Chapter VI: The Indirect Method of Inference

1. The Indirect Method of Inference 81

2. Simple Illustrations 83

3. Employment of the Contrapositive Proposition 84

4. Contrapositive of a Simple Identity 86

5. Miscellaneous Examples of the Method 88

6. Mr. Venn’s Problem 90

7. Abbreviation of the Process 91

8. The Logical Alphabet 94

9. The Logical Slate 95

10. Abstraction of Indifferent Circumstances 97

11. Illustrations of the Indirect Method 98

12. Second Example 99

13. Third Example 100

14. Fourth Example 101

15. Fifth Example 101

16. Fallacies Analysed by the Indirect Method 102

17. The Logical Abacus 104

18. The Logical Machine 107

19. The Order of Premises 114

20. The Equivalence of Propositions 115

21. The Nature of Inference 118

CHAPTER VII.

INDUCTION.

1. Induction 121

2. Induction an Inverse Operation 122

3. Inductive Problems for Solution by the Reader 126

4. Induction of Simple Identities 127

5. Induction of Partial Identities 130

6. Solution of the Inverse or Inductive Problem, involving
Two Classes 134

7. The Inverse Logical Problem, involving Three Classes 137

8. Professor Clifford on the Types of Compound Statement
involving Four Classes 143

9. Distinction between Perfect and Imperfect Induction 146

10. Transition from Perfect to Imperfect Induction 149

BOOK II.

NUMBER, VARIETY, AND PROBABILITY.

CHAPTER VIII.

PRINCIPLES OF NUMBER.

1. Principles of Number 153

2. The Nature of Numbe 156

3. Of Numerical Abstraction 158

4. Concrete and Abstract Number 159

5. Analogy of Logical and Numerical Terms 160

6. Principle of Mathematical Inference 162

7. Reasoning by Inequalities 165

8. Arithmetical Reasoning 167

9. Numerically Definite Reasoning 168

10. Numerical meaning of Logical Conditions 171

CHAPTER IX.

THE VARIETY OF NATURE, OR THE DOCTRINE OF COMBINATIONS
AND PERMUTATIONS.

1. The Variety of Nature 173

2. Distinction of Combinations and Permutations 177

3. Calculation of Number of Combinations 180

4. The Arithmetical Triangle 182

5. Connexion between the Arithmetical Triangle and the
Logical Alphabet 189

6. Possible Variety of Nature and Art 190

7. Higher Orders of Variety 192

CHAPTER X.

THEORY OF PROBABILITY.

1. Theory of Probability 197

2. Fundamental Principles of the Theory 200

3. Rules for the Calculation of Probabilities 203

4. The Logical Alphabet in questions of Probability 205

5. Comparison of the Theory with Experience 206

6. Probable Deductive Arguments 209

7. Difficulties of the Theory 213

CHAPTER XI.

PHILOSOPHY OF INDUCTIVE INFERENCE.

1. Philosophy of Inductive Inference 218

2. Various Classes of Inductive Truths 219

3. The Relation of Cause and Effect 220

4. Fallacious Use of the Term Cause 221

5. Confusion of Two Questions 222

6. Definition of the Term Cause 224

7. Distinction of Inductive and Deductive Results 226

8. The Grounds of Inductive Inference 228

9. Illustrations of the Inductive Process 229

10. Geometrical Reasoning 233

11. Discrimination of Certainty and Probability 235

CHAPTER XII.

THE INDUCTIVE OR INVERSE APPLICATION OF THE THEORY
OF PROBABILITY.

1. The Inductive or Inverse Application of the Theory 240

2. Principle of the Inverse Method 242

3. Simple Applications of the Inverse Method 244

4. The Theory of Probability in Astronomy 247

5. The General Inverse Problem 250

6. Simple Illustration of the Inverse Problem 253

7. General Solution of the Inverse Problem 255

8. Rules of the Inverse Method 257

9. Fortuitous Coincidences 261

10. Summary of the Theory of Inductive Inference 265

BOOK III.

METHODS OF MEASUREMENT.