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CONTENTS. 



PAGE 



CnAPTKE XVI. Of Empirical Laws. 

 § 1. Definition of an empirical law 366 



2. Derivative laws commonly depend on col- 



locations 367 



3. The collocations of the permanent causes 



are not reducible to any law 36T 



4. Hence empirical laws can not be relied on 



beyond the limits of actual experience. . . 368 



5. Generalizations which rest only on the 



Method of Agreement can only be re- 

 ceived as empirical laws 309 



6. Signs from which an observed uniformity 



of sequence may be presumed to be re- 

 solvable 369 



7. Two kinds of empirical laws 371 



Chapter XVII. 0/ Chance, and its Elimination. 

 §1. The proof of empirical laws depends on 



the theory of chance 372 



2. Chance defined and characterized 373 



' 3. The elimination of chance 376 



4. Discovery of residual phenomena by elim- 

 inating chance 377 



6. The doctrine of chances 37S 



Chapter XVIII. 0/ the Calculation of Chances. 



§1. Foundation of the doctrine of chances, as 



taught by mathematics 379 



2. The doctrine tenable 380 



3. On what foundation it really rests 381 



4. Its ultimate dependence on causation 383 



5. Theorem of the doctrine of chances which ' 



relates to the cause of a given event 385 



6. How applicable to the elimination of 



chance 380 



Ch APTEK XIX. Of the Extension of Derivative Laws 

 to Adjacent Cases. 



§ 1. Derivative laws, when not casual, are al- 

 most always contingent on collocations. . 3S8 



2. On what grounds they can be extended to 



cases beyond the bounds of actual expe- 

 rience 389 



3. Those cases must be adjacent cases 390 



Chapter XX. Of Analogy. 

 5 1. Various senses of the word analogy 393 



2. Nature of analogical evidence 393 



3. On what circumstances its value depends. . 396 



Chapter XXI. Of the Evidence of the Law of Uni- 

 versal Causation. 

 § 1. The law of causality does not rest on an 



instinct 397 



2. — but on an induction by simple enumera- 



tion 400 



3. In what cases such induction is allowable. 402 



4. The universal prevalence of the law of cau- 



sality, on what grounds admissible 403 



Chaptee XXII. Of Uniformities of Co-existence 

 not dependent on Causation. 



§1. Uniformities of co-existence which result 



from laws of sequence 400 



2. The properties of Kinds are uniformities 



of co-existence 408 



3. Some are derivative, others ultimate 409 



4. No universal axiom of co-existence 410 



6. The evidence of uniformities of co-exist- 

 ence, how measured 411 



PAGE 



§ 6. When derivative, their evidence is that of 

 empirical laws 412 



7. So also when ultimate 413 



8. The evidence stronger in proportion as the 



law is more general 413 



9. Every distinct Kind must be examined 414 



Chapter XXIII. Of Approximate Generalizations, 

 and Probable Evidence. 



§ 1. The inferences called probable, rest on ap- 

 proximate generalizations 416 



2. Approximate generalizations less useful 



in science than in life 416 



3. In what cases they may be resorted to 417 



4. In what manner proved 418 



5. With what precautions employed 420 



6. The two modes of combining probabilities. 421 



7. How approximate generalizations may be 



converted into accurate generalizations 

 equivalent to them. 423 



Chapter XXIV. Of the Remaining Laws of Na- 

 ture. 



§ 1. Propositions which assert mere existence. 425 



2. Resemblance, considered as a subject of 



science . 426 



3. The axioms and theorems of mathematics 



comprise the principal laws of resem- 

 blance 427 



4. — and those of order in place, and rest on 



induction by simple enumeration 428 



6. The propositions of arithmetic alHrm the 

 modes of formation of some given num- 

 ber 429 



6. Those of algebra afllrm the equivalence 



of diflTereut modes of formation of num- 

 bers generally 432 



7. The propositions of geometry are laws of 



outward nature ' 433 



8. Why geometry is almost entirely deduct- 



ive 436 



9. Function of mathematical truths in the 



other sciences, and limits of that function. 436 



Chapter XXV. Of the Grounds of Disbelief. ^ 

 § 1. Improbability and impossibility 438 



2. Examination of Hume's doctrine of mir- 



acles 438 



3. The degrees of improbability correspond 



to differences in the nature of the gener- 

 alization with which an assertion con- 

 flicts .441 



4. A fact is not incredible because the chances 



are against it 443 



5. Are coincidences less credible than other 



facts? 444 



6. An opinion of Laplace examined 446 



BOOK IV. 



OF OPERATIONS SUBSIDIARY TO IN- 

 DUCTION. 



Chapter I. Of Observation and Description. 

 §1. Observation, how far a subject of logic — 449 

 2. A great part of what seems observation is 

 really inference 460 



