the world gave rise toperceptual judgments that brought with themuniversal propositions, in a manner that was"not controllable and therefore not fullyconscious."192 Peirce viewed thosepropositions as hypotheses, coming to lifethrough "an act of insight" that arose "like aflash."193 Peirce named this process"hypothesis inference" (or "abductiveinference").

In some of his writings, Peirce divided non-deductive reasoning into three types:

Let us now consider non-necessaryreasoning. This divides itself, accordingto the different ways in which it may bevalid, into three classes: probablededuction; experimental reasoning, whichI now call Induction; and processes ofthought capable of producing noconclusion more definite than aconjecture, which I now callAbduction.194

Peirce described Abductive Reasoning as aprocess of “examining a mass of facts and inallowing these facts to suggest a theory. Inthis way we gain new ideas; but there is noforce in the reasoning.”195 AbductiveReasoning works the opposite direction fromdeduction: with deduction, the Antecedent isused to get to the Consequent. Looked atsyllogistically, Abduction takes a knownConclusion and an known Major Premise andintuits the Minor Premise. Looked at from thestandpoint of Conditionals, in AbductiveReasoning the Consequent is used to get to theAntecedent.196

The abductive process may originate withintuition, but through a process of verificationcertain hypotheses may be eliminated becausethey do not square with the facts. Ahypothesis is “valid” if it is the bestexplanation of the correlations underconsideration. Abduction has been describedas a process where a theory and some data arecombined to derive a premise. Examples:

All humans are mortal.Socrates is mortal.Therefore, Socrates must be human.

To use an example suggested by Peirce:

The surprising fact, C, is observed;But if A were true, C would be a matter ofcourse,Hence, there is reason to suspect that A istrue.197

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The foregoing Syllogism exhibits the Fallacyof the Undistributed Middle, and is not Valid.It does, however, suggest an hypothesis thatcould be true, and can be subjected toverification.

If you have the flu, you have a mild fever.You have a mild fever.Therefore, you may have the flu.

The foregoing Conditional Syllogism exhibitsthe Fallacy of Affirming the Consequent, andis not logically Valid. It does, however,suggest an hypothesis that can be confirmedor rejected by testing.

The purely-logical interpretation of Peirce’sconcept leaves out an important component ofPierce’s beliefs. Peirce did not considerperceptual judgment to be discrete fromhypothetical inference; he viewed perceptualjudgments as extreme cases of hypotheticalinference. In science, the hypothesis, arisingfrom perception becomes an ongoing tool formaking observations and applying themethods of deductive and inductive logic toarrive at objectively verified conclusions.198

Peirce went beyond the conceptual frameworkjust outlined, however, because he associatedhypothetical inference with a feeling of greatintensity, which he identified as emotion.

Peirce identified two types of logic: logicautens and logica docens. Logica utens is arudimentary sense of logic-in-use, whichproduces insight through a process not visibleto the conscious mind and not susceptible toexplanation. Logica docens is a con-sciously-developed skill set that we aretaught, or that we develop, to us in ananalytical fashion in our daily lives andwork.199

Peirce believed that if two or more hypothesesare consistent with the data, there is a long-standing preference for the simpler of the two.See Occam’s Razor and the Rule of

Parsimony. In Peirce’s words, Pearcesuggested that the least extraordinaryhypothesis is preferred.

X. REASONING IN UNCERTAINTY.Some theorists have suggested that ordinaryreasoning is not based on valid deductivemethods because deductive reasoning dealswith absolutes while everyday reasoning isuncertain. While it is true that reasoning isuncertain when people are called upon tomake choices that can affect outcomes, thelogic structure of Modus Ponens (especiallywhen expressed in the cause-and-effectrelationship) nevertheless underlies mostpeople’s assessments of the way the presentrelates to the future. Apart from that,Deductive Logic’s approach of constructingand attacking arguments by identifyingPremises and Conclusions, and seeing howthey relate, is the way most legal argumentsare approached.

Deductive Logic assumes that therelationships it asserts between Terms orbetween Propositions are absolute, guaranteedrelationships that are either true or false.Inductive Logic assumes that absolutecertainty is unattainable, and that the supportfor Conclusions comes in degrees of strength,most often characterized as probabilities.200

Thus, Inductive Logic involves the degree ofevidentiary support for contingent claims.201

Probability is a world unto itself. Themathematical study of probabilities startedwith Balise Pascal and Pierre de Fermat in the1600s, was expanded by Pierre De Laplace inthe 1800s, was introduced into formal logic byGeorge Boole in 1854, and was furtheradvanced by John Venn in 1876. The actualcalculation of probabilities is outside therealm of normal decision-making. However,understanding the essential aspects ofprobability theory can be useful in evaluatingarguments, even in normal speech.

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There are many situations where it is notpossible to assign probabilities to conclusions.People still apply reasoning to those kinds ofissues. Some theorists apply belief-basedapproaches to conditionals.

A. T H E B A S I C R U L E S O FPROBABILITY. In probability theory, theprobability of an outcome or that a conditionexists ranges from zero to one, and is stated asa percentage. Something that will not happenhas a probability of 0%, and something that iscertain to happen has a probability of 100%.Something that is as likely to happen as nothappen has a probability of 50%. Todetermine the probability of any one or moreof a series of events will occur, you add theprobabilities of each event happening. Todetermine the probability that each and everyone of a series of events will occur, youmultiply the probabilities of each event.

B. CONDITIONAL PROBABILITY.“Conditional Probability” is in one sense theprobability that event “q” will occur giventhat event “p” has occurred. The conditionalprobability of “q”, given “p”, is indicated bythe symbol “P(q|p)”. Conditional Probabilitycan also involve our level of confidence thata condition or circumstance exists, based onthe information we know. In such an instance,“P(q|p)” describes not probability of outcomesof a series of future events, but instead theprobability that a particular condition “q”exists given that condition “p” has beenproven to exist. Conditional Probability canalso be used as a way to quantify InductiveLogic, when you assess the probability that ahypothesis is true given new evidence. Thisformulation would be “P(h|e)” , or theprobability of hypothesis “h” given evidence“e”.

1. Where Probabilities Can BeDetermined With Certainty. In someinstances, all possible outcomes and theprobability of each are known in advance. An

example is the probabilities of “heads” or“tails” in a series of coin tosses.

a. Prior Probability. In a particularsituation, it may be possible to determine theprobabilities of different outcomes in advance.This would be an instance of “PriorProbability.” The Prior Probability of theoutcomes from tossing two coins can be easilydetermined: Example:

You are going to toss a nickel and then toss adime, and determine the likelihood of havingtwo “tails.” There are four possible outcomes,reflected in the following table (where “H”means “heads” and “T” means “tails”:

Nickel Dime H H H T T H T T

The table is similar to a Truth Table becauseboth analyses are bivalent (True-False andHeads-Tails). It can be seen that, before anycoin tossing is done, the probability of two“heads” is 1 out of four 4 (1/4), the probabilityof one “head” and one “tail” is two out of four(½), and the probability of two “tails” is oneout of four (1/4), for a total of 1. By the way,it doesn’t matter if the coins are flipped insequence or simultaneously, the probabilitiesof outcome are the same.

b. The Monty Hall Dilemma. The MontyHall Dilemma is named after the Monty Hall,the host for the television games show Let'sMake a Deal, which aired from 1963 to 1976.The problem came to the world's attentionthrough two 1990-91 Parade Magazinecolumn of Marilyn Vos Savant, reputedly theworld's smartest person. Craig F. Whitaker, ofColumbia, Maryland, sent the followingquestion:202

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Suppose you're on a game show, andyou're given the choice of three doors.Behind one door is a car, behind theothers, goats. You pick a door, say #1,and the host, who knows what's behindthe doors, opens another door, say #3,which has a goat. He says to you, "Doyou want to pick door #2?" Is it to youradvantage to switch your choice ofdoors?

Vos Savant answered:

Yes; you should switch. The first doorhas a 1/3 chance of winning, but thesecond door has a 2/3 chance. Here's agood way to visualize what happened.Suppose there are a million doors, andyou pick door #1. Then the host, whoknows what's behind the doors and willalways avoid the one with the prize,opens them all except door #777,777.You'd switch to that door pretty fast,wouldn't you?

Vos Savant's answer created a storm ofcontroversy. She received nearly 10,000letters, including letters of protest fromhighly-degreed individuals who disagreedwith her, and were sometimes condescending.An example:

You blew it, and you blew it big! Sinceyou seem to have difficulty grasping thebasic principle at work here, I'll explain.After the host reveals a goat, you nowhave a one-in-two chance of beingcorrect. Whether you change yourselection or not, the odds are the same.There is enough mathematical illiteracyin this country, and we don't need theworld's highest IQ propagating more.Shame!

Scott Smith, Ph. D. University of Florida

Vos Savant answered these complaints asfollows:

Good heavens! With so much learnedopposition, I'll bet this one is going tokeep math classes all over the countrybusy on Monday.

My original answer is correct. Butfirst, let me explain why your answer iswrong. The winning odds of 1/3 on thefirst choice can't go up to 1/2 just becausethe host opens a losing door. To illustratethis, let's say we play a shell game. Youlook away, and I put a pea under one ofthree shells. Then I ask you to put yourfinger on a shell. The odds that yourchoice contains a pea are 1/3, agreed?Then I simply lift up an empty shell fromthe remaining other two. As I can (andwill) do this regardless of what you'vechosen, we've learned nothing to allow usto revise the odds on the shell under yourfinger.

The benefits of switching are readilyproven by playing through the six gamesthat exhaust all the possibilities. For thefirst three games, you choose #1 and"switch" each time, for the second threegames, you choose #1 and "stay" eachtime, and the host always opens a loser.Here are the results.

Game Door 1 Door 2 Door 3 Result

#1 Auto Goat Goat Switch/Lose#2 Goat Auto Goat Switch/Win#3 Goat Goat Auto Switch/Win#4 Auto Goat Goat Stay/Win#5 Goat Auto Goat Stay/Lose#6 Goat Goat Auto Stay/Lose

When you switch, you win 2/3 of the timeand lose 1/3, but when you don't switch, youonly win 1/3 of the time and lose 2/3. Youcan try it yourself and see. Alternatively,you can actually play the game with another

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person acting as the host with three playingcards—two jokers for the goat and an acefor the prize. However, doing this a fewhundred times to get statistically validresults can get a little tedious, so perhapsyou can assign it as extra credit—or forpunishment! (That'll get their goats!)

The foregoing is an example of ConditionalProbability, and the fact that in certainsituations one event can affect the probabilityof the next event. Recalculating odds based onnew information is determining posteriorprobability, discussed in the next section.

c. Posterior Probability. If the probabilityof a sequence of events is considered, theprobability of the ultimate outcome canchange from its Prior Probability as eachevent occur. In the example of two coinsflipped in succession, consider theprobabilities calculated after the first coin istossed. If the first coin came up “heads,” theprobability of having two “heads” after thenext coin toss is ½, the probability of havingone “head” and one “tail” is 1/2, and theprobability of having two “tails” is zero. Theprobability after the first coin toss is called“Posterior Probability.” In a multi-eventseries, the Posterior Probability can berecalculated after each event.

The Posterior Probability, or “what is theprobability of q given p?”, can vary from zero(when p 6 ¬q) to one (when p 6 q), oranywhere in between, when the implicationrelationship is not absolute. Symbolically, theprobability of “q” given “p” is shown as“P(q*p)”.

The accepted way to calculate the ConditionalProbability of an event or condition, based oninformation received after the InitialProbability was calculated, is Bayes’Formula.203 The theorem behind Bayes’Formula is that the probability that event Bwill occur, given that event A has occurred,

depends not only on the relationship betweenB and A but also on the likelihood of Bwithout regard to A, and the likelihood of Awithout regard to B. Stated differently, thereare three parameters involved in Bayes’Theorem: the prior degree of belief in theclaim, how likely the evidence would be if theclaim were true, and how likely the evidencewould be if the claim were false.204

Conditional Probability applies not just tooutcomes of sequential events. It also appliesto recalculating the probability that a certaincondition exists, based on increasing amountsof information. An example would be: what isthe probability that a female patient has breastcancer, given a mammogram indicating thepresence of cancer? Bayes’s Formula appliedto updating a hypothesis based on newinformation is:

P(H*D) = P(D*H) P(H)P(D)

where, H is the hypothesis, D is the data, P(H)is the prior probability of H (i.e., theprobability that H is correct before seeing thedata D), P(D*H) is the conditional probabilityof seeing the data D given that H is true(called “the likelihood”), P(D) is the marginalprobability of D (i.e, the probability ofwitnessing the data under all possiblehypotheses), and P(H*D) is the posteriorprobability (the probability that H is true,given the prior belief regarding H, and D).205

A Bayes’ Formula Calculator is available on-line.206 Bayes’ Formula can be used for“assessing the likelihood of an event byupdating a prior probability in light of newevidence.”207

2. Where Probabilities Cannot BeDetermined With Certainty. In mostinstances in real life, the probabilities ofdifferent outcomes cannot be determined byprobability theory alone. For example, the

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probability of Barak Obama’s winning theU.S. presidency was generally discountedbefore the Iowa caucuses. With the additionalinformation that Obama won the Iowacaucuses, the probability of his electionincreased. With the additional informationthat Hillary Clinton won the New Hampshireprimary, Obama’s probability of electiondiminished. When Obama won the SouthCarolina primary, his chances of being electedpresident increased again. When Obama wonthe Democratic nomination, his chances ofelection became very high. In each instance,the probability of Obama’s being electedpresident changed as new events cameforward. This is a form of PosteriorProbability, “P(q|p)”, only with multipleevents: “P(q|p1, p2, p3, p4, p5 . . . pn,)”, where“q” is the probability that Obama would beelected president and where “p1" is the firstpiece of information, “p2" is the second pieceof information, and “pn” is the final piece ofinformation.

Expressed in terms of Conditional Probability,Modus Ponens (“p 6 q”) is expressed“P(q*p)”. Expressed in terms of ConditionalProbability, Modus Tollens (“¬p 6 ¬q”) isexpressed “P(¬p*¬q)”.

The late Berkeley Logician Earnest W. Adamssuggested that people normally don’t suggestprobabilistic Conditional Propositions unlessthey think the “subjective probability” of theImplication is high. Subjective Probability inthis sense is: P(b*a) = P(ba) ÷ P(a).

C. BELIEF REVISION. It is sometimesnecessary to apply reasoning to Conditionalsthat do not fit the True-False dichotomy ofbivalent Logic or even differing degrees ofprobability. Some theorists have proposed abelief-based approach for those situations.“Belief revision” refers to the process ofchanging beliefs based on new information. In1929, Frank Ramsey suggested that whenpeople accept a Conditional Proposition “if A

then C” they are “fixing their degree of beliefin C given A.” Ramsey proposed what hasbecome known as The Ramsey Test: to decidewhether to believe a Conditional Propositionin the face of new information, provisionallyor hypothetically add the updated Antecedentto your stock of beliefs, and consider whetherto believe the Consequent.208 The Bayesianapproach to conditional probability relatesprobabilities to subjective degrees of belief.209

But belief revision must still occur even whenprobabilities cannot be determined.

XI. REASONING BY ANALOGY. InLogic, an analogy is an inference that,because two things are similar in somerespects, they are therefore similar in otherrespects. When we reason by analogy, wecompare something new to something familiarand, if the comparison is close enough, wetreat the new like we would the familiar. If thefamiliar is A, and the new is B, the validity ofthe inference that B is like A depends on thedegree of similarity between B and A. If thesimilarities are few, then the inference isweak. If the similarities are not relevant to thematter at hand, then the inference is weak.Analogy operates with points of comparison,where aspects of the familiar, A, are matchedto aspects of the new, B. The forensicmatching of fingerprints using points ofcomparison is a classic example of reasoningby analogy. But the strength of the analogy isnot just quantitative; it is also qualitative. Thequality of the analogy is more compellingwhen the similarities are relevant to the matterunder consideration. Dissimilarities betweenthe two items being compared can degrade theanalogy.

In discussions about reasoning by analogy, thefamiliar item is called the “Source” and thenew item we are comparing is called the“Target.” Because analogy operates from theparticular to the particular, it is oftendifferentiated from deductive reasoning(which moves from the general to the specific)

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and inductive reasoning (which moves fromthe specific to the general). Francis Bacon andJohn Stuart Mill, however, believed thatanalogy is just a special case of inductivereasoning, where the Source has features A,B, and C, while the Target has features A andB, and the conclusion is reached that theTarget likely also has feature C. Stateddifferently, reasoning by analogy is reasoningfrom the existence of some similaritiesbetween two items to the existence of othersimilarities between those items. Anotherdistinction is that analogy is based on oneSource, whereas Inductive Logic is generallybased on a large number of samples, the morethe better. Reasoning based on a number ofcommon features is called “homology.”210

However, reasoning by analogy can beviewed more abstractly, where things that arephysically dissimilar can be viewed asmatching from a conceptual perspective. Thistype of analogy is described: “A is to B” as “Cis to D”. Example: “Hand is to palm as foot isto sole.” The palm of the hand and the sole ofa foot are physically dissimilar, but therelationship between the hand and the palmcan be said to be analogous to the relationshipbetween the foot and the sole. This has beencalled “shared abstraction.”

An analogy is strong or weak baseddepending on the competition between thesimilarities and dissimilarities of the objectsbeing compared and the extent of the“unexplored region of unascertainedproperties.”211 However, there may also be acompetition between competing analogies.212

Where the similarities between the objectsbeing compared are many, and thedissimilarities minor, then argument fromanalogy can approach in strength a validdeduction.213 Where the similarities are weak,or the dissimilarities strong, or the“unexplored region” very great, then theanalogy reduces to a mere guide-post pointingthe direction for more rigorous examination.214

Analogies are a common method ofargumentation, where something unfamiliar toan audience is analogized to somethingfamiliar, or something complex is analogizedto something that is easier to understand.Many trials of complex issues end up beingpresented to juries as a contest between twocompeting simplified analogies.

“False Analogy” or “questionable analogy” isa belief or perception that two different itemsare sufficiently similar that the principles thatapply to one are applicable to the other whenthe similarities are not strong enough tosupport that Conclusion. In common parlancewe say: “That’s comparing apples andoranges.” This flaw is based on the context ofthe analogy, not a flaw in reasoning. A legalargument that a prior case is “distinguishable”is a claim of false analogy. There are nearlyalways differences between the Source andthe Target. The question is whether thesedifferences are material.

In argumentation, analogy sets up theargument that, where two situations aresimilar in some ways, then what holds true forone situation must hold true for the othersituation. In legal disputes, analogy is oftenused to determine which principles of lawshould be applied to resolve the dispute.Professor Edward Levi suggested thatreasoning by analogy in the common lawinvolves three steps: (1) establishing that thecurrent case is similar to an earlier case; (2)determining the rule of law used to resolve theearlier case; (3) applying the same rule of lawto the current case.215

A clear example of reasoning by analogy isthe case of Kyllo v. U.S.,216 where the U.S.Supreme Court had to decide whether thegovernment’s use, at a distance, of a “thermalimaging device” (heat sensor) to detect whe-ther a person was using high intensity lights inhis home that are needed to grow marijuana,constituted a “search” that required probably

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cause and a search warrant under the FourthAmendment. The Supreme Court analogizedthe technique as being similar to the soundwaive interception that was held, in Katz v.United States, to require probable cause and asearch warrant. Thus, because of the similaritybetween the non-physical detection of voicewaves and the non-physical detection of heatwaves, the rule applying to sound waves(Katz) was applied to the case heat waves(Kyllo).

Here is an example of a court rejecting aproposed analogy:

Avenell contends, “Once a landlord conveysthe property to a third-party, he is no longerentitled to collect rent on the property.” Thecases he cites to support this contention,however, are inapposite. First, in Ellison v.Charbonneau, a 1936 case from the FortWorth court of appeals, the court concludedthat when a landlord evicts a tenant, he isnot entitled to the rent due under the lease.See 101 S.W.2d 310, 314-15 (Tex. Civ.App.--Fort Worth 1936, writ dism'd). ButChrisman did not evict Avenell; instead,Avenell defaulted on the lease.217

XII. INFORMAL LOGIC. Informal Logicis the study of argumentation in naturallanguage settings. As Aristotle noticed, themost frequent use of logical principles is indiscussions and arguments. Because thenatural language is easier to understand, manyteachers prefer Informal Logic over FormalLogic as an approach to teachingargumentation in their classes, and muchInformal Logic literature has to do withteaching and learning good and badapproaches to argumentation.

An historical example of what is today calledInformal Logic is the dialogues of Plato. Thereasoning demonstrated in Plato’s dialoguesare dialectical, meaning that truth is pursuedthrough a dialogue of two or more persons,

whose point-counter-point discussion leads toan unmasking of weak arguments and agreater understanding of the point beingdebated. The Socratic Method is a type ofdialectical process, where two individualswith opposing views ask each other questionsand give each other answers in an effort toprove that the argument of the other wrong.The Socratic Method has been loosely adaptedto law school education, where the professorcalls upon a student to explain a court rulingand then defend it against counter-argumentsor reconfigured hypotheticals requiring thatthe legal principle in question be applied toshades of different facts.

Nowadays Informal Logic talks about manyof the same subjects addressed by FormalLogic, but in more conversational terms. Therequirement of Deductive Logic that Premisesbe true is abandoned as not reflecting theissues most people deal with in their dailylives. And the structure attributed toargumentation is not Deductive Logic.

The first International Symposium onInformal Logic occurred in 1978. Early workon argumentation schemes focused onfallacies, as examples of argumentationschemes to avoid. This approach has beencriticized on the ground that it is hard to teachgood argumentation skills by studying thebad. Another criticism is that in manyinstances supposedly-fallacious arguments areappropriate. For example, in legalargumentation it is expected that both sideswill appeal to legal authorities that favor theirpositions. Many times ad Hominem attacksare valid attacks on the credibility of theperson whose statements are being evaluated.And even logical fallacies can lead to validinsights or can be used to generate plausiblehypotheses.218 This suggests that the invalidityof a fallacy is determined not just by thestructure of the fallacy, but also by itscontent.219

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Informal Logic has also developed what itcalls “argumentation schemes,” which aremodels of how arguments are constructed andpresented in everyday discourse, includinglaw and science. They include elements ofLogic but are not controlled by the principlesof Logic. See Section XVII.

An important part of Informal Logic isaccepting uncertainty or even inaccuracyabout one’s propositions. Arguments need notbe 100% right; they may be “defeasible,”meaning subject to invalidation. It is possiblethat a partially-false or even entirely-falsePremise might support the Conclusion of agood defeasible argument. In this light a goodargument is not just one that is Valid andSound. A good argument is also one thatfulfills its purpose even if it is Invalid orUnsound.220

XIII. THE SPECIAL LOGIC OFSTATUTORY INTERPRETATION. Whilemuch of what is written above applies tocourts determining the meaning of statutes,statutory interpretation raises fundamentalissues about how humans interact withlanguage and how meaning is derived from orattributed to words and other symbols.221

Additionally, a set of rules of interpretationhave developed that are designed for thepurpose of interpreting statutes. Statutoryinterpretation problems can arise fromvagueness or ambiguity or amphiboly in thestatutory language, conflicts between statutes,and conflicts with constitutional provisions.Statutory interpretation problems can alsoarise when it is not clear, in a particular case,whether a statute applies, and if so, how itshould be applied to resolve the dispute. Thisapproach to resolving these difficulties isinfluenced by a person’s philosophy oflanguage, political philosophy, and method ofperceiving and reasoning.

A. PHILOSOPHY OF INTERPRETINGSTATUTES. Much has been written about

the philosophy of interpreting statutes, bothby judges and by law professors and evenprofessors in other fields. In all instances thecourts say that they are attempting todetermine legislative intent.222 As JusticeReed pointed out:

The interpretation of the meaning ofstatutes, as applied to justiciablecontroversies, is exclusively a judicialfunction. This duty requires one body ofpublic servants, the judges, to construe themeaning of what another body, thelegislators, has said.223

At the present time there are three mainschools of thought about statutoryinterpretation: textualist; intentionalist; andpurposivist. The differences can be explainedas a debate over what information a courtshould consider in interpreting a statute. ChiefJustice John Marshall once wrote: “Where themind labors to discover the design of thelegislature, it seizes everything from whichaid can be derived.”224 Analysis indicates thatsome judges who have identified themselveswith a particular philosophy of statutoryinterpretation sometimes use that approachand sometimes do not, depending on whetherit adds to or detracts from their position in aparticular case. Additionally, although legalwriters have published many weighty writingsabout different approaches to statutoryinterpretation, it is not at all clear that thejudiciary is influenced by the intellectualdebate.

1. Textualist Approach. The strictstatement of the textualist view was given bythe Texas Supreme Court in 1920:

Courts must take statutes as they find them.More than that, they should be willing totake them as they find them. They shouldsearch out carefully the intendment of astatute, giving full effect to all of its items.

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But they must find its intent in its languageand not elsewhere . . . .225

Textualists no longer subscribe to such a rigidview. Generally, however, the textualistposition says that legislative intent should bederived from the words of the statute. Afterall, it is only the language of the statute thatpassed both houses of the legislature and wassigned by the chief executive. Committeereports, bill analyses and testimony atcommittee hearings were voted on by no one.Proponents of the textualist view argue thatwords have fixed meanings that can beobjectively discerned. In case of vagueness orambiguity, descriptive canons can be used toresolve uncertainties. Textualists do notapprove looking at legislative history, becausecommittee reports and floor debates reflect theviews of only a few legislators, and becausesuch information is not as readily available tothe public as the language of the statute itself,raising an issue as to whether the statute givesfair notice of what is allowed and what isprohibited.226

2. Intentionalist Approach. The intentiona-list approach calls for courts to use allrelevant indicators of legislative intent, notjust the language of the statute. Going beyondthe words of the statute exposes the analysisto the risk that the additional information maynot be representative of all, or even amajority, of legislators. The fact that a witnessmay testify to opinions regarding the statute,or the problem addressed by the statute, in acommittee hearing where some of thecommittee members are absent and others areengaged in conversation, is of limitedusefulness in determining legislative intent.

Psychologists who study decision-makingsuggest that, after a point, adding moreinformation can reduce the quality of thedecision.227

What is legislative intent anyway? Possibleanswers to this question are problematic.Legislation typically has several sponsors,who are not necessarily of one mind regardingintent, and a bill often undergoes changessuggested by non-sponsors as it passesthrough the legislative process.228 The TexasSupreme Court said that “the intent of anindividual legislator, even a statute's principalauthor, is not legislative history controllingthe construction to be given a statute. It is atmost persuasive authority as might be giventhe comments of any learned scholar of thesubject.”229 Professor Levi said “it cannot beforgotten that to speak of legislative intent isto talk of group action, where much of thegroup may be ignorant or misinformed.”230

And true intent of Congress or a statelegislature is a fiction anyway, because manyvotes are along party lines, some bills(especially in the U.S. Congress) are too bigfor any Congressman or Senator to read, andit is self-evident that the Congress and Senate(or upper and lower house in a statelegislature) cannot be said to have a unifiedintent on anything, except for the simplest,most cut-and-tried propositions. JusticeCardozo wrote:

'The fact is,' says Gray in his lectures on the'Nature and Sources of the Law,' 'that thedifficulties of so-called interpretation arisewhen the legislature has had no meaning atall; when the question which is raised on thestatute never occurred to it; when what thejudges have to do is, not to determine whatthe legislature did mean on a point whichwas present to its mind, but to guess what itwould have intended on a point not presentto its mind, if the point had been present.'231

3. Purposivist Approach. The purposivistapproach to statutory interpretation says thatthe meaning of a statute should evaluated inlight of the purpose behind the legislation.U.S. Supreme Court Justice Stephen Breyer isa noted proponent of this view. He has

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explained and justified his position in writingsand speeches over the years. In his 2005 book,ACTIVE LIBERTY: INTERPRETING OUR

DEMOCRATIC CONSTITUTION, Justice Breyerwrote:

At the heart of a purpose-based approachstands the “reasonable member ofCongress”—a legal fiction that applies, forexample, even when Congress did not infact consider a particular problem. Thejudge will ask how this person (real orfictional), aware of the statute’s language,structure, and general objectives (actually orhypothetically), would have wanted a courtto interpret the statute in light of presentcircumstances in the particular case.232

In a 1991 law review article, Judge Breyer(then Chief Judge of the First Circuit Court ofAppeals) articulated five instances wherelegislative history was important: “(1)avoiding an absurd result; (2) preventing thelaw from turning on a drafting error; (3)understanding the meaning of specializedterms; (4) understanding the “reasonablepurpose” a provision might serve; and (5)choosing among several possible “reasonablepurposes” for language in a politicallycontroversial law.”233 Justice Breyerinterpreted the “intent” of Congress asCongress’s “purpose.” He argued that thepurpose of a statute could be determinedwithout regard to the private motive of eachlegislator in voting for or against the statute.234

In Houston Bank & Trust Co. v. Lee, 345S.W.2d 320, 322-23 (Tex. Civ. App.--Houston1961, writ dism'd), in arriving at legislativeintent, the court cited and quoted from articlespublished by members of the State Barcommittee that drafted the Texas ProbateCode.

B. CANONS OF STATUTO RYCONSTRUCTION.

1. Code Construction Act. The startingpoint for interpreting a Texas statute is theTexas Code Construction Act, Tex. Gov’tCode ch. 311, which contains a number ofrules that the Legislature has given to courtsto control and standardize the way courtsinterpret Texas statutes. Tex. Gov't Code Ann.§ 311.021 says that, in construing codes, theLegislature intends: that the statute beconstitutional, that the entire statute beeffective, that a just and reasonable result, thatexecution be feasible, and that public interestbe favored over private interest.

The Texas Government Code settles thetextualist-intensionalist-purposivist debate inTexas. Section 311.023 says that, inconstruing a code, whether or not ambiguous,the court may consider: the object sought tobe attained, circumstances under which thestatute was enacted; legislative history;common law and former statutes;consequences of a particular construction;administrative construction of the statute; andtitle, preamble and emergency provision.Section 312.005 says, "[i]n interpreting astatute, a court shall diligently attempt toascertain legislative intent and shall considerat all times the old law, the evil, and theremedy." Section 312.006 says that “[t]heRevised Statutes are the law of this state andshall be liberally construed to achieve theirpurpose and to promote justice.” The pros andcons of each interpretive approach remain asconsiderations that courts should keep in mindin selecting and weighing the extrinsicevidence it will consider on statutory intent.

2. Common Law Canons of Construction.In addition to the Code Construction Act,there are a number of “canons” of statutoryconstruction that have been set out in caselaw. This discussion is a thumbnail sketch, asa full discussion would take an entire article toitself.

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Theorists divide the canons of statutoryconstruction into “descriptive canons” and“normative canons.”235 Descriptive canons aredesigned to aids courts in determining themeaning of the words in the statute.Normative canons, which involve policy-based choices, come into play when thestandard methods of discerning the meaningof the words fails to pinpoint the meaning.

Descriptive canons include:

• Plain/Common Meaning236

• Ejusdem generis237

• Expressio unius est exclusio alterius238

• In pari materia239

• Noscitur a sociis240

• Reddendo singula singulis241 • Generalia specialibus non derogant242

• Construe the statute as a whole243

• Construe the statute to have effect244

• Presume adoption of court interpretations ofidentical prior statutes245

• “And” and “or” are not interchangeable246

Normative canons include:

• Avoid constitutional issues247

• Assume constitutionality248

• Presumption against retroactivity249

• Consider all laws bearing on the samesubject250

• If statutes conflict, find the dominantlegislative intent251

• Harmonize with other relevant statutes252

• Avoid an interpretation that would make aprovision absurd or meaningless253

Some normative canons for federal courtsinclude:

• Avoidance of constitutional issues254

• "Charming Betsy" canon255

• Interpretation in light of fundamentalvalues256

• Rule of lenity257

• Avoidance of abrogation of state sovereign-ty258

• Deference to administrative interpretations259

Problems occur when two or more canonsapply to an issue, and the court mustdetermine which canon receives precedence.It is generally held that normative canons aresubordinate to descriptive canons, and shouldbe used only when descriptive canons fail toresolve the uncertainty.260

XIV. RHETORIC. Ancient Greece wasgoverned by a council of landed aristocrats,who selected certain individuals of the groupto serve as executives. Around 590 B.C., theruling council appointed one of theirmembers, named Solon, to draft politicalreforms to stimulate economic growth andpolitical cohesion. Solon’s reforms allowedmore participation in government processesby a broader range of Greeks. In 508 B.C., theGreeks opened government further bycreating the Assembly, which was a policy-making body made up of all male citizensover the age of twenty. A court system wasestablished, that allowed citizens to seek legalredress but, as there was no class of lawyers,litigants had to plead their own cases to a juryof citizens. The structure of Greekgovernment permitted advantages to thosewho could speak effectively in public insupport of their own goals and interests, andagainst inimical goals and interests. Overtime, the Greeks studied effective persuasivespeaking and developed approaches toteaching the ways to communicate effectively.While philosophers like Plato were interestedin how to effectively communicatephilosophical truths, his student Aristotle wasmore interested in techniques of effectivecommunication independent of the subjectmatter, regardless of whether the occasionwas a funeral oration, a religious speech, alegal proceeding, deciding a politicalquestion, or just having a conversation withfriends.

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Here are some definitions of Rhetoric, overthe ages261:

Plato: Rhetoric is "the art of winning thesoul by discourse."

Cicero: "Rhetoric is one great art comprisedof five lesser arts: inventio, dispositio,elocutio, memoria, and pronunciatio."Rhetoric is "speech designed to persuade."

Quintillian: "Rhetoric is the art of speakingwell."

Francis Bacon: Rhetoric is the applicationof reason to imagination "for the bettermoving of the will."

George Campbell: “[Rhetoric] is that art ortalent by which discourse is adapted to itsend. The four ends of discourse are toenlighten the understanding, please theimagination, move the passion, andinfluence the will.”

A. Richards: “Rhetoric is the study ofmisunderstandings and their remedies.”

Kenneth Burke: "Wherever there ispersuasion, there is rhetoric, and whereverthere is rhetoric, there is meaning."

Aristotle wrote a book about techniques ofpersuasive argumentation, entitled Rhetoric.To quote Aristotle:

Rhetoric may be defined as the faculty ofobserving in any given case the availablemeans of persuasion.

