CONTENTS. 



^ 7. The dctluctive method henceforth 

 the main instrument of scientilic 

 iniiuir>' 286 



CHAPTER XIV. 

 Of the Limits to the Explanation of Laws of 



Aature ; and of Hypotheses. 

 ^ 1. Can all the sequences in nature be 

 resolvable into one law ? 



2. Ultimate laws cannot be less numer 



ous than the distinguishable feel 

 ings of our nature .... 287 



3. Ill what sense ultimate facts can be 



explained 289 



•1. The proper use of scientific liypoth 



eses 290 



5. Their indispensableness . . . 294 

 ti. Legitimate, how distinguished from 



illegitimate hypotheses 

 7. Some inquuies apparently hypothet 



ical are really ijiductive 



CHAPTER XV. 



Of Progressive Effects ; and of the Continued 

 Action of Causes. 



<;> 1. How a progressive effect results 

 from the simple continuance of 

 the cause 300 



2. — and from the progressiveness of 



the cause 302 



3. Derivative laws generated from a 



single ultimate law . . . 301 



CHAPTER XVI. 



Of Empirical Laws. 

 § 1. Definition of an empirical law . 305 



2. Derivative laws commonly depend 



upon collocations .... 306 



3. The collocations of the permanent 



causes are not reducible to any law 307 



■i And hence empirical laws cannot be 

 relied upon beyond the limits of 

 actual experience .... ib. 



5. Generalizations which rest only on 

 the Method of Agreement can only 

 be received as empirical laws . 308 



C. Signs from which an observed uni- 

 formity of sequence may be pre- 

 sumed to be resolvable . . . 309 



7. Most, if not all, cases of sequence 

 from very complex antecedents, 

 are resolvable . . . .311 



3. Two kinds of empirical laws . . 312 



CHAPTER XVII. 



Of Chance, and its Elimination. 

 % 1. The proof of empirical laws depends 



on the theon,' of chance . . 312 



2. Chance defined and characterized .313 



3. The elimination of chance . . 316 



4. Discovery of a residual phenomena 



by eliminating chance . . .317 



5. The doctrine of chances . . . 318 



CHAPTER XVJII. 

 Of the Calculation of Chances. 

 <i 1. The foundation of the doctrine of 

 chances, as taught by Laplace, de- 

 fective 319 



2. The real foundation, what . . 320 



Pago 



§ 3. Theorem of the doctrine of chances, 

 which relates to the cause of a 

 given event 322 



4. In what cases the doctrine is practi- 



cally applicable .... 320 



5. How applicable to the elimination 



oi chance ib. 



CHAPTER XIX. 



Of the Extension of Derivative Laws to adjacent 

 Cases. 



^ 1. Derivative laws, when not causal, 

 are almost always contingent upon 

 collocations 327 



2. On what grounds they can be ex- 



tended to cases beyond the bounds 

 of actual experience . . . 328 



3. Those cases must be adjacent cases 329 



CHAPTER XX. 



Of Analogy. 

 ^ 1. Various senses of the word analogy 332 



2. Nature of analogical evidence . ib. 



3. On what circumstances its value 



depends 335 



CHAPTER XXI. 



Of the Evidence of the Law of Universal 

 Causation. 

 ^ 1. The law of causality rests upon an 



induction by simple enumeration . 337 



2. In what cases such induction is 



allowable 339 



3. The universal prevalence of the law 



of causality may once have been 

 doubtful. 340 



4. Ground of its present certainty . 341 



5. Limits of the reliance due to it . 342 



CHAPTER XXU. 



Of Uniformities of Coexistence 7wt dependent 

 upon Causation. 

 ^ 1. The uniformities of coexistence 

 which result from laws of se- 

 quence 343 



2. The properties of Kinds are unifor- 



mities of coexistence . . . 344 



3. Some are derivative, others ultimate 345 



4. No universal axiom of coexistence . 346 



5. The evidence of uniformities of co- 



existence, how measured . . 347 

 0. When derivative, their evidence is 

 that of empirical laws . . . 348 



7. So also when ultmiaie . . .349 



8. The evidence stronger in proportion 



as the law is more general . . ib. 



9. Every distinct Kind must be ex- 



amined 350 



CHAPTER XXIIL 

 Of Approximate Generalizations, and Probable 



Evidence. 

 % 1. The inferences called probable, rest 



upon approximate generalizations 351 



2. Approximate generalizations less 



useful in science than in life . 352 



3. In what cases they must bo re- 



sorted to 353 



4. In what manner proved . . . 354 



5. With what precautions employed . 356 



