A System of Logic: Ratiocinative and Inductive, 7th Edition, Vol. I

Chapter V. _of the Import of Propositions._

§ 1. Doctrine that a proposition is the expression of a relation between two ideas 96

2. Doctrine that it is the expression of a relation between the meanings of two names 99

3. Doctrine that it consists in referring something to, or excluding something from, a class 103

4. What it really is 107

5. It asserts (or denies) a sequence, a coexistence, a simple existence, a causation 110

6. --or a resemblance 112

7. Propositions of which the terms are abstract 115

Chapter Vi. _of Propositions Merely Verbal._

§ 1. Essential and Accidental propositions 119

2. All essential propositions are identical propositions 120

3. Individuals have no essences 124

4. Real propositions, how distinguished from verbal 126

5. Two modes of representing the import of a Real proposition 127

Chapter Vii. _of the Nature of Classification, and

the Five Predicables._

§ 1. Classification, how connected with Naming 129

2. The Predicables, what 131

3. Genus and Species 131

4. Kinds have a real existence in nature 134

5. Differentia 139

6. Differentiæ for general purposes, and differentiæ for special or technical purposes 141

7. Proprium 144

8. Accidens 146

Chapter Viii. _of Definition._

§ 1. A definition, what 148

2. Every name can be defined, whose meaning is susceptible of analysis 150

3. Complete, how distinguished from incomplete definitions 152

4. --and from descriptions 154

5. What are called definitions of Things, are definitions of Names with an implied assumption of the existence of Things corresponding to them 157

6. --even when such things do not in reality exist 165

7. Definitions, though of names only, must be grounded on knowledge of the corresponding Things 167

BOOK II.. Of Reasoning.

OF REASONING.

CHAPTER I. Of Inference, or Reasoning, in general.

§ 1. Retrospect of the preceding book 175

2. Inferences improperly so called 177

3. Inferences proper, distinguished into inductions and ratiocinations 181

Chapter Ii. _of Ratiocination, or Syllogism._

§ 1. Analysis of the Syllogism 184

2. The dictum de omni not the foundation of reasoning, but a mere identical proposition 191

3. What is the really fundamental axiom of Ratiocination 196

4. The other form of the axiom 199

Chapter Iii. _of the Functions, and Logical Value, of the

Syllogism._

§ 1. Is the syllogism a petitio principii? 202

2. Insufficiency of the common theory 203

3. All inference is from particulars to particulars 205

4. General propositions are a record of such inferences, and the rules of the syllogism are rules for the interpretation of the record 214

5. The syllogism not the type of reasoning, but a test of it 218

6. The true type, what 222

7. Relation between Induction and Deduction 226

8. Objections answered 227

9. Of Formal Logic, and its relation to the Logic of Truth 231

Chapter Iv. _of Trains of Reasoning, and Deductive

Sciences._

§ 1. For what purpose trains of reasoning exist 234

2. A train of reasoning is a series of inductive inferences 234

3. --from particulars to particulars through marks of marks 237

4. Why there are deductive sciences 240

5. Why other sciences still remain experimental 244

6. Experimental sciences may become deductive by the progress of experiment 246

7. In what manner this usually takes place 247

Chapter V. _of Demonstration, and Necessary Truths._

§ 1. The Theorems of geometry are necessary truths only in the sense of necessarily following from hypotheses 251

2. Those hypotheses are real facts with some of their circumstances exaggerated or omitted 255

3. Some of the first principles of geometry are axioms, and these are not hypothetical 256

4. --but are experimental truths 258

5. An objection answered 261

6. Dr. Whewell's opinions on axioms examined 264

Chapter Vi. _the Same Subject Continued._

§ 1. All deductive sciences are inductive 281

2. The propositions of the science of number are not verbal, but generalizations from experience 284

3. In what sense hypothetical 289

4. The characteristic property of demonstrative science is to be hypothetical 290

5. Definition of demonstrative evidence 292

Chapter Vii. _examination of Some Opinions Opposed to

the preceding doctrines._

§ 1. Doctrine of the Universal Postulate 294

2. The test of inconceivability does not represent the aggregate of past experience 296

3. --nor is implied in every process of thought 299

4. Sir W. Hamilton's opinion on the Principles of Contradiction and Excluded Middle 306

BOOK III.. Of Induction.

