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