CONTENTS. xiii 



SECTION PAGE 



10. Illustrations of the Indirect Method . . . .113 



11. Fallacies analysed by the Indirect Method . . .117 



12. The Logical Abacus . . . . . .119 



13. The Logical Machine . . . . .123 



14. The Order of Premises . . . . .131 



15. The Equivalency of Propositions . . . .132 



16. The Nature of Inference . . . . .136 



CHAPTER VII. 



INDUCTION. 



1. Induction . . . . . . .139 



2. Induction an Inverse Operation . . . .140 



3. Induction of Simple Identities . . . .146 



4. Induction of Partial Identities . . . .149 



5. Complete Solution of the Inverse or Inductive Logical Pro 



blem . . . . . . .154 



6. The Inverse Logical Problem involving Three Terms . 157 



7. Distinction between Perfect and Imperfect Induction . 164 



8. Transition from Perfect to Imperfect Induction . .168 



BOOK II. 



NUMBER, VARIETY, AND PROBABILITY. 

 CHAPTER VIII. 



PRINCIPLES OF NUMBER. 



1. Principles of Number . . . . .172 



2. The Nature of Number . . . . .175 



3. Of Numerical Abstraction . . . . .177 



4. Concrete and Abstract Numbers . . . .178 



5. Analogy of Logical and Numerical Terms . . .180 



6. Principle of Mathematical Inference . . . .183 



7. Reasoning by Inequalities . . . . .186 



8. Arithmetical Reasoning . . . . .188 



9. Numerically Definite Reasoning . . . .190 



CHAPTER IX. 



THE VARIETY OP NATURE, OR THE DOCTRINE OP COMBINATIONS 

 AND PERMUTATIONS. 



1. The Variety of Nature . . . .195 



2. Distinction of Combinations and Permutations . . 200 



3. Calculation of Number of Combinations . . . 204 



4. The Arithmetical Triangle . . . . .206 



