The Principles of Science: A Treatise on Logic

Jevons

1879

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Selected pages

FORMAL LOGIC DEDUCTIVE AND INDUCTIVE CHAPTER I	1

Simple Illustrations	2

Employment of the Contrapositive Proposition	3

The Powers of Mind concerned in the Creation of Science	4

Laws of Identity and Difference	5

The Nature of the Laws of Identity and Difference	6

Symbolic Expression of the Law of Contradiction	7

Certain Special Conditions of Logical Symbols PAGE 29	8

The Terrestrial Standard	314

The Pendulum Standard	315

Unit of Density	316

Unit of Mass	317

Natural System of Standards	319

Subsidiary Units	320

Derived Units	321

Provisional Units	323

The Process of Inference	9

Abstraction of Indifferent Circumstances	10

Deduction and Induction	11

Second Example	12

Symbolic Expression of Logical Inference	13

Expression of Identity and Difference	14

Fifth Example	15

Fallacies Analysed by the Indirect Method	16

General Formula of Logical Inference	17

The Logical Machine	18

The Order of Premises	19

The Propagating Power of Similarity	20

Anticipations of the Principle of Substitution	21

The Logic of Relatives	22

CHAPTER II	24

Twofold meaning of General Names	25

Abstract Terms	27

Substantial Terms	28

PROPOSITIONS	36

Propositions	39

Simple Identities 3 Partial Identities	40

Limited Identities	42

Negative Propositions	43

Conversion of Propositions	46

Twofold Interpretation of Propositions	47

CHAPTER IV	49

Deductive Reasoning 2 Immediate Inference 3 Inference with Two Simple Identities	51

Inference with a Simple and a Partial Identity	53

Inference of a Partial from Two Partial Identities	55

On the Ellipsis of Terms in Partial Identities 7 Inference of a Simple from Two Partial Identities	58

Inference of a Limited from Two Partial Identities	59

Miscellaneous Forms of Deductive Inference	60

Fallacies	62

INDUCTION PAGE	64

CHAPTER V	66

Expression of the Alternative Relation	67

Nature of the Alternative Relation	68

BOOK II	69

Laws of the Disjunctive Relation	71

Symbolic Expression of the Law of Duality	73

Various Forms of the Disjunctive Proposition	74

Inference by Disjunctive Propositions	76

Induction 121 C	117

Induction an Inverse Operation	122

Inductive Problems for Solution by the Reader	126

Induction of Simple Identities	127

Induction of Partial Identities	130

Solution of the Inverse or Inductive Problem involving Two Classes	134

The Inverse Logical Problem involving Three Classes	137

Professor Clifford on the Types of Compound Statement in volving Four Classes 137	143

Distinction between Perfect and Imperfect Induction	146

Transition from Perfect to Imperfect Induction	149

NUMBER VARIETY AND PROBABILITY CHAPTER VIII	153

Principles of Number PAGE	155

The Nature of Number	156

Of Numerical Abstraction	158

Concrete and Abstract Number	159

Analogy of Logical and Numerical Terms	160

Principle of Mathematical Inference	162

Reasoning by Inequalities	165

Arithmetical Reasoning	167

Numerically Definite Reasoning	168

Numerical meaning of Logical Conditions 162 165 167 168	171

CHAPTER IX	173

36	177

Calculation of Number of Combinations	180

The Arithmetical Triangle	182

PAGE 399	183

Ende des frunden Tails	187

Connexion between the Arithmetical Triangle and the Logical Alphabet	189

Possible Variety of Nature and	190

Higher Orders of Variety	192

BOOK VI	193

CHAPTER X	197

SECTION PAGE 5 Comparison of the Theory with Experience	206

37	208

Theory of Probability	209

400	210

Difficulties of the Theory	213

CHAPTER XI	218

Various Classes of Inductive Truths	219

The Relation of Cause and Effect	220

Fallacious Use of the Term Cause	221

Confusion of Two Questions	222

Definition of the Term Cause	224

Distinction of Inductive and Deductive Results	226

The Grounds of Inductive Inference	228

Illustrations of the Inductive Process	229

43	230

146	232

Geometrical Reasoning	233

Discrimination of Certainty and Probability	235

CHAPTER XII	240

Principle of the Inverse Method	242

Simple Applications of the Inverse Method	244

Fundamental Principles of the Theory 3 Rules for the Calculation of Probabilities 4 The Logical Alphabet in questions of Probability 173	247