Aristotle distinguished Rhetoric from otherfields of study, like medicine (which dealswith what is healthy and unhealthy), orgeometry (which deal with the properties ofmagnitudes), or arithmetic (which deals withnumbers). Other fields deal with their specialcontent. Rhetoric involves “the power of

observing the means of persuasion on almostany subject presented.”

Aristotle broke Rhetoric down into threeareas:

Of the modes of persuasion furnished bythe spoken word there are three kinds. Thefirst kind depends on the personalcharacter of the speaker; the second onputting the audience into a certain frameof mind; the third on the proof, orapparent proof, provided by the words ofthe speech itself.

Today, Aristotle’s three parts are called Ethos,Pathos, and Logos. “Ethos” (the Greek wordfor “character”) is the perceivedtrustworthiness of the speaker. “Pathos” (theGreek word for “suffering” or “experience”)is an appeal to an audience’s emotions.“Logos” (the Greek word for “word”) is anargument based on reason.262

In the years since Aristotle, much has beenadded to Aristotle’s analysis of Rhetoric. Forexample, Rhetoric has been divided into fiveparts: invention, arrangement, style, memory,and delivery. Aristotle’s concepts sometimesseem quaint, or even strange, but hisperspective has proven durable, and with theelaborations developed in the Middle Ages,plus the recent additions of communicationstheory, psychology, and neuropsychology,have created an important body of knowledgeregarding effective communication.

A. APPEALS TO ETHOS. In traditionalRhetoric theory, Ethos is persuasivenessattributable to the actual or perceivedcharacter of the speaker or writer. Aristotleviewed Ethos as something invented by thespeaker and created during the speech.Aristotle commented: “[There is persuasion]through character whenever the speech isspoken in such a way as to make the speakerworthy of credence . . . . And this should

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result from the speech, not from a previousopinion that the speaker is a certain kind ofperson.”263 Roman Rhetoricians viewed Ethosdifferently, for in Rome a person’s credibilityand the weight of his words were intertwinedwith his family history.264 It is said that Ethosis influenced by the speaker’s attitude towardthe audience. The attitude can vary fromformal to informal, and can vary inside onespeech. Attitude is conveyed to the audiencethrough tone. Tone is the feeling the audienceperceives about the speaker’s attitude. Tone isconveyed through word choice and sentencestructure.

B. APPEALS TO PATHOS. Pathos is theapproach of swaying the audience byemotional appeal, rather than by logicalargument. Such emotions might include love,fear, patriotism, guilt, hate, joy, pity,attraction, etc. Emotional effect is oftenachieved through vivid and concrete language,emotionally-loaded words, honorific andpejorative words, emotional narratives oranecdotes that bring the issue beingconsidered “to life,” metaphors, similes, andsymbols that trigger emotional reactions.Some writers include in Pathos appeals to anaudience’s sympathies, an effort to have theaudience identify with the speaker or writer.Many of the Rhetorical Fallacies are in facttried-and-true effective appeals to Pathos.

While an emotional appeal today is sometimesseen as inferior to intellectual argument,Aristotle did not view it that way. Aristotlesaw humans as having a rational element andan irrational element.265 Since both theintellect and emotions are a part of human-ness, any study of persuasion by necessitymust attend to the way that speakers andwriters can affect emotions.266

An explicit appeal to emotions, by telling theaudience how to feel, is seldom successful.Instead, the speaker or writer must use words

to create or re-create situations in whichemotions naturally arise.

C. APPEALS TO LOGOS. The Greek word“Logos” has a rich background in the historyof ancient philosophy. As used by Aristotle inRhetoric, “Logos” is an argument thatpersuades through reasoning, often sequentialsteps, and often arguing from premises toconclusions. To Aristotle, the typical structurefor arguments that appeal to Logos is theSyllogism and the Enthymeme.

1. Syllogism. A Syllogism is a three-prongeddeductive argument with two overlappingPremises that lead with certainty to aConclusion. If the two Premises are proven,then the Conclusion necessarily follows. SeeSection VII.B.

2. Enthymeme. In the section of this Articlerelating to Deductive Logic, an Enthymemewas described as a truncated Syllogism ortruncated Conditional Proposition in whichpart or all of one or more of the Premises orConclusion is not explicitly stated. It usuallyhas the form of the Conclusion coupled witha reason (typically the Major Premise).267

Unlike pure deductive arguments, Enthyme-mes are not required to lead to the Conclusionwith absolute certainty. In Rhetoric, anEnthymeme has an additional aspect. InRhetoric, an Enthymeme is an argument insyllogistic form that has as its premise a beliefor value that the or writer speaker thinks isshared by the audience.268 These sharedbeliefs or values are sometimes called“Commonplaces.” Aristotle made clear thatrhetorical Enthymemes appeal to the rational,not the emotional, part of the audience. ButEnthymemes substitute a kind of InformalLogic for formal Deductive Logic developedelsewhere by Aristotle.269

(a) Advantages and Disadvantages ofCommonplaces. Using Premises that theaudience will accept without preliminary

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justification avoids the difficulties of provingthat the Premises are true. This allows thespeaker to move directly into the argumentphase in which s/he attempts to persuade theaudience that the Premises of the argumentleads to the Conclusion. Because manyCommonplaces that might be used in anEnthymeme are (i) ill-defined, (ii) true only toa degree or depending on circumstances, (iii)contradict other beliefs or feelings held by theaudience, or (iv) may have different effects ondifferent audiences, the process ofconstructing and winning arguments does nothave the clarity of valid Deductive Logic(where true Premises lead by necessity to acorrect Conclusion), or even valid InductiveLogic (where a sufficient number of well-chosen particulars support a general principleto an acceptable degree of likelihood).270

(b) Selection of Enthymemes. An importantand interesting part of Aristotle’s writing onEnthymemes relates to the “places” (in Greektopoi) where a speaker can go to findCommonplaces to use in an argument. The300-400 enthymatic topics suggested byAristotle in his books TOPICS and RHETORIC

are only partially relevant for the present time,but recent publications have modernizedAristotle’s topics271 and the Internet givestopic-hunters a limitless number ofopportunities to find Commonplaces forEnthymemes. You can search for currentevents, jokes, quotations, proverbs, maxims,272

adages,273 aphorisms, gnomes,274 paroemia,275

sententia,276 quotations from famous persons,and even for lists of enthymatic structures andtopics.277 In legal arguments, theCommonplaces include rules of law, legalmaxims, court decisions that have becomesymbolic (e.g., Miranda, Roe v. Wade, etc.),iconic documents (e.g., the Declaration ofIndependence, the U.S. Constitution, theEmancipation Proclamation, King’s letterfrom Birmingham jail, etc.); the list goes on.

3. Sorites. A Sorites in Rhetoric is aconcatenated Enthymeme, or a chain of claimsreasoned from an original premise to aconclusion. See Section XIV.C.3. A Sorites isneeded when there are many steps betweenthe initial premise and the conclusion. The1961 song popularized by the Kingston Trio,Where Have All the Flowers Gone?, is apoetic example of a Sorites Enthymeme.278

4. Inductive Inference. Inductive Inferenceis deriving a probable conclusion about alarge number of people or things based on asmall number of instances. In modern times,this usually takes the form of test results orsurveys that are subjected to statisticalanalysis to arrive at conclusions.Occasionally, however, when it is necessaryto develop a new rule of law (rare) or a newapplication of existing rules (infrequent), thiscan be done by inductive reasoning fromindividual rulings.

5. Analogy. An analogy is a comparisonbetween two different things used to highlightsome point(s) of similarity. Linguistically, ananalogy sets up a comparison between twoitems, but does not suggest a totalidentification, like a metaphor does.279 From alogical perspective, arguing from analogy isreasoning from parallel cases or parallel factpatterns.280 The greater the similaritiesbetween the items being compared, thestronger the analogy and the conclusions thatcan be drawn from it.

6. Simile. A simile is a figure of speech inwhich two dissimilar things are explicitlycompared, usually in a phrase introduced by“like” or “as.” Example: “Life was like a boxof chocolates; you never know what you’regonna get.” See “Metaphor,” next section.281

7. Metaphor. A metaphor is a figure ofspeech in which an implied comparison ismade between two unlike things that actuallyhave something in common. “The relationship

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between simile and metaphor is close,metaphor often being defined as a condensedsimile, that is, someone who runs likelightning can be called a lightning runner.Sometimes, simile and metaphor blend so wellthat the join is hard to find . . . .”282 From alogical standpoint, metaphors assume theproposition which they are brought to prove.Their use is to make clear and vivid the pointthat is intended by the metaphor.283

8. Aetiologia. “Aetologia” is reasoning thatgives a cause or a reason for a statement orclaim.

9. Anthypophora. “Anthypophora,” or“hypophora,” is a figure of speech in whichthe speaker poses a question, and thenanswers the question in a definitive tone. Itcan be done where the question embodies theopposing argument, which is soundly rejected.An example is Winston Churchill’s speech ofMay 13, 1940, regarding war againstGermany:

You ask, what is our policy? I will say: It isto wage war, by sea, land, and air, with allour might and all the strength that God cangive us; to wage war against a monstroustyranny, never surpassed in the dark,lamentable catalog of human crime. That isour policy. You ask, what is our aim? I cananswer in one word: Victory, victory at allcosts, victory in spite of all terror; victory,however long and hard the road may be; forwithout victory, there is no survival.

“Ratiocinatio” is like anthypophora, exceptthat it is done internally. It is the mentalprocess of reasoning with oneself by askingquestions.

10. Apophasis. “Apophasis” is the process ofrejecting alternatives until only the best one isleft. This is a form of the familiar “process ofelimination.”

11. Contrarium. “Contrarium” is juxtaposingtwo opposing statements in such a way as toprove the one from the other. It is a “figure ofopposition.”

12. Definitions. A definition is a passage thatexplains the meaning of a word or term usingother words that are more familiar. Apersuasive definition is a definition designedto influence the audience’s attitudes orfeelings about the subject. See SectionXXIII.C.12.

13. Epitrope. Epitrope is part of a class ofargumentative concessions. With an Epitropea speaker either pretends to express agreementwith an opponent or encourages an opponentto do something that the speaker actuallyobjects to.

14. Expeditio. “Expiditio” is listing allpossibilities and then excluding all but one.Also called “process of elimination.”284

15. Proecthesis. “Proecthesis”is providing ajustification at the end of an argument.285

16. Prosapodosis. “Prosapodosis” is wherethe statement of a thing is followed by theantithesis of its cause.

17. Paromologia. “Paromologia” is part of anargumentative class of concessions, where adisputant concedes a weaker point in order tostrengthen her/his overall position.

18. Dirimens Copulatio. “Dirimens Copula-tio” is the technique of mentioning opposingconsiderations in order to avoid an argument’sappearing to be one-sided. The techniqueexhibits fairness which increases the speaker’sEthos. It has tactical value, as well. Forexample, in drafting an appellant’s brief, byanticipating your opponent’s arguments, youcan present them in the worst light while youhave the reader’s attention, before the

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appellee has a chance to present his argumentsin the best light.

19. Commoratio. “Commoratio” isemphasizing something by repeating it severaltimes in different words.

20. Hyperbole. “Hyperbole” is a rhetoricaldevice where statements are exaggerated inorder to emphasize or achieve an effect.

21. Rhyming. One would think that rhymingwould have no place in legal arguments.However, Johnny Cochran used rhyming inhis closing argument in the O.J. Simpsonmurder prosecution, speaking of the state’scircumstantial evidence: “If it doesn’t fit, youmust acquit.”286

22. Similiarities/Differences. Comparisonsand contrasts between things are an importantpart of Rhetoric. This can be done in ananalogy, but also can be accomplished byjuxtaposition, parallel construction of the text,etc.

D. THE FIVE CANONS OF RHETORIC.The Five Canons of Rhetoric are invention,arrangement, style, memory, and delivery.

1. Invention. Invention is the process ofdesigning a successful argument. To design anargument, it is important to consider (1) theaudience’s needs, desires, thoughts,prejudices, etc.; (2) available evidence (facts,testimony, statistics, maxims, examples,laws); (3) appeal to the audience (Ethos,Pathos, Logos); (4) topics; and (5) timing andopportunity, coupled with accurate targeting(Kairos).287

2. Arrangement. Arrangement involvesputting the argument into an effective order.Rhetoricians have developed a 5-part structurefor presentations:

(1) Introduction

(2) Statement of Fact(3) Confirmation or Proof(4) Refutation(5) Conclusion.

The introduction not only acquaints theaudience with the issues, but it is where thespeaker must begin to establish good Ethos.The statement of fact lays the foundation forthe argument. It also permits the use of Pathosto build emotional support or generate enmityagainst your opponent. Confirmation/proof isthe presentation of your argument, that buildson the facts to lead to the conclusion oroutcome you desire. Refutation is addressingthe arguments made, or that you expect to bemade, by your opponent. Conclusion is whereyou summarize, and show how the facts andthe argument lead to action or inaction on thepart of the audience.

3. Style. Style is not about what things aresaid; it is about how things are said.288 Stylehas been described as the way to “equip one'sthoughts with verbal expression appropriatefor accomplishing one's intentions.”289 Stylehas been broken down into virtues, levels,qualities, and figures of speech.290 The virtuesof style are Correctness, Clarity, Evidence,Propriety, and Ornateness. The Roman OratorCicero described three levels of style, basedon the purpose of the speech: to move, toplease, and to teach.291 Rhetoricians have alsoidentified qualities of style.292 There is a longlist of figures of speech.293

4. Memory. As a canon of Rhetoric,“memory” describes the ability to deliver aspeech without reading it. In former times,those who could speak extemporaneously did;those who could not, memorized. Withteleprompters, modern American politicianscan feign extemporaneousness or memory.Power Point presentations sometimes serve asthe poor man’s teleprompter.294

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5. Delivery. Delivery involves voice,posture, dress, gestures,295 text, and images.296

E. STRUCTURE. The structure of anargument is an important aspect of making theargument clear and persuasive. If the physicalstructure of the writing reflects the intellectualstructure of the argument, then the twostructures offer each other mutual support.297

1. Appellate Briefs. The arrangement ofappellant’s brief is set out in TRAP 38.1, of apetition in an original proceeding in TRAP52.3, of a petition for review in TRAP 53.2,and of a brief on the merits in the SupremeCourt in TRAP 55.2. This arrangement isdesigned to give the appellate court theinformation it needs in the sequence it needsit. The prescribed arrangement of anappellant’s brief is:

• Identity of the Parties• Table of Contents• Index of Authorities• Statement of the Case• Statement Regarding Oral Argument• Issues Presented• Statement of Facts• Summary of the Argument• Argument• Prayer• Appendix

Many appellate lawyers alter this arrangementwhile still conforming to it. Examples include:setting out the Issues Presented in the Table ofContents; putting a succinct version of thePrayer in the Statement of the Case, or in theSummary of the Argument, or in theArgument; and putting portions of theStatement of Facts or Argument in theAppendix. The arrangement of the parts of thebrief is different from the arrangement of thepresentation, which has to do (on the higherend) with the sequence in which informationand ideas are introduced, and (on the lowerend) with the use of writing techniques such

as lists, section headings and subheadings,cross-references, numbering, and sometimeseven hyperlinks, to control the path that theappellate court takes through the presentation.

2. Appellate Opinions. Appellate opinions(excluding memorandum opinions) generallyfall into three parts: the facts, the law, and theconclusion. Appellate opinions establishpremises, then move through the argument tothe conclusion. Losing arguments should beidentified and refuted or rejected. Where therule to apply is not clear, or the way acontrolling rule should be applied to the caseat hand is uncertain, reasoning by analogy toclearer cases may be useful.

3. The Courtroom. In the trial courtroom,the judge is up high and up front. In Americancourtrooms, everyone looks toward the judge,except for court staff and the witness. Thewitness is close to the judge. The jury issegregated from other participants by beingplaced in a box. The legal actors are separatedfrom the audience by the “bar” or rail. All ofthese placements have practical and symboliceffect. In appellate courts, the bench iselevated, the process is highly structured andcounsel speak only from the podium, notcounsel table.

F. PUNCTUATION. Punctuation has beendescribed as the marks and signs, used inwriting and printing, to separate words intophrases and sentences. This is true, butpunctuation does much more when itseparates words into phrases and sentences.Punctuation shapes the meaning of the phrasesand sentences. Example: The sentence“woman without her man in nothing” can bepunctuated “woman, without her man, isnothing,” or “woman: without her, man isnothing.” The law school story, about the wifewho telegrammed her husband for permissionto buy an extravagantly expensive bracelet,and he telegrammed back “no price too high,”but the telegram company left out the comma

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after “no,” so she bought the bracelet and thehusband later sued Western Union, is a vividbut apparently apocryphal example of how theuse of punctuation can even reversemeaning.298 Professor Lawrence Tribe tells astory about Article I, Section 8, Paragraph 1of the United States Constitution. The clausesays “Congress shall have power to lay andcollect Taxes, Duties, Imposts, and Excises topay the Debts and provide for the commonDefense and general Welfare of the UnitedStates.” Professor Tribe suggests that if thecomma had been a semicolon, it would havegiven Congress “sweeping lawmaking powerto ‘provide for the general welfare,’ which hesays would have been “a source of powervastly broader than even the CommerceClause has ever conferred,” a power thatwould have been “essentially boundless.”Professor Tribe says that the chief draftsmanof the Constitutional Convention’s Committeeof Style, Gouvernor Morris, substituted asemicolon instead of a comma, but thesemicolon was eventually removed.299 Thisstory is confirmed in historical publications,but there remains some controversy overwhether Morris acted surreptitiously.300

In addition to helping to construct meaning,punctuation can also be used to help phrasesand sentences convey emotions effectively.So, while the rules of grammar givepunctuation the power to affect meaning, wemust also remember that punctuation canaffect feelings in a way that goes beyondgrammar. Thus, punctuation is part ofRhetoric.

• Period. A period ends a sentence. It dividesideas into constituent parts. It determineshow long a sentence will be, and thereforehow easy the sentence will be to understand.It gives a speaker the chance to inhale. Itasks the reader to stop and reflect. Thebiggest problem with periods is that they arenot used enough.

• Comma. In grammar, a comma has fouruses: it separates items in a list; it joins twocomplete sentences; it indicates theomission of a word; and it acts as thedelimiter of a clause. When reading outloud, a comma signals a pause. Commasshould be used to avoid amphiboly(ambiguity arising from confusing sentencestructure). A comma can separate thoughtsin instances where a period would impairthe flow of the mind or the voice. Above all,commas should be used to improve clarity.

• Colon. A colon signals an explanation. Itsignals a list. It suggests that supportfollows for what was just stated. Accordingto Strunk and White: “A colon tells thereader that what follows is closely related tothe preceding clauses. The colon has moreeffect than the comma, less power toseparate than the semicolon, and moreformality than the dash.”301

• Semicolon. A semicolon is used to connecttwo sentences that are not joined by aconjunction. It is also used when the secondsentence is connected to the first by aconjunctive adverb, such as “however” or“nevertheless.” A semicolon is also used toseparate parts of a list when a component ofthe list contains a comma. In joining twosentences, a semicolon is a compromisebetween a comma and a period. AbrahamLincoln said: “With educated people, Isuppose, punctuation is a matter of rule;with me it is a matter of feeling. But I mustsay I have a great respect for the semi-colo-n; it's a useful little chap."

• Hyphen. The hyphen is used to break upcompound words that would otherwise behard to understand (one-of-a-kind).Hyphens are used in numbers under ahundred, and when a word is divided at theend of a printed or typed line. Hyphens areused when a “compound modifier” is usedbefore a noun (e.g., computer-basedrecords). Joining two words with a hyphencan be used, like a metaphor, to cause the

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audience to juxtapose different concepts thatare brought together by the hyphen.

• Bullet. A “bullet” is an elevated dot on theleft extreme of a word or phrase, used toindicate membership in a list. Bullets areused when numbering the list is notimportant or would be distracting. Bulletslend emphasis to the individual items in alist more effectively than joining theconcepts in a sentence, separated bycommas or semi-colons.

• Dash. A dash interrupts the grammar of asentence. It can enclose a parentheticalstatement. It can connect two independentclauses. It can connect a phrase to the rest ofthe sentence. A hyphen joins; a dashseparates.302 Strunk and White say: “A dashis a mark of separation stronger than acomma, less formal than a colon, and morerelaxed than parentheses.”303 A dash, like apause, emphasizes what follows.

• Parentheses. Parentheses are used fornumbers in a numbered list, or to segregatean interjected explanatory remark or anaside from the main flow of the sentence inwhich it appears. They can also be used tosignify plurals (e.g., “one or moreperson(s)”). Parentheticals can be usedeffectively for disambiguation. They can beused to establish an equivalency (i.e., adefinition), or to give an example (to-wit:this), or to exclude certain meanings (butnot others). A parenthetical is like a speak-er’s “aside” to the audience.

• Brackets. “Square brackets” (i.e., [ ]) areused to signify the inclusion of material inquoted text by someone other than thequoted person. In this Article, “anglebrackets” (i.e., < >) are used to delimit aURL citation to a World Wide Web page.

• Asterisk. An asterisk is used as a cross-reference mark to indicate furtherexplanation at the bottom of the page. It islike a an unnumbered footnote, but you arelimited to one per page. Asterisks are alsoused like “bullet points” in a list, and asomitted letters in profanity.

• Apostrophe. An apostrophe is used toindicate a contraction or a possessive.Contractions are informal speech, anddetract from the seriousness of the writing.

• Question Marks. A question mark signals aquestion. In a parenthetical, it reflectsuncertainty about a date, name, etc. Inpersuasive speech, it signals a RhetoricalQuestion. See Section XIV.M.

• Slash. A slash mark is a separator (e.g.“and/or”). It sometimes replaces an “and.”

• Indentation. Indentation is commonly usedat the start of a paragraph, and also todifferentiate lists and block quotations fromregular text.

• Quotation Marks. Quotation marks signalthe use of another’s words. They also signala special meaning for a word or phrase.They also can be used to disparage a wordor phrase used by your opponent (called“scare quotes”--example, “his only‘authority’ for this extraordinary assertion isa unpublished opinion”).

• Ellipsis. An ellipsis signals an omissionfrom a quotation. It also invites a reader tostop, and dwell on a thought, before goingforward. It also can represent an interval oftime, setting up a dramatic pause.

• Footnotes. A footnote is a super-scriptedand numbered cross-reference that directsthe reader to the bottom of the page forfurther information. Footnotes can cross-refer to other footnotes more easily than textcan cross-refer to other text. The legalcommunity is divided on the desirability ofusing footnotes in legal writing. Somereaders consider it to be a distraction tohave to look at the bottom of the page to seesupporting authority. Others prefer to readthe main ideas in the text without having toread or skip through citations. Without adoubt, however, footnotes allow the writermore freedom to give explanatory remarksand more extensive references to underlyingauthority.

• Endnotes. Endnotes are footnotes placed atthe end of the document. Readers who find

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footnotes to be a nuisance will find endnotesaggravating. Endnotes are used in thisArticle because the article would beunreadable if citations to sources, withURLs, were in the main text. Endnotes alsowere used instead of footnotes, in thisArticle, to respect the convention thatcontinuing legal education articles are lessformal than footnote-rich law journalarticles, while still providing the utility offootnotes.

G. EMPHASIS. Emphasis, sometimes called“accent,” can be used to give more importanceto some words than others, with the effectsometimes operating at a subconscious level.There are ways to emphasize in writing,304 andways to emphasize verbally. An excessiveamount of emphasis blunts the effect of allemphasis and irritates some readers orlisteners.305 When written emphasis appears ina quotation to avoid ambiguity, it is necessaryto indicated in brackets whether the emphasiswas in the original or was added. Emphasis inverbal speech is an important component ofthe communication. Written emphasis in somesenses is an effort to translate into the writtenword the emphasis so readily accomplished inverbal speech.

Oral

• Loudness–one can emphasize by speakingthe first syllable of the word more loudlythan others. Words or even entire phrasescan be spoken more loudly for emphasis.

• Repetition–repetition can emphasize (e.g.,“this is really, really important”).

• Softness–speaking more softly can be a formof emphasis. If not too frequent or tooprolonged, speaking softly inclines theaudience to listen more attentively to catchthe words.

• Speed–speaking a word or phrase moreslowly than the rest emphasizes.

• Pitch–you can change your pitch(“modulation”) for emphasis, to getattention, to distract.

• Pause–pauses can be used at the start of aspeech, or right before or after an importantpoint,

• Silence–silence preceding or following animportant point can be used for emphasis.

• Movement–moving while speaking, ormoving and then stopping, can be used foremphasis.

• Placement–placement of speakers indifferent locations can signify importance.A lawyer standing behind his/her client inclosing argument is emphasis.

• Inflection–alteration in the pitch or tone ofthe voice.

• Accent–accent, or emphasis, can be used tostress certain words. It is sometimes used ina way that changes the meaning, even thou-gh the words remain the same.

• Mimicry–mimicry is using the voice andtone of another person. This can be funny,but it can be disrespectful and thus damageEthos.

• Cadence–a slight falling in pitch of thevoice in speaking or reading, as at the end ofa declarative sentence.

• Body language–gestures can be used forexpression or for emphasis. Posture, bodytilt, turning the head, turning the body,moving the eyes–all can be used foremphasis.

• Interruptions–interruptions can be used toemphasize, whether they are staged orspontaneous.

Written

• Italics–italics gives light emphasis to words.• Underscore–underscoring is used for

emphasis, probably left over from the daysof typewriters that could not type italics.When used for emphasis, underscoring fallsbetween italics and bold in strength.Underscoring is often used to differentiateparagraph headings (see for example, this

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very paragraph) and, in an appellate brief,underscored paragraph headings can bepresented in the table of contents of anappellate brief to show the reader a lowerlevel of the structure of the presentation.

• Bold–bold gives heavy emphasis to words.Bold can also be used to differentiatedparagraph headings from ordinary text.

• ALL CAPS–All caps, or upper case letters,emphasizes a word or phrase. Words thatare entirely upper case are more difficult toread than normal text. Upper case issometimes considered the written version ofshouting, and thus should be used sparingly.

• Exclamation Point! – An exclamation pointsuggests surprise or shock (and whenspoken–a shout). Excessive use ofexclamation points is considered to beamateurish and tiresome; so are doubled andtripled exclamation points.306

• Color–changing color can be used foremphasis, and is often used that way onWorld Wide Web pages.

• Centering–Centering on a line is animportant way to emphasize a phrase, or anidea. Centering is frequently used inappellate briefs, to signify the sectionheadings for different parts of a brief.

• Repetition--Repetition can be used foremphasis. Repetition can be used for effect.Consider the emphasis imparted byrepetition in the apocryphal statement, “Thethree most important things about real estateare: location; location; location.”307

President John F. Kennedy used repetitionfor effect in his June 26, 1963 speech inBerlin, where he repeated the phrase: “Letthem come to Berlin.”308

• Question--A Rhetorical Question can beused for emphasis. Example: “Can this beright? Does this mean what it says? Who dothey think they are? Are we going to letthem get away with this?”

Choice of Words

• Nouns–Nouns, with their associated verbs,are the building blocks of a sentence. In anappellate brief, the nouns are mostlysupplied by the underlying facts. However,in discussions of hypothetical propositionsand in analogies, the writer is free to usenouns chosen for effect. A careful selectionof new nouns can be an effective persuasivedevice.

• Euphemisms–A euphemism is aninoffensive word or phrase substituted forone considered offensive or hurtful. TheRhetorical term is “paradiastole,” which isthe use of euphemism to soften the impactof a vice or virtue. Euphemisms are oftenused for certain body parts, procreation,excretion, disabilities, death, and othertopics that make people uncomfortable, etc.Example: “health” insurance is reallysickness insurance; “life” insurance is reallydeath insurance. “Meiosis” is an euphemismthat downplays or understates something.

• Litotes--A figure of speech consisting of anunderstatement in which an affirmative isexpressed by negating its opposite.Example: "The grave's a fine and privateplace, But none, I think, do there embrace."Andrew Marvell, To His Coy Mistress.Example: "We made a difference. We madethe city stronger, we made the city freer, andwe left her in good hands. All in all, notbad, not bad at all." Ronald Reagan’sFarewell Address to the Nation, January 11,1989.

• Pronouns–A pronoun takes the place of anoun. There are personal pronouns,309

demonstrative pronouns,310 relativepronouns,311 indefinite pronouns,312

interrogative pronouns,313 possessivepronouns,314 and reflexive pronouns.315

Pronouns are the bane of clear writing.There is often confusion as to what theantecedent referred to by a pronoun maybe.Using nouns in that situation can avoid thisconfusion. Pronouns (along with thepassives “his” and “her”) can confound thewriter who is sensitive to the female

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reaction to the use of the male pronoun toapply to both genders (as in “all men arecreated equal”). Won’t someone invent aneutral gender to rid us of this problem?

• Possessives–A possessive noun or pronounindicates that the following word belongs tothe possessive noun or pronoun. When aninanimate object is given a possessive, it cansuggest personification. There arecomplicated rules for making possessivesout of words ending with different letters. Itis easy to miss the proper form withpossessives, which may cause some readersto think you don’t know grammar, andtherefore are not knowledgeable on the topicyou are espousing.

• Adjectives–An adjective is used to modifya noun or pronoun, giving more informationabout the word that is modified. Adjectivescan be used argumentatively, to enhance ordiminish the nouns they modify. If used tooargumentatively, adjectives can detract fromthe sense of decorum and fairness that helpto support the speaker’s or writer’s Ethos.

• Intensifiers–An “intensifier” is a word thatadds no meaning to a sentence but insteadserves to magnify the meaning of the wordor phrases it modifies. Examples are “very,”“extremely,” “clearly,” “obviously,” etc.

• Verbs–A verb is a word that conveys actionor a state of being. Verbs can be selectedthat have emotional content and persuasiveeffect.

• Adverbs–Adverbs modify any part oflanguage other than nouns (which aremodified by adjectives). Adverbs canmodify verbs, adjectives, other adverbs,clauses, etc.

• Verb tenses–English has three main tenses:past, present, and future. Each has aprogressive form (ongoing action), a perfectform (completed action), and a perfectprogressive form (ongoing action completedat a definite time). The pluperfect tense is apast act completed before another past act.Using past, present, and future tenses lendsto clear, declarative writing. Other tenses

are more complicated but in certainsituations more accurate.

• Verb moods–The mood of a verb suggeststhe manner in which an action or conditionis conceived by the speaker. The threemoods in English are indicative (stating afact or asking a question), imperative (acommand), and subjunctive (doubt, desire,supposition, or condition contrary to fact).The choice of mood is a subtle but powerfulway to convey secondary meaning to thereader.

• Quotations–When citing supportingauthorities, quotations can eliminate thenecessity that the reader look up and readthe cited material. Well-written quotedmaterials can be more persuasive thanwords the author might choose to expressthe same idea. Quoted contractualprovisions or quoted testimony can be moreeffective then a record reference in a brief.

• Paraphrase–A paraphrase is a reconstructionof a quotation. While a pithy quotation isbetter than an excellent paraphrase,sometimes it is not possible to find a pithyquotation that conveys the point you want tomake. Chopping up a verbose quotationwith elipses introduces doubt as to whetherthe quotation fairly reflects the originalstatement. If the brief-writer can do a betterjob of conveying the message than theoriginal writer being quoted, thenparaphrase. On balance, a good paraphraseis better than a poorly-phrased quotation.

• Jargon–Jargon is vocabulary, associatedwith a topic, group, trade, profession, andthe like, that has a special meaning. Jargontends to develop into short-hand terms oracronyms that are unintelligible to theuninitiated.

• Slang–Slang is a manner of speaking,typically in private conversations, using aninformal vocabulary. Much slang containselements of sexuality, humor, irreverence,disrespect of social conventions, and thelike. Some slang is like jargon, using wordsthat are incomprehensible to the general

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public. Slang is usually avoided in formalwriting and speaking.

• Profanity–Profanity is verboten in formalwriting and speaking. If quoting a witnesswho used profanity, the profanity should beused delicately, so that the negativeimpression the profanity creates is notattributed to the writer. Substitutingasterisks for internal letters can soften theeffect. Example: “sh*t happens.” A populareuphemism: “he used the F-word”.

H. CITATION SIGNALS. When citinglegal authority in support of a statement in abrief or appellate opinion, “citation signals”can be used to indicate the degree of supportthat the cited authority gives to the statement.The citation signals are:• [No Signal] indicates direct support.• “e.g.” indicates that the cited authority is oneof several examples that could be cited.• “accord,” used after the primary authority,means that the cited authority agrees withprimary authority; “accord” is also used whenciting legal authorities from anotherjurisdiction.• “see” is used instead of “no signal” when theauthority does not explicitly support thestatement, but supports it in principle, or whenthe support is in dictum.• “contra” is used when the cited authoritydirectly contradicts the statement.• “but see” is used like “see,” but when theauthority is generally to the contrary.• “see generally” is used to cite backgroundmaterials that are relevant but do not providedirect support for the statement.• “compare with” or “cf.” (which means“compare” in Latin) indicates that value canbe derived from comparing the indicatedauthorities to one another. This citation signalrequires a parenthetic explanation to explainwhat the comparison shows.

