xiv CONTENTS. 



SECTION PAGE 



5. Connexion between the Arithmetical Triangle and the 



Logical Abecedarium . . . . .214 



6. Possible Variety of Nature and Art . . . .216 



7. Higher Orders of Variety . . . . .219 



CHAPTER X. 



THEORY OF PROBABILITY. 



1. Theory of Probability . . . . .224 



2. Fundamental Principles of the Theory . . . 228 



3. Rules for the Calculation of Probabilities . . .231 



4. Employment of the Logical Abecedarium in questions of 



Probability . . . . . .234 



5. Comparison of the Theory with Experience . . . 236 



6. Probable Deductive Arguments .... 239 



7. Difficulties of the Theory . . . . .243 



CHAPTER XL 



PHILOSOPHY OF INDUCTIVE INFERENCE. 



1. Philosophy of Inductive Inference .... 250 



2. Various Classes of Inductive Truths . . . .251 



3. The Relation of Cause and Eifect .... 253 



4. Fallacious Use of the Term Cause . . . .254 



5. Confusion of Two Questions . . . . .256 



6. Definition of the Term Cause .... 257 



7. Distinction of Inductive and Deductive Results . .260 



8. On the Grounds of Inductive Inference . . .262 



9. Illustrations of the Inductive Process . . .263 



10. Geometrical Reasoning . . . . .268 



11. Discrimination of Certainty and Probability in the Inductive 



Process ....... 271 



CHAPTER XII. 



THE INDUCTIVE OR INVERSE APPLICATION OF THE THEORY 

 OF PROBABILITIES. 



1. The Inductive or Inverse Application of the Theory of 



Probabilities . . . . . .276 



2. Principle of the Inverse Method . . . .279 



3. Simple Applications of the Inverse Method . . .281 



4. Application of the Theory of Probabilities in Astronomy . 285 



5. Statement of the General Inverse Problem . . .289 



6. Simple Illustration of the Inverse Problem . . .292 



7. General Solution of the Inverse Problem . . . 295 



8. Rules of the Inverse Method . . . .297 



9. Fortuitous Coincidences ..... 302 

 10. Summary of the Theory of Inductive Inference . . 307 