OF INDUCTION.

CHAPTER I. Preliminary Observations on Induction in general.

§ 1. Importance of an Inductive Logic 313

2. The logic of science is also that of business and life 314

Chapter Ii. _of Inductions Improperly So Called._

§ 1. Inductions distinguished from verbal transformations 319

2. --from inductions, falsely so called, in mathematics 321

3. --and from descriptions 323

4. Examination of Dr. Whewell's theory of Induction 326

5. Further illustration of the preceding remarks 336

Chapter Iii. _on the Ground of Induction._

§ 1. Axiom of the uniformity of the course of nature 341

2. Not true in every sense. Induction per enumerationem simplicem 346

3. The question of Inductive Logic stated 348

Chapter Iv. _of Laws of Nature._

§ 1. The general regularity in nature is a tissue of partial regularities, called laws 351

2. Scientific induction must be grounded on previous spontaneous inductions 355

3. Are there any inductions fitted to be a test of all others? 357

Chapter V. _of the Law of Universal Causation._

§ 1. The universal law of successive phenomena is the Law of Causation 360

2. --i.e. the law that every consequent has an invariable antecedent 363

3. The cause of a phenomenon is the assemblage of its conditions 365

4. The distinction of agent and patient illusory 373

5. The cause is not the invariable antecedent, but the unconditional invariable antecedent 375

6. Can a cause be simultaneous with its effect? 380

7. Idea of a Permanent Cause, or original natural agent 383

8. Uniformities of coexistence between effects of different permanent causes, are not laws 386

9. Doctrine that volition is an efficient cause, examined 387

Chapter Vi. _of the Composition of Causes._

§ 1. Two modes of the conjunct action of causes, the mechanical and the chemical 405

2. The composition of causes the general rule; the other case exceptional 408

3. Are effects proportional to their causes? 412

Chapter Vii. _of Observation and Experiment._

§ 1. The first step of inductive inquiry is a mental analysis of complex phenomena into their elements 414

2. The next is an actual separation of those elements 416

3. Advantages of experiment over observation 417

4. Advantages of observation over experiment 420

Chapter Viii. _of the Four Methods of Experimental

Inquiry._

§ 1. Method of Agreement 425

2. Method of Difference 428

3. Mutual relation of these two methods 429

4. Joint Method of Agreement and Difference 433

5. Method of Residues 436

6. Method of Concomitant Variations 437

7. Limitations of this last method 443

Chapter Ix. _miscellaneous Examples of the Four Methods._

§ 1. Liebig's theory of metallic poisons 449

2. Theory of induced electricity 453

3. Dr. Wells' theory of dew 457

4. Dr. Brown-Séquard's theory of cadaveric rigidity 465

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

Chapter Xi. _of the Deductive Method._

§ 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._

§ 1. Explanation defined 518

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

6. Example from mental science 538

7. Tendency of all the sciences to become deductive 539

INTRODUCTION.

§ 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.

This diversity is not so much an evil to be complained of, as an inevitable and in some degree a proper result of the imperfect state of those sciences. It is not to be expected that there should be agreement about the definition of anything, until there is agreement about the thing itself. To define, is to select from among all the properties of a thing, those which shall be understood to be designated and declared by its name; and the properties must be well known to us before we can be competent to determine which of them are fittest to be chosen for this purpose. Accordingly, in the case of so complex an aggregation of particulars as are comprehended in anything which can be called a science, the definition we set out with is seldom that which a more extensive knowledge of the subject shows to be the most appropriate. Until we know the particulars themselves, we cannot fix upon the most correct and compact mode of circumscribing them by a general description. It was not until after an extensive and accurate acquaintance with the details of chemical phenomena, that it was found possible to frame a rational definition of chemistry; and the definition of the science of life and organization is still a matter of dispute. So long as the sciences are imperfect, the definitions must partake of their imperfection; and if the former are progressive, the latter ought to be so too. As much, therefore, as is to be expected from a definition placed at the commencement of a subject, is that it should define the scope of our inquiries: and the definition which I am about to offer of the science of logic, pretends to nothing more, than to be a statement of the question which I have put to myself, and which this book is an attempt to resolve. The reader is at liberty to object to it as a definition of logic; but it is at all events a correct definition of the subject of these volumes.

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