I. LEGALESE. Lawyers are victims of thefact that their first exposure to legal writing inlaw school is to significant but old appellate

opinions written in a somewhat archaic styleby judges selected on some basis other thanthe clarity of their writing. Most cases arechosen for casebooks because of the legalproposition decided, and not the quality of thewriting. Today’s appellate judges universallycondemn legalistic writing in the briefs theyhave to read (what about in the opinions theyhave to write?). Antonin Scalia: “[Too manylawyers believe that] it is essential to legalEnglish that one write as pompously aspossible, using words and phrases that havelong since disappeared from normal Englishdiscourse.’’316 Words to avoid include:whereas, hereby, herein, hereinabove,hereinbefore, hereinafter, hereto, therefor,therefrom, therein, thereof, therewith, to wit,unto, vis-à-vis, viz., whereby, and wherein.Replace “said,” “such,” “aforecited,”“aforementioned,” “aforesaid” with “the,”“this,” or “these.” The words “forthwith,”“herewith,” “and/or” can be made more exact.There are a number of sources of suggestionson good legal writing style.317

J. FIGURES OF SPEECH. A “figure ofspeech” is a rhetorical device that achieves aspecial effect by using words in distinctiveways. The figure of speech could be a wordthat is used in a way that diverges from itsnormal meaning, or a phrase that has aspecialized meaning not based on the literalmeaning of the words in it. Figures of speechalso include well-known techniques ofarranging and presenting words or conceptsfor special effect. Hundreds of figures ofspeech have been identified, although only afew are routinely used in modern times.Figures of speech include: alliteration(repetition of an initial consonant sound),allusion (an unstated reference to anotherwell-known writing), anaphora (repetition ofthe same word or phrase at the beginning ofsuccessive clauses or verses), anastrophe(inversion of the usual word order), antithesis(juxtaposition of contrasting ideas in balancedphrases), anticlimax (arranging words in order

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of decreasing importance), antithesis(juxtaposing opposing or contrasting ideas),apophasis (invoking an idea by claiming notto invoke it), aposiopesis (interrupting speechfor dramatic or emotional effect), cacophony(juxtaposing words in a way that produces aharsh sound); chiasmus (a verbal pattern inwhich the second half of an expression isbalanced against the first, but with the partsreversed), climax (arranging words in order ofincreasing importance), dysphemism (thesubstitution of a more troubling or offensiveword for another more innocuous word),enumeratio (amplifying a topic by dividing itinto parts, and detailing them), euphemism(the substitution of an inoffensive term forone considered too harsh or explicit),hyperbole (the use of exaggerated terms forthe purpose of emphasis or heightened effect),innuendo (a secondary meaning of a statementthat differs from the primary meaning), irony(the use of words to convey the opposite oftheir literal meaning, or making a statement ordescribing a situation that implies the oppositeof what appears on the surface), juxtaposition(presenting two things together so as tosuggest similarities or differences), litotes (anunderstatement in which an affirmative isexpressed by negating its opposite), metaphor(an implied comparison between twodissimilar things that suggests that they havesomething in common), metonymy (where oneword or phrase is substituted for another withwhich it is closely associated, or describingsomething indirectly by referring to thingsaround it), onomatopoeia (words that imitatethe sounds associated with the objects oractions they refer to), oxymoron (incongruousor contradictory terms that are joinedtogether), paradox (a statement that appears tocontradict itself but can sometimes bereconciled at a deeper level), personification(where an inantimate object or abstraction isendowed with human qualities or abilities),pun (a play on words, sometimes on differentsenses of the same word and sometimes on thesimilar sense or sound of different words),

simile (a comparison, usually formed with"like" or "as," between two dissimilar things),repetition (using a word or phrase again andagain for emphasis or to establish correlationsbetween different parts of a speech orwriting), rhetorical question (making astatement by way of posing a question), sinedicendo (a statement so obvious that it is self-evident), synecdoche (a description where apart is used to represent the whole, and vice-versa), understatement (where a writer or aspeaker deliberately makes a situation seemless important or serious than it is).318

K. NARRATIVE. A narrative is story told asa sequence of events, usually presented inchronological order. Narrative has particularappeal to an audience, since most books,movies, and television dramas are narratives.Narrative theorist Porter Abbott said that“narrative is the principal way in which ourspecies organizes its understanding oftime.”319 “Narrative structure” is the structuralframework that underlies the order andmanner in which a narrative is presented.Narrative structure consists of fabula and sujet(sometimes called “story” and “narrative”respectively). “Fabula” is the underlyingstory, the order in which the actual eventstranspired. “Sujet” (also “sjuzhet”) is theorder in which the events are told, which maybe but need not be chronological.320 Abbottcommented:

The juxtaposition of the two kinds of timemakes the difference clear. Clock time, likeother forms of abstract or regular time,always relates to itself, so that one speaks interms of numbers of seconds (minutes,hours) and fractions (nanoseconds).Narrative time, in contrast, relates to eventsor incidents.321

“Progression” is the movement of a narrativefrom beginning to end and the principlesgoverning that movement.322 It is important torecognize that the same story can be narrated

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in different ways, with different results.Designing a narrative for use in a brief orspeech is very much a Rhetorical process. Thefacts can be ordered chronologically, butdecisions must be made about what facts toinclude and what to omit from the narrative.In a legal argument, inclusion and exclusionmay be dictated by the legal theories or by thedesired outcome. There are many narrativepatterns (“grand narratives”) that audienceswill be able to consciously or unconsciouslyidentify with (e.g., Adam and Eve, David andGoliath, Jesus of Nazareth, the Pilgrims andThanksgiving, 1776, Sleeping Beauty,Cinderella, cowboys and Indians, the voyageof discovery, the murder mystery, to name afew). As Aristotle taught regarding the use ofEnthymemes that will be familiar to theaudience, so the Commonplaces of Rhetoricinclude the grand narratives and meta-narratives that percolate through our society.In making a legal argument, the way the caseis narrated can be an important part ofpersuasive effect. If the argument inherentlyinvolves abstractions, then perhaps examplescan be used imbue the argument with thequalities of a narrative.

L. CONTRAST. Contrast can be a powerfultool in constructive sentences andconstructing arguments. Abraham Lincolnsaid: “You may fool all the people some of thetime, you can even fool some of the people allof the time, but you cannot fool all of thepeople all the time.” Winston Churchill said:“Never in the field of human conflict was somuch owed by so many to so few.” CharlesDickens began A TALE OF TWO CITIES withthis sentence:

It was the best of times, it was the worst oftimes; it ws the age of wisdom, it was theage of foolishness; it was the epoch ofbelief, it was the epoch of incredulity; it wasthe season of Light, it was the season ofDarkness; it was the spring of hope, it wasthe winter of despair; we had everything

before us, we had nothing before us; wewere all going directly to Heaven, we wereall going the other way.

M. TYPES OF QUESTIONS. Questionsplay a variety of important roles in persuasivespeech and writing. Questions have beendivided into categories, discussed below.

1. Loaded Question. A loaded question,sometimes called a “plurium interrogatio-num,” is a question that is structured so thatthe answer will impliedly confirm a tacitassumption that is built into the question. Theclassic example is the question: “When didyou stop beating your wife?” This questiontacitly assumes that you have a wife that youhave beaten. The best defense is to directlyaddress the tacit assumption. An examplewould be: “I am not married,” or “I love mywife and I would never beat her.” Or theanswer could be humorous: “Sir, if you sawmy wife, you would not ask that question.” Abad answer would be: “How I discipline mywife is none of your business.” A loadedquestion has been called a “misleadingquestion,” or a question that contains a “falsesupposition.”323 A noted example occurredwhen Lesley Stahl, an interviewer on thetelevision program Sixty Minutes, asked US.Ambassador to the U.N. Madeleine Alrightthe following question about economicsanctions in effect against Iraq: “We haveheard that half a million children have died. Imean, that is more children than died inHiroshima. And, you know, is the price worthit?”324 Ambassador Albright responded, “Ithink that is a very hard choice, but the price,we think, the price is worth it.” While therewas little public outcry in the United Statesover the answer, it received much negativepress in the Middle East. She was nonethelesslater confirmed as President Clinton’sSecretary of State. In her memoirs, MadameSecretary said:

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I must have been crazy; I should haveanswered the question by reframing it andpointing out the inherent flaws in thepremise behind it. Saddam Hussein couldhave prevented any child from sufferingsimply by meeting his obligations.... Assoon as I had spoken, I wished for the powerto freeze time and take back those words.My reply had been a terrible mistake, hasty,clumsy and wrong. Nothing matters morethan the lives of innocent people. I hadfallen into the trap and said something Isimply did not mean. That was no one’sfault but my own.325

2. Leading Questions. A leading question isa question that suggests the answer that thequestioner desires. In a Texas courtproceeding, Tex. R. Evid. 611 prohibitsleading questions on direct examination butpermits them on cross-examination. Outsidethe courtroom, leading questions caninvalidate a forensic interrogation. Dr.Elizabeth Loftus has published researchsuggesting that leading questions can implantfalse memories in examinees.326

3. Rhetorical Question. A rhetoricalquestion is a question posed in a speech inorder to set up an answer that the speaker willprovide. Some rhetorical questions are posedfor the audience to provide its own answer.Example: “Why would anyone want a child tohave no health insurance?” The foregoingquestion is a form of Reductio ad Absurdum.An apocryphal historical example is KingHenry II’s rhetorical question: “Who will ridme of this troublesome priest?” which resultedin Archbishop Thomas Becket’s assassination.Chief Justice Roberts used forty imponderableRhetorical Questions in his dissent in Caper-ton v. A.T. Massey Coal Co.,327 to attack thesubjectivity of the standard for when judicialrecusal would be constitutionally required forcampaign contributions. Justice Roberts’rhetorical device is called a “parade ofhorribles,” where the speaker argues against a

course of action by listing a number ofextremely undesirable events which willostensibly result from the action.

4. Speaking Questions. A “speakingquestion” is a question that purports to solicitan answer when the real purpose is to assert aproposition regardless of the answer.Example: “Isn’t it true, Sir, that you intendedto provoke an angry reaction from my client?”The obvious answer is “no,” but the real effectof the question is to suggest a “yes” answerdespite the expected denial. Skilled trialadvocates can conduct a cross-examinationwhere the insinuations in the questions canprove a point even when the witness answersall the questions “no”.

5. “Buttering Up” Questions. “Buttering-up” occurs when a two-step question is asked,the first part of which is designed to lead thequestionee to answer yes to the second part ofthe question. For example: “Would you be adear and hand me my glasses?”

6. A “Hook” Question. A hook question isdesigned to cause the questionee to engage ina dialogue. For example, a man standing on46th Street in New York City approaches atourist and asks “Can I help you findsomething?” when his real purpose is toengage the passer-by in conversation in orderto direct the passer-by into a particularjewelry store to buy diamonds.

N. TENSE, MOOD, AND VOICE OFVERBS.

1. Tense. The tense of a verb is the timeframe in which the action took place: past,present, or future. There are four ways to stateeach tense (past, progressive, perfect, andperfect progressive), and three “aspects”(indefinite, complete, and continuing).328

2. Mood. In English there are four moods ofverbs: the indicative mood, the imperative

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mood, the subjunctive mood, and theinfinitive. The indicative mood is the mostcommon, and is used to make an unqualifiedassertion of fact or opinion. The imperativemood is used to give orders or to makerequests. The subjunctive mood is used tostate a hypothesis, a contingency, somethingthat is contrary to fact, a wish, and oftenappears in a clause beginning with the word“if.” The infinitive is used with other verbs tocreate tense and mood.

3. Voice. English sentences have the activeor passive “voice.” In the active voice, thesubject acts through the verb upon the objectof the sentence. In the passive voice, theobject of the sentence receives the action ofthe verb from the subject. In some passivevoice sentences the subject is omitted. Whilethe meaning of the sentence is the same, thepassive voice leads to a more round-aboutway of saying things, that can reduce clarity.The active voice emphasizes the subject oreven the action in the sentence, while thepassive voice emphasizes the object and de-emphasizes the subject of the sentence. Thereare times where you want to de-emphasize theactor, as in a criminal trial where thedefendant says “the the gun went off,” or in acar wreck case when the defendant says “thenthe car spun out of control.” President Lincolnused the passive voice in his statement toCongress justifying his suspending the writ ofhabeas corpus. See Section VII.L.13. Morerecently, Texas Governor Rick Perry, on May3, 2010, talking about the British Petroleumoil spill, said: “From time to time there aregoing to be things that occur that are acts ofGod that cannot be prevented.” His statementde-emphasized British Petroleum’sinvolvement in the well blow out and assignedthe role of the acting agent to chance. Thereare times when the actor is unimportant (e.g.,“the mail was delivered late today”). Thereare times when the actor is unknown (e.g.,“the fire started at 3am” or “the cat was run

over during the night”). And there are timeswhen there is no actor (e.g., “it rained”).

William Strunck Jr., author of THE ELEMENTS

OF STYLE, wrote in 1918 that “[t]he habitualuse of the active voice . . . makes for forciblewriting.”329 Contrast “I will always rememberthe first time we met” to “the first time wemet will always be remembered by me.” Asthe professor succinctly put it to the student:“Don’t tell me you’re sorry the paper waspoorly written; tell me you’re sorry you wrotea bad paper.”

O. KAIROS. “Kairos” is an importantancient Greek word with different meanings atdifferent times. Kairos first appears in Hom-er’s Iliad, to describe a vital or lethalvulnerability in the human body.330 Whenused by Aristotle in connection with Rhetoric,Kairos had the sense of the “right” or“opportune” moment to enter a conversation,or to make a point in a debate. Kairos goesbeyond “what to say” or “how to say it” andconsiders “when to say it.” While Kairos hasbeen an overlooked part of Rhetoric, a fewmodern writers have written about it withinterest. Carl Glover combined physicalvulnerability with timing when he said: “Thearcher must exercise 'due measure andproportion' in aiming the arrow and drawingthe bow string; he must hit a 'vital part of thebody' to fell his prey; he must release thearrow at the 'exact or critical time' to strike amoving target.”331 Glover’s conceptioninvolves not just timing, but also knowingwhere to strike to land a decisive blow.Anyone who has worked on a committeeknows that the timing of when statements aremade in a committee meeting can influencethe direction that a committee takes. Also, theopportunity to make a comment at a certainpoint in the discussion can expire, as thediscussion moves on to a different topic.

In a larger sense, Kairos applies to theappropriateness of Ethos, Pathos, and Logic,

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since the appropriateness and effectiveness ofcertain appeals to the audience depends on thetemper of the times. For example, Marxistrationales were ahead of the times when Marxwrote them, were influential amongintellectuals and third-world political leadersfrom 1917 to the 1970's, and are essentiallydead letter at the present time.

XV. F A L L A C I E S O FARGUMENTATION. Some arguments arefallacious because their underlying logic failsto adhere to the rules of deductive or inductivereasoning. Logical Fallacies are discussed inSections VII.B.10 (syllogistic), VII.K(deductive) and VIII.F (inductive). Then thereare arguments that are fallacious because ofproblems with word meanings, syntax, andsemantics, or because they divert the focus ofthe audience from the merits of the dispute toirrelevant considerations. These latter types ofargument are called “Fallacies ofArgumentation.” While Logical Fallacies areclearly flawed, Fallacies of Argumentation areright or wrong in degrees, depending on thecontent of the argument and the context of theargument.332

Spotting Rhetorical Fallacies in everydaylanguage is sometimes difficult because manyof these techniques are so familiar that wehave become used to them. The best antidoteis to become familiar with a list of RhetoricalFallacies, to be better able to spot one when itarises. Sometimes fallacious arguments aremade out of ignorance. However, manyfallacious rhetorical techniques are usedprecisely because they are effective inobscuring the merits of an argument. Since thegoal of Rhetoric is persuasion and notadhering to Logic, many areas of discourseare prone to fallacious techniques, includingpolitical propaganda, international diplomacy,advertising, editorials, news programs thatappeal to particular constituencies, and,unfortunately, legal advocacy.

In appellate court opinions, the term “fallacy”is often loosely used to characterize a positionas being generally illogical, or sometimeswrong for any reason. This use of the term“fallacy” is so loose that it is connected totraditional fallacies only in the sense that theuser seeks to add the historical weight of theword “fallacy” behind his criticism of acontrary position, even when the reasoningbeing criticized is not truly fallacious.

There are many lists of Rhetorical Fallaciesavailable on the worldwide web, and thecategories and individual items in these listsare somewhat subjective and can amount toshades of grey. Latin names were introducedfor many fallacious arguments in the MiddleAges, and are mentioned where applicable.The following list contains the majorRhetorical Fallacies, but by no means all ofthem.

1. Accident. The Fallacy of Accident, alsocalled “Destroying the Exception” or “Sweep-ing Generalization,” occurs when oneattempts to apply a legitimate general rule toan irrelevant situation that should berecognized as an exception to the general rule.“Guilt by association” is an instance of theFallacy of Accident.

2. Ambiguity. The Fallacy of Ambiguityarises when a word used in an argument hasmore than one meaning, and the intendedmeaning is unclear. When someoneintentionally creates an Ambiguity, in order togain from the uncertainty of meaning, it iscalled “Equivocation.”

The Fallacy of Ambiguity was mentioned inPowers v. Texas Mut. Ins. Co., 2010 WL337144, *4 (Tex. App.--Eastland 2010, nopet.) (memorandum opinion), the court said:

Powers's challenge on appeal is that theblood alcohol test results should not havebeen admitted as evidence because there

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were gaps in the chain of custody;therefore, the expert opinions of Dr.Avery and Hambrick that relied on theblood sample should have been excluded.Powers cites Gammill v. Jack WilliamsChevrolet, Inc., 972 S.W.2d 713, 726(Tex. 1998), for the proposition thatexpert testimony is unreliable if “there issimply too great an analytical gap betweenthe data and the opinion proffered.” Thepart of his argument that relies on Gam-mill commits the fallacy of ambiguity(equivocation). The “gap” referred to inGammill is one of analytical reasoning.The “gap” challenged here is whether thechain of custody from the time the bloodsample was taken until it was analyzed byHambrick was established by theevidence; it was not a “gap” in an expert'sanalytical reasoning.

3. Amphiboly. “Amphiboly” (from theGreek “ampho,” which means "double" or "onboth sides"), also called “amphibology,”occurs where an ambiguity arises not from theunclear meaning of one word, but rather fromthe way the words are arranged. There aremany humorous examples:

• "Toilet Out Of Order ... Please Use FloorBelow"

• "Automatic Washing Machines: PleaseRemove All Your Clothes When The LightGoes On"

• "After Tea Break Staff Should Empty TheTeapot And Stand Upside Down On TheDraining Board"

• “I cannot praise her work too highly.”• “If you attack the Persians, you will destroy

a mighty empire.”333

Ambiguity and Amphiboly should bedistinguished from Vagueness. Vagueness isan indistinctness of meaning.

4. Appeal to Authority (ad Verecundiam).An appeal to authority is an argument that a

proposition should be accepted or rejectedbecause a person in authority has accepted orrejected the proposition. This argument isfallacious when there is no necessaryconnection between who the person is and thecorrectness of her views. It is notobjectionable to suggest that opinions ofauthoritative persons support a view; theproblem is in arguing that such opinionsestablish the point. The fallacy was identifiedby John Locke, who wrote: “When men areestablished in any kind of dignity, it is thoughta breach of modesty for others to derogate anyway from it, and question the authority of menwho are in possession of it.”

This technique is evident in advertising whenclaims are made like: “According to anationwide survey: More doctors smokeCamels than any other cigarette;” or “Tridentis so good for your teeth that 4 out of 5dentists would recommend Trident sugarlessgum for their patients who chew gum.”

The Fallacy of Appeal to Authority has twomanifestations. First, the person held up as anexpert may be well-known but not an expertin the subject matter in question. Celebrityendorsements of products or services are aform of this fallacy, as are health productadvertisements with actors wearing whitecoats and stethoscopes hanging around theirnecks. On June 9, 2010, actor Kevin Costnertestified to a committee of the U.S. Congresson the oil spill in the Gulf of Mexico.334 Since1969, more than 400 celebrities have appearedas witnesses in 288 congressional committeehearings.335 A second problem occurs with anAppeal to Authority when the authority is anexpert in the area, but his/her opinion may beflawed due to bias, corruption, inaccuracy,etc. This concern has driven the scientificresearch community to require disclosure ofresearchers’ ties to parties who are financiallyinterested in the results of the study, and totreat undisclosed connections as a scandal.

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The revolution in the role of expert witnessesushered in by the Daubert case336 involves thevery issues raised by this fallacy. Expertsmust now back up their opinions with reliabledata and valid technique. As stated by thecourt in Burrow v. Arce337: “it is the basis ofthe witness's opinion, and not the witness'squalifications or his bare opinions alone, thatcan settle an issue as a matter of law; a claimwill not stand or fall on the mere ipse dixit ofa credentialed witness.” Will Rogers put it thisway: “An economist’s guess is liable to be asgood as anybody else’s.”

An Appeal to Authority is not fallacious whena legal argument relies on binding caseprecedent, although the argument is fallaciousif the authority is not binding because theauthority is dictum, or a plurality opinion, orhas been attenuated by the amendment of anunderlying statute, etc.

5. Appeal to Belief. An Appeal to Belief isan argument that because many people believean argument, it is therefore true. It takes theform: “Many people believe X; therefore, X istrue”. Depending on the issue, the fact thatsomething is widely believed may make theview important for practical reasons, butdoesn’t establish the truth of the belief. Overhistory, a majority of the people have at timesbelieved something we now know to be false,like a flat earth, or a geocentric universe, orthat Columbus was the first European todiscover America.

6. Appeal to Emotion. The Appeal toEmotion Fallacy occurs when an arguerappeals to the audience’s emotions rather thanreason in order to persuade. This Fallacy isprevalent in political speech and incommercial and political advertising.Indicators of an appeal to emotion areconcepts or symbols that engender strongfeelings, like patriotism, racism, religiousfervor, pity, etc. Non-verbal symbols can beused as latent components of an appeal to

emotion, like patriotic or religious music, anational flag, a religious symbol, persons ofcertain age, race, or gender, positioned behindthe speaker’s podium for effect, etc.

7. Appeal to Fear (ad Baculum). TheFallacy of Appeal to Fear occurs when thespeaker attempts to provoke fear in support ofan argument when the fear is unrelated to themerits of the argument.338 It is an argumentthat uses explicit or implicit threats orotherwise causes fear in order to gainacceptance. Example: “You’d better agreewith me, or else . . . .”

8. Appeal to Flattery. An Appeal to Flatteryis an attempt to persuade a listener byflattering or complimenting the listener. Suchan appeal is unrelated to the merits of theclaim.339

9. Appeal to Novelty. An Appeal to Noveltyoccurs when it is argued that somethingshould be accepted because it is new.340 Justbecause an idea or process is new does notmake it better than existing ideas or processes.

10. Appeal to Pity (ad Misericordiam). AnAppeal to Pity occurs when someone tries toengender support or opposition by invokingpity among the audience.341 The argument isfallacious when the feeling of pity isextraneous to the merits of the argument.

11. Appeal to Ridicule. An Appeal toRidicule, or Appeal to Mockery, is anargument designed to persuade by ridiculingor mocking the opponent.342

12. Appeal to Tradition. An Appeal toTradition is an argument that somethingshould be supported or rejected based ontradition, or the way things have always beendone.343

13. Argumentum ad Hominem. An “adHominem” argument is an argument that

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attacks an idea by attacking its proponents onirrelevant grounds. The term “ad Hominem”means “against the man.” The structure of anad Hominem attack is:

Person A makes claim X.Person B discredits person A.Therefore, person A's claim should berejected.

Example: unwarranted attacks on the integrityof opposing counsel are improper, and aresometimes held to be incurable error. SeeAmelia’s Auto., Inc. v. Rodriguez, 921 S.W.2d767 773-774 (Tex. App.–San Antonio 1996,no writ) (asking a party if he knew that hislawyer was a convicted felon and had beendisbarred for five years for filing a frivolouslawsuit, was incurable error).

A “direct” ad Hominem attack is a personalattack on the opponent, including an attack onher/his character. The structure of the attackis: “Person A has a certain negative quality orfeature; therefore, Person A’s argumentshould be rejected.” A “circumstantial” andHominem attack attempts to refute a claim byshowing that the proponent has beeninconsistent in his support of the claim.

The ad Hitlerum Fallacy is an instance of adHominem. Ad Hitlerum occurs when anopponent is likened to Hitler or the Nazis as away of discrediting his argument. Discreditingan argument because the proponent is of acertain race, religion, or gender, is adHominem.

An ad Hominem attack is legitimate when theattack targets something relevant to the meritsof the argument.

14. Argumentum Ad Hominem Tu Quoque.An “ad hominem tu quoque” attack is one thatcriticizes an opponent for having previouslysaid something inconsistent, or havingpreviously acted in a manner inconsistent with

his or her current position in a dispute. Thefact that the proponent previously espoused adifferent view doesn’t establish which of theconflicting views is incorrect. Actinginconsistently may show the proponent is ahypocrite, but it doesn’t disprove theargument itself.344 Additionally, changingone’s position, when an earlier position is nolonger convincing, is a sign of goodreasoning, not bad.

15. Argument From Fallacy (ad Logicano).The Fallacy of Argument From Fallacy is anargument that, because an opponent’sargument is fallacious, it therefore followsthat his/her conclusion is false. A fallaciousargument does not prove that its conclusion istrue, but the fact it is fallacious does notestablish that the conclusion is false. Youmust distinguish failure to prove fromdisproof.

16. Argument from Ignorance (ad Ignoran-tiam). Argument from Ignorance is thecontention that a proposition is false becauseit has not been proved, or is true because ithas not been disproved. Example: “P isunproved; therefore, not-P is true.”345 This isa shifting of the burden of proof. This kind ofreasoning is not fallacious in instances, like atrial, where the law assigns a burden ofpersuasion to a party and the failure to meetthat burden has the effect of negating theproposition. For example, in a criminal trialthe defendant is either “guilty” or “not guilty.”By law, the failure of the prosecution to proveguilt beyond a reasonable doubt results in thenegative of the proposition being taken astrue. Another example would be a belief thata medicine is safe because no clinical studieshave demonstrated negative side-effects. If thebelief is based on one study, the conclusion isstrongly fallacious. As more studies areconducted, the conclusion becomes less-and-less fallacious.346 One psychologicalexperiment reflects that examinees rated a

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conclusion based on one study to be weakerthan a conclusion based on 50 studies.347

17. Argument From Popular Appeal (adPopulum). Arguing From Popular Appeal isclaiming that someone should accept anargument because a large number of peopleapprove the argument. The argument has theform: “Most people approve of X; therefore Xis true”.

18. Argument to Moderation (adTemperantiam). Argument to Moderation,also called the Fallacy of the Middle Ground,or Fallacy of False Compromise, is acceptingan argument because it lies between twocompeting positions. The Fallacy has thestructure: Party A and Party B are arguing twopositions, position A and position B. PositionC falls between A and B. Therefore, C is thecorrect position.348 The flaw is in thinking thatthe middle ground is always preferable.Sometimes the choice really does boil downto either of two positions (i.e., a woman iseither pregnant or she is not).

19. Bandwagon Effect. The BandwagonEffect, sometimes called “Peer Pressure,” isan argument where the listener’s discomfort atbeing left out of the group is used to persuade,rather than the merits of the argument.

20. Complex Question. The “Fallacy of theComplex Question” occurs when a question ispredicated on an unstated assumption, so thatany answer to the question tacitly affirms theassumption. This is sometimes called a “load-ed question” or a “trick question.” Example:“When did you stop beating your wife?” Tomeet the trick question head on, you canidentify the unstated assumption and disagreewith it. Sometimes a person will ask a loadedquestion without realizing that the questioncontains a false premise. In that instance thefallacy can be pointed out in a friendly way.See Section XIV.M.

21. Converse Accident. “Converse AccidentFallacy” occurs when you form a general rulebased on a few cases that are notrepresentative of the norm. It is a form ofHasty Generalization.

22. Equivocation. “Equivocation” occurswhen someone uses the same term in differentsenses in an argument. When it occurs withthe Middle Term of a Syllogism, it causes theFallacy of Four Terms. See SectionVII.B.10.a. In George Orwell’s ANIMAL

FARM, once the pigs established ascendancyover the other farm animals, they avoidedhaving to rescind the animals’ motto byadding a second part, which usedEquivocation: “All animals are equal. Someanimals are more equal than other animals.” Asubtle form of Equivocation can result from“Semantic Shift,” which involves slowlychanging the context in which the same wordsare repeated so as to achieve Equivocation bytreating distinct meanings of the word asequivalent.

23. False Cause. The Fallacy of False Causeoccurs when a cause is wrongly identified.

24. False Dilemma. Also known as “FalseDichotomy,” the Fallacy of False Dilemmaoccurs when a proposition requires you tochoose between the specified choices, and inreality both choices are false or there are otherchoices available. The dichotomy has thestructure: “Either A is true or B is true; B isfalse; therefore, A is true”. The dichotomy isfalse when both A and B are false, and whenthe choices presented are not collectivelyexhaustive. False Dilemma can be expressedby the proposition “You are either with us, oragainst us.” This was both Hillary Clinton’s349

and George W. Bush’s350 reaction to theSeptember 11, 2001 attacks on the WorldTrade Towers and the Pentagon. Although thelogic may be fallacious, the economic andmilitary might of the United States couldforce such a choice on other nations.

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25. Genetic Fallacy. The Genetic Fallacyoccurs when the support of, or opposition to,a claim is based on the source of the claim,rather than the merits of the claim. Anexample would be supporting an argument byshowing that it originated with a popularperson, or a respected institution, etc., ordiscrediting an argument based on anunpopular source.351

26. Guilt by Association. The fallacy of Guiltby Association is an ad Hominem attack thata claim should be rejected because it isendorsed by unsavory characters. The form is:“People you don’t like accept claim A;therefore you should reject claim A.”

27. Irrelevant Conclusion (IgnoratioElenchi). The Fallacy of IrrelevantConclusion occurs where a proponent of oneconclusion offers an argument that supports adifferent conclusion.

28. Misapplied Burden of Proof. TheFallacy of a Misapplied Burden of Proofoccurs when a contesting party is required toprove a contention when the proposing partyshould have the burden of proof.352 How aburden of proof is assigned, outside oflitigation, can be tricky. Usually the personwho wishes to change the status quo has theburden of proof because, as a practical matter,if people are not persuaded to change theywill continue to do things in the same way.

29. Misleading Vividness. The Fallacy ofMisleading Vividness occurs when a single orsmall number of dramatic examples are givengreater weight that a significant amount ofcontrary evidence.353

30. Moving the Goalposts. Moving theGoalposts occurs when the standard foracceptance is moved to fit an argument, eitherto make it acceptable or make is unacceptable.

31. No True Scotsman Fallacy. The No TrueScotsman Fallacy occurs when a personmakes an ad hoc adjustment to a propositionin order to keep from admitting that it isInvalid. The Fallacy was presented by Britishphilosopher Antony Flew:

Imagine Hamish McDonald, a Scotsman,sitting down with his Glasgow MorningHerald and seeing an article about how the"Brighton Sex Maniac Strikes Again." Ham-ish is shocked and declares that "NoScotsman would do such a thing." The nextday he sits down to read his GlasgowMorning Herald again and this time finds anarticle about an Aberdeen man whose brutalactions make the Brighton sex maniac seemalmost gentlemanly. This fact shows thatHamish was wrong in his opinion but is hegoing to admit this? Not likely. This time hesays, "No true Scotsman would do such athing."354

32. Poisoning the Well. The Fallacy ofPoisoning the Well occurs when someoneattempts to defeat an argument by discreditingits proponent in advance of the proponentpresenting his/her argument.

33. Questionable Cause. The Fallacy ofQuestionable Cause occurs when a causalconnection is asserted between A and Bwithout sufficient justification.355 The PostHoc Ergo Propter Hoc Fallacy is a specificinstance of Questionable Cause, in that thePost Hoc Fallacy concludes that, becauseevent A preceded event B, therefore event Acaused event B.356

34. Special Pleading. The Fallacy of SpecialPleading occurs when a proponent of anargument proposes the adoption of laws orrules while exempting himself/herself fromthem without sufficient cause. For example,the United States Congress will sometimesexempt itself from laws it enacts thateveryone else is required to obey.

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35. Red Herring. A Red Herring is anirrelevant point introduced into a debate inorder to divert attention from the merits beingdebated. The term derives from the fact that afish, typically a herring, that has been cured inbrine and heavily smoked, is reddish coloredand has a pungent odor, supposedly strongenough to throw a sniffing bloodhound off thetrail of its game. Red Herrings are especiallyeffective when they trigger emotionalreactions. An inappropriate analogy can be aRed Herring under the guise of an acceptableargument.

36. Relativist Fallacy. The Relativist Fallacyarises when an opponent argues that aproposition may apply to others but not to himor her, because s/he is unique. This couldinclude the extreme position that all validity isrelative. This Fallacy side-steps the validity ofpropositions that do apply universally.

37. Straw Man. The Straw Man Fallacyoccurs when an advocate ignores hisopponent’s actual position and substitutes aweaker one that the advocate can more easilyrefute. Because the argument refuted is not thegenuine argument, the Straw Man attack doesnot disprove the opponent’s real argument. Astraw man attack can be effectuated byquoting an opponent’s words out of context,or by choosing to respond to an adversarywho has presented a weak argument for theproposition, or by attacking an over simplifiedversion of the argument, or by attacking afictitious adversary.

XVI. CATEGORIZING FALLACIES.Fallacies have been described as “reasoningthat is not cogent, which means reasoning thateither (1) does not provide sufficiently goodgrounds for its conclusion; (2) employsunwarranted premises; or (3) ignores oroverlooks relevant information.”357

Throughout this Article, Fallacies have beendivided into two categories: logical fallaciesand rhetorical fallacies, with logical fallacies

being further subdivided into deductivefallacies and inductive fallacies. Over themillennia, Fallacies have been categorized inmany different ways. Aristotle categorizedFallacies in 300 BC. Roman writers refinedthese categories and added more. TheseFallacies were elaborated and multiplied (andgiven Latin names) during the Middle Ages.In 1620, Francis Bacon identified fourFallacies. In 1843, John Stuart Mill identifiedfive categories of Fallacies. More recently,researchers using Bayesian conditional logichave evaluated the traditional Fallacies likearguments from Ignorance, CircularArguments, Slippery Slope arguments, adPopulum, ad Hominem, and the like.

Some writers distinguish formal frominformal Fallacies. Formal Fallacies are errorsin the logical form of the argument, whileinformal Fallacies are errors of reasoning thatcannot easily be expressed in our system offormal logic, but are nonetheless criticized asbeing wrong.358 Other writers distinguishdeductive from inductive fallacies, which isthe approach taken in this Article.

Here are some alternative divisions offallacies into different categories.

A. ARISTOTLE’S FALLACIES. In hisbook Sophistici Elenchi (SophisticalRefutations), Aristotle listed thirteen“sophistical arguments” (fallacies), anddivided them into two groups: “materialfallacies” and “verbal fallacies.” MaterialFallacies included: Accident, Ignorance ofRefutation, Affirming the Consequent,Begging the Question, Converse Accident,Complex Question, Irrelevant Conclusion,Missing the Point, and False Cause. VerbalFallacies included: Accent, Amphiboly,Equivocation, Composition and Division, andFigure of Speech.359

B. FRANCIS BACON’S FALLACIES.Francis Bacon perceived that the human mind

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had certain predispositions that could causedistortions in perceptions of the world. Baconassociated these predispositions withFallacies, but he didn’t call them fallacies. Inhis 1620 book NOVUM ORGANUM, Baconcalled them “idols,” and he had four of them:Idols of the Tribe, Idols of the Den, Idols ofthe Market, and Idols of the Theater.

