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 XI. 



PHILOSOPHY OF INDUCTIVE INFERENCE. 



1. Philosophy of Inductive Inference . . . .250 



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

 <S3. The Relation of Cause and Effect . . . .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 



1 1 . 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 