The General Inverse Problem	250

Simple Illustration of the Inverse Problem	253

46	254

General Solution of the Inverse Problem	255

Rules of the Inverse Method	257

Fortuitous Coincidences	261

402	263

Summary of the Theory of Inductive Inference	265

274	274

282	282

180	294

UNITS AND STANDARDS OF MEASUREMENT 1 Units and Standards of Measurement	305

Standard Unit of Time	307

The Unit of Space and the Bar Standard	312

305	326

182	330

CHAPTER XVI	357

On the Average or Fictitious Mean	363

50	367

Determination of Maximum Points	371

Herschels Geometrical Proof	377

189	383

51	384

409	386

307	388

Rejection of the Mean Result	389

Detection of Constant Errors	396

314	398

Distinction of Observation and Experiment	400

Mental Conditions of Correct Observation	402

Instrumental and Sensual Conditions of Correct Observation 5 External Conditions of Correct Observation	407

Apparent Sequence of Events	409

Negative Arguments from NonObservation	411

CHAPTER XIX	416

Experiment 2 Exclusion of Indifferent Circumstances	419

Simplification of Experiments	422

Failure in the Simplification of Experiments	424

Removal of Usual Conditions	426

Interference of Unsuspected Conditions	428

190	429

192	430

Blind or Test Experiments	433

Negative Results of Experiment	434

Limits of Experiment	437

CHAPTER XX	439

The Variable and the Variant	440

Measurement of the Variable	441

Maintenance of Similar Conditions	443

Collective Experiments	446

Periodic Variations	447

Combined Periodic Changes	450

197	451

Integrated Variations	452

SECTION	457

Successive Approximations to Natural Conditions	465

Mathematical Principles of Approximation	471

Four Meanings of Equality	479

Quantitative Induction	485

The Graphical Method	492

53	496

Illustrations of Empirical Quantitative Laws	499

The Use of Hypothesis	508

Consistency with the Laws of Nature	514

Descriptive Hypotheses	522

ACCORDANCE OF QUANTITATIVE THEORIES	551

Discordance of Theory and Experiment	558

200	563

Agreement of Distinct Modes of Measurement	564

55	569

CHAPTER XXVI	574

The Newtonian Method the True Organum	581

The Philosophic Character of Faraday	587

GENERALISATION ANALOGY AND CLASSIFICATION CHAPTER XXVII	594

Distinction of Generalisation and Analogy	596

Two Meanings of Generalisation	597

Value of Generalisation	599

Comparative Generality of Properties	600

Uniform Properties of all Matter	603

Variable Properties of Matter	606

Extreme Instances of Properties	607

The Detection of Continuity	610

The Law of Continuity	615

Failure of the Law of Continuity	619

Negative Arguments on the Principle of Continuity	621

Tendency to Hasty Generalisation	623

CHAPTER XXVIII	627

Analogy as a Guide in Discovery	629

Analogy in the Mathematical Sciences	631

Analogy in the Theory of Undulations	635

316	638

Failures of Analogy	641

CHAPTER XXIX	644

Imaginary or False Exceptions	647

Apparent but Congruent Exceptions	649

Singular Exceptions	652

Divergent Exceptions	655

317	656

Accidental Exceptions	658

Novel and Unexplained Exceptions 1	661

Limiting Exceptions	663

Real Exceptions to Supposed Laws	666

Unclassed Exceptions	668

416	726

CHAPTER XXXI	735

The Meaning of Natural	737

Infiniteness of the Universe	738

The Indeterminate Problem of Creation	740

Hierarchy of Natural Laws	742

The Ambiguous Expression Uniformity of Nature	745

Possible States of the Universe	749

Speculations on the Reconcentration of Energy	751

The Divergent Scope for New Discovery	752

149	765

Infinite Incompleteness of the Mathematical Sciences 11 The Reign of Law in Mental and Social Phenomena 12 The Theory of Evolution 13 Possibil...	766

205	771

57	772

419	773

59	774

66	775

68	776

439	777

71	780

441	785

452	786

Common terms and phrases

abC abc ABcd AbCd analogy apparent approximate ascertain assert body calculation cause character classification colour combinations consists Contrapositive crystals deductive deductive reasoning density detect discovered discovery disjunctive proposition earth effect electricity equal equation equivalent error exactly existence experiment expression fact force give gravity heat hypothesis identity induction inference infinite instance inverse inverse logical investigation J. S. Mill knowledge Laws of Identity laws of nature Laws of Thought Leibnitz light Logical Alphabet logical conditions logicians magnetic manner mathematical matter meaning measure metal method mind mode motion negative Newton objects observation phenomena Philosophical planets possess possible premises principle principle of substitution probability properties proposition qualities quantity reasoning refraction regards relation scientific scientific method similar simple stars substances substitution supposed syllogism symbols temperature theory things tion triangle true truth velocity

Bibliographic information

Title	The Principles of Science: A Treatise on Logic
Author	Jevons
Edition	3
Published	1879
Original from	University of Bern
Digitized	Jul 16, 2021

Export Citation	BiBTeX EndNote RefMan

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