Aphorism 41: The idols of the tribe areinherent in human nature, and the very tribeor race of man. For man's sense is falselyasserted to be the standard of things. On thecontrary, all the perceptions, both of thesenses and the mind, bear reference to man,and not to the universe, and the human mindresembles those uneven mirrors, whichimpart their own properties to differentobjects, from which rays are emitted, anddistort and disfigure them.

Aphorism 42: The idols of the den are thoseof each individual. For everybody (inaddition to the errors common to the race ofman) has his own individual den or cavern,which intercepts and corrupts the light ofnature; either from his own peculiar andsingular disposition, or from his educationand intercourse with others, or from hisreading . . . .

Aphorism 43: There are also idols formedby the reciprocal intercourse and society ofman with man, which we call idols of themarket, from the commerce and associationof men with each other. For men converseby means of language; but words are formedat the will of the generality; and there arisesfrom a bad and unapt formation of words awonderful obstruction to the mind. . . .

Aphorism 44: Lastly, there are idols whichhave crept into men’s minds from thevarious dogmas of peculiar systems ofphilosophy, and also from the pervertedrules of demonstration, and these wedenominate idols of the theatre. For we

regard all the systems of philosophy hithertoreceived or imagined, as so many playsbrought out and performed, creatingfictitious and theatrical worlds. . . .

In Aphorism 40, Bacon wrote that these idolscould be avoided by forming notions andaxioms on the foundation of true induction.

C. JOHN STUART MILL’S FALLACIES.John Stuart Mill wrote that “Logic is notconcerned with the false opinions which‘people’ happen to entertain, but with themanner in which they come to entertainthem.”360 In his book ON FALLACIES, Millstates five categories of Fallacies: (i) Fallaciesà priori (or Fallacies of Inspection), (ii)Fallacies of Observation, (iii) Fallacies ofGeneralization, (iv) Fallacies of Ratiocination,and (v) Fallacies of Confusion. Fallacies àpriori occur with no actual inference takingplace, where a person mistakenly assumes thathis/her subjective awareness is a reflection ofobjective reality.361 Fallacies of Observationresult from error in sufficiently ascertainingthe facts on which a theory is grounded.362

Fallacies of Generalization includeunverifiable generalizations, attempts toresolve into one things that are radicallydifferent, mistaking empirical for causal laws,Post Hoc Fallacy, and the Fallacy of FalseAnalogies.363 Fallacies of Ratiocination arearguments that rely on false Premises andthose with true Premises that do not supportthe Conclusion. These include the failure todistinguish the contrary from thecontradictory, syllogistic Fallacies, and theFallacy of Changing the Premises.364 Fallaciesof Confusion have their source in language,whether vagueness or ambiguity, or casualassociations with words, and they aremisconceiving the import of the Premises,forgetting what the Premises are, andmistaking the Conclusion that is proved.365

Mill points out, however, that the distinctionsbetween these categories of Fallacies fail uponclose inspection.

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D. A MODERN TAXONOMY OFFALLACIES. In THEORY AND PROBLEMS OF

LOGIC (2d ed.), by Nolt, Rohatyn, andVarzl,366 the authors divide fallacies into sixcategories: Fallacies of Relevance, CircularReasoning, Semantic Fallacies, InductiveFallacies, Formal Fallacies, and Fallacies ofFalse Premises. Their Fallacies of Relevanceoccur when the Premises of an Argument haveno bearing on the Conclusion, includingArguments that have a distractive element thatdiverts attention away from the lack ofrelevance. This category includes: adHominem abusive attacks, Guilt byAssociation, Tu Quoque attacks, VestedInterest arguments, Circumstantial adHominem attacks, Straw Man arguments,Appeals to Force, Appeals to Authority,Appeals to Pity, Appeals to Ignorance,Missing the Point, and Red Herring. Fallaciesof Circular Reasoning involve assuming whatyou are trying to prove. Semantic Fallaciesoccur when the language used in an argumentis ambiguous or so vague that it interfereswith the ability to assess the cogency of theargument. Their Semantic Fallacies includeambiguity, amphiboly, vagueness, and accent.Inductive Fallacies occur when the probabilityof the Argument’s Conclusion, given thePremises, is too low. Formal Fallacies occurwhen a valid rule of inference is misapplied orthe rule followed is not Valid. Their finalcategory is Arguments with False Premises,including False Dichotomy and SlipperySlope.367

XVII. M O D E R N A R G U M E N TTHEORIES.

A. THE TOULMIN MODEL OFARGUMENT. Informal Logic is a loosely-integrated variety of approaches to reasoningand argumentation. An important theorist inthe field was British philosopher Stephen E.Toulmin (died in 2009), later a professor atUSC, whose 1958 book THE USES OF

ARGUMENT is considered a seminal work inthe field of Informal Logic. In the book,Toulmin suggested the Toulmin Model ofArgument. Many found Toulmin’s model tobe an easier way to teach argumentation thaneither traditional Logic or traditional Rhetoric.Toulmin’s Model has three main components:the Claim, the Support, and the Warrant; andthree additional components: Quantifiers,Rebuttals, and Backing.

1. Claims. A Claim is a proposition or thesisthat an arguer is trying to make. To make agood argument, the Claim should be stated instrong and unequivocal terms. However,Claims stated in terms of absolutes (all, none,always, never) are vulnerable to refutation bya single counter-example. To avoid this,Claims can be stated with Qualifiers thatsoften the statement somewhat. Qualifiers thatsoften the Claim include few, some, most,seldom, sometimes, often, usually, nearlyalways.

In legal arguments, the Claim is usually thereason the client should win. It is wise to limita legal Claim to the narrowest scope that willassure a victory, in order to avoid having toprove more than you need to win.

The Claim should be tailored to thesupporting evidence.

Toulmin recognized three types of claims: fact(verifiable conditions in the real world),judgment/value (opinions, attitudes,subjective assessments), and policy (futurecourse of action).

2. Data. Data are the supports, grounds,evidence, or information that back up theClaim. Data can include assertions based onthe arguers personal authority, quotationsfrom famous people or respected writings,statements by experts, test results, statistics,physical evidence, statements of eyewitnesses,

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and the like. Data can also include appeals tohuman desires, needs, or values.

3. Warrants and Backing. Warrants are theassumptions, or principles, or logicalstatements, that link the Claims to the support.A Warrant could be a deductive inference, aninductive inference, an analogical comparison,an Enthymeme, or it could be a Rhetoricalthing, like Ethos, Pathos, Logos. Backing isstatements that support the Warrants, asopposed to supporting the Claims. Backingcan show that the Warrant is supported byLogic or by observations of the real world.368

4. Rebuttals. Even carefully constructedarguments can be subjected to rebuttalarguments. Rebuttal arguments have their ownstructure of Claim, Data, Warrant, andBacking.

5. Comparison to Syllogism. Toulmin’sModel of Argument, expressed in the form ofa Syllogism, would have the followingcorrelations: The Warrant would be the MajorPremise; the Evidence would be the MinorPremise; and the Claim would be theConclusion.

B. DEFEASIBLE REASONING. In recentyears there has been strong interest in whatare called “Defeasible Arguments.” ADefeasible Argument is an argument offeredto support a Conclusion with recognition thatthe Argument is subject to being invalidatedby subsequent information or contraryArguments that may later arise.369 In contrastto an Argument founded on DeductiveLogic--where the Argument is presented asbeing conclusive--it is understood with aDefeasible Argument that the Argument isprovisional only, more like a hypothesis, to beused until something stronger or better comesalong.

Defeasible Reasoning was suggested by legalphilosopher H.L.A. Hart in 1948, was picked

up by epistomologist (concerned with thenature of knowledge) philosopher RoderickM. Chisholm who applied it to perceptionsabout the world, and was later carried forwardby American philosopher John L. Pollock,who developed a scheme of argumentationbased on Defeasible Arguments. In Pollock'sview, reasoning “proceeds by constructingarguments for conclusions.”370 Arguments arebased on Premises. In Deductive Logic, theConclusions we draw from the Premises arenot defeasible (i.e., subject to being defeated).With Inductive Logic, however, as we learnmore information we sometimes find that ouroriginal Premises remain true but theConclusions we drew from these Premises areno longer supportable, and must be retracted(see the black swan discussion in SectionVII.B.1). Thus, in Inductive Logic ourConclusions are always defeasible, andsubject to being disproved by what Pollocktermed "defeaters," either "rebuttingdefeaters" or "undercutting defeaters."371

C. ARGUMENTATION SCHEMES.Modern writings on argument theory aretending away from argument patterns basedon formal Logic and toward “argumentationschemes” or semi-formal argument patternsthat loosely copy the premise-and-conclusionpattern or Modus Ponens structure of FormalLogic, but without the requirement of truePremises and certain Conclusions.372 Theseargumentation schemes are believed to betterapproximate everyday conversation and thetype of reasoning that occurs in law andmedical diagnosis.373 One theorist, DouglasWalton, has offered an extensive list ofargumentation schemes, including argumentfrom sign, argument from example, argumentfrom commitment, argument from position toknow, argument from expert opinion,argument from analogy, argument fromprecedent, argument from gradualism, andslippery slope arguments.374 Theseargumentation schemes are presumptive,meaning that they are defeasible. They are

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thus different from the “context-free kinds ofdeductive and inductive arguments so longstudied in logic.”375 Each argument scheme ismatched with a series of “critical questions”that are used to test the validity and strengthof the argument. Taking an example from oneof Walton’s articles, here is the argumentscheme for “argument from expert,” includingits logical structure and related criticalquestions:

Major Premise: Source E is an expert insubject domain S containing proposition A.Minor Premise: E asserts that proposition A(in domain S) is true (false).Conclusion: A may plausibly be taken to betrue (false).

Here are the “critical questions” that matchthis argumentation scheme:

1. Expertise Question: How credible is E asan expert source?2. Field Question: Is E an expert in the fieldthat A is in?3. Opinion Question: What did E assert thatimplies A?4. Trustworthiness Question: Is E personallyreliable as a source?5. Consistency Question: Is A consistentwith what other experts assert?6. Backup Evidence Question: Is E'sassertion based on evidence?376

This modern approach to argumentationschemes does not turn its back on 2,300 yearsof Logic and Rhetoric. It draws justificationsfrom Aristotle’s ideas of Enthymemes andTopics, only interpreted in a nontraditionalway. Modern argument theory is an effort totake the principles suggested by Formal Logicand Formal Rhetoric and adapt them to theway argumentation actually occurs in modernlife.

XVIII. DEGREES OF CERTAINTY.Legal propositions or arguments can have

different degrees of certainty, usuallydiscussed in terms of probability. In law,recognized degrees of certainty are usuallydiscussed as degrees of proof: legallyinsufficient; colorable;377 prima facie;factually sufficient; preponderance; clear andconvincing; beyond a reasonable doubt; andconclusive.

XIX. CATEGORIES VS. GRADA-TIONS.

A. PHILOSOPHICAL PERSPECTIVE. Asthe Sorites Paradox (Section VII.L.1)indicates, categorical distinctions can be hardto apply and hard to justify near theborderlines of the categorical boundaries. Theproblem exists for any taxanomicclassification scheme. The AmericanPsychiatric Association’s DIAGNOSTIC AND

STATISTICAL MANUAL OF MENTAL

DISORDERS (4th ed.) addressed this issue as itapplies to diagnosing mental illness:

This naming of categories is the traditionalmethod of organizing and transmittinginformation in everyday life and has beenthe fundamental approach used in allsystems of medical diagnosis. A categoricalapproach to classification works best whenall members of a diagnostic class arehomogeneous, when there are clear bound-aries between classes, and when thedifferent classes are mutually exclusive.378

Categories work when (i) the things insideeach category are homogenious, (ii) theboundaries of the categories are clear, and (iii)the categories are mutually exclusive. If anyof the three elements are missing, categoriesdo not work well.

As an alternative to categories, people usedimensional approaches to differentiation.This is true in incremental measurements,such as height, length, weight, etc. However,things that can not be counted can not be dealt

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with easily using a dimensional standard, andtherein lies the difficulty since so manyimportant things in life cannot be quantified.As Einstein is reported to have said: “. . . . noteverything that counts can be counted.”379

B. LOGICAL PERSPECTIVE. ClassicalDeductive Logic has no problems withgradations because Logic is “bivalent,”meaning that a Term, Proposition, orArgument is either totally true or totally false,and any other possibility lies outside ofDeductive Logic. Probabilistic approaches toLogic recognize the limitations of bivalence,and address it by assigning different degreesof likelihood to Premises and Conclusions.Inductive Logic addresses gradations bydetermining the probability that something fitsin a particular category. Analogical reasoningabsorbs gradations into the process of makingindividual comparisons between objects.

C. LEGAL PERSPECTIVE. The law hasfaced and accommodated gradations indifferent ways.

Example: The late Professor Keith Morrison,of the University of Texas School of Law,used to tell his students: “Any fool knows thedifference between midnight and noon. Butfew know when night ends and day begins.”Professor Morrison, who taught federalincome taxation, was also known to say:“There is a fine line between tax avoidanceand tax evasion and a high price is paid for theability to discern it.” Few would expect toencounter such philosophical or even poeticinsights in the study of federal income taxlaw. This goes to show that some lawyers arepoets. But these examples also highlight theproblems, and the opportunities, of gradationsof the law.

Here are some gradations in the law, to namea few out of many:When does a driver have to turn on his lights,under Texas law?

What is the minimum amount of cocainenecessary to constitute possession?When is a defendant too crazy to be put ontrial? When is a published piece too humorous to bedefamatory?When is a convicted murderer toounintelligent to execute?When is a fetus too alive to abort?When are words or images of sexual behaviortoo artistic to be prosecuted?When does free speech become treason?When can a child be prosecuted as an adult?When does an activity impact interstatecommerce?What constitutes “reasonable force” inprotecting property?When is information sufficient to constituteprobable cause for a search?When is a casual connection too remote tosupport liability?

Unlike philosophy, the legal process cannotafford to get lost in the blank spaces betweenwords, since the law must arrive at a result. Soeven at the edge of the meaning of a word, orthe limit of a concept, where distinctions areblurred, the law must make the choices thathave to be made in order to reach a result.

XX. VAGUENESS. Vagueness is the baneof communicating with words or symbols.Vagueness is the center of one of the mostcontentious multi-disciplinary controversiesof the last fifty years–whether wordsthemselves have meanings, or whether wordshave only the meanings that people attributeto them. The debate is too far advanced toenter into here, but there is much to gain fromidentifying the fundamentals.

Vagueness is a form of indeterminacy ofmeaning. The problem can be at the wordlevel, where the word chosen is more generalthan what is needed of the word. Example:“Please identify State’s Exhibit 23.” “Afirearm.” “What kind of firearm?” “A pistol.”

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“What kind of pistol?’ “A Colt 45 caliberrevolver.” Whose Colt 45 caliber revolver?”“Mine.” Another example: “Obligee shallmake timely payment of all sums due underthis contract.” Q. How long after the due datedoes Obligee have to make payment? A. Areasonable time. Q. What is a “reasonable”time? A. I don’t know.

Even a precise word or term can have avagueness of meaning. Take the legal term“Due Process of Law.” We can divide theterm into procedural due process andsubstantive due process, but those terms arestill too imprecise to have a definitivemeaning. We can define due process of lawusing other words, but those words havemeanings that in turn are imprecise. When theterm “due process of law” is used in aparticular case, it is most often conclusory. Adefendant either was or was not afforded dueprocess of law. That particular case becomesan example of due process, or an example ofa denial of due process. But examples arevague themselves, because the facts of onecase always differ from the facts of the nextcase. So examples help with vagueness butthey can’t eliminate it. This calls to mindJustice Potter Stewart’s famous commentabout how to define pornography: “I know itwhen I see it.” That is an honest appraisal ofthe problem, but it is unsatisfactory as a legalstandard that would permit people to knowwhere the line is drawn as a guide to theiractivities.

Another challenging problem with vaguenessinvolves a classification scheme that isapplied to something continuous in nature. Asyou approach the dividing line betweencategories, the justification for puttingsomething on one side of the dividing line andnot the other begins to look arbitrary, and theitems are hard to distinguish. This is theproblem of “borderlines.” It is reflected in theSorites Paradox.380 See Section VII.L.1.

XXI. DISAMBIGUATION. Disambigua-tion is a process of clarifying the meaning ofa word or concept by stating what is notmeant. This can be done using definitions thatboth include and exclude. It can be done byusing parentheticals and footnotes, and otherclarifying asides. It can be done by restatingpoints in different ways. At a higher level,disambiguation means striving for clarity ofmeaning in what you write and say. In orderto write and speak clearly, you must first thinkclearly. Thinking clearly requires practice andeffort.

XXII. HEURISTICS AND COGNITIVEBIASES. Psychologists have noticed thatpeople have approaches to thinking that bothhelp and hurt an accurate assessment of asituation.381

A. HEURISTICS. "Heuristics" are simplerules that describe how judgments are made.Cognitive heuristics include: therepresentativeness heuristic, the availabilityheuristic, the primacy effect, the anchoring-and-adjustment heuristic, and thepast-behavior heuristic.

The "representativeness heuristic" occurswhen a judgment is made by deciding if anobject or person is representative of a knowncategory.

The "availability heuristic" occurs whenjudgments are influenced by the ease withwhich objects and events can be remembered.

The "primacy effect" exists when a personmakes judgments quickly, sometimes withoutcollecting sufficient data.

The "anchoring-and-adjustment heuristic"occurs when judgments vary depending uponthe order of presentation of information in thediagnostic assessment process. For example,if the evaluator's judgment changes dependingupon whether a piece of information is

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obtained early or late in the process, then theanchoring-and-adjustment heuristic applies.

The "past-behavior heuristic" occurs whenpredictions of future behavior are based on aperson's past behavior.

The “recency effect” is the observedphenomenon that people asked to remember alist of items remember better the items that arelast on the list. This has been generalized to aproposition that in a narrative, or in a trial,people remember what they heard recentlybetter than what they heard prior to that.

B. COGNITIVE BIASES. A cognitive biasis a distortion in the way we see the world.There is a long list of recognized cognitivebiases. Some of these are reflected in the listsof Fallacies discussed earlier in this Article. Apartial list of recognized cognitive biasesincludes the following.

Mis-Estimation of Covariance--Mis-estimation of covariance occurs whensomeone analyzing a situation does notcorrectly describe the relationship betweentwo events. Studies suggest that, in attemptingto see if a correlation exists between anindicator and a result, people tend to assesscovariance based on the portion of the samplethat has the indicator while ignoring instancesthat do not have the indicator. In reality,knowing the correlation in both groups isnecessary to make an accurate assessment.

Preconceived notions or expectan-cies–Psychological research suggests thatpreconceived notions affect not only aperson’s perception of the correlation betweenfactors but that preconceived notions alsoimpede the accurate processing of both newand remembered data.

Lack of Awareness–Studies of the problemsuggest that person have negligible awarenessof the factors that influence their judgment.

This keeps them from implementingsafeguards against influences that might colortheir judgment.

Overconfidence–Some psychologists arguethat a person’s overconfidence in his or herabilities impedes the improvement of theirprocess of arriving at judgments. Thus, it iscommonly accepted that more informationimproves a judgment, when studies haveshown that too much information can degradethe ability to make a good judgment. Thisargument has been raised as an argumentagainst expanding the information used tointerpret a statute from the literal language ofthe statute to include legislative history.

Confirmation Bias–Research suggests thatpersons often form tentative conclusions in ashort period of time, and that once thosetentative conclusions are formed they caninfluence what additional information issought, and how additional information isprocessed. The danger is that the person willunconsciously tend to want to confirm theirpreliminary hypothesis, rather than keeping anopen mind until the data has been fullyacquired and analyzed. So, Confirmation Biasis the tendency to selectively seek andconsider evidence that confirms thehypothesis currently under consideration andnot contrary evidence.382

Hindsight Bias--"Hindsight bias" occurs whenknowledge of the outcome of an event altersa person’s memory of what s/he expectedbefore the event.383 It results from thetendency of people to want to believe thatthey were accurate in their predictions orexpectations.

Halo effect--A long-standing view holds thatthere is a halo effect for physicalattractiveness–where an attractive person willbe judged more positively than a lessattractive person. It is hard not to notice thatcable news programs are currently dominated

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by young, attractive journalists, not so muchold or overweight ones. And yet buxomfemale commentators are not prevalent on thenews shows, suggesting that the producersmay think that sexuality may detract from thecredibility that they would like to project.

XXIII. USING LOGIC AND RHETORICTO CONSTRUCT AND EVALUATELEGAL ARGUMENTS. The principles ofDeductive and Inductive and AnalogicalLogic examined in this Article can be used inconstructing legal arguments. Some thoughtson applying these principles to legalarguments are set out in this Section.Likewise, the principles of Rhetoric can beused in constructing and delivering legalarguments. The Canons of Rhetoric have beendiscussed in Section XIV.D. and will not berepeated here, for as Lincoln noted, even greatskill at speaking does not relieve a lawyerfrom “the drudgery of the law.”384 Recall that,in Rhetoric, “Commonplaces” are beliefs orvalues that the speaker or writer thinks areheld by the audience. This Section of theArticle examples legal Commonplaces thatcan be used to construct legal arguments.

A. ADAPTING LOGIC CONCEPTS TOLEGAL ARGUMENTS. Logical reasoningis a process that can be applied to legalargumentation. Abraham Lincoln wrote thisabout Deductive Logic:

In the course of my law reading I constantlycame upon the word demonstrate. I thought,at first, that I understood its meaning, butsoon became satisfied that I did not. I said tomyself, What do I do when I demonstratemore than when I reason or prove? Howdoes demonstration differ from any otherproof? I consulted Webster’s Dictionary.They told of certain proof, proof beyond thepossibility of doubt; but I could form noidea of what sort of proof that was. I thoughta great many things were proved beyond thepossibility of doubt, without recourse to any

such extraordinary process of reasoning asI understood demonstration to be. Iconsulted all the dictionaries and books ofreference I could find, but with no betterresults. You might as well have defined blueto a blind man. At last I said, Lincoln, younever can make a lawyer if you do notunderstand what demonstrate means; and Ileft my situation in Springfield, went hometo my father’s house, and stayed there till Icould give any proposition in the six booksof Euclid at sight. I then found out whatdemonstrate means, and went back to mylaw studies.385

1. Use Syllogisms. Syllogistic reasoning hasbeen considered to be the core of deductivereasoning for over 2,000 years. Syllogisticreasoning can be used to construct ordeconstruct a legal argument to see if itfollows the rules of Deductive Logic,expressed through the Rules of Syllogismsand syllogistic Fallacies. Example: In aparticular case, the defendant supplementedhis list of persons with knowledge of relevantfacts 29 days before trial. Tex. R. Civ. P.163.5(b) says that an amended orsupplemental discovery response made lessthan 30 days prior to trial is presumed not tohave been amended reasonably promptly afterthe party discovers the necessity for such aresponse. Stated as a Syllogism, the issuewould be: “Discovery supplementation madeless than 30 days before trial is presumptivelyuntimely. Tex. R. Civ. P. 163.5(b). Thedefendant supplemented its discoveryresponse 29 days before trial. Therefore, thesupplementation is presumptively untimelyand should not be allowed.”

Another way to introduce a Syllogism into alegal argument is to use a simile and constructa Syllogism that is analytically similar to theproposition in question. Some psychologicalstudies reflect that a strong disposition amongpersons to assess the validity of a Syllogismbased on the believability of its content–called

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“Belief Bias.”386 To leverage Belief Bias inyour favor, analogize the legal proposition inquestion to a Syllogism with content that iseasily recognized as Valid (or Invalid,depending on the point you wish to make).

2. Use Enthymemes. Aristotle drew hisinsights on Logic from observingargumentation, and he used examples fromargumentation to illustrate many of his points.Aristotle noticed that Greek speakers did notspeak in Syllogisms–they spoke inEnthymemes, or truncated Syllogisms. Atypical Enthymeme is a Conclusion supportedby the Major Premise, leaving the MinorPremise unmentioned. In constructing yourargument, and considering how to formulatean Enthymeme, you may find that it is betterto state the Minor Premise explicitly, or youmay not. It is a choice you can makeconsciously, once you are aware of the choice.You may find that it is better to emphasize theMiddle Term of a Syllogism, or better tounderstate it. These are conscious choices,once you know the structure of syllogisticreasoning.

Here is the example given in the previoussection, stated as an Enthememe: “Becausethe defendant supplemented discovery within30 days of trial, the supplementation wasuntimely and should be stricken. Tex. R. Civ.P. 163.5(b).” In this Enthememe, the MajorPremise is left unstated: “Discoverysupplementation made less than 30 daysbefore trial is presumptively untimely.”

3. Use Conditional Propositions(Implication). Conditional Propositions areImplications, which have the form “P impliesQ” or “if P then Q”. Many legal issues can beexpressed at Conditional Propositions. Theexample used in the two foregoing sectionscan be stated as a Conditional Proposition: “Ifa party supplements discovery within 30 daysof trial, then the supplementation is untimelyand should be stricken. Tex. R. Civ. P.

163.5(b). The defendant supplementeddiscovery 29 days before trial. Therefore, thediscovery supplementation should bestricken.”

A n o t h e r e x a m p l e : C o n f i d e n t i a lcommunications between a client and his/herlawyer are privileged. Tex. R. Evid. 503(5).The problem may be stated: “If the email fromJones to his lawyer fits the definitions in Tex.R. Evid. 503, then it is privileged.” Proceed toconfirm whether the email meets thedefinitions in the Rule.

Another example: An out-of-court statementis hearsay if it is offered into evidence toprove the truth of the matter asserted. Tex. R.Evid. 801(d). Unless an exception applies,hearsay evidence is inadmissible. Tex. R.Evid. 802. The problem can be stated: “If anout-of-court statement is offered for the truthof the matter asserted, then it is inadmissible.Tex. R. Evid. 802.”

Another example: A successful plaintiff canrecover attorney’s fees if the claim is for: (1)rendered services; (2) performed labor; (3)furnished material; (4) freight or expressovercharges; (5) lost or damaged freight orexpress; (6) killed or injured stock; (7) asworn account; or (8) an oral or writtencontract. Tex. Civ. Prac. & Rem. Code§ 38.001. The legal issue may be stated: “Ifthe plaintiff’s claim fits any category listed inSection 38.0001, then the award of attorney’sfees must be upheld on appeal.”

Another example: Driving while intoxicated isan offense under Tex. Penal Code § 49.04. Aperson is intoxicated if either (i) her/hisalcohol content exceeds 0.08%, or (ii) s/hedoes not have normal use of mental orphysical faculties by reason of taking alcoholor other drug. Id. § 49.01(1). If either (i) or (ii)apply (the Inclusive Disjunction), then anoffense was committed. If the defendant hadnot drunk alcohol but had smoked marijuana,

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then (i) is ruled out and an offense wascommitted only if (ii) applied.

The common element of these examples isthat a specific legal rule applies to the issue inquestion, and determining whether the facts ofthe case fall within the operation of the ruledetermines the outcome. This type of legalproblem can be resolved using DeductiveLogic.

4. Use Inductive Reasoning. InductiveReasoning moves from particular instances toa general Conclusion. The more individualinstances there are that support theConclusion, the Stronger the Conclusion willbe. Suppose that the issue on appeal iswhether the trial court committed reversibleerror in denying the defendant a continuancedue to the fact that its lead counsel wasalready in trial in another case, requiring thedefendant to go forward with second-chaircounsel who was an associate attorney withlittle trial experience. Citing one case thatfound reversible error on similar facts is somesupport. Finding three is more support.Finding ten would be strong support. If thereare no Texas cases on point, then includingout-of-state cases may raise the level ofsupport to the winning point.

Any time a decision is addressed to the trialcourt’s discretion, then the outcome is notdictated by legal rules, and DeductiveReasoning cannot be used. By finding casesinvolving the same exercise of discretion, andfact patterns that are similar to the case athand, a general rule can be abstracted that,given a certain set of facts, prior judges haveexercised their discretion in a certain way.Even if the appellate courts have nearlyalways affirmed the trial court’s decision,perhaps some kind of precedent can beinductively developed based on the way thetrial courts exercised their discretion in theindividual cases.

5. Use Analogical Reasoning. AnalogicalReasoning can be used when Deductive andInductive Reasoning do not lead to a solution.

Example: “Boating while intoxicated” is anoffense under Tex. Penal Code § 49.06. Theoffense involves “operating a watercraft.”“Watercraft” is defined as a “vessel . . . orother device used for transporting or carryinga person on water, other than a devicepropelled only by the current of water.” Id.§ 49.01(4). The term “operating” is notdefined in the Penal Code. On one Saturdayafternoon, ten U.T. fraternity bothers werearrested on the Guadalupe River south ofAustin. All were intoxicated. At the time ofarrest: two were in a canoe, but only the boyin the stern had a paddle; two were in a rubberraft, which had a rudder but no paddles; onewas in an innertube and had a paddle, butwhen he paddled he only turned in a circle;one was in an innertube that was tethered tothe canoe; two were standing on a shallowdam tugging on the raft to drag it over thedam and back into the flow of the river. Whocommitted the offense of boating whileintoxicated?

Example: under the case of Kyllo v. U.S.,387

the U.S. Supreme Court held that thegovernment must have probable cause inorder to “search” a person’s home using a“thermal imaging device,” which would detecthigh intensity lights that are used to growmarijuana. The Transportation SafetyAdministration plans to install full-bodyscanners388 at John F. Kennedy Airport inSeptember 2010, and to require personspassing through security to undergo the scans.Is probable cause required to conduct anelectronic full body scan of a person seekingto board an airplane?

6. Use Fallacies. While Fallacies areimproper reasoning, there are instances wherethe Premises and the Argument may notsupport a Conclusion 100% but may support

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them to a sufficient degree. In argumentation,where deductive certainty is not required, it isfine to use fallacious reasoning. InductiveFallacies are usually a matter of degree, andcan be used in argumentation to the extentthey are considered persuasive. RhetoricalFallacies might be wrong in some instancesand right in others. Known Fallacies shouldtherefore be considered Commonplaces foruse in argumentation.

7. Indirect Argument. In Logic, an indirectargument assumes the negative of the Premiseand shows that it leads to a logicalcontradiction. More loosely, in argumentationan indirect argument supports the proponent’sConclusion by showing that the opposingargument leads to illogical or undesirableconsequences. Using the opponent’s Premiseto construct an argument that refutes theopposing argument--and confirms your own--is doubly successful. Abraham Lincoln didjust this in his famous Cooper Union speech.

Lincoln’s speech at Cooper Union in NewYork City on February 27, 1860, was anessential step in his proving to theRepublicans of the Atlantic states that thisungainly prairie lawyer was a credible choiceto be the Republican Party’s nominee forPresident. But the speech is also an superbexample of indirect argument. At the outset ofthe speech, Lincoln identified as his chiefantagonist Stephen A. Douglas, the DemocratSenator from Illinois, who argued that theFederal government did not have the power toexclude slavery from the new states beingcreated in the westward expansion of thewhite race. Lincoln held the opposite view. Inopening his Cooper Union speech, Lincolnidentified the following statement that hadbeen offered by Douglas to support his view:

“Our fathers, when they framed theGovernment under which we live,understood this question just as well, andeven better, than we do now."389

Lincoln went on to say: “I fully indorse this,and I adopt it as a text for this discourse. I soadopt it because it furnishes a precise and anagreed starting point for a discussion betweenRepublicans and that wing of the Democracyheaded by Senator Douglas. It simply leavesthe inquiry: ‘What was the understandingthose fathers had of the question mentioned?’”Having adopted Douglas’s Premise, Lincolnproceeded to recount the instances in whichindividual signers of the United StatesConstitution had voted in favor of federallimitations on the expansion of slavery, or hadpublicly endorsed such a limitation. Lincolnestablished that a majority of the “fathers” hadpublicly supported such a limitation. Byadopting Douglas’s premise, and showing thatit led to the opposite of the conclusionDouglas espoused, Lincoln both refutedDouglas’s argument and proved his own.

B. USE OF AUTHORITIES TOSUPPORT A LEGAL ARGUMENT. In adebate against Stephen A. Douglas, AbrahamLincoln said:

There are two ways of establishing aproposition. One is by trying to demonstrateit upon reason, and the other is, to show thatgreat men in former times have thought soand so, and thus to pass it by the weight ofpure authority.390

Lincoln captured an important aspect of legalargumentation–that is the use of authority asa substitute for logically demonstrating apoint. Many legal arguments take as theirstarting point some rule or principle that isauthoritative and needs no justification (i.e.,an Axiom). This is why advocates strive tocome within or fall without the scope of alegal rule, and why lawyers and judgesencounter difficulties with legal reasoningwhen a problem arises that does not clearlyfall within the established scope of any rule.But there are other forms of authority besides

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the constitution, statutes, and past appellateopinions.

1. Invoking the Diety. Many a successfulargument has been predicated on invoking theDiety. The Law of Moses--the TenCommandments–is an unassailable premisefor making a moral argument to certaingroups. Likewise, for many people a biblicalquotation of Jesus of Nazareth or Paul ofTarsus is a rock-solid foundation for a moralor even political argument. Many Christianpreachers build entire sermons around anappeal to the Diety, particularly Protestantpreachers who base their sermons on biblicalpassages that are accepted as Axioms forpurposes of their arguments. Since they arepreaching to believers, both the preacher andthe audience assume the truth of the biblicalpassage as a starting point for the argument. Ifthe Protestant preacher were to address anaudience of atheists, or Buddhists, or Hindus,the audience would first require somevalidation of the Premise of biblical validitybefore they would be persuaded by thereasoning that follows from the Premise.

Appeals to the Diety appear in law, althoughless today than in the past. Blackstone madean appeal to the Diety to support his theory ofnatural law as the foundation for human law.See Section IV. Take Jefferson’s statement inthe Declaration of Independence that “Wehold these truths to be self-evident, that allmen are created equal, that they are endowedby their Creator with certain unalienableRights . . . .” The terms “created” and“endowed by their Creator” are appeals to theDiety. In contrast, “We hold these truths to beself-evident” is a logic-based explanation whyno proof is offered or needed to support theConclusions that Jefferson is proposing.

