5. Examples of the Method of Residues 471
6. Dr. Whewell's objections to the Four Methods 475
CHAPTER X. _Of Plurality of Causes; and of the Intermixture of Effects._
§ 1. One effect may have several causes 482
2. --which is the source of a characteristic imperfection of the Method of Agreement 483
3. Plurality of Causes, how ascertained 487
4. Concurrence of Causes which do not compound their effects 489
5. Difficulties of the investigation, when causes compound their effects 494
6. Three modes of investigating the laws of complex effects 499
7. The method of simple observation inapplicable 500
8. The purely experimental method inapplicable 501
§ 1. First stage; ascertainment of the laws of the separate causes by direct induction 507
2. Second stage; ratiocination from the simple laws of the complex cases 512
3. Third stage; verification by specific experience 514
CHAPTER XII. _Of the Explanation of Laws of Nature._
2. First mode of explanation, by resolving the law of a complex effect into the laws of the concurrent causes and the fact of their coexistence 518
3. Second mode; by the detection of an intermediate link in the sequence 519
4. Laws are always resolved into laws more general than themselves 520
5. Third mode; the subsumption of less general laws under a more general one 524
6. What the explanation of a law of nature amounts to 526
CHAPTER XIII. _Miscellaneous Examples of the Explanation of Laws of Nature._
§ 1. The general theories of the sciences 529
2. Examples from chemical speculations 531
3. Example from Dr. Brown-Séquard's researches on the nervous system 533
4. Examples of following newly-discovered laws into their complex manifestations 534
5. Examples of empirical generalizations, afterwards confirmed and explained deductively 536
7. Tendency of all the sciences to become deductive 539
§ 1. There is as great diversity among authors in the modes which they have adopted of defining logic, as in their treatment of the details of it. This is what might naturally be expected on any subject on which writers have availed themselves of the same language as a means of delivering different ideas. Ethics and jurisprudence are liable to the remark in common with logic. Almost every writer having taken a different view of some of the particulars which these branches of knowledge are usually understood to include; each has so framed his definition as to indicate beforehand his own peculiar tenets, and sometimes to beg the question in their favour.