2. Invoking a Higher Authority. Invokinga higher authority has been a defense inprosecutions of combatants for extraordinarilybad behavior in times of war. The defense of

“Superior Orders” was successfully used in apost-World War I trial by a Germansubmarine captain who sank a British hospitalship, acting on orders provided by a superior.The defense was specifically excluded by theLondon Charter of the International MilitaryTribunal, adopted to govern the trialproceedings of German military and politicalfigures in Nuremburg in 1945, afterGermany’s unconditional surrender at the endof World War II.391

3. Invoking the Founding Fathers. Oncertain issues, particularly of constitutionallaw, advocates and judges will look forsupport in the writings of the leaders of theAmerican Revolution, or proponents of theratification of the U.S. Constitution.Peculiarly, not much attention is paid to JamesMadison’s detailed notes of the debates andcompromises on a day-by-day basis during theconstitutional convention, which becameavailable after his death on July 4, 1836.392

Also, advocates and courts seldom cite thewell-documented debates pro and con at thevarious colonies’ ratification conventions. Thepro-constitution writings of Madison,Hamilton, and Jay, published originally asletters to the editor and later as The FederalistPapers, seem to be given paramountconsideration in such matters. Appellateopinions continue to quote the FoundingFathers on occasion.

a. Lincoln’s Cooper Union Speech.Lincoln’s 1860 Cooper Union speech was atriumph of legal research in determining theFounding Fathers’ views on the power ofCongress to regulate slavery in new states. Hisconclusion: “The sum of the whole is, that ofour thirty-nine fathers who framed the originalConstitution, twenty-one--a clear majority ofthe whole-certainly understood that no properdivision of local from federal authority, norany part of the Constitution, forbade theFederal Government to control slavery in thefederal territories....” Lincoln’s argument was

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an appeal to the Founding Fathers coupledwith an Appeal to the Majority.

b. Lincoln’s Gettysburg Address. AbrahamLincoln began his Gettysburg Address “Fourscore and seven years ago our fathers broughtforth on this continent a new nation,conceived in liberty, and dedicated to theproposition that all men are created equal.”[Emphasis added]. Lincoln conflated theDeclaration of Independence with the U.S.Constitution. The Gettysburg Address wasgiven in 1863, which was 87 years (four scoreand seven years) after the Declaration ofIndependence was signed. The “new nation,”meaning the United States of America,actually started functioning in 1789, only 74years before Lincoln’s speech. It was theDeclaration that confirmed the propositionthat “all men are created equal.” In contrast,the Constitution–without actually using theword--recognized the condition of slavery aspart of the plan of government. For example,persons held in bondage were counted as 3/5of a person for purposes of determining thenumber of Congressmen to be allocated toslave states. The Fugitive Slave clauserequired Free States to return escaped slavesto their owners. The right of states to importslaves was guaranteed through 1808, byArticle I, Section 9 of the U.S. Constitution.Lincoln was not appealing to law in thisfamous quotation. He was appealing to theFounding Fathers.

4. Self-Evident Propositions (Axioms). AnAxiom is a Premise that treated as truewithout proof of its truth. Jefferson’s words inthe Declaration of Independence presented aseries of startling assertions as if they weretoo obvious to require proof. This included theassertion that all men are created equal, andthat all men have the right to life, liberty, andthe opportunity to pursue happiness. Inappellate opinions, we sometimes encounteran Axiom when the court uses words like: “Itis too well-established to need citation that . .

. .” Any legal argument that takes aconstitutional provision, statute, or courtholding, as a given, is using that authority asan Axiom. John Stuart Mill observed thatAxioms are necessary, because if eachPremise required proof of its underlyingPremises, every argument would require “aninfinite series of proof, a chain suspendedfrom nothing.”393

5. Affirmation by the Majority. In thequasi-democratic society we live in, we arequite familiar with the process of resolvingdisputes by majority vote.394 This is(approximately) the way we elect thePresident, this is the way bills become law,and it is the way most other elective officesare filled (excepting those few instanceswhere the election is won by the largestplurality). Outside of politics, many times agroup will not take action unless there is aconsensus on such action is taken. In courtcases, a super-majority is required to reach ajury verdict in a civil case and a unanimousvote is required to reach a verdict convictingsomeone of a crime. Regardless, legaldecisions are often based on the views of themajority, whether that be the majorityreflected by a vote, or by surveys, or byintuition. The argument will be phrased: “amajority of the states do so-an-so,” or “amajority of the courts who have addressed theissue.....”

The same process exists for determining whowins an appellate case that has been acceptedfor review. The winner is determined bymajority vote regarding the proper dispositionof the appeal, without regard to the degree ofconcurrence on the reasons for each Justice’svote. Where an appellate court decides a case,and issues opinions, but no opinion garnersthe support of a majority of the members ofthe court, then the lead opinion is a pluralityopinion, and it is not accorded precedentalweight and does not constitute stare decisis.See Section XXIII.B.7.

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6. The Hierarchy of Legal Authorities.Law is hierarchical, in the sense that rules andprinciples are ranked so that, if they collide,some rules or principles will prevail overother rules and principles. Hierarchicalstructure is reflect in Tex. R. Evid.101(c),which provides the following hierarchyof governance in criminal proceedings:

Hierarchical governance shall be in thefollowing order: the Constitution of theUnited States, those federal statutes thatcontrol states under the supremacy clause,the Constitution of Texas, the Code ofCriminal Procedure and the Penal Code,civil statutes, these rules, and the commonlaw.

In general terms, of legal principles and rulesin the United States, the pre-eminent source oflegal authority to which all other laws aresubordinate is the U.S. Constitution, but onlyin areas where the Constitution applies.Beneath the Constitution are federal statutesand treaties, then federal regulations, thenfederal court pronouncements (which carrythe weight of the authority upon which theyare based, whether that be the Constitution,federal statues, or federal case law). However,constitutions speak in broad terms aboutgeneral principles, and leave much for thelegislature and courts to determine.

Federal law in the United States is supremeonly in areas where preemption of state lawhas occurred. Preemption is limited in someareas, such as the law governing manyproperty rights, contracts, divorce, parent-child issues, and probate, to name a few.Federal law augments and overlaps with statecriminal laws. Special considerations apply tothe question of which parts of the Bill ofRights to the U.S. Constitution apply to thestates. State law has a similar hierarchy, withthe state constitution being superior to statestatutes, which has priority over state courtdecisions (except when the court says that the

statute conflicts with a law superior to thelegislation). Federal court opinionsinterpreting state law have no precedentialeffect in state courts.

Inside the court system, supreme court casesprevail over decisions of intermediate courtsof appeals. Trial court decisions have noweight, other than that they bind the parties tothe law suit through the doctrines of claimpreclusion and issue preclusion.

7. Stare Decisis. Stare decisis is the rule inAnglo-American law that prior decisions of acourt of last resort are binding on subsequentdecisions of courts who are faced with thesame question between different parties. Thisrule of consistency can be simply stated, but itis more complicated in its application.

a. Prior Appellate Decisions. Like all courtsin America, the courts in Texas recognize thedoctrine of stare decisis, or the binding effectof decisions issued by appellate courts. Thedoctrine requires courts to follow the lawpreviously declared and applied by a highercourt. Thus trial courts are bound byintermediate appellate court decisions issuedby the appellate court in whose district theyreside, and by Supreme Court decisions (or incriminal cases the Texas Court of CriminalAppeals decisions). Intermediate appellatecourts are bound only by Supreme Court orCourt of Criminal Appeals decisions, althoughsome intermediate courts consider themselvesbound by earlier decisions issued by thatintermediate appellate court. However, staredecisis only operates when there is sufficientsimilarity between the facts of the earlier caseand the current case. Meyer v. Texas Nat.Bank of Commerce of Houston, 424 S.W.2d417, 420 n. 2 (Tex. 1968) (“The bindingnessof a prior decision under the rule of statedecisis cannot be determined apart from aconsideration of the facts of the case, orperhaps stated more accurately, the factswhich the deciding judges deemed

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important”). Prior cases whose legalprinciples or underlying facts are too differentfrom the case at hand are said to be“distinguishable,” meaning that they do notoperate as precedent for the case at hand.

b. Holding, Dictum and Judicial Dictum.Considering appellate opinions themselves,stare decisis effect is accorded only theholding, together with statements in thecourt’s opinion that are necessary to thatholding, but not obiter dicta. The rationaleannounced by the appellate court in support ofits decision has no precedential weight unlessit is necessary to the holding and is supportedby a majority of the justices sitting in the case.While this point is often lost, the SupremeCourt said so in Marmon v. Mustang Aviation,Inc., 430 S.W.2d 182, 193 n. 1 (Tex. 1968):

The bindingness of a series of holdings of acourt of last resort under the rule of staredecisis is determined by the ‘decision’rather than the opinion or rationale ad-vanced for the decision. 21 C.J.S. Courts §§181, 186, pp. 289, 297. The controllingprinciple of a case is generally determinedby the judgment rendered therein in the lightof the facts which the deciding authoritydeems important. Goodhart, ‘Determiningthe Ratio Decidendi of a Case,’Jurisprudence in Action, p. 191.

You can glean precedent from plurality andconcurring opinions by comparing thedifferent opinions issued in the case to findviews or propositions that are necessary to theholding and are shared by a majority of themembers of the court. Dissenting opinionshave no precedential weight at all. In Texas,unpublished appellate court opinions have noprecedential value. Tex. R. App. P. 47.7. Fora more detailed discussing precedentialweight, see Richard R. Orsinger, The Role ofPrecedent, TEXAS SUPREME COURT MANUAL

ch. 11 (State Bar of Texas 2005).

8. Appeals to History. Appeals to historyare sometimes used to support legalarguments, particularly when interpreting theConstitution. Johnny Cochran, in his closingargument in the O.J. Simpson murder trial,read a quotation from former slave FrederickDouglass to the jury, written he said “shortlyafter the slaves were freed.”395 It is noteworthywho Cochran chose to quote, given theracially-charged atmosphere of that case andthe fact that eight members of the jury wereAfrican-American.

9. Policy Arguments. Beginning early in theTwentieth Century, the U. S. Supreme Courtbegan to discuss the policy implications oftheir decisions in cases as an important factorin reaching their decision. It is nowcommonplace, in difficult cases, to appendpolicy arguments onto legal argument as away of supporting a ruling or a dissent from aruling. While policy is in a sense subordinateto the letter of a statute or the holding of aprior case, since many legal disputes becomeissues of interpreting statutory language ordetermining the ramifications of prior courtrulings, policy can be an important part of alegal argument.

10. Appeals to Statistics. In some instances,the issues in a legal dispute fall in a domainwhere statistics are available to supportarguments in the case. In El Chico Corp. v.Poole, 732 S.W.2d 306, 311 (Tex. 1987),Justice Franklin Spears wrote:

In addressing foreseeability, we know bycommon knowledge that alcohol distortsperception, slows reaction, and impairsmotor skills, while operation of anautomobile requires clear perception, quickreaction, and adept motor skills. Oureveryday use and reliance on the automobileis unquestionable. Also unquestionable isthe tragic relationship between intoxicateddrivers and fatal or injury-producingaccidents. The most recent available

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statistics show that in 1985, there were30,794 total motor vehicle traffic accidentsin Texas involving intoxicated drivers. SeeTEX. DEP'T OF PUBLIC SAFETY, ALOOK AT DWI ... ACCIDENTS,VICTIMS, ARRESTS 1-4 (1985 ed.). Inthose accidents, 989 persons were killed and25,461 were injured. The 1985 figuresrepresent a 6% decrease over 1984, due inpart to society's increased awareness of thedanger of drunk driving and an increase in“driving while intoxicated” arrests. Id. Therisk and likelihood of injury from servingalcohol to an intoxicated person whom thelicensee knows will probably drive a car isas readily foreseen as injury resulting fromsetting loose a live rattlesnake in a shoppingmall.

Reasoning from statistics is discussed abovein connection with Inductive Reasoning. SeeSection XIII.C.4 & 5. Statistical Fallacies arediscussed in Section VIII.F.9.

C. LEGAL “COMMONPLACES” TO USEIN LEGAL ARGUMENTS. There are manyCommonplaces that can be used in legalarguments. Some important legalCommonplaces are discussed below.

1. Failure to Contest and Concession.When a disputant fails to contest a point, itmay be taken as conceded, but that is notalways the case. For example, under Tex. R.Civ. P. 239, the failure of a defendant totimely file an answer on appearance dayallows the plaintiff to take a default judgment.However, under Rule 243, in a case withunliquidated damages, only liability isconceded by the failure to answer, not theamount of unliquidated damages. UnderTRAP 38.8(a)(3), if the appellant fails to filea brief but the appellee does, the appellatecourt can rely on appellee’s brief as correctlypresenting the case and may rule withoutexamining the appellate record. In Strackbeinv. Prewitt, 671 S.W.2d 37, 39-40 (Tex. 1984),

the Supreme Court held that the failure tocontest affidavits, attached to a motion fornew trial explaining why an answer was nottimely filed before a default judgment, meantthat there was no factual dispute and themovant need only make a prima facie showingof no conscious indifference.

Where a point is conceded by a disputant, it istaken as conclusively established and nolonger needs to be proved. Appellate courts,particularly Supreme Courts, in oral argumentwill sometimes try to get the oral advocate toconcede some point that will narrow thedispute or sometimes even undermine theadvocate’s position. In preparing for oralargument, it is important to evaluate theweaknesses in an argument and to decide, inadvance, what to concede and when toconcede it. In making concessions the lawyermust realize that his role is to advocate, notjudge. However, refusing to make reasonableconcessions can call the advocate’s sincerityand credibility (Ethos) into question, therebyweakening other, more convincing arguments.

2. Acquiescence. Acquiescence is tacit orpassive assent or agreement to something.There are instances where acquiescencecomes to play in legal disputes. This occurswith adverse possession of land, acceptinglate performance of a legal obligation, andlaches.

3. Waiver. “Waiver” has been defined as theintentional relinquishment of a known right.Ulico Casualty Co. v. Allied PilotsAssociation, 262 S.W.3d 773 (Tex. 2008).However, there is a distinction between thepurposeful waiver defined above, andinadvertent waiver that is by its natureunintentional. A person can inadvertentlywaive legal rights in a variety of ways. Theinequity of a criminal defendant unknowinglywaiving procedural safeguards was thedriving force behind the Conclusion that theSixth Amendment guaranteed a criminal

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defendant the right to appointed counsel,announced for federal prosecutions inJohnson v. Zerbst, 304 U.S. 458, 457 (1938)and extended to state prosecutions in Gideonv. Wainwright, 372 U.S. 335 (1963). Waiveris an ever-present concern for appellatelawyers, who may be unable to raise validarguments on appeal because the right to raisethe complaint was not preserved in the trialcourt. Tex. R. Evid. 103(a)(1) (error may notbe predicated on evidentiary ruling without“timely objection . . . stating the specificground of objection”); Tex. R. App. P. 33.1(“[a]s a prerequisite to present a complaint forappellate review, the record must show” atimely and specific complaint that wasoverruled by the trial judge).

4. Action vs. Inaction. Most legal disputesinvolve an act that is illegal or is actionable.However, certain failures to act can becriminal or actionable, as well. The TexasPenal Code criminalizes certain types of“conduct,” which includes an act or anomission, but an omission counts only whenthe person has a duty to act. Tex. Penal Code§§ 6.01(a), 1.07(10). In some instances aperson can be held criminally responsible foractions he did not commit, or for failing tostop another from acting. See Tex. Penal Code§ 7.02 (criminal responsibility for conduct ofanother). Houstonians in their sixties willremember the trial of Dr. John Hill, accusedof murdering his wife Joan Robinson Hill bywithholding medication. His jury hung, but hewas later murdered (just desserts?).

5. Mental State. The mental state of aperson can be an important determiner of theoutcome of a legal dispute.

a. Culpability in Criminal Law. Under theTexas Penal Code, a person can be convictedonly if he acts (or fails to act when legallyobligated to do so) if he has one of fourculpable mental states: intentional, knowing,reckless, or criminal negligence. Tex. Penal

Code § 6.02(d). Intent requires a consciousobjective or desire to engage in the conduct orcause the result. Tex. Penal Code § 6.03(a).Knowing requires an awareness that theconduct is reasonably certain to cause theresult. Id. § 6.03(b). Reckless meansawareness but conscious disregard of asubstantial and unjustifiable risk thatconstitutes a gross deviation from the standardof care of an ordinary person under all thecircumstances viewed from the actor’sviewpoint. Id. § 6.03(c). Criminal negligenceis the failure to perceive a substantial andunjustified risk that constitutes a grossdeviation from the standard of care that anordinary person would exercise under all thecircumstances as viewed from the actor’sstandpoint. Id. § 6.03(d). If a person provesthat he committed the offense under duress,meaning he was compelled to act “by threat ofimminent death or serious bodily injury tohimself or another,” then he is not guilty ofthe offense. Tex. Penal Code § 8.05.

b. Culpability in Tort Law. TheRESTATEMENT (SECOND) OF THE LAW OF

TORTS (1965) distinguishes between tortiousbehavior that is intentional, negligent, andreckless. See Restatement § 500, Comment f(intent v. reckless) and Comment g (recklessvs. negligent). Intent is defined in § 8A (“theactor desires to cause consequences of his act,or that he believes that the consequences aresubstantially certain to result from it”).Reckless is defined in § 500 (“knowing orhaving reason to know of facts which wouldlead a reasonable man to realize, not only thathis conduct creates an unreasonable risk ofphysical harm to another, but also that suchrisk is substantially greater than that which isnecessary to make his conduct negligent”).Negligence is defined in § 282 (“conductwhich falls below the standard established bylaw for the protection of others againstunreasonable risk of harm”). In Louisi-ana-Pacific Corp. v. Andrade, 19 S.W.3d 245,246-47 (Tex. 1999), the Texas Supreme Court

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distinguished negligence and gross negligencein this manner: “what separates ordinarynegligence from gross negligence is thedefendant's state of mind; in other words, theplaintiff must show that the defendant knewabout the peril, but his acts or omissionsdemonstrate that he did not care.”

c. Mental Competency. Mental competencyto testify is governed by Tex. R. Evid. 601.Everyone is competent to testify except forinsane persons and children who do notpossess sufficient intellect to relate thetransactions in question. Mental incompetencyfor purposes of commitment into state custodyrequires proof that the person is sufferingfrom a mental illness and that hospitalizationis necessary for the protection of the personhimself or for the protection of others.396

Insanity can also affect whether the state canprosecute a person accused of a crime, and issometimes a defense to prosecution. Tex.Penal Code § 8.01 (“at time of conductcharged, the actor, as a result of severe mentaldisease or defect, did not know that hisconduct was wrong”). Texas law recognizes“temporary insanity caused by intoxication”as a factor in punishment, but not as adefense. The state cannot prosecute a personwho was less than 15 years of age at the timeof the crime, except for perjury, vehicularviolations, misdemeanors subject to fine only,and certain felonies. Tex. Penal Code § 8.07.The death penalty cannot be assessed if theactor was under age 18 when the offense wascommitted. Texas Penal Code § 8.04. TheU.S. Bill of Rights prohibits the execution ofa person who is mentally retarded. Atkins v.Virginia, 536 U.S. 304, 311 (2002).

6. Subjective Vs. Objective Points-of-View. In law, a subjective point-of-view is thepoint-of-view of the individual under scrutinyat the relevant point-in-time. An objectivepoint-of-view is the point-of-view of areasonable person who is hypothetically

placed in the same situation as the individualunder scrutiny at the relevant point-in-time.

Evaluating a situation subjectively requires aninquiry into the actual awareness of theindividual at the relevant point-in-time, whichin law is ordinarily an issue of fact to bedetermined by the finder of fact. Sinceappellate courts do not engage in fact-finding,appellate review of subjective determinationsis limited to sufficiency of the evidencereview.

In contrast, an objective point-of-view is anabstract evaluation, divorced from the actualawareness of a particular individual. Becausethe “objective” determination is not based onthe actual awareness of a particular individual,it is not a factual determination, and so ismore appropriate to analysis by an appellatecourt.

There are examples throughout the law; threeexamples are discussed below.

a. Negligence. In Texas, “negligence” meansfailure to use ordinary care, that is, failing todo that which a person of ordinary prudencewould have done under the same or similarcircumstances or doing that which a person ofordinary prudence would not have done underthe same or similar circumstances. “Ordinarycare” means that degree of care that would beused by a person of ordinary prudence underthe same or similar circumstances. Thedefinition of “ordinary care” is redundant tothe definition of “negligence.” But bothdefinitions involved objective standards,requiring the fact finder to imagine anabstraction, the “person of ordinary pru-dence,” and to imagine how such a personwould have acted in the same or similarcircumstances. So the standard of negligenceis unrelated to the defendant’s actual state-of-mind.

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b. Gross Negligence. Under Burke RoyaltyCo. v. Walls, 616 S.W.2d 911, 922 (Tex.1981), the essential feature of grossnegligence was the mental attitude of thedefendant--the defendant must know about theperil, while his acts or omissions show that hedid not care. This was a subjective standard.In Transportation Ins. Co. v. Moriel, 879S.W.2d 10, 23 (Tex. 1994), a seven-to-twomajority of the Supreme Court held that grossnegligence would henceforth require proof oftwo components: (1) viewed objectively fromthe actor's standpoint, the act or omissioncomplained of must involve an extremedegree of risk, considering the probability andmagnitude of the potential harm to others; and(2) the actor must have actual, subjectiveawareness of the risk involved, butnevertheless proceed in conscious indifferenceto the rights, safety, or welfare of others.Because the two grounds are conjunctivelyjoined, both must exist to find grossnegligence. The Court thus engrafted anobjective standard onto the former subjective-only standard for gross negligence, with theresult that findings of gross negligence couldbe reversed based on an objective standardthat was more susceptible to appellate reviewthan the subjective standard. The Legislaturehas codified the objective and subjectivestandards for gross negligence, in Tex. Civ.Prac. & Rem. Code § 41.001(11).

c. Recusal. Another example of subjectiveversus objective points-of-view relates to thegrounds for recusal of Texas judges. UnderTex. R. Civ. P. 18b(2), a trial judge mustrecuse himself/herself in instances, amongothers: (a) if his impartiality mightreasonably be questioned; or (b) if he has apersonal bias or prejudice concerning thesubject matter or a party, or personalknowledge of disputed evidentiary factsconcerning the proceeding. The first ground isan objective standard, viewed from theperspective of a third person. The secondground is a subjective standard, having to do

with the mental processes and emotions of thejudge in question. See Caperton v. A.T.Massey Coal Co., 129 S.Ct. 2252 (2009),where the U.S. Supreme Court side-steppedthe subjective test for recusal applied by alower court justice and and held, instead, thatunder an objective test the Due Process ofLaw required the lower court justice to recusehimself from the case.

7. Legal Duty. A legal duty is an obligationowed by one person to another person, as anindividual or owner of a thing. Legal dutiesoften arise in the context of liability suits fordamages, but legal duties exist betweenfamily members, the individual and thegovernment, and in many other significantrelationships. Legal duties can issue from anyaspect of government, from the Constitutionon down to the raised hand of a traffic cop ona city street. Statutes create duties, andexceptions as well. Courts created duties,when deciding cases. In the tort system inAmerica, there is a long-standing conflictbetween two different visions of legal duty:should judges decide the existence and extentof legal duties in their rulings on motions andin the instructions and questions submitted tojuries; or should juries determine the existenceand extent of duties in answering factualquestions like liability, causation, anddamages? The judge-versus jury questionaffects the power of appellate courts, becauselower court decisions on “the law” are moresusceptible to appellate review than arejurors’ decisions on “the facts.”

The Texas Supreme Court has said that “[t]hedefinition of a legal duty is an issue for thecourt involving questions of legal policy.”397

The Court has characterized the process ofdetermining common-law duty as “balancingthe risk, forseeability, and likelihood of injuryagainst the social utility of the actor's conduct,the magnitude of the burden of guardingagainst the injury, and the consequences ofplacing the burden on the defendant.”398 Legal

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duty is a powerful Commonplace where thelaw applicable to a legal dispute is not clearlyestablished by a statute or case law precedent.

8. Causation. Causation has been a matter ofdeep concern for philosophers as long ashuman thoughts have been recorded. A causeis something that precedes and brings aboutan effect or a result. The legal system mustdeal with causation in a practical way, and ithas developed special concepts of causation.

< First Cause – “First cause” is aphilosophical concept of the uncreated orself-created cause to which all other of causesmust ultimately be traced. The first cause isthe stopping point of the infinite regression ofcausation.

< Sufficient Cause – A “sufficient cause” is acause that, if it occurs, guarantees that theresult follows; however, the existence of theresult does not guarantee the existence of thethat cause. Stated differently: if X is asufficient cause of Y, then the presence of Xnecessarily implies the presence of Y.However, the existence of Y does notguarantee the presence of X, because anothercause, Z, may be the cause of Y.

< Necessary Cause – A “necessary cause” isone that must be present for the effect tooccur, but where the presence of the necessarycause does not necessitate the effect. If X isthe necessary cause of Y, then the presence ofY necessarily implies the presence of X. Thepresence of X, however, does not imply that Ywill occur.

< Contributing Cause – A "contributingcause" is a cause that is not a necessary orsufficient cause, but does contribute to theeffect in question. To be contributory, a causecannot, acting alone, bring about the result. Acontributing cause must precede the effect,and altering the contributing cause must alterthe effect.

< Direct Cause – For a cause to be direct,there must be no known variable interveningbetween the cause and the effect.

< Legal Cause – “Legal cause” is a cause thattriggers some recognition by the legal system,for example liability for damages or criminalliability. There are policy reasons why the lawmay not recognize something as a legal causewhen is was an actual cause. "At some pointin the causal chain, the defendant's conduct orproduct may be too remotely connected withthe plaintiff's injury to constitute legalcausation." Union Pump Co. v. Allbritton, 898S.W.2d 773, 775 (Tex. 1995).

< "But For" Cause – “But for” causation existswhen the event in question could not haveoccurred without the act or omission inquestion occurring first. The test is acounterfactual Conditional: “If X had nothappened, would Y have happened?” “Butfor” causation is another way of saying“necessary cause.”

< Criminal Cause – Causation for criminalpurposes is defined in Texas Penal Code§ 6.04(a):

A person is criminally responsible if theresult would not have occurred but for hisconduct, operating either alone orconcurrently with another cause, unless theconcurrent cause was clearly sufficient toproduce the result and the conduct of theactor clearly insufficient.

This requires that the act or omission be a“but for” cause. However, it is not necessaryfor the act or omission standing alone to be asufficient cause, as long as it is sufficient incombination with another cause, unless thatother cause is sufficient standing alone andthe actor’s action standing alone is not.

< Cause-in-Fact – “Cause in fact means thatthe act or omission was a substantial factor in

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bringing about the injury and without whichno harm would have occurred.” McClure v.Allied Stores of Texas, Inc., 608 S.W.2d 901,903 (Tex. 1980). This concept of causationinvolves two component parts: subtantialfactor and “but for” causation.

< Proximate Cause – “Proximate cause” is aconcept used in negligence cases. Proximatecause incorporates two elements: cause-in-factand foreseeability. Southwest Key Program,Inc. v. Gil-Perez, 81 S.W.3d 269, 274 (Tex.2002). The test for foreseeability is whether aperson of ordinary intelligence would haveanticipated the danger his or her negligencecreates. Id. at 274.

< Independent Intervening Cause – An“independent intervening cause” is a separateact or omission that breaks the directconnection between the defendant’s actionsand an injury or loss to another person. Thiscause may relieve the defendant of liabilityfor the injury or loss

< Good Cause – “Good cause” is a legallysufficient reason. Good cause is often theburden placed upon a litigant ... to show whya request should be granted or an actionexcused.399

< Probable Cause – “Probable cause” is alegal standard used in criminal cases.Probable cause is required before agovernment official may search a person orhis property. In this sense, probable cause isinformation sufficient to warrant a prudentperson's belief that a search would revealevidence of a crime or contraband. Probablecause is also required before the governmentmay arrest and initiate criminal proceedingsagainst a person. In this sense, probable causemeans a reasonable belief that a person hascommitted a crime.

Causation is not a Logic concept. In ahypothetical proposition the Antecedent is the

"reason" for the Consequent, and not the"cause" of the Consequent. To say that "P isthe reason for Q" is a matter of Logic; to saythat "P is the cause of Q" is a matter ofscience, or law.

9. Res Judicata Vs. Stare Decisis. In Texas,the doctrine of res judicata prohibits a partyfrom litigating, in a later law suit, “not onlyon matters actually litigated, but also oncauses of action or defenses which arise out ofthe same subject matter and which might havebeen litigated in the first suit.” Getty Oil Co.v. Insurance Co. of North America, 845S.W.2d 794, 798 (Tex. 1992). In contrast, theSupreme Court said in Lubbock County v.Trammel's Lubbock Bail Bonds, 80 S.W.3d580, 585 (Tex. 2002), that “the doctrine ofstare decisis dictates that once the SupremeCourt announces a proposition of law, thedecision is considered binding precedent. . . .However, circumstances occasionally dictatereevaluating and modifying prior decisions.This Court may modify judicially createddoctrines . . . .” Stare decisis is the reason whyindividuals, companies, trade organizations,and interest groups file amicus curiae briefs incases to which they are not a party. Thirdparties are not bound by res judicata to theoutcome of the case, but they may be boundby the ruling in the case as a result of thedoctrine of stare decisis.

10. The Principle of Parsimony. In sciencethere is a widely-shared preference forfavoring the simplest explanation of aphenomenon over more complicated ones.400

In philosophy, the least complex argument isthe preferred one. In reasoning, when anoutcome can be justified by a narrower rule ora broader one, there is a preference to use thenarrower one. In law, there is a rule ofinterpretation that, if two statements in awriting cannot be reconciled, the specificstatement prevails over the general statement.The rule applies both to statutes and tocontracts. Nelson v. Texas Employment

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Comm'n, 290 S.W.2d 708, 711 (Tex. Civ.App.--Galveston 1956, writ ref'd) (statute);Sefzick v. Mady Dev., L .P., 231 S.W.3d 456,461 (Tex. App.--Dallas 2007, no pet.)(contract). The rationale was explained in SamBassett Lumber Co. v. City of Houston, 198S.W.2d 879, 881 (Tex. 1947):

[W]hen the law makes a generalprovision, apparently for all cases, and aspecial provision for a particular class, thegeneral must yield to the special in so faras the particular class is concerned. Thisrule is based upon the principle that allacts and parts thereof must stand, ifpossible, each occupying its proper place,and that the intention of the Legislature ismore clearly reflected by a particularstatute than by a general one. Accordinglya specific act is properly regarded as anexception to, or qualification of, a generallaw on the same subject previouslyenacted. In such a case both statutes arepermitted to stand, the general one beingapplicable to all cases except theparticular one embraced in the specificact.

The rule, that in deciding cases constitutionalquestions are avoided if a non-constitutionalbasis for the decision is available, is anexpression of the principle of parsimony.

11. Escaping a General Rule. If youradversary invokes a rule that works to yourclient’s disadvantage, you can try to defeat therule, and if that is not possible, then try toundercut it (weaken it) to the point that someother rule (that is more favorable to yourclient) is applied instead. In some situations,the best approach is to show that the facts ofthe case do not trigger the rule. Alternatively,you can find legal reasons why the rule doesnot apply. These arguments include waiver ofthe rule, as well as the failure to meetprocedural requirements that are preconditionsto asserting the rule. Sometimes you can find

a superior rule that would block the adverserule; examples would be federal preemption,conflict of laws principles, or contractualterms that supplant or modify the adverse rule.To confront the rule head-on, you can argueexceptions to the rule, to establish that the ruledoes not apply to your case. Failing that, youcan attack your opponent’s interpretation ofthe rule, by showing that vagueness orambiguity in the language of the rule makesits application uncertain given the facts of thecase, or by denying that definitions and otherterms in the rule mean what your opponentcontends they mean. You can also invokepolicy arguments or appeals to equity that thecourt should not apply the rule to your client,or should modify the rule enough to allowyour client to escape the rule, or shouldoverturn the rule. The following recent case demonstrates thedifficulties that can arise from applying a rulethat has exceptions that are vague enough toleave broad opportunities to escape the rule.In the case of In re ADM Investor ServicesInc., 304 S.W.3d 371 (Tex. 2010), theSupreme Court stated that a forum-selectionclause is enforceable unless the partyopposing enforcement of the clause canclearly show that (1) enforcement would beunreasonable or unjust, (2) the clause isinvalid for reasons of fraud or overreaching,(3) enforcement would contravene a strongpublic policy of the forum where the suit wasbrought, or (4) the selected forum would beseriously inconvenient for trial. The Courtstated the general rule and four exceptions.Justice Willett called for the Court, in the nextcase, to specify the parameters of “seriouslyinconvenient” and “unreasonable or unjust”when a party is alleging a medical hardship asgrounds to escape a forum selection clause.Id. at 377.

The following principles can serve to win byavoiding the merits of a dispute: waiver,estoppel, standing, ripeness, case or

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controversy (no advisory opinions), politicalquestion, and religious question.

12. Definitions. Definitions are symbols,words, or phrases used to define a symbol,word, or phrase in more familiar terms. Thereare five types of definitions: lexical ordescriptive definitions (a dictionary definition,which explains how a word is actuallyused);401 stipulative definitions (given by awriter or speaker to establish a specialmeaning for purposes of that document orspeech);402 persuasive definitions (designed toinfluence a person’s attitude or feelingstowards the subject matter);403 precisingdefinitions (removes vagueness by giving amore precise description);404 and theoreticaldefinitions (suggesting how a concept can andshould be viewed in all circumstances).405

Some legal arguments involve a fight overstipulative definitions that are reallypersuasive definitions in disguise, for examplewhere the definition determines whethercertain parties do or do not fall within thescope of the statute, rule of law, or contractterm, that uses the defined word.

13. C o n v e r t i n g L i m i t a t i o n s o nGovernmental Power to Rights ofIndividuals. The main body of the AmericanConstitution gives the central governmentcertain powers, denies it other powers, andleaves other typical governmental powersunmentioned. The Bill of Rights limits thepowers of the central government, sometimesby imposing limits, and sometimes byrecognizing rights in individuals and thestates. Over time, there has been a generalshift in perspective, from the view thatindividuals are autonomous and should be freefrom governmental control except in certainareas of life, to the view that individuals haverights and that one function of government isto intervene in the lives of its citizens to besure that those rights are met. These twoperspectives were contrasted in the last seriesof presidential debates, when a citizen in a

“town hall” format debate asked bothcandidates whether people had a right tohealth insurance coverage. One candidate said“no,” the other “yes.” Neither candidatementioned the legal basis for his view. Inkeeping with the times, legal situations canarise where a prohibition reflects a right.

14. Using Supporting Rationales to Limitthe Rule. Oftentimes a principle of law willbe announced, together with a supportingrationale. An example is the SecondAmendment to the U.S. Constitution, whichreads:

A well regulated Militia, being necessary tothe security of a free State, the right of thepeople to keep and bear Arms, shall not beinfringed.

The form of the statement is an Enthymeme,where a Conclusion is stated together with itsPremise. The right to keep and bear arms isstated in unqualified terms. However, becausethis otherwise unqualified statement includesits rationale, some have interpreted the rule tobe limited to its rationale, i.e.: only personsacting as part of a well regulated Militia areentitled to keep and bear arms. This reflectsthe risk that including an explanation of therationale for a law in the statement of the lawmay later be seen as a limitation on the rule oflaw.

The same thing can happen with statements ofintent, which are particularly popular asintroductory terms in contracts. Thesestatements of intent can be used to resolvevagueness or ambiguity in the contract terms,but they can also be used to argue for broaderor narrower applications of the operativecontract terms. And yet draftsmen tend tofocus less on general statements of intent atthe beginning of the contract and more on thespecific obligations in the operative part of thecontract.

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15. Appeal to Consistency. One of thefundamental underpinnings of law isconsistency, meaning that the norms by whichbehavior will be judged are stable and thusmay be relied upon in taking actions andplanning the future. The principle of staredecisis is largely attributable to this need forconsistency. An appeal to consistency istherefore a powerful legal argument when youwant to have your case treated in the sameway that similar cases have been treated in thepast.

16. Appeal to Fairness. One of the oldesttenets of law in a free society is the idea ofequal justice under the law. That is the“motto” engraved above the entrance to theUnited States Supreme Court. It is the sourceof Jefferson’s assertion that ‘all men arecreated equal.” It is embodied in the EqualProtection Clause of the FourteenthAmendment. It was an argument that JohnnyCochran made to the jury in the O.J. Simpsonmurder trial.406 Equal justice under the law hasa wonderful historical pedigree, dating back toThucydides’ HISTORY OF THE PELOPONNE-SIAN WAR, where he related a funeral orationby Pericles, the political leader of Athens, in430 B.C.:

Our constitution does not copy the laws ofneighbouring states; we are rather a patternto others than imitators ourselves. Itsadministration favours the many instead ofthe few; this is why it is called a democracy.If we look to the laws, they afford equaljustice to all in their private differences; ifno social standing, advancement in publiclife falls to reputation for capacity, classconsiderations not being allowed to interferewith merit; nor again does poverty bar theway, if a man is able to serve the state, he isnot hindered by the obscurity of hiscondition.407

17. Appeal to Majority. “Majority rule” is aprevailing tenet of group action in our culture.

See Section XXIII.B.5. Showing that aposition has been adopted by a majority ofjurisdictions is considered as justification foradopting a position. For example, in El ChicoCorp. v. Poole, 732 S.W.2d 306, 310 (Tex.1987), the Texas Supreme Court decided toimpose tort liability on commercial purveyorsof alcoholic beverages when a drunk patrondrives away and causes injury. JusticeFranklin Spears wrote:

Of fifty American jurisdictions (includingthe District of Columbia and excludingTexas), twenty-nine recognize a commonlaw cause of action against an alcoholicbeverage purveyor for injuries caused by anintoxicated customer.FN1 Additionally,nineteen state legislatures have enacted civildramshop liability,FN2 seven of which alsohave recognized a complementary andsupplemental common law cause ofaction.FN3 In total, a civil cause of actionexists in forty-one jurisdictions with asubstantial majority basing the cause ofaction upon the common law principles ofnegligence, negligence per se, or both.Focusing on the carnage inflicted uponinnocent victims by drunk drivers, courtshave rejected the rationale supporting noliability as outdated and unrealistic and thusinvalid. Injury to a third person is no longerunforeseeable in an age when death anddestruction occasioned by drunk driving isso tragically frequent.

18. Invoking Trends. If a court is required toextend existing law or create new law toresolve a legal dispute, a simple determinationof a majority rule is often not satisfactorybecause new rules replace old rules veryslowly. In these situations, courts andadvocates often look to see whether there is atrend reflected in recent decisions of otherjurisdictions. Fifty-state surveys can be usedfor this purpose.

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D. A D A P T I N G R H E T O R I C A LC O N C E P T S T O L E G A LARGUMENTATION. There are many moreconcepts of Rhetoric than there areopportunities to use them in legalargumentation. More generally, it is useful toremember that Enthymemes are truncatedSyllogisms, and that Enthymemes can be usedin deductive-type arguments where theconclusion is only possible or probable, andnot certain. Another equally important aspectof Enthymemes comes from Aristotle’s studyof Rhetoric. Recall that Aristotle observedthat effective speakers would adopt as thePremises of their Arguments propositions thatthe audience would naturally agree with,either intellectually or emotionally, whichAristotle called “Commonplaces.” Law andlife abound with potential Commonplaces.There is a host of legal Commonplaces--that-is, legal concepts and procedures--that can beused as Premises in a legal Argument. Thenthere are religious, historical, cultural,geographical, race-based, gender-based, class-based, and age-based Commonplaces, allavailable to use in legal arguments. Tworhetorical arguments used frequently in legalarguments are discussed below.

1. Reductio Ad Absurdum. In Logic,Reductio ad Absurdum is a form of indirectproof where an Argument is proved Sound bynegating the Premise and showing that thenegated Premise leads to a logicalcontradiction. In the bivalent world of FormalLogic, disproving the negative of the Premiseproves that the Premise is true. In normalargument, as opposed to Formal Logic,Reductio is more often used by an advocate torefute the opponent’s Argument, by taking theopponent’s Argument and applying it todifferent Premises that lead to an absurd orundesirable result. This shows that theArgument is untenable. Used in this way theArgument is called “Reductio ad Incommo-dum,” or reduction to an implausibility oranomoly.408 One instance of this type of

Reductio technique is the Straw Man Fallacy,where the changed Premise does not fairlyrepresent the opponent’s case. A Reductioattack, when used in a legal argument, isbased on the tacit assumption that for theopponent’s rule or Warrant (to use InformalLogic terminology) to be used in the presentcase, then consistency requires that it be usedin all cases. The answer to this is that any ruleor Warrant can have exceptions that avoidsthe extreme cases. A Reductio ad Absurdumcan be imbedded in a question. Example: Ina political speech, Abraham Lincoln answeredthe accusation that he was two-faced byasking the audience "If I were two-faced,would I be wearing this one?" This is a formof Reductio ad Absurdum, in which Lincolnassumed his opponent’s Premise and showedthat it led to an absurdity.

Example: in a presidential debate on October13, 1988, the moderator, Bernard Shaw, askedCandidate Michael Dukakis, "Governor, ifKitty Dukakis were raped and murdered,would you favor an irrevocable death penaltyfor the killer?" Dukakis replied, "No, I don't,and I think you know that I've opposed thedeath penalty during all of my life", and wenton to explain his stance.409

A somewhat facetious but nonethelessfrequent form of Reductio is called “Reductioad Hitlerum.” This describes a discourse inwhich, at some point, one disputant willattempt to discredit the argument of anotherby drawing a parallel between the opponent’sposition and a view or policy held by theGerman Nazi party in the 1930s and 1940s.This is really an ad Hominem attack, butpopular usage treats it as a Reductioargument.

2. Using the Extreme to Reach the Middle.Argument to Moderation is the name of theFallacy of accepting an argument because itlies between two competing positions. SeeSection XV.18. It is a common practice in

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negotiations and litigation to ask for morethan you want in hopes that you will end up ata mid-point, between the parties’ two extremepositions, that your client finds satisfactory.The thinking is that if you make a reasonabledemand, and your opponent makes anunreasonable demand, that you will end upsomewhere between the middle and youropponent’s extreme. Therefore there is somerisk in advocating a reasonable position whenyour opponent advocates an unreasonable one.

XXIV. REFRAMING. A mental frameworkis a conceptual structure that we impose on asituation. Lawyering and judging operate onmental frameworks that by training and habitwe impose on disputes. In litigation, theplaintiff establishes the original frame byfiling a claim detailing certain actions orinactions and asserting causes of action. Thedefendant may accept the plaintiff’s framing,or the defendant may try to reframe the case ina different way, where the facts or the lawwork to better advantage. The appellatelawyer receives the case as it was framed bythe trial lawyers and trial judge. That framingmay be inescapable, or it may be mostadvantageous to the client. But in someinstances the client will do better on appeal ifthe contest is reframed. Appellate judges facethe same issue, faced with a frame establishedby the trial lawyers and judges or by theappellate lawyers. The appellate judges maywant to consider reframing the case anddisposing of it based on the principles thatapply in the reframed conception of the case.This was done in Katz v. United States,involving incriminatory information gatheredby the government by attaching an electroniclistening device to the outside of a telephonebooth. Justice Potter Stewart, writing for theCourt, said:

Because of the misleading way the issueshave been formulated, the parties haveattached great significance to thecharacterization of the telephone booth from

which the petitioner placed his calls. Thepetitioner has strenuously argued that thebooth was a ‘constitutionally protectedarea.’ The Government has maintained withequal vigor that it was not.FN8 But thiseffort to decide whether or not a given‘area,’ viewed in the abstract, is‘constitutionally protected’ deflectsattention from the problem presented by thiscase.FN9 For the Fourth Amendmentprotects people, not places.410

XXV. A SYNTHESIS OF THECONCEPTS DISCUSSED IN THISARTICLE. This Section attempts tosynthesize the principles of Logic, Rhetoric,reasoning, and argumentation discussed in thisArticle.

A. CONSTRUCTING ARGUMENTS.Remember what the psychologists say aboutthe two types of reasoning (see Section III),that is, the intellect versus feelings andexperience. Try to construct an argument thatappeals to both the conscious, deliberative,and analytical part of the audience as well asthe part that is intuitive, automatic, natural,non-verbal, narrative, categorical, andexperiential.

1. Preserve the Right to Argue. There is noopportunity to argue unless you preserve theright to argument. In appellate practice, thatmeans preservation of error in the trial court.

2. Assemble the Facts. For the advocate, thedesired conclusion is known from the start.For the judge, the desired conclusion shouldcome toward the end of the process. In eitherevent, it is best to assemble the facts first,although having an eye on the conclusion orpossible conclusions can affect which factsare sought and which facts are used in theargument.

3. Frame (or Reframe) the Problem. Onappeal, regardless whether the client won or

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lost in the trial court, the advocate shouldevaluate the case to see if it was framed by thetrial lawyers and trial judge in the way that ismost advantageous to your client on appeal. Ifyour client lost in the trial court, you may beable to reframe the case in the appellate courtand win there. If your client won, but thevictory is vulnerable to reversible, then try toreframe the case into a more favorableposture. For the appellate judge, reframing thecase appropriately may mark the way to theultimate disposition of the case. A case shouldnot be reversed because it was framed wrong-ly; it should be reversed only if it reached thewrong result.

4. Determine Possible Then PreferableArguments. Arguments work from Premisesto Conclusions. In creating an Argument, youmay need to start with the Conclusion youwant in order to determine the Premises youneed, but once the Premises are identified, thenormal Argument asserts and then proves thePremises, and then shows how those Premiseslead to the Conclusion. The Premises must beproven, or assumed for purposes of theArgument. Then the Argument is presented,consisting of deductions, or inductions, oranalogies, or Enthymemes, or emotionalappeals, or any combination of these. If thePremises are true (or probable), and theArgument Valid (or acceptable to theaudience), then the Conclusion should follow.In constructing an Argument, it is helpful todetermine whether the Logic is Deductive,Inductive, or Analogical. If Deductive,attention should be paid to whether thePremises and the Conclusion can be provenwith certainty. If not, then the Argumentshould be formulated as Enthymemes, with aConclusion that is highly-likely, or at leastmore probable than not. If the Argument isInductive, then attention should be paid to thenumber and representativeness of theinstances that are used to support theConclusion. If the proof is Analogical, thenattention should be paid to the number and

relevance of similarities between the Sourceand the Target, and any dissimilarities thatmight be used to attack the analogy. Indirectproof involves stating your Premises clearly,then assuming that your Premises are false,and using an Argument to show that the falsePremises lead to a logical contradiction orabsurd consequence, which thus indirectlysupport the idea that, if your Argument isValid, then your Premises must be true. Anindirect argument will not be effective if it istoo complex.

In Informal Logic you would identify yourClaims (properly Qualified), Data, andWarrants. You would find the backing foryour Warrants. You would identify andprepare for Rebuttals.

5. Identify Commonplaces to Use in theArgument. The principles of Rhetoric suggestthat Arguments are best constructed usingCommonplaces. You would identify themesthat the audience will intuitively accept andmake them your Premises or part of yourArgument. Examples abound, but the poorguy litigating against the rich corporationmight use a David-and-Goliath theme. Acriminal defendant who is a member of aracial minority might reframe a prosecutionfrom an issue of guilt-or-innocence to an issueof racial bias versus fairness, or the use oftainted evidence, as O.J. Simpson’s attorneysdid in his murder trial.

6. Select Rhetorical Tools. Attend to Ethos,Pathos, and Logos. Someone constructing anargument might lay out the rhetorical tools inadvance of constructing an argument like asurgeon might lay out a scalpel, clamps, andsponges in advance of the operation. Somerhetorical tools operate at the general level,like the Five Canons of Rhetoric. Otherrhetorical tools are specific, like vividexamples, juxtaposition, contrast, climax,emphasis, etc. Tools must be picked to fit theoccasion, and also to fit the style of the

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advocate, and also to fit the temperament ofthe audience. Rhetorical items could includeanalogies that simplify or clarify the issues.Analogies are also a way to introduceemotional elements into the process.

B. TESTING ARGUMENTS. A goodargument wins only when it is not refuted. Sopart of constructing a winning argument is toanticipate counter-arguments. This allows youto construct your argument in a way that willprotect weaknesses in your position. Reviseyour argument to eliminate the weaknesses,and if that is not possible, then construct yourargument to contain the damage that might becaused by the counter-arguments.

Psychological experiments suggest thatindividuals working alone find it harder todevelop counter-arguments than to developsupporting arguments.411 The ancient Greeksdeveloped a form of argumentation, called the“dialectic,” to test arguments, find their flaws,and revise them or even replace them withbetter arguments. Later thinkers developed thesequence of thesis-antithesis-synthesis. Adialectic can be conducted alone, or with otherpersons. Find a colleague or friend to play theDevil’s advocate. Conduct a mock trial ormock argument with a questioning audience.Broad experience, or experience arguing theopposite of your current position, helps inidentifying counter-arguments.

C. PRESENTING ARGUMENTS.Arguments are prepared in writing and orally.Most of the rhetorical analysis has been onoral argumentation, but you can write with a“voice” that opens your written argument upto many of the tools of oral argumentation.Writing is better suited to a logical argument;oral is better suited to an emotional argument.However, the enduring popularity of writtenfiction shows that emotions can be conveyedthrough writing, if you know how to do it.

In presenting the argument, attend to Ethos,Pathos, and Logos.

D. REFUTING YOUR OPPONENT’SARGUMENTS. In a normal refutation, youare seeking to have the audience reject ouropponent’s Conclusion. You can attack (i) theConclusion, or (ii) the Premises, or (iii) thelogic of the Argument connecting thePremises to the Conclusion. Under (i), youattack the opponent’s Conclusion directly, byusing evidence to show that the Conclusion isnot true, or by showing that the Conclusion isnot desirable for legal or moral reasons, andthe like. Under (ii), you accept the opponent’sArgument and attack one or more of thePremises, proving them to be false, orimprobable. An example would be a claimthat a sample used to support a statisticalargument was too small to be representativeof the relevant population, or was selected ina biased (non-random) manner. Anotherexample would be attacking the credibility ofan expert whose opinion is a Premise of theopposing Argument. Proving that a Premise isfalse means that the argument is Unsound.Proving a Premise to be unlikely means thatthe Argument is likely to be Unsound. Itshould be remembered that disproving aPremise does not establish that the opponent’sConclusion is false; however, in law thefailure to support a claim with evidence isfatal to the claim. Under (iii), you attack youropponent’s Argument, which is the reasoningused to connect the Premises to theConclusion. One way to attack an Argumentis to prove that it is Invalid, by showing thatthe Conclusion can be false when thePremises are true. This attack is somewhattheoretical for many audiences. A betterapproach is to produce a vivid counter-example, which is a way of showing byspecific instance that the Argument is notdeductively Valid (because it does notnecessarily lead to a true Conclusion). Insome instances the opponent has protectedher/himself against counter-examples by

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asserting less than 100% certainty of theConclusion, in which event you must findmore than sufficient counter-examples toreduce the probability below a successfullevel. One way to attack an Argument is todiscredit it through the Reductio ad Absurdumprocess, by taking the opponent’s Argumentand applying it to hypothetical fact situationsthat show that the Argument can lead toabsurd or undesirable consequences.

The rules of Rhetoric suggest that theaudience may be induced to reject anargument based on non-ra t ionalconsiderations, like rejecting a Premisebecause of its source (i.e., the GeneticFallacy), or rejecting an Argument because itsConclusion is inconsistent with the audience’spreconceived beliefs.

Strictly speaking, a successful direct attack onyour opponent's argument does not prove thatyour argument is a good one. However, ifyour opponent has the burden of persuasion,a successful attack means you win. If youhave the burden of persuasion, and you mere-ly defeat your opponent's rebuttal argument,you must still prove the merit of yourargument.

XXVI. IMPORTANT DISTINCTIONS.In many instances the clarity of our thoughtscan be improved by understanding thedifference between terms that are similar andoften confused. This is a form of disambigua-tion. See Section XXI. Here are someimportant distinctions.

Ambiguous vs. Vague. Applied to words orconcepts, ambiguity involves a multiplicity ofmeaning, while vagueness is an indistinctnessof meaning.412

Ambiguity vs. Equivocation. Ambiguity is amultiplicity of meanings of a word, whileEquivocation occurs when someone uses thesame term in different senses in an argument.

Ambiguity vs. Amphiboly. Ambiguity is amultiplicity of meaning at the word level,while Amphiboly is multiplicity of meaning atthe sentence level. The uncertainty arisingfrom Amphiboly has to do with the way thewords are arranged. A frequent source ofAmphiboly is the mixing of Universal andParticular Quantifiers in the same sentence.413

Conjunction vs. Disjunction. In Logic,Conjunction and Disjunction are two LogicOperators that connect Terms in aProposition, or connect Propositions in aCompound Proposition. Conjunction joinsterms; disjunction separates terms.Conjunction requires that all conjunctiveelements be true for the condition stated in theconjunction to be met. Disjunction requiresonly one of the several conjunctive elementsto be true for the condition stated in thedisjunction to be met.

Consistent vs. Inconsistent. Two LogicPropositions are “Consistent” with each otherwhen it is possible for both Propositions to beTrue. If it is not possible for both Propositionsto be True, then the Propositions are“Inconsistent.” Stated differently, if a TruthTable is constructed for the Conjunction ofthe two Propositions, if there is at least onerow where the conjoined Propositions areTrue, then they are Consistent. If there is nosuch row, then they are Inconsistent.414

Contrary vs. Contradictory. In Logic, twoPropositions are contraries if they cannot bothbe true but can both be false. TwoPropositions are contradictories if they cannotboth be true and both be false.

Converse vs. Obverse. The Converse of aCategorical Proposition results fromexchanging the subject and predicate terms ofthe Proposition. Example: the Converse of “Pe Q” is “Q e P”. The Obverse of aCategorical Proposition results from replacingthe predicate term with its complement.

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Example: the Converse of “P e Q” is “P e¬Q”.

Conversion vs. Contraposition. Conversion isa Logic process in which a new ConditionalProposition is created by switching the subjectand the predicate of the original ConditionalProposition. Example: the Converse of “P eQ” is “Q e P”. Contraposition is a Logicprocess in which a new ConditionalProposition is created by switching the subjectand predicate of a Proposition and thenNegating both. Example: the Contrapositiveof “P e Q” is “¬Q e ¬P”. Example: ModusTollens is the Contrapositive of ModusPonens. The original Proposition and itsContrapositive are Logically Equivalent; theoriginal Proposition and its Converse are not.

Cogent vs. Sound Argument. An inductiveargument is “Cogent” when its Premises aretrue and the Conclusion is more likely to betrue than not true. A deductive argument is“Sound” when its Premises are true and thetruth of the Premises guarantees that theConclusion is true.

Deduction vs. Induction vs. Analogy.Deduction is a form of reasoning orargumentation where the Conclusion followsby necessity from the Premises. Induction is aform of reasoning or argumentation where thelikelihood that the Conclusion follows fromthe Premises is less than certain. In manyinstances, the likelihood can be assigned aprobability. Analogy is a form of reasoning orargumentation where something unfamiliar iscategorized based on its similarities anddissimilarities to things that are familiar andhave already been categorized.

Deductive vs. Inductive Logic vs. AnalogicalLogic. Deductive Logic is based on thejoining of two or more Premises in such a waythat they suggest a necessary Conclusion.Inductive Logic is based on analyzing specificthings and inferring from them general rules

that apply to a wider group of things.Analogical Logic is based on comparing twospecific instances, to see whether thesimilarities outweigh the differences so thatthey can both be treated the same way.Deductive Logic moves from the general tothe specific, while Inductive Logic movesfrom the specific to the general, andAnalogical Logic moves from the specific tothe specific. Deductive Logic leads toConclusions that are certain, while InductiveLogic leads to Conclusions that are at bestprobable, and Analogical Logic leads to aConclusion that is limited to the items beingcompared.

Direct vs. Indirect Arguments. A DirectArgument consists of proof that the Premisessupport the Conclusion, either with certainty(in Deductive Logic) or to a high degree ofprobability (in Inductive Logic). Using ModusTollens to disprove an Antecedent bydisproving the Consequent is also a DirectArgument, called Proof by Contrapositive. AnIndirect Argument, sometimes called “Proofby Contradiction” or “negation introduction,”establishes the Soundness of a LogicProposition by Negating the Premise andshowing that the Negated Premise leads to alogical contradiction, thereby establishing thatthe Proposition as originally stated must betrue.

Disjunction vs. Conjunction. A disjunction(like the English word “or”) separates items,while a conjunction (like the English word“and”) joins them. In Logic, InclusiveDisjunction is a Operation contained in aLogic Proposition that results in theProposition being True when one or more ofthe Terms of the Proposition are true.Exclusive Disjunction is a Logic Operationcontained in a Logic Proposition that resultsin the Proposition being True when one andonly one of the Terms of the Proposition aretrue. Conjunction is a Logic Operation insidea Logic Proposition that results in the

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Proposition being True only when all of theTerms of the Proposition are true.

Distributed vs. Undistributed. In CategoricalPropositions, a Term is said to be Distributedif all members of that category are mentionedor accounted for. In the categorical statement"all men are mortal," the term “men” isdistributed. Likewise, in the Statement “nomen are immortal,” the term “men” isdistributed. A Term is “Undistributed” if notevery member is mentioned or accounted for.See Section VII.B.7.

Equal vs. Equivalent. “Equal” means twothings are the same. “Equivalent” means thattwo things are the same for some but not allpurposes. In Logic, two Terms or Propositionsare Logical Equivalents if they have identicalTruth Tables.

Entailment vs. Implication. The term“entailment” was introduced by G.E. Moore,in his book PHILOSOPHICAL STUDIES 291(1923). Moore likened “entailment” to the tiethat exists between the Antecedent and theConclusion in a Conditional Proposition,where the Antecedent is constructed bycombining the two Premises of a CategoricalSyllogism. From Deductive Logic we knowthat the relationship between the two Premisesand the Conclusion of a Syllogism is one ofnecessity. Thus, “entailment” has beendescribed in this way: “where P and Q arecontingent propositions, P entails Q onlywhen ‘P and not-Q’ is self-contradictory.”415

Entailment is thus the strongest form ofImplication possible. In contrast, the term“Implication” has a multiplicity of meanings,including the Material Conditional, indicativeConditional, subjunctive Conditional, counter-factual Conditional, and more. In Logic,Implication is a relationship between theterms “P” and “Q” in which the occurrence orexistence of “P” means the occurrence orexistence of “Q”. Usually written “P 6 Q” or“P e Q” where “P and Q” are Terms or

Propositions. The Implication is True exceptwhen P (the Antecedent) is true and Q (theConsequent) is false. The strength of anImplication can range from slightly abovezero to certainty. As used in Deductive Logic,the term Implication connotes certainty. Asused in Inductive Logic, the term Implicationconnotes some degree of probability less than100%.

Inclusive vs. Exclusive Disjunction. In Logic,two or more Statements or Propositions joinedby Disjunction are true if at least one of theStatements of Propositions are true. InclusiveDisjunction allows the Statement orProposition to be true if one or more of thecomponents are true. Exclusive Disjunctionallows the Statement or Proposition to be trueif and only if just one of the components istrue.

True vs. Valid vs. Sound. As applied toStatements, “true” means accurate in the realworld. A Logic Proposition is True when theTruth Value of the Proposition, taken as awhole, is True given the Terms and the LogicOperations contained in the Proposition. ALogic Proposition is Valid when theConclusion is true whenever the Premises aretrue. A Logic Proposition is Sound when it islogically Valid and the Premises are true.

Universal vs. Particular. CategoricalPropositions have three quantifiers, thatindicate how many of the subject category areincluded in the predicate category: all, none,and some. The two Universal quantifiers are“all” and “none.” The Particular quantifier is“some.” See Section VII.B.7.

Valid vs. Sound. See “True vs. Valid vs.Sound.”

Valid vs. Strong. A deductive proposition orargument is Valid if the Conclusion is alwaystrue when the Premises are true. An inductiveproposition is Strong when it is improbable

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that the Premises are true and the Conclusionfalse.

XXVII. GLOSSARY.

Abduction - A term, invented by CharlesSanders Peirce, to describe perceptualjudgments that suggest universal propositionsthrough an intuitive process that is not subjectto conscious awareness or control, and has anemotional component to it. See Section IX.

Abductive Reasoning - The process offorming an explanatory hypothesis, using aninductive-like process of moving from theparticular to the general that has no assuranceof Validity or Strength. See Section IX.

Ambiguity - A multiplicity of meaning.Distinguished from Vagueness. See SectionXV.2. Also distinguished from Equivocation.See Section XV.22.

Analogy - In Logic, a method of reasoningthat infers that because different items sharesome features they therefore share morefeatures. See Section XI. In argumentation,analogy is an approach that says that, becausesomething new is similar to somethingfamiliar, therefore the categories or rulesassociated with the familiar thing shouldapply to the new thing. See Section XIV.C.5.

Antecedent - The statement or Proposition “P”that is the subject of the ConditionalProposition “P implies Q” or “if P then Q”.See Section VII.C.

Axiom - An Axiom, also called a "Postulate,"is a statement regarded as being self-evidentlytrue so that it need not be proved. Inargumentation, using an Axiom puts a stop tothe otherwise infinite regressing to some firstpremise (or First Cause). See Section VII.I.

Bayes’ Formula - A method of calculating theConditional Probability of event or condition

“B” given the occurrence or existence of anevent or condition “A”, using the PriorProbability of “A”, the Prior Probability of“B”, and the Probability of “A” given “B”.See Section X.B.1.

Case-Based Reasoning - The process ofsolving new problems based on the solutionsto similar past problems. In law, the argumentthat the present case should be resolved usinglegal rules applied in an earlier case that issufficiently similar.

Categorical Statement - A statement thatincludes the subject Term in, or excludes itfrom, the category described in the predicateTerm. Must be in either A-, E-, I- or O-form,or their negation. See Section VII.B.

Conclusion - The ending point of a LogicProposition or Logic Argument or rhetoricalArgument. The conclusion of a rhetoricalargument may not be the end of the reasoningprocess, where the ending is a restatement orsumming up of the argument. See SectionVII.A.

Conditionals - See “Conditional Proposition.”

Conditional Probability - The probability ofan event or condition given the occurrence orexistence of another event or condition. SeeSection X.B.

Conditional Proposition - An Implication,expressed in Logic by “P implies Q” or “if Pthen Q”, or in natural language by “Q only ifP” or “Q provided that P”. See Section VII.C.

Consequent - The statement or LogicProposition “Q” that is the predicate of theConditional Proposition “P implies Q” or “ifP then Q”. See Section VII.C.

Contradiction - a pair of propositions whereone asserts what the other denies."Contradictions do not exist. Whenever you

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think that you are facing a contradiction,check your premises. You will find that one ofthem is wrong." Ayn Rand, ATLAS SHRUGGED

(1957). See Section VII.A.2.

Contrapositive - A Conditional Propositioncreated from another Conditional Proposition,by reversing and then Negating the subjectand predicate of the first ConditionalProposition. Example: the Contrapositive of“P e Q” is “¬Q e ¬P”. Proving theContrapositive establishes that the originalPremise “P” is false, in a form of proof calledModus Tollens. A Proposition and itsContrapositive are Logically Equivalent (i.e.,have the same Truth Tables). See SectionsVII.C.2 & XXVI.

Conversion - The process of exchanging theplaces of the subject and predicate terms in acategorical statement. See Sections XII.B.7 &XXVI.

Copula - The verb (a form of “to be”) thatjoins the subject and predicate of a categoricalstatement. See Section VII.C.4.

Deductive Logic - See “DeductiveReasoning.”

Deductive Reasoning - A form of reasoning inwhich two or more Premises are associated insuch a way as to lead with certainty to aConclusion. See Section VII.

Defeasible Argument - Argument that isrationally compelling but not DeductivelyValid.416 See Section XVII.B.

Defeasible Reasoning - A non-demonstrativeform of reasoning that does not result in afinal demonstration of a claim, but rather aprovisional assertion of an argument that issubject to undercutting or rebuttal as furtherevidence is discovered or further argumentsare brought to bear. See Section XVII.B.

Enthymeme - In Deductive Logic, a Syllogismthat is missing a Premise, or missing parts oftwo or more Premises, or that implies that theConclusion is only probable and not certain.See Section VII.B.3. In argumentation, anargument that utilizes themes that the rationalcomponent of the audience will identify with.See Section XIV.C.2.

Equivocation - Using the same term atdifferent points of an argument, but indifferent senses. When this occurs in aSyllogism, it is the Fallacy of Four Terms. SeeSection XV.22.

Euler Circles - A way of depicting CategoricalPropositions and syllogistic reasoning in agraphical manner, by using circles thatrepresent each category used in theProposition. See Section VII.D.

Fallacy - A flawed argument. Fallacies havebeen categorized. See Sections VII.B.10(syllogistic), VII.K. (deductive), VIII.F(inductive), XV (argumentation), and XVI(alternate characterizations).

Fallacy of Relevance - An argument that iserroneous because the Premises are notsufficiently relevant to the Conclusion. SeeSection VII.M.

Implication - A relationship between two ormore Terms or Propositions where theexistence or occurrence of one means that theother exists or will occur. In natural EnglishImplication is expresses as “P implies Q” or“if P then Q”. In Symbolic Logic, Implicationis expressed “P 6 Q” or for MaterialImplication “P e Q”. See Section VII.C.

Indirect Argument - validating a LogicProposition by assuming the Proposition isfalse and showing by deductive argument thatthis leads to a logical contradiction. Alsocalled “Proof by Contradiction.” See SectionXXIII.A.7.

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Inductive Logic - See “Inductive Reasoning.”

Inductive Reasoning - Inferring fromparticular instances a general principle thatapplies, with some degree of likelihood shortof certainty, to a larger number of instances.See Section VIII. Statistical generalizationsare a form of inductive reasoning, where arandomly-chosen sample is believed torepresent an entire class of persons or things,to some degree of probability. See Section X.Some people see Reasoning by Analogy as aform of inductive reasoning where a givennumber of similarities between items beingcompared suggests that more similaritiesexist. See Section XI.

Invalid - A Deductive Proposition for whichthere is at least one instance where thePremises are true and the Conclusion is false.See Section VI.C.2.

Inverse - A Conditional Proposition formedby Negating both the subject and predicate ofanother Conditional Proposition. Example: theInverse of “P e Q” is “¬P e ¬Q”. See SectionVII.C.2.

Major Premise - The first Premise of aSyllogism that is in Standard Order, andwhich contains the Major Term. See SectionVII.B.1.

Major Term - The Term that occurs in thepredicate of the Major Premise of aCategorical Syllogism, and appears again inthe predicate of the Conclusion. See SectionVII.B.1.

Material Conditional - A ConditionalProposition that is true if and only if theConsequent is true whenever the Antecedentis true and the Antecedent is false wheneverthe Consequent is false. Expressed inSymbolic Logic as "P e Q " or "P Y Q". SeeSection VII.C.3.

Middle Term - The Term that occurs in thesubject of the Major Premise, and predicate ofthe Minor Premise, of a CategoricalSyllogism, and which does not appear in theConclusion. The Middle Term joins the MajorPremise to the Minor Premise so that theConclusion may be deduced. See SectionVII.B.1.

Minor Premise - The second Premise of aSyllogism that is in Standard Order, andwhich contains the Minor Term. See SectionVII.B.1.

Minor Term - The Term that occurs in thesubject of the Minor Premise of a CategoricalSyllogism, and appears again in the subject ofthe Conclusion. See Section VII.B.1.

Modus Ponens - A Conditional Proposition inthe following form: “if P is true, then Q istrue; P is shown to be true; therefore Q mustbe true”. See Section VII.C.4.

Modus Tollens - A Conditional Proposition inthe following form: "If P is true, then Q istrue; Q is shown to be false; therefore, P isfalse". See Section VII.C.5.

Negation - In Logic, the opposite of the termor Proposition being Negated. Also, theprocess of reversing the Truth Value of aLogic Term, Proposition, or CompoundProposition. See Sections VII.F.1 & VII.Q.1.

Non Sequitur - An argument reflecting aFallacy of Relevance. See Section VII.K.4.

Paradox - In Logic, a Valid argument thatleads to a logical contradiction. Inargumentation, a seemingly self-contradictorystatement or argument that invites analysis ofone’s assumptions or reasoning. See SectionVII.L.

Posterior Probability - A term from BayesianTheory, meaning the Conditional Probability

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assigned to an event or condition afterreceiving additional information. See SectionVII.L.

Premise - In Deductive Logic, a suppositionfrom which something else results ofnecessity; the beginning point of an argumentdesigned to lead inexorably from the Premiseto a Conclusion that is by necessity true; aknown fact from which other facts can beinferred.

Prior Probability - A term from BayesianTheory, meaning the probability assigned toan event or condition before receivingadditional information. See Section X.B.1.a.

Proposition - In Logic, a Statement thatasserts a Logic-based relationship betweenTerms, or between two or more Propositions.See Section VI.B.

Reasoning by Analogy - See “Analogy.”

Reductio ad Absurdum - In Logic, a form ofargument in which a Proposition is disprovenby showing that it leads to a logicalcontradiction. An Indirect Proof is a form ofReductio, in which an Argument is provedSound by showing that negating the Premiseleads to a logical contradiction. See SectionXXIII.A.7. In argumentation, Reductio arefutation where an opponent's Argument iscarried to the extreme and to show that itreaches an absurd or undesirable result.Technically, the latter form of argument iscalled “reductio ad incommodum.” SeeSection XXIII.D.1.

Sampling Bias - An error in statisticalgeneralization that results from the selectionof a sample that is not representative of thepopulation as a whole, because for somereason it is not randomly selected. See SectionVIII.F.9.a(1).

Sorites - In Logic, a chain of incompleteSyllogisms in which the predicate of eachPremise (except the first) is the subject of thenext Premise, continuing until the Conclusion.See Sections VII.B.4 and XIV.C.3.

Sorites Paradox - A logic-based argument thatexploits the vagueness associated withcategories applied to a continuousphenomenon to show that focusing onincremental changes defeats the categorizationscheme. See Section VII.L.1.

Sound - In Logic, a Proposition that is bothValid and has true Premises. See SectionVI.C.3.

Square of Opposition - A diagram showingthe possible relationships between thePremises and Conclusions of CategoricalSyllogisms that are stated in the StandardForm. See Section VII.B.8.

Standard Form - The Standard Form is theconfiguration of a Categorical Propositioninto one of the four forms described as a A, E,I, and O. See Section VII.B.7.

Standard Order - The ordering of the parts ofa Categorical Syllogism, with the MajorPremise first, followed by the Minor Premise,and finally the Conclusion. See SectionVII.B.1.

Strong - Said of an inductive argument whereit is unlikely that the Premises could be trueand the Conclusion false. See SectionVIII.“Strong” is the Inductive Logic analogue tothe concept of “valid” in Deductive Logic,except that “valid” deals with certainty while“strong” deals with likelihood.

Syllogism - In Deductive Logic, a method ofreasoning whereby the joining of twoPremises establishes a Conclusion thatnecessarily follows. See Section VII.B.

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1. The principles of Logic and of Rhetoric have been stated and restated so many times that the selection of a particular source asauthority is arbitrary. In this Article, some citations are picked based on their most famous proponent, some based on the clarityof the source language, some based on the availability of the original writing on the internet (to permit confirmation by thereader), some based on historical significance, and some for entertainment value.

2. Where possible, references for further study are made to materials available for free on the internet. This convenience has aprice: links go dead. If that happens, conduct an internet search using key words or phrases to find new materials for furtherstudy. The author recommends Google for internet-wide searches. Google is preferred over other search engines because ofGoogle’s access to Google Books, which gives access to copyrighted material. The date that the author of this article lastaccessed the URL is given in parenthesis, i.e. (8-10-2010).

Term - A component part of a LogicProposition. A term can be a Statement or aLogic Proposition. See Section VII.A.1.

Truth Tables - A table listing the Truth Valuesof a Logic Proposition under all possiblecombinations of true and false Terms. SeeSection VII.E.

Truth Value - The truth or falsity or a Term orLogic Proposition. See Section VII.E.

Unsound - A deductive argument that is Validbut has false Premises. See Section VI.C.3.

Vagueness - An indistinctness of meaning.Distinguished from ambiguity. See SectionXX.

Valid - A deductive argument for which,when the Premises are true, the Conclusion isnecessarily true. See Section VI.C.2.

Warrant - Part of the structure of argumentsproposed in 1958 by Stephen E. Toulmin andwidely accepted in Informal Logic circles, inwhich arguments are constructed of threec o m p o n e n t s - - C l a i m s , D a t a , a n dWarrants--where Warrants are theassumptions, or principles, or logicalstatements, or themes, that link the Data to theClaims. Warrants can be deductive orinductive inferences, an analogicalcomparison, an Enthymeme, or a principle ortechnique of Rhetoric. See Section XVII.A.3.

XXVIII. ENDNOTES.

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3. See David R. Shanks, Implicit Learning, in K. Lamberts and R. Goldstone, HANDBOOK OF COGNITION p. 202 (2005)<http://www.psychol.ucl.ac.uk/david.shanks/Implicit%20learning%20review%20chapter.pdf> (8-1-2010), for a discussion of the“implicit learning” process.

4. Ian Tattersall, Macroevolutionary Patterns, Exaptation, and Emergence in The Evolution of the HumanBrain and Cognition,in Stephen Cunnane (Ed.), Kathlyn Stewart (Ed.), THE EVOLUTION OF THE HUMAN BRAIN AND COGNITION, IN HUMAN BRAIN

EVOLUTION : THE INFLUENCE OF FRESHWATER AND MARINE FOOD RESOURCES 2 (June 2010) <http://media.wiley.com/product_data/excerpt/84/04704526/0470452684.pdf> (8-1-2010).

5. Gottfrieb Leibniz,THE ART OF DISCOVERY (1685).

6. Magda Osman, An evaluation of dual-process theories of reasoning, 11 PSYCHONOMIC BULLETIN & REVIEW 988, 988 (2004) <http://pbr.psychonomic-journals.org/content/11/6/988.full.pdf> (8-1-2010). British theorist Jonathan St. B.T. Evansdistinguishes dual systems from dual processes, and points out that the fact that people process information in two ways doesnecessarily mean that they have two separate cognitive systems. In fact, he suggests, the issue of whether there is one system orare two systems for processing information is not important to researchers attempting to account for experimental results. Evansproposes two reasoning processes, one heuristic (implicit) and one analytic (explicit). Evans proposes that people heuristicallyuse incoming information to generate a plausible model, which they stick with until there is a good reason to replace it withanother. Thus, deductive reasoning, instead of being the central intellectual activity, "may be seen as no more than ananalytic-level strategy that bright people can be persuaded to adopt by the use of special instructions." In his view, "[d]eductiveeffort, when made, attempts to modify pragmatic processes, and not the other way around." Jonathan St. B. T. Evans, Theheuristic-analytic theory of reasoning: Extension and evaluation, 13 PSYCHONOMIC BULLETIN & REVIEW 378 (2006)<http://pbr.psychonomic-journals.org/content/13/3/378.full.pdf> (8-18-2010).

7.Brian Ogren, Aristotle's Rhetoric and the Cognition of Being: Human Emotions and the Rational-Irrational Dialectic, 8MINERVA - AN INTERNET JOURNAL OF PHILOSOPHY 1, 1-6 (2004) < http://www.mic.ul.ie/stephen/vol8/aristotle.pdf> (8-16-2010).

8. Id.

9. Id. p. 988-989. See Seymour Epstein, Integration of the Cognitive and thePsychodynamic Unconscious, 49 AMERICAN

PSYCHOLOGIST 709 (1994) <http://ocean.st.usm.edu/~w535680/Epstein%20(1994).pdf> (8-1-2010).

10. Osman, supra n. 6 p. 988-989.

11. Osman, supra n. 6 p. 996.

12. Osman, supra n. 6 p. 995.

13. William Blackstone, COMMENTARIES ON THE LAW OF ENGLAND, Vol. I, Book I, Section III [“Commentaries”]<http://www.archive.org/details/blackstonescomm00unkngoog>. A version of Blackstone’s Commentaries that can beelectronically copied and pasted is at <http://avalon.law.yale.edu/subject_menus/blackstone.asp.> Alternate printings can beviewed at <http://openlibrary.org/works/OL2417578W/Commentaries_on_the_laws_of_England> (8-16-2010).

14. Blackstone, COMMENTARIES, Vol. I, Book I, Section III.

15. Blackstone, COMMENTARIES, Vol. I, Book I, Section III.

16. William Blackstone, A Discourse on the Study of the Law 16 (1758),<http://www.lonang.com/exlibris/blackstone/bla-001.htm> (6-19-2010) [“Discourse”].

17. Pollock and Maitland, THE HISTORY OF ENGLISH LAW BEFORE THE TIME OF EDWARD I 138 (1895).

18.Edward Rubin, What’s Wrong with Langdell’s Method and What to do About it, 60 VAND. L. REV. 609, 628-29 (2007)(“Rubin”).

19. Littleton’s The Tenures was one of the first books published in London and was the first legal treatise published on Englishlaw. The three volume set was an effort to achieve a comprehensive classification of rights in land. Littleton’s approach was tostate a definition and description of the rights in question, followed by hypothetical illustrations and in some instances referencesto some of the court decisions that had been assiduously recorded in “year books” for some years prior.

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20. The first part is at <http://www.archive.org/details/firstpartinstit03nottgoog> (6-19-2010). The second part is at<http://www.archive.org/details/secondpartinsti02cokegoog.> (6-20-2010): The third part is at<http://www.archive.org/details/thirdpartinstit01cokegoog> (8-16-2010).

21. William Blackstone, An Analysis of the Laws of England, Preface p. v. Ranulf de Glanville (d. 1190) served as Chief Justiciar(i.e., prime minister) for Henry II of England. He is reputed to have authored the Treatise on the Laws and Customs of theKingdom of England in 1188–the first treatise on English law. The Treatise detailed the complicated practice of writs, whichwere used to remove legal disputes from a local court (dominated by the local noble) to one of the King’s Courts.

22. Blackstone, An Analysis of the Laws of England, Preface p. v <http://www.constitution.org/cmt/blackstone/ale1762.htm> (6-20-2010). Henry de Bracton (1210-1268) wrote a treatise in Latin On the Laws and Customs of England in around 1260. As aclerk to William de Raley, an important judge during the time of King Henry III, Bracton had access to the records ofunpublished cases, which he used to annotate the statements of principles contained in his book. Bracton thus facilitated thedevelopment of the doctrine of stare decisis. He introduced the mens rea requirement for criminal conviction, and many otherinnovations.

23. Blackstone, An Analysis of the Laws of England, Preface p. v. “Britton” is the name attributed to the author of acomprehensive statements of laws, also given the name “Britton,” that were published 1291-1292 by the authority of Edward I,in an effort to regularize the law across England and Ireland under his ultimate authority. Edward gave notice in the Prologue tothe work that all contrary local laws were preempted. See Francis Morgan Nichols, Britton (1865)<http://www.archive.org/details/brittonenglishtr00nichiala> (6-19-2010). This 615-page book, written in Law French, gives acomprehensive listing of the remedies available from the courts, and through them the rights they vindicate. <www.archive.org/details/brittonenglishtr00nichiala>.

24. Blackstone, An Analysis of the Laws of England, Preface p. v.


26. Blackstone, An Analysis of the Laws of England, Preface pp. v-vi


28. Blackstone, An Analysis of the Laws of England, Preface p. vi.

29. Blackstone, An Analysis of the Laws of England, Preface p. v. See A Memoir of Sir William Blackstone, George Sharswood(1860) <www.archive.org/details/commentariesonl00shargoog> (8-16-2010).

30. Blackstone, COMMENTARIES, (Clarendon Press 2001, ed. Wayne Morrison,) Preface xxxvii-viii.

31. Blackstone, COMMENTARIES, p. xxxvii-viii.

32. Blackstone, COMMENTARIES, p. xxxvi.

33. Blackstone, An Analysis of the Laws of England, Preface p. iv.

34. Blackstone, An Analysis of the Laws of England, Preface p. xxxviii.

35. Blackstone, An Analysis of the Laws of England, Preface p. xxxviii.

36. Blackstone, An Analysis of the Laws of England,, Preface p. viii.

37. Blackstone, An Analysis of the Laws of England, Preface p. vii.

38. A scan of John Adams personal copy is on-line at<http://www.archive.org/stream/generalabridgmen06vine#page/n1/mode/2up> (8-16-2010).

39. <http://www.lonang.com/exlibris/blackstone/bla-001.htm> (6-19-2010) [“Discourse”].

40. Blackstone, Discourse, p.6.

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41. Blackstone, Discourse, pp. 36-37.

42. <http://openlibrary.org/books/OL7025510M/Commentaries_on_the_laws_of_England.> (6-19-2010).

43.Thomas Acquinas, SUMMA THEOLOGICA Pt. I, Q. 90, Art. 4.

44. Blackstone, COMMENTARIES, Vol. I, Book I, Section II.

45. Id.

46. Id.

47. Id.

48. Id.

49. Id.

50. Blackstone, COMMENTARIES, Book I, Part I, Section III.

51. Id.

52. Blackstone, COMMENTARIES, Vol. I, Book I, Section II. Blackstone wrote: “The fairest and most rational method to interpretthe will of the legislator, is by exploring his intentions at the time when the law was made, by signs the most natural andprobable. And these signs are either the words, the context, the subject matter, the effects and consequence, or the spirit andreason of the law.“

53. Id. William Blackstone said: “For it is an established rule to abide by former precedents, where the same points come againin litigation; as well to keep the scale of justice even and steady, and not liable to waver with every new judge's opinion; as alsobecause the law in that case being solemnly declared and determined, what before was uncertain, and perhaps indifferent, is nowbecome a permanent rule, which it is not in the breast of any subsequent judge to alter or vary from, according to his privatesentiments: he being sworn to determine, not according to his own private judgment, but according to the known laws andcustoms of the land; not delegated to pronounce a new law, but to maintain and expound the old one. yet this rule admits ofexception, where the former determination is most evidently contrary to reason; much more if it be contrary to the divine law.But even in such cases the subsequent judges do not pretend to make a new law, but to vindicate the old one frommisrepresentation. For if it be found that the former decision is manifestly absurd or unjust, it is declared, not that such asentence was bad law, but that it was not law; that is, that it is not the established custom of the realm, as has been erroneouslydetermined.”

54. Tucker’s Blackstone can be accessed at <http://www.constitution.org/tb/tb-0000.htm> (6-20-2010).

55. Donald S. Lutz analyzed the European sources most cited by the Founding Fathers, and Blackstone finished third behind thePaul of Tarsus and Montesquieu. See <http://www.constitution.org/primarysources/influences.html> (8-16-2010). Daniel J.Boorstin, in the preface to the paperback edition of his book The Mysterious Science of the Law (Boston: Beacon Press, 1958)commented: “In the history of American institutions, no other book—except the Bible—has played so great a role asBlackstone's Commentaries on the Laws of England." Blackstone’s image is carved into the frieze in the U.S. Supreme Court’scourtroom, along with Justinian, Mohammed, Charlemagne, King John, St. Louis, Grotius, Marshall, and Napoleon. See<http://www.wm.edu/news/stories/newssidebars/2009/warren-speech-to-marshall-wythe-blackstone-ceremony,-sept.-1954.php>(8-16-2010).

56. The American Declaration of Independence begins: “When in the Course of human events it becomes necessary for onepeople to dissolve the political bands which have connected them with another and to assume among the powers of the earth, theseparate and equal station to which the Laws of Nature and of Nature's God entitle them, a decent respect to the opinions ofmankind requires that they should declare the causes which impel them to the separation.” [Emphasis added]

57. In The Federalist No. 84, Alexander Hamilton quoted Blackstone: “‘To bereave a man of life, [says he] or by violence toconfiscate his estate, without accusation or trial, would be so gross and notorious an act of despotism, as must at once convey thealarm of tyranny throughout the whole nation; but confinement of the person, by secretly hurrying him to jail, where hissufferings are unknown or forgotten, is a less public, a less striking, and therefore a more dangerous engine of arbitrarygovernment.’ And as a remedy for this fatal evil he is everywhere peculiarly emphatical in his encomiums on the habeas corpus

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act, which in one place he calls ‘the BULWARK of the British Constitution.’” Hamilton had previously quoted Blackstone in hisletter of February 23, 1775, entitled “The Farmer Refuted.” Hamilton quoted Blackstone to the effect “that the first and primaryend of human laws, is to maintain and regulate these absolute rights of individuals.”

58. Marbury v. Madison, 5 U.S. 137, 163, 1803 WL 893, *17 (1803) (quoting Blackstone’s definition of writ of mandamus) .

59. Blackstone, COMMENTARIES, Vol. III, ch. 8.

60. Blackstone, COMMENTARIES, Vol. I, Book I, Section II.

61. Carl Landauer, Social Science on a Lawyer's Bookshelf: Willard Hurst's Law and the Conditions of Freedom in theNineteenth-Century United States 18 LAW AND HISTORY REV. 59 n. 61 (2000).<http://www.historycooperative.org/journals/lhr/18.1/landauer.html#foot61> (6-20-2010).

62. The following is a letter from Abraham Lincoln to James T. Thornton on December 2, 1858:

Dear SirYours of the 29th, written in behalf of Mr. John W. Widmer, is received. I am absent altogether too much to be asuitable instructor for a law student. When a man has reached the age that Mr. Widner has, and has already been doingfor himself, my judgment is, that he reads the books for himself without an instructor. That is precisely the way I cameto the law. Let Mr. Widner read Blackstone's Commentaries, Chitty's Pleadings's -- Greenleaf's Evidence, Story'sEquity, and Story's Equity Pleading's, get a license, and go to the practice, and still keep reading. That is my judgmentof the cheapest, quickest, and best way for Mr. Widner to make a lawyer of himself. Yours trulyA. Lincoln

<http://showcase.netins.net/web/creative/lincoln/speeches/law.htm> (7/29/2010).

63.See Bruce A. Kimball, Warn Students That I Entertain Heretical Opinions, 25 LAW AND HISTORY REVIEW 1, 4 (2007)<http://www.historycooperative.org/journals/lhr/17.1/kimball.html> (8-12-2010): “But Langdell’s mode of reasoning –even onissues traditionally invoked to demonstrate his formalism–is actually three-dimensional, exhibiting a comprehensive yetcontradictory integration of induction from authority, deduction from principle, and analysis of justice and policy.”

64. Id. at 19.

65. Id. at 21.

66. Id., quoting Langdell, CASES ON CONTRACTS (1871), Preface.

67. Id. at 22-23, 37.

68. Oliver Wendell Holmes, Jr., The Path of the Law, 10 HARVARD LAW REVIEW 457 (1897).

69. “The common law is not a brooding omnipresence in the sky...," Southern Pacific v. Jensen, 244 U.S. 205, 222 (1917)(Holmes, J., dissenting).

70. “The life of the law has not been logic; it has been experience...The law embodies the story of a nation's developmentthrough many centuries, and it cannot be dealt with as if it contained only the axioms and corollaries of a book of mathematics.” Oliver W. Holmes, Jr., THE COMMON LAW (1881), p. 1.

71. Professor Pound’s 1908 Columbia Law Review article, entitled Mechanical Jurisprudence, is available on-line at GoogleBooks, but the URL is unwieldy. Go to Google Books and search for “Roscoe Pound's Mechanical Jurisprudence.”

72. Professor Corbin wrote: “[T]he law does not consist of a series of unchangeable rules or principles engraved upon anindestructible brass plate or, like the code of Hammurabi, upon a stone column. Every system of justice and of right is of humandevelopment, and the necessary corollary is that no known system is eternal. In the long history of the law can be observed thebirth and death of legal principles. They move first with the uncertain steps of childhood, then enjoy a season of confidentmaturity, and finally pass tottering to the grave. . . . The law is merely a part of our changing civilization. The history of law isthe history of . . . society. Legal principles represent the prevailing mores of the time, and with the mores they must necessarilybe born, survive for the appointed season, and perish.” Arthur L. Corbin, ANSON ON CONTRACTS v-vi (3d Am. ed. 1919).”Corbin wrote in a private letter: “I have read all the contract cases for the last 12 years; and I know that ‘certainty’ does not exist

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and the illusion perpetrates injustice.” See Joseph M. Perillo, Twelve Letters From Arthur L. Corbin to Robert Braucher, 50WASH. & LEE L. REV. 755 (1993).

73.Edward H. Levi, AN INTRODUCTION TO LEGAL REASONING 12 (1949).

74. Professor Levi described the process this way: ”It is a three-step process described by the doctrine of precedent in which aproposition descriptive of the first case is made to a rule of Harvard then applied to a next similar situation. The steps are these:similarity is seen between cases; next the rule of law inherent in the first case is announced; then the rule of law is madeapplicable to the second case." Id. at 11. Professor Levi said this process had a dynamic quality “because the scope of the rule oflaw, and therefore its meaning, depends upon a determination of what facts will be considered similar to those present when therules was first announced. The finding of similarity or difference is the key step in the legal process." Id.

75. U.S. Supreme Court Associate Justice Stephen Breyer recently said that “law is an example of reasoned power.” PanelDiscussion, Law vs. Power: Who Rules? Who Makes the Rules? (November 1, 2009)<http://fora.tv/2009/11/21/Law_Versus_Power#chapter_05> (8-1-2010).

76. See Zarefsky n. David Zarefsky, 2 ARGUMENTATION: THE STUDY OF EFFECTIVE REASONING 176 (2d ed. TheTeaching Company 2005) <http://www.teach12.com> (8-17-2010).

77. Aristotle, POSTERIOR ANALYTICS Book I, Part 1 <http://classics.mit.edu/Aristotle/posterior.1.i.html> (8-7-2010).

78. Logical systems have been devised that do not assume that an assertion must be either true or false. Such systems are notcovered in this Article.

79. Logical systems have been devised that do not assume that all logical Propositions have a Truth Value. One such systemasks whether a connection between Statements or Propositions is “necessary.” Another system includes a parameter reflectingthe “relevance” of the Terms being connected in a Proposition. Such systems are excluded from this Article.

80. The first Premise is also false, in that ostriches have wings but cannot fly.

81. In the English language, verbs have four “moods”: indicative, imperative, subjunctive, and infinitive.

82.This is the Logic rule known as Modus Tollens. See Section VII.C.5.

83. Note how the present tense “fits” better with declarative statements, while the future tense “fits” better with conditionalstatements.

84. In this Article, the term “Statement” is used for a clause or sentence that appears as part of a Logical Proposition, and thatcan be said to be true or false in the real world. Thus, in this Article the phrase “red blueberries” would be considered to be alogical Statement, even though it is not a complete sentence.

85. Stanford Encyclopedia of Philosophy, Aristotle’s Logic <http://plato.stanford.edu/entries/aristotle-logic> (8-16-2010).

86. The Proposition that “A is A” is called a “Tautology.”

87. Aristotle, METAPHYSICS 4.4, W.D. Ross (trans.), GBWW 8, 525–526.

88. Under the Law of Contradiction, “A” and “not-A” are “mutually exclusive.”

89. Under the Law of Excluded Middle, “A” and “not-A” are “collectively exhaustive.”

90. See <http://www.thelogician.net/2_future_logic/2_chapter_02.htm> (8-16-10).

91. This Rule of Inference is called “Modus Ponens.” See Section VII.C.4.

92. This is the Rule of Inference called “Modus Tollens.” See Section VII.C.5.

93. So-called “birthers,” who believe that President Obama was born in Kenya, would say that this Syllogism “Begs theQuestion,” in that it assumes what it purports to prove, i.e., that President Obama was born in America.

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94. <http://classics.mit.edu/Aristotle/prior.mb.txt> (8-16-2010).

95. Aristotle's Metaphysics, Stanford Encyclopedia of Philosophy <http://plato.stanford.edu/entries/aristotle-metaphysics> (8-7-2010).

96. Roy A. Sorenson, Are Enthymemes Arguments?, 29 NOTRE DAME JOURNAL OF FORMAL LOGIC 155, 155 (1988)<http://projecteuclid.org/euclid.ndjfl/1093637779> (8-17-2010)

97. See <http://yesfine.com/carroll_symbolic_logic_simplified_statements.htm> (8-12-2010).

98. See Francine F. Abeles, Lewis Carroll's Method of Trees: its Origins in Studies in Logic, 1 MODERN LOGIC 25 (1990) <http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.rml/1204834538> (7-4-2010).

99. Conclusion: babies cannot manage crockodiles.

100. Conclusion: none of my presents are of tin.

101. Conclusion: all of my potatoes are old.

102. Conclusion: none of your sons are fit to serve on a jury.

103. Conclusion: no bird in this aviary lives on mince pies.

104. Conclusion: these sorites-examples are difficult.

105. Conclusion: all my dreams come true.

106. The Validity of a Disjunctive Syllogism can depend on context. When Neil Armstrong was standing on the moon, his senseof day and night was quite different from persons on Earth.

107. The Traditional Square of Opposition, Stanford Encyclopedia of Philosophy <http://plato.stanford.edu/entries/square> (8-6-2010).

108. The conventional translation from Aristotle’s DE INTERPRETATIONE for I is “Some S is P”. This creates problems when S isa set containing no members. Id. p. 5. However, one translator phrased the English “Not every S is P”, which makes the problemgo away. Id.

109. Id. at 2-3.

110. Id. at 3.

111. Aristotle, POSTERIOR ANALYTICS Book I, Part 3 <http://classics.mit.edu/Aristotle/posterior.1.i.html> (8-7-2011).

112. <http://www.fallacyfiles.org/undismid.html> (8-5-2010).

113. Osman, supra n. 6 p. 1001.

114. See Aldisert, Clowney, and Peterson, Logic for Law Students: How to Think Like a Lawyer, 69 UNIV. PITT. L. REV. 1, 1-13(2007).

115. Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579, 592-593 (1993) (quoting Karl Popper for the proposition that“the criterion of the scientific status of a theory is its falsifiability, or refutability, or testability”).

116. People commonly assume that disproving the Antecedent disproves the Consequent as well. This is incorrect. Disprovingthe Antecedent proves that the Conditional is Unsound. However, even an Unsound Proposition may have a Conclusion that istrue. Thus, disproving the Antecedent does not prove that the Conclusion is false.

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117. It is commonly assumed that showing the Implication relationship to be Invalid disproves the Consequent. This is incorrect.An Implication is Invalid when there is at least one instance where the Antecedent is true and the Consequent is false. Thus, anInvalid Implication may have a Conclusion that is true 99% of the time.

118. Gene Harmon Ford, Inc., v. David McDavid Nissan, Inc., 997 S.W.2d 298, 306 n. 10 (Tex. App.--Austin, 1999, pet.denied). See Joseph Heller, CATCH-22 46 (1961).

119. <http://www.washingtonpost.com/ac2/wp-dyn/A37288-2002Dec10?language=printer> (8-16-2010).

120. Tex. Code. Crim. P. art. 38.03.

121. Tex. Fam. Code § 3.003(a).

122. Diagrams, Stanford Encyclopedia of Philosophy <http://plato.stanford.edu/entries/diagrams> (8-15-2010); Mario Savio, AE(Aristotle-Euler) Diagrams: An Alternative Complete Method for the Categorical Syllogism, 30 Notre Dame J. Formal Logic 581(1998) http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.ndjfl/1039118872(8-16-2010).

123.Note that it is sometimes easier to see a Fallacy using real life examples rather than abstract variables.

124. <http://www.butte.edu/~wmwu/iLogic/3.2/iLogic_3_2.html> (8-7-2010).

125. “Idempotence” is the property of something that has the same effect if used multiple times as if it was used only once.

126. <www.eartham.edu/upeters/courses/log/transtip.htm> (8-12-2010).

127. “Idempotence” is the property of something that has the same effect if used multiple times as if it was used only once.

128. Tex. Fam. Code § 1.104.

129. <http://mathworld.wolfram.com/Axiom.html> (8-12-2010).

130. John Stuart Mill, ON FALLACIES ch. 3, § 1 (1843) <http://oll.libertyfund.org/title/247/40031> (8-12-2010).

131. <www.iep.utm.edu/prop-log>, p. 13.

132. <www.iep.utm.edu/prop-log>, p. 12.

133. <www.iep.utm.edu/prop-log>, p. 13 (8-12-2010).

134. The “Converse” of a Categorical Proposition exchanges the Term in the subject and the Term in the predicate. For example,the Converse of “P implies Q” is “Q implies P”, or the Converse of “Some S is P” is “Some P is S”.

135.John Nolt, Dennis Rohatyn, Achille Varzi, THEORY AND PROBLEMS OF LOGIC 92-93 (2d ed. 1998) [“Nolt”].

136. See Internet Encyclopedia of Philosophy <http://www.iep.utm.edu/fallacy> (8-7-2010).

137. See <http://mathworld.wolfram.com/Fallacy.html> (8-12-2010).

138. In U.S. v. Kincade, 379 F.3d 813, 873 (9th Cir. 2004) (Kozinski, J., dissenting), Judge Kozinski used a slippery slopeargument, that the court’s condoning the government’s expansive use of DNA technology would set a new baseline of acceptableabridgement of privacy rights that would become the foundation for subsequent expansion of the government’s authority tointrude. His quotation: “Not only do [Fourth Amendment opinions] reflect today's values by giving effect to people's reasonableexpectations of privacy, they also shape future values by changing our experience and altering what we come to expect from ourgovernment.” Id. at 873.

139. Eugene Volokh, The Mechanisms of the Slippery Slope, 116 HARV. L. REV. 1026 (2003); Ruth E. Sternglantz, Raining onthe Parade of Horribles: of Slippery Slopes, Faux Slopes, and Justice Scalia’s Dissent in Lawrence v. Texas, 153 UNIV. OF PENN.L. REV. 1097 (2005).

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140. John Stuart Mill, ON FALLACIES ch. 6, § 4 (1843) <http://oll.libertyfund.org/title/247/40039> (8-12-2010).

141. Jason Glenn, Many Judges Sometimes Lie: Remarks on Sorensen’s Views on Vagueness and Law (2007)<www.sorites.org/Issue__18/glenn.htm> (8-17-2010).

142. Sorites Paradox, Stanford Encyclopedia of Philosophy <http://plato.stanford.edu/entries/sorites-paradox/#1> (8-7-2010).

143. The attribution of this epistle to Paul has been questioned. Seehttp://en.wikipedia.org/wiki/Epistle_to_Titus#Pauline_Authenticity. (8-17-2010).

144. See Internet Encyclopedia of Philosophy <http://www.iep.utm.edu/par-liar/> (8-7-2010).

145. See<http://www.statemaster.com/encyclopedia/Autoinfanticide> (8-12-2010).

146. Two envelopes problem <http://en.wikipedia.org/wiki/Two_envelopes_problem> (8-7-2010).

147. Exchange paradox, <http://en.wikipedia.org/wiki/Exchange_paradox> (8-7-2010).

148. Interestingly, the same pattern occurred with Lincoln’s Emancipation Proclamation, which was difficult (if not impossible)to justify under the Constitution prior to the adoption of the Thirteenth Amendment. His first Emancipation Proclamation wasessentially an offer of compromise to the states in rebellion. In his final Emancipation Proclamation, Lincoln “freed” the slavesin states that did not recognize his executive authority, while leaving in bondage the slaves in Tennessee, Maryland, andDelaware, which did recognize his Executive Authority. Thus, the Emancipation Proclamation freed no slaves. This and manyother of Lincoln’s actions as President reflect his sophisticated sense of legal reasoning, just as his political and Presidentialspeeches reflect his consummate skill in Rhetoric. Based on his career as a successful lawyer and his actions and statements asPresident, one could justifiably say that Lincoln was the greatest lawyer that America ever produced.

149. Nolt, supra n. 135 p. 33.

150. Nolt, supra n. 135 pp. 33-34.

151. Audun Jøsang, Conditional Reasoning with Subjective Logic, 15 J. OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING 2(2008) <http://persons.unik.no/josang/papers/Jos2008-JMVLSC.pdf> (8-6-2010).

152. Ruth M. J. Byrne and Alessandra Tasso, Deductive reasoning with factual, possible, and counterfactual conditionals, 27MEMORY & COGNITION 726, 727 (1999)<http://www.tara.tcd.ie/bitstream/2262/39510/1/Deductive%20reasoning%20with%20factual,%20possible,%20and%20counterfactual%20conditionals.pdf> (8-7-2010).

153. Id.

154. Ruth M. J. Byrne, Deductive reasoning with factual, possible, and counterfactual conditionals, 27 MEMORY & COGNITION

726 (1999)<http://www.tara.tcd.ie/bitstream/2262/39510/1/Deductive%20reasoning%20with%20factual,%20possible,%20and%20counterfactual%20conditionals.pdf> (8-18-2010).

155. See Douglas Walton, FUNDAMENTALS OF CRITICAL ARGUMENTATION 7 (2006).

156. Huhn, The Stages of Legal Reasoning: Formalism, Analogy, and Realism, 48, VILL. L. REV. 305, 309 (2003).

157.Sangeet Khemlani & P.N. Johnson-Laird, Disjunctive Illusory Inferences and How to Eliminate Them, 37 MEMORY &COGNITION 615, 615 (2009).

158.Id. at 616.

159.Id. at 614.

160. Hugo Mercier and Dan Sperber, Why do humans reason? Arguments for an argumentative theory, BEHAVIORAL AND BRAIN

SCIENCES p. 14 (2010) <http://www.dan.sperber.fr/wp-content/uploads/2009/10/MercierSperberWhydohumansreason.pdf> (8-17-2010).

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161. Turn the “8-card” and the “brown card.” The “3-card” will not validate or invalidate the conditional. The “red card” will notvalidate or invalidate the conditional either, because even if the reverse of the “red card” is an odd number, it doesn’t address theConditional, which only applies when the Antecedent is an even number. If the brown card has an even number on the reverseside, it will invalidate the Conditional, because the Antecedent (8) will be true when the Consequent (reverse side) is false.

162. Osman, supra n.6 p. 1002.

163. Osman, supra n. 6 p. 1002.

164. Osman, supra n. 6 p. 1001.

165. Aidan Feeney (Ed.), Evan Heit (Ed), INDUCTIVE REASONING: EXPERIMENTAL, DEVELOPMENTAL, AND COMPUTATIONAL

APPROACHES xiii (1990).

166. John Stuart Mill, A SYSTEM OF LOGIC, Book 3, ch. 2, § 1 <http://oll.libertyfund.org/title/246/39835> (8-12-2010).

167. This conceptualization was taken from a letter of Charles Sanders Peirce in 1905. See Abduction<http://www.helsinki.fi/science/commens/terms/abduction.html> (8-9-2010).

168. <http://www.mhhe.com/mayfieldpub/ct/ch11/glossary.htm> (8-9-2010).

169. John L. Pollock, Defeasible Reasoning 2 < http://oscarhome.soc-sci.arizona.edu/ftp/PAPERS/Defeasible%20Reasoning-Adler&Rips.pdf> (8-16-2010).

170. Mercier, supra n. 160 p. 15.

171. See Spatial Cognition and Computation <http://www.sis.pitt.edu/-scc> (8-17-2010); Memory and Cognition<http://mc.psychonomic-journals.org> (8-18-2010).

172. <http://www.nizkor.org/features/fallacies/ignoring-a-common-cause.html> (8-12-2010).

173. Jøsang, supra n. 151 p. 4

174. Osman, supra n. 6 p. 1000.

175. Id.

176. Id.

177. Bruce D. Burns and Bryan Corpus, Randomness and inductions from streaks: “Gambler’s fallacy” versus “hot hand,” 11PSYCHONOMIC BULLETIN & REVIEW 179, 179 (2004).

178. Id. at 170.

179. Id. at 182.

180. Jonathan J. Koehler, Misconceptions About Statistics and Statistical Evidence (2007) (draft)<http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.140.215&rep=rep1&type=pdf> (8-9-2010).

181. Id. at 3-4.

182. Id. at 4-5.

183. Id. at 6-7.

184. Id. at 8-9.

185. Id. at 10.

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186. Id. at 12.

187. Id. at 12-14.

188. Id. at 14-15

189. Id. at 15-16.

190. Bertrand Russell described Peirce as “the greatest American thinker ever.” Karl Popper called him “one of the greatestphilosophers of all time.” <http://en.wikipedia.org/wiki/Charles_Sanders_Peirce> (8-9-2010).

191. Charles S. Peirce, quoted in Thomas Sebcok, You Know My Method: A Juxtaposition of Charles S. Peirce and SherlockHolmes, p. 8 <http://www.aber.ac.uk/media/Documents/short/abduction.html> (8-9-2010).

192. Id. at p. 8.

193. Id.

194. Abduction <http://www.helsinki.fi/science/commens/terms/abduction.html> (8-9-2010).

195. Id.

196. Id.

197. Taken from Peirce’s 1903 lecutres at Harvard <http://www.helsinki.fi/science/commens/terms/abduction.html> (8-9-2010).



200. James Hawthorne, Stanford Encyclopedia of Philosophy, Inductive Logic p. 8 (2008)<http://plato.stanford.edu/entries/logic-inductive> (8-17-2010) (“Hawthorne”).

201. Id. at 11.

202. All of the following quoted material regarding the Monty Hall Dilemma comes from the following URL:<http://www.marilynvossavant.com/forum/viewtopic.php?t=64&postdays=0&postorder=asc&start=0&sid=bc22dd63985958bf395e9e22dc5b0024> (8-7-2010).

203. Hawthorne, supra n. 200 pp. 21-25.

204. Ulrike Hahn, Adam J.L. Harris, Adam Corner, Argument Content and Argument Source: An Exploration, 29 INFORMAL

LOGIC 337, 340 (2009) <http://www.phaenex.uwindsor.ca/ojs/leddy/index.php/informal_logic/article/download/2903/2340> (8-6-2010).

205. <http://en.wikipedia.org/wiki/Bayesian_probability> (8-6-2010).

206. Bayes’ Rule Calculator <http://stattrek.com/Tools/BayesRuleCalculator.aspx> (8-17-2010).

207. Gaëlle Villejoubert and David R. Mandel, The Inverse Fallacy: An Account of Deviations From Bayes’s Theorem and theAdditivity Principle, 30 MEMORY AND COGNITION 171, 171 (2002)<http://mc.psychonomic-journals.org/content/30/2/171.full.pdf> (8-17-2010).

208. Jøsang, supra n.151 p. 2.

209. Hahn, supra n. 204 p. 341.

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210. Fabrizio Macagno and Douglas Walton, Argument From Analogy in Law: The Classical Tradition, and Recent Theories 42PHILOSOPHY AND RHETORIC 158 (2009) <http://www.dougwalton.ca/papers%20in%20pdf/09Analogy.pdf> (8-15-2010).

211. John Stuart Mill, A SYSTEM OF LOGIC Book III, ch. 20 §§ 2 & 3 <http://oll.libertyfund.org/title/246/39874> (8-12-2010).

212. Id.

213. John Stuart Mill, A SYSTEM OF LOGIC Book III, ch. 20 § 3 <http://oll.libertyfund.org/title/246/39874> (8-12-2010).

214. Id.

215. Aldisert, supra n.114 p. 17.

216. Kyllo v. U.S., 533 U.S. 27, 28 (2001).

217. Avenell v. Chrisman Properties, L.L.C. 2010 WL 1379972 *4 (Tex. App.--Houston [14 Dist.] 2010, no pet.).

218. Leo Groarke, Argumentation Schemes<http://philosophysother.blogspot.com/2009/03/groarke-leo-review-of-douglas-walton-et.html> (8-6-2010).

219. Hahn, supra n. 204 p. 341.

220. Patrick Bondy, Truth and Argument Evaluation, 30 INFORMAL LOGIC 142, 142 (2010)<http://www.phaenex.uwindsor.ca/ojs/leddy/index.php/informal_logic/article/download/2931/2406> (8-6-2010).

221. Julie Dickson, Interpretation and Coherance in Legal Reasoning, <http://plato.stanford.edu/entrier/legal-reas-interpret>(8-16-2010).

222. Jessen Associates, Inc. v. Bullock, 531 S.W.2d 593, 599 (Tex. 1976) (“A fundamental rule in the construction of statutes isto ascertain and give effect to the intent of the Legislature”).

223. United States v. American Trucking Ass'ns, 310 U.S. 534, 541-44 (1939).

224. United States v. Fisher, 6 U.S. (2 Cranch) 358, 386 (1805).

225. Simmons v. Arnim, 220 S.W. 66, 70 (Tex. 1920).

226. Caleb Nelson, Statutory Interpretation and Decision Theory, 74 UNIV. OF CHICAGO L. REV. 329, 353 (2007).

227. See Nelson, supra n. 226 p. 336.

228. See R. Posner, THE PROBLEMS OF JURISPRUDENCE 268 n. 10 (1990) ("Statutory drafting is often a rushed and carelessprocess").

229. General Chemical Corp. v. De La Lastra, 852 S.W.2d 916, 923 (Tex. 1993).

230. E. Levi, AN INTRODUCTION TO LEGAL REASONING 31 (1949).

231. Benjamin Cardozo, THE NATURE OF THE JUDICIAL PROCESS 15 (1921) (quoting Gray, NATURE AND SOURCES OF THE LAW).

232. Stephen Breyer, ACTIVE LIBERTY: INTERPRETING OUR DEMOCRATIC CONSTITUTION 88 (2005).

233. Stephen Breyer, On the Uses of Legislative History in Interpreting Statutes, 65 S.CAL.L.REV. 845, 861 (1992).

234. Id. at 865.

235. Nelson, supra n. 226 at 349.

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236. Caminetti v. United States, 242 U.S. 470, 485 (1917) ("[i]t is elementary that the meaning of a statute must, in the firstinstance, be sought in the language in which the act is framed, and if that is plain... the sole function of the courts is to enforce itaccording to its terms"); Satterfield v. Satterfield, 448 S.W.2d 456, 459 (Tex. 1969) ("Words in common use, when used by theLegislature in a statute, . . . are to be interpreted as intending to express the meaning in which they are ordinarily understood").

237. "Under the rule of ejusdem generis, where specific and particular enumerations of persons or things in a statute arefollowed by general words, the general words are not to be construed in their widest meaning or extent, but are to be treated aslimited and applying only to persons or things of the same kind or class as those expressly mentioned." Stanford v. Butler, 142Tex. 692, 181 S.W.2d 269, 272 (1944). The rule of ejusdem generis gives way to statutory language which discloses a contrarylegislative intent. Carbide Intern., Ltd. v. State, 695 S.W.2d 653, 658 (Tex. App.--Austin 1985, no writ).

238. Sometimes it is not clear whether a listing in a statute is exhaustive or merely illustrative. Nelson, supra n. 226 p. 337;Maley v. 7111 Southwest Freeway, Inc., 843 S.W.2d 229, 231 (Tex. App.--Houston [14th Dist.] 1992, writ denied) (“an expresslisting of certain persons, things, consequences, or classes is equivalent to an express exclusion of all others”).

239. City of Tacoma, Washington v. FERC, 331 F.3d 106, 115 (D.C. Cir. 2003).

240. Words of a feather flock together. Jarecki v. G.D. Searle & Co., 367 U.S. 303, 307 (1961) ("a word is known by thecompany it keeps").

241. The last antecedent rule: Saade v. Villarreal, 280 S.W.3d 511, 519 n. 9 (Tex. App.--Houston [14th Dist.] 2009, pet. dism’d)(“generally, a relative or qualifying clause applies only to the immediately preceding words or clause”).

242. West Cameron Port v. Lake Charles Harbor & Terminal, 38 So.3d 577, 583 n. 2 (La. App. 2010) (“The doctrine holdingthat general words in a later statute do not repeal an earlier statutory provision dealing with a special subject.”)

243. Big H Auto Auction v. Saenz Motors, 665 S.W.2d 756, 758 (Tex. 1984).

244. Duson v. Poage, 318 S.W.2d 89, 96 (Tex. Civ. App.--Houston 1958, writ ref'd n.r.e.).

245. Lane v. Ross, 249 S.W.2d 591, 594 (Tex. 1952).

246. Bayou Pipeline Corp. v. Railroad Commission, 568 S.W.2d 122, 125 (Tex. 1978) (“Bayou relies on . . . cases in whichcourts have construed the word ‘and’ in a statute to mean ‘or.’ While there may be circumstances which call for such aconstruction, ordinarily the words ‘and’ and ‘or’ are not interchangeable. ”).

247.NLRB v. Catholic Bishop of Chicago, 440 U.S. 490, 501 (1979).

248. Welch v. Welch, 369 S.W.2d 434, 437 (Tex. Civ. App.--Dallas 1963, no writ).

249. Quick v. City of Austin, 7 S.W.3d 109, 132 (Tex. 1998). This canon has both descriptive and normative qualities. Nelson,supra n. 226 p. 357.

250. Jessen Associates, Inc. v. Bullock, 531 S.W.2d 593, 600 n. 9 (Tex. 1976); Lenhard v. Butler, 745 S.W.2d 101, 105 (Tex.App.--Fort Worth 1988, writ denied) (discussing the doctrine of "in para materia" as applied to two or more statutory provisionspertaining to the same subject).

251. Tex. Dep't. of Public Safety v. Schaejbe, 687 S.W.2d 727, 728 (Tex. 1985).

252. LaSara Grain Co. v. First Nat. Bank of Mercedes, 673 S.W.2d 558, 565 (Tex. 1984).

253. Maley v. 7111 Southwest Freeway, Inc., 843 S.W.2d 229, 231 (Tex. App.--Houston [14th Dist.] 1992, writ denied) ("wewill not adopt a construction that would render a law or provision absurd or meaningless").

254. Harris v. U.S., 536 U.S. 545, 555 (2002) (“when ‘a statute is susceptible of two constructions, by one of which grave anddoubtful constitutional questions arise and by the other of which such questions are avoided, our duty is to adopt the latter””).

255. Murray v. The Schooner Charming Betsy, 6 U.S. (2 Cranch) 64, 118, 2 L.Ed. 208 (1804) (Marshall, C.J.) (“an act ofCongress ought never to be construed to violate the law of nations if any other possible construction remains, and consequentlycan never be construed to violate neutral rights, or to affect neutral commerce, further than is warranted by the law of nations as

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understood in this country”) [1804 WL 1103].

256. Holy Trinity Church v. United States, 143 U.S. 457 (1892) ("It is a familiar rule, that a thing may be within the letter of thestatute and yet not within the statute, because not within its spirit, nor within the intention of its makers").

257. McNally v. United States, 483 U.S. 350 (1987).

258. United States v. Bass, 404 U.S. 336, 349 (1971) ("[U]nless Congress conveys its purpose clearly, it will not be deemed tohave significantly changed the federal-state balance").

259. Chevron v. Natural Resources Defense Council, 467 U.S. 837 (1984), which was substantially narrowed in U.S. v. MeadCorp., United States v. Mead Corp., 533 U.S. 218, 226-227 (2001).

260. Nelson, supra n. 226 p. 329.

261. The list is taken from <http://www.stanford.edu/dept/english/courses/sites/lunsford/pages/defs.htm> (8-5-2010).

262. Jeanne Fahnestock The Appeals: Ethos, Pathos, and Logos <http://members.tripod.com/butler_s/f2002-1002/appeals.html> (8-11-2010).

263. Aristotle, RHETORIC <http://grammar.about.com/od/il/g/inventedethos.htm> (8-17-2010).

264. <http://grammar.about.com/od/rs/g/situatedethos.htm> (8-12-2010).

265. Orgren, supra n. http://rhetoric.byu.edu/figures/e/enthymeme.htm pp. 4-5.

266. Brian Ogren, Aristotle’s Rhetoric and the Cognition of Being: Human Emotions and the Rational-Irrational Dialectic, 8MINERVA 4-5 (2004) <http://www.ul.ie/~philos/vol8/aristotle.html> (8-1--2010).

267. <http://rhetoric.byu.edu/figures/e/enthymeme.htm> (8-12-2010).

268. Zarefsky, supra n. 76 Vol. 2 p. 58 (2d ed. The Teaching Company 2005) <http://www.teach12.com>.

269. See Section XII.

270. Zarefsky, supra n. 76 vol. 2 p. 58.

271. Douglas Walton and Fabrizio Macagno, Enthymemes, Argumentation Schemes and Topics, LOGIQUE & ANALYSE 39, 43(2009) <http://www.dougwalton.ca/papers%20in%20pdf/09ScmTopEnt.pdf> (8-16-2010).

272. A “maxim” is a short, pithy saying. <http://rhetoric.byu.edu> (8-17-2010).

273. An “adage” is a short, pithy saying, or traditional expression of conventional wisdom. <http://rhetoric.byu.edu> (8-17-2010).

274. “Gnome” is one of several terms describing short, pithy sayings. <http://rhetoric.byu.edu> (8-17-2010).

275. “Paroemia” is one of several terms describing short, pithy sayings. <http://rhetoric.byu.edu> (8-17-2010).

276. “Sententia” is one of several terms describing short, pithy sayings. <http://rhetoric.byu.edu> (8-17-2010).

277. See Silva Rhetoricae (the Forest of Rhetoric) <http://rhetoric.byu.edu> (8-17-2010).

278. The song was written by Pete Seeger in 1955, based on a sentence taken from a Ukranian folk song, and was then added toand put into its final shape by Joe Hickerson in 1960. The song was popularized by the Kingston Trio in 1961.

279. Richard Nordquist, What Is an Analogy? <http://grammar.about.com/od/rhetoricstyle/f/qanalogy07.htm> (8-9-2010).

280. Richard Nordquist, Analogy? <http://grammar.about.com/od/ab/g/analogy.htm> (8-9-2010).

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281. Richard Nordquist, Analogy? <http://grammar.about.com/od/rs/g/simileterm.htm> (8-9-2010).

282.Tom McArthur, THE OXFORD COMPANION TO THE ENGLISH LANGUAGE (1992).

283. John Stuart Mill, A SYSTEM OF LOGIC Book V, ch. 5 § 7.

284. <http://rhetoric.byu.edu/Figures/E/expeditio.htm> (8-5-2010).

285. <http://rhetoric.byu.edu/figures/P/proecthesis.htm> (8-5-2010).

286. YouTube < http://www.youtube.com/watch?v=jRth45yU_2Q> (8-17-2010).

287.Andrew R. Cline, Rhetorica: A Rhetorical Primer (2006) <http://rhetorica.net/textbook/invention.htm> (8-17-2010).

288. Style <http://rhetoric.byu.edu/canons/Style.htm> (8-11-2010).



291. Style: Levels of Style <http://rhetoric.byu.edu/canons/Style/Style-Levels.htm> (8-11-2010).

292. Qualities of Style <http://rhetoric.byu.edu/canons/Style/Style-Qualities.htm> (8-11-2010).

293. Figures of Speech <http://rhetoric.byu.edu/Figures/Figures-Overview.htm> (8-11-2010).

294.See Cline, supra n.287.

295. <http://www.psych.ucsb.edu/~hegarty/papers/SCCgestures.pdf >(8-17-2010).

296.See Cline, supra n. 287.

297.See Figures of Order <http://rhetoric.byu.edu/Figures/Groupings/of%20order.htm> (8-17-2010).

298. Snopes <http://www.snopes.co25, 2008) m/language/mistakes/noprice.asp> (8-12-2010).

299.Laurence Tribe, The Invisible Constitution, Ford Hall Forum (September 25, 2008)<http://fora.tv/2008/09/25/Laurence_H_Tribe_The_Invisible_Constitution#chapter_03 > (8-1-2010). The incident is detailed inJames J. Kirschke, GOUVERNEUR MORRIS: AUTHOR, STATESMAN, AND MAN OF THE WORLD 169 (2005).

300.Richard Brookhiser, GENTLEMAN REVOLUTIONARY: GOUVERNEUR MORRIS, THE RAKE WHO WROTE THE CONSTITUTION 90(2003).

301. Strunk & White, ELEMENTS OF STYLE 7 (3d ed. 1979).

302. Copperud, AMERICAN USAGE AND STYLE: THE CONSENSUS 188 (1980).

303. Strunk & White, ELEMENTS OF STYLE 9 (3d ed. 1979).

304. See <http://changingminds.org/techniques/language/modifying_meaning/emphasis_writing.htm> (8-17-2010).

305. “Italic is sometimes used to differentiate or to give greater prominence to words, phrases, etc. However, an excessive amount of italic defeats this purpose and should be restricted.” U.S. Government Printing Office Style Manual § 11.1 (2008)<http://frwebgate.access.gpo.gov/cgi-bin/getdoc.cgi?dbname=2008_style_manual&docid=f:chapter11.wais> (8-17-2010).

306. Edward D. Johnson, THE HANDBOOK OF GOOD ENGLISH 249-50 (1982) [“Johnson”].

307. <http://www.nytimes.com/2009/06/28/magazine/28FOB-onlanguage-t.html> (8-17-2010).

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308. “There are many people in the world who really don't understand, or say they don't, what is the great issue between the freeworld and the Communist world. / Let them come to Berlin. / There are some who say -- There are some who say thatcommunism is the wave of the future. / Let them come to Berlin. / And there are some who say, in Europe and elsewhere, we canwork with the Communists. / Let them come to Berlin. / And there are even a few who say that it is true that communism is anevil system, but it permits us to make economic progress. / Lass' sie nach Berlin kommen. / Let them come to Berlin. . . .”<http://www.americanrhetoric.com/speeches/jfkberliner.html> (8-17-2010).

309. Personal pronouns are: I, we, you, thou, he, she, it, they.

310. Demonstrative pronouns are: this, these, that, and those. See René Magritte’s painting The Treachery of Images (1928-29),which is a drawing of a pipe with the phrase in French: “This is not a pipe.” If “this” means the image depicted, then the paintingif false. If “this” means the painting, then the statement is true.

311. Relative pronouns are: who, which, that, as.

312. Indefinite pronouns include: each, all, everyone, either, one, both, any, such, somebody.

313. Interrogative pronouns are: who, which, what.

314. Possession pronouns are: my, your, his, her, our, their.

315. Reflexive pronouns are: myself, himself, herself, and itself.

316. Bryan A. Garner, Judges on Effective Writing: The Importance of Plain Language, MICHIGAN B. J. (Feb. 2005) http://www.michbar.org/journal/pdf/pdf4article845.pdf (8-17-2010).

317. See e.g., NLRB STYLE MANUAL 51-66 (2000) <http://www.nlrb.gov/nlrb/legal/manuals/stylemanual.pdf> (8-17-2010).

318. Richard Nordquist, Top 20 Figures of Speech <http://grammar.about.com/od/rhetoricstyle/a/20figures.htm> (7/28/2010);Figure of Speech, Wikipedia <http://en.wikipedia.org/wiki/Figure_of_speech> (on 7/28/2010).

319. H. Porter Abbott, THE CAMBRIDGE INTRODUCTION TO NARRATIVE 3 (2d ed. 2002).

320. James Phelan, NARRATIVE AS RHETORIC: TECHNIQUE, AUDIENCES, ETHICS, IDEOLOGY 219 (1996)<http://www.ohiostatepress.org/books/complete%20pdfs/phelan%20narrative/14.pdf> (8-9-2010).

321. Abbott, supra n. 319 p. 4.

322. Id. at 219.

323. Maggie Bruck and Stephen J. Ceci, The Suggestibility of Children’s Memory, 50 ANNU. REV. PSYCHOL. 419, 421 (1999)<http://www.arts.uwaterloo.ca/~doneill/cogsci600/Kenyon.pdf > (8-17-2010).

324. <http://www.youtube.com/watch?v=FbIX1CP9qr4> (8-12-2010).

325. <http://www.fff.org/comment/com0311c.asp> (8-12-2010).

326.E. F. Loftus, EYEWITNESS TESTIMONY (1996). Elizabeth F. Loftus, Leading Questions and the Eyewitness Report, 7COGNITIVE PSYCHOLOGY 550 (1975) (to locate Dr. Loftus’ seminal article, go to Google’s search page and search for “LeadingQuestions and the Eyewitness Report”).

327. Caperton v. A.T. Massey Coal Co., 556 U.S. ----, ----, 129 S.Ct. 2252, 2261, 2269-2272 (2009) (Roberts, C. J., dissenting).

328. <http://www.uottawa.ca/academic/arts/writcent/hypergrammar/usetense.html> (8-15-2010).

329. <http://www.bartleby.com/141/strunk5.html> (8-12-2010).

330. Phillip Sipiora, Introduction: the Ancient Concept of Kairos http://www.sunypress.edu/pdf/60473.pdf (8-17-2010), FROM

RHETORIC AND KAIROS : ESSAYS IN HISTORY, THEORY, AND PRAXIS, Phillip Sipiora and James S. Baumlin, editors.

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331. Carl Glover, Kairos and Composition: Modern Perspectives on an Ancient Idea, (dissertation), quoted in Steven D. Krause,The Immediacy of Rhetoric: Definitions, Illustrations, and Implications, ch. 1 (dissertation)<http://www.emunix.emich.edu/~krause/Diss/> (8-17-2010).

332.Mercier, supra n. 160 p. 15.

333. According to the Greek historian Heroditus, ch. 1.91, Lydian King Croesus, sent extravagant gifts to the Oracle at Delphi,inquiring whether he should attack Cyrus the Great, founder of the Persian Empire. The Oracle responded that "if he attacked thePersians, he would destroy a mighty empire." Croesus initiated the attack, was defeated and enslaved, but blamed his decision toattack on the Oracle. Cyrus sent to Delphi for an explanation, and the Oracle said: "he ought, if he had been wise, to have sentagain and inquired which empire was meant, that of Cyrus or his own; but if he neither understood what was said, nor took thetrouble to seek for enlightenment, he has only himself to blame for the result."<http://www.iranchamber.com/history/herodotus/herodotus_history_book1.php> (8-17-2010).

334. See <http://www.huffingtonpost.com/2010/06/09/kevin-costner-testifies-b_n_606542.html> (8-17-2010).

335. “In June, 2002, Senator George Voinovich (R – Ohio) refused to attend the Senate’s Environment and Public Works CleanAir Subcommittee hearing to protest the appearance of Kevin Richardson, member of the pop music group, the Backstreet Boys.According to Voinovich, ‘It’s just a joke to think that this witness can provide members of the United States Senate withinformation on important geological and water quality issues. We’re either serious about the issues or we are running asideshow.’”(Rulon 2002, 1). Harry C. Strine IV, “Your Testimony Was Splendid: The Treatment of Celebrities andNon-Celebrities in Congressional Hearings,”<http://www.allacademic.com//meta/p_mla_apa_research_citation/0/9/3/7/8/pages93788/p93788-2.php> (8-17-2010).

336. Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579 (1993).

337. Burrow v. Arce, 997 S.W.2d 229, 235 (Tex. 1999).

338. <http://www.nizkor.org/features/fallacies/appeal-to-fear.html> (8-12-2010).

339. <http://www.nizkor.org/features/fallacies/appeal-to-flattery.html> (8-12-2010).

340. <http://www.nizkor.org/features/fallacies/appeal-to-novelty.html> (8-12-2010).

341. <http://www.nizkor.org/features/fallacies/appeal-to-pity.html> (8-12-2010).

342. <http://www.nizkor.org/features/fallacies/appeal-to-ridicule.html> (8-12-2010).

343. <http://www.nizkor.org/features/fallacies/appeal-to-tradition.html> (8-12-2010).

344. <http://www.nizkor.org/features/fallacies/ad-hominem-tu-quoque.html> (8-12-2010).

345. <http://philosophy.lander.edu/logic/appendb.html> (8-12-2010).


347. Mercier, supra n. 160 p. 15

348. <http://www.nizkor.org/features/fallacies/middle-ground.html> (8-17-2010).

349.Hillary Clinton said, on September 13, 2001: “Every nation has to either be with us, or against us. Those who harborterrorists, or who finance them, are going to pay a price.” < http://www.youtube.com/watch?v=DbYGYiGjpUs> (8-17-2010).

350.In his address on September 13, 2001to a joint session of congress, President George W. Bush said: “Either you are with us,or you are with the terrorists.”

351. <http://www.nizkor.org/features/fallacies/genetic-fallacy.html> (8-12-2010).

352. <http://www.nizkor.org/features/fallacies/burden-of-proof.html> (8-12-2010).

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353. <http://www.nizkor.org/features/fallacies/misleading-vividness.html> (8-12-2010).

354. Antony Flew, THINKING ABOUT THINKING (1975).

355. <http://www.nizkor.org/features/fallacies/confusing-cause-and-effect.html> (8-12-2010).

356. <http://www.nizkor.org/features/fallacies/post-hoc.html> (8-12-2010).

357. Hausman, Alan, Howard Kahane, and Paul Tidman, Logic and Philosophy: A Modern Introduction 357 (2007), quoted inBrian Lightbody and Michael Berman, The Metaphoric Fallacy to a Deductive Inference, 30 INFORMAL LOGIC 185, 189 (2010)<http://www.phaenex.uwindsor.ca/ojs/leddy/index.php/informal_logic/article/download/1192/2410> (8-6-2010).

358. Internet Encyclopedia of Philosophy <http://www.iep.utm.edu/fallacy> (8-7-2010).

359. “Figures of speech” in this context related to ambiguity arising when Greek words had different cases or genders that werespelled the same way. We don’t have that problem in English.

360. John Stuart Mill, A SYSTEM OF LOGIC Book 5, ch. 2, § 1 (1843) <http://oll.libertyfund.org/title/247/40031> (8-12-2010).



363. John Stuart Mill, A SYSTEM OF LOGIC Book 5, ch. 5 (1843) <http://oll.libertyfund.org/title/247/40041> (8-12-2010).



366. Nolt, supra n. 135 ch. 8.

367. Nolt, supra n. 135 ch. 8.

368. Toulmin’s invention of warrants has been described as “the most important contribution since Aristotle distinguishedpremises from conclusions.” David Hitchcock, Johnson’s “Rise of Informal Logic”, 18 INFORMAL LOGIC 273, 275 (1996).<http://ojs.uwindsor.ca/ojs/leddy/index.php/informal_logic/article/download/2385/1827> (8-6-2010).

369. Walton, supra n. 271 p. 45.

370. Id. at 3.

371. Id. at 4-5.

372. Id. at 39.

373. Id. at 39.

374. Id. at 41.

375. Id. at 41.

376. Id. at 42.

377. A “colorable claim for relief” is a claim that, on appropriate proof, would support a recovery in a bankruptcy context. In reSTN Enterprises, 779 F.2d 901, 904 (2d Cir.1985). For example, the examiner appointed by the court to conduct an investigationinto the Lehman Brothers bankruptcy found that colorable claims existed against high management and against Lehman’sauditors, Ernst and Whinney. See <http://lehmanreport.jenner.com/VOLUME%201.pdf> (8-3-2010).

378. DSM-IV-TR p. xxxi (2000).

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379. http://www.brainyquote.com/quotes/quotes/a/alberteins100201.html (8-18-2010).

380. Jeremy Waldron, Vagueness in Law and Language: Some Philosophical Issues, 82 CAL. L. REV. 509, 517 (1994).

381. See e.g., Jonathan St. B. T. Evans, The heuristic-analytic theory of reasoning: Extension and evaluation, 13PSYCHONOMIC BULLETIN & REVIEW 378 (2006) <http://pbr.psychonomic-journals.org/content/13/3/378.full.pdf>(8-18-2010) (suggesting that heuristic-analytic reasoning is the basic mode of thought, that is sometimes assisted or supplantedby logical thinking.)

382. Hal R. Arkes, Impediments to Accurate Clinical Judgment, 49 JOURNAL OF COUNSELING & CLINICAL PSYCHOLOGY 323(1981), citing M. Snyder, Seek and Ye Shall Find . . ., in E.T. Higgins, C.P. Herman, & M.P. Zanna (eds.) SOCIAL COGNITION:THE ONTARIO SYMPOSIUM ON PERSONALITY AND SOCIAL PSYCHOLOGY (1981).

383. Howard N. Garb, STUDYING THE CLINICIAN 183 (1998).

384. Abraham Lincoln, circa 1850. The expanded quotation is: “Extemporaneous speaking should be practiced and cultivated. Itis the lawyer’s avenue to the public. However able and faithful he may be in other respects, people are slow to bring himbusiness, if he cannot make a speech. And yet there is not a more fatal error to young lawyers, than relying too much on speechmaking. If any one, upon his rare powers of speaking, shall claim exemption from the drudgery of the law, his case is a failure inadvance.” <http://showcase.netins.net/web/creative/lincoln/speeches/lawlect.htm> (7-29-2010).

385. Abraham Lincoln, quoted in The Independent for September 1, 1864, cited at<http://www.math.lsu.edu/~madden/M4005s2006/geometry1.pdf> (7-29-2010).

386. Osman, supra n. 6 p. 1001.

387. Kyllo v. U.S., 533 U.S. 27 (2001).

388. The TSA website has posted sample images. <http://www.tsa.gov/blog/uploaded_images/untitled-717391.JPG> (8-16-2010).

389. <http://www.sonofthesouth.net/slavery/abraham-lincoln/abraham-lincoln-cooper-union-speech.htm>.

390. Abraham Lincoln, Debate with Douglas, Columbus, Ohio, Sept. 1859.

391. Nuremberg Principle IV provided: “The fact that a person acted pursuant to order of his Government or of a superior doesnot relieve him from responsibility under international law, provided a moral choice was in fact possible to him.”<http://www.icrc.org/ihl.nsf/full/390> (8-17-2010).

392. Madison died on the day of the 50th anniversary of the signing of the Declaration of Independence, as did John Adams. Thetribulations of reassembling and preserving Madison’s entire body of writing is detailed at<http://memory.loc.gov/ammem/collections/madison_papers/mjmabout2.html> (8-17-2010).

393. John Stuart Mill, 8 A SYSTEM OF LOGIC RATIONCINATION AND INDUCTIVE, Beck V, Ch. 3 § 1 (1843)<http://oll.libertyfund.org/index.php?option=com_staticxt&staticfile=show.php%3Ftitle=247&layout=html#chapter_40033> (8-17-2010

394. Hélène Landemore, Majority Rule and the Wisdom of Crowds: the Task-Specificity of Majority Rule as a Predictive Tool<www.sas.upenn.edu/ppe/documents/MajorityRule_Landemore.pdf> (8-5-2010).

395. Johnny Cochran’s closing argument in the O.J. Simpson case <http://www.youtube.com/watch?v=jRth45yU_2Q&NR=1>(8-17-2010).

396. Taylor v. State, 671 S.W.2d 535, 538 (Tex. App.--Houston [1st Dist.] 1983, no writ).

397. Universe Life Ins. Co. v. Giles, 950 S.W.2d 48, 71 (Tex. 1997).

398. Read v. Scott Fetzer Co., 990 S.W.2d 732, 736 (Tex. 1998).

399. In re M.C.F., 121 S.W.3d 891, 896 (Tex. App.--Fort Worth 2003, no pet.).

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400. This preference for the simple explanation over the more complex is known as the Rule of Parsimony, or Occam’s Razor.

401. Austin Cline, Lexical Definitions <http://atheism.about.com/od/logicalarguments/a/def_lexical.htm> (8-9-2010).

402. Austin Cline, Stipulative Definitions <http://atheism.about.com/od/logicalarguments/a/def_stipulative.htm> (8-9-2010).

403. Austin Cline, Persuasive Definitions <http://atheism.about.com/od/logicalarguments/a/def_persuasive.htm> (8-9-2010).

404. Austin Cline, Precising Definitions <http://atheism.about.com/od/logicalarguments/a/def_precising.htm> (8-9-2010).

405. Austin Cline, Theoretical Definitions <http://atheism.about.com/od/logicalarguments/a/def_theoretical.htm> (8-9-2010).

406. <http://www.youtube.com/watch?v=jRth45yU_2Q&NR=1> (8-17-2010).

407. Richard Crawley translation (1874).

408. Reductio ad Absurdum, Internet Encyclopedia of Philosophy <http://www.iep.utm.edu/reductio/#H1> (8-15-2010).

409. This type of question had been anticipated, and an answer rehearsed, but Dukakis didn’t give the rehearsed answer. See<http://archive.newsmax.com/archives/articles/2004/9/27/103737.shtml> (8-12-2010).

410. Katz v. United States, 389 U.S. 347, 351 (1967).


412. Nolt, supra n. 135 p. 206.

413. Nolt, supra n. 135 p. 207.

414.<www.iép.utm.edu/prop-log>4 p. 10 (8-17-2010).

415. Norman Malcolm, The Nature of Entailment, 49 MIND 333 (1940) <http://www.jstor.org/pss/2250488> (8-14-2010).

416. Defeasible Reasoning, Stanford Encyclopedia of Philosophy <http://plato.stanford.edu/entries/reasoning-defeasible> (8-15-2010).