The principles of science

by William Stanley Jevons

I may add that Professor Clerk Maxwell’s words seem to countenance the same view, for he says,‍[23] “This is only one of the cases in which a consideration of the dissipation of energy leads to the determination of a superior limit to the antiquity of the observed order of things.” The expression “observed order of things” is open to much ambiguity, but in the absence of qualification I should take it to include the aggregate of the laws of nature known to us. I should interpret Professor Maxwell as meaning that the theory of heat indicates the occurrence of some event of which our science cannot give any further explanation. The physical writers thus seem not to be so clear about the matter as Professor Clifford assumes.

So far as I may venture to form an independent opinion on the subject, it is to the effect that Professor Clifford is right, and that the known laws of nature do not enable us to assign a “beginning.” Science leads us backwards into infinite past duration. But that Professor Clifford is right on this point, is no reason why we should suppose him to be right in his other opinions, some of which I am sure are wrong. Nor is it a reason why other parts of my last chapter should be wrong. The question only affects the single paragraph on pp. [744]–5 of this book, which might, I believe, be struck out without necessitating any alteration in the rest of the text. It is always to be remembered that the failure of an argument in favour of a proposition does not, generally speaking, add much, if any, probability to the contradictory proposition. I cannot conclude without expressing my acknowledgments to Professor Clifford for his kind expressions regarding my work as a whole.

2, The Chestnuts,
West Heath,
Hampstead, N. W.

August 15, 1877.

CONTENTS.

BOOK I.
FORMAL LOGIC, DEDUCTIVE AND INDUCTIVE.
CHAPTER I.
INTRODUCTION.
SECTION		PAGE
1.	Introduction	[1]
2.	The Powers of Mind concerned in the Creation of Science	[4]
3.	Laws of Identity and Difference	[5]
4.	The Nature of the Laws of Identity and Difference	[6]
5.	The Process of Inference	[9]
6.	Deduction and Induction	[11]
7.	Symbolic Expression of Logical Inference	[13]
8.	Expression of Identity and Difference	[14]
9.	General Formula of Logical Inference	[17]
10.	The Propagating Power of Similarity	[20]
11.	Anticipations of the Principle of Substitution	[21]
12.	The Logic of Relatives	[22]
CHAPTER II.
TERMS.
1.	Terms	[24]
2.	Twofold meaning of General Names	[25]
3.	Abstract Terms	[27]
4.	Substantial Terms	[28]
5.	Collective Terms	[29]
6.	Synthesis of Terms	[30]
7.	Symbolic Expression of the Law of Contradiction	[31]
8.	Certain Special Conditions of Logical Symbols	[32]
CHAPTER III.
PROPOSITIONS.
1.	Propositions	[36]
2.	Simple Identities	[37]
3.	Partial Identities	[40]
4.	Limited Identities	[42]
5.	Negative Propositions	[43]
6.	Conversion of Propositions	[46]
7.	Twofold Interpretation of Propositions	[47]
CHAPTER IV.
DEDUCTIVE REASONING.
1.	Deductive Reasoning	[49]
2.	Immediate Inference	[50]
3.	Inference with Two Simple Identities	[51]
4.	Inference with a Simple and a Partial Identity	[53]
5.	Inference of a Partial from Two Partial Identities	[55]
6.	On the Ellipsis of Terms in Partial Identities	[57]
7.	Inference of a Simple from Two Partial Identities	[58]
8.	Inference of a Limited from Two Partial Identities	[59]
9.	Miscellaneous Forms of Deductive Inference	[60]
10.	Fallacies	[62]
CHAPTER V.
DISJUNCTIVE PROPOSITIONS.
1.	Disjunctive Propositions	[66]
2.	Expression of the Alternative Relation	[67]
3.	Nature of the Alternative Relation	[68]
4.	Laws of the Disjunctive Relation	[71]
5.	Symbolic Expression of the Law of Duality	[73]
6.	Various Forms of the Disjunctive Proposition	[74]
7.	Inference by Disjunctive Propositions	[76]
CHAPTER VI.
THE INDIRECT METHOD OF INFERENCE.
1.	The Indirect Method of Inference	[81]
2.	Simple Illustrations	[83]
3.	Employment of the Contrapositive Proposition	[84]
4.	Contrapositive of a Simple Identity	[86]
5.	Miscellaneous Examples of the Method	[88]
6.	Mr. Venn’s Problem	[90]
7.	Abbreviation of the Process	[91]
8.	The Logical Alphabet	[94]
9.	The Logical Slate	[95]
10.	Abstraction of Indifferent Circumstances	[97]
11.	Illustrations of the Indirect Method	[98]
12.	Second Example	[99]
13.	Third Example	[100]
14.	Fourth Example	[101]
15.	Fifth Example	[101]
16.	Fallacies Analysed by the Indirect Method	[102]
17.	The Logical Abacus	[104]
18.	The Logical Machine	[107]
19.	The Order of Premises	[114]
20.	The Equivalence of Propositions	[115]
21.	The Nature of Inference	[118]
CHAPTER VII.
INDUCTION.
1.	Induction	[121]
2.	Induction an Inverse Operation	[122]
3.	Inductive Problems for Solution by the Reader	[126]
4.	Induction of Simple Identities	[127]
5.	Induction of Partial Identities	[130]
6.	Solution of the Inverse or Inductive Problem, involving Two Classes	[134]
7.	The Inverse Logical Problem, involving Three Classes	[137]
8.	Professor Clifford on the Types of Compound Statement involving Four Classes	[143]
9.	Distinction between Perfect and Imperfect Induction	[146]
10.	Transition from Perfect to Imperfect Induction	[149]
BOOK II.
NUMBER, VARIETY, AND PROBABILITY.
CHAPTER VIII.
PRINCIPLES OF NUMBER.
1.	Principles of Number	[153]
2.	The Nature of Numbe	[156]
3.	Of Numerical Abstraction	[158]
4.	Concrete and Abstract Number	[159]
5.	Analogy of Logical and Numerical Terms	[160]
6.	Principle of Mathematical Inference	[162]
7.	Reasoning by Inequalities	[165]
8.	Arithmetical Reasoning	[167]
9.	Numerically Definite Reasoning	[168]
10.	Numerical meaning of Logical Conditions	[171]
CHAPTER IX.
THE VARIETY OF NATURE, OR THE DOCTRINE OF COMBINATIONS AND PERMUTATIONS.
1.	The Variety of Nature	[173]
2.	Distinction of Combinations and Permutations	[177]
3.	Calculation of Number of Combinations	[180]
4.	The Arithmetical Triangle	[182]
5.	Connexion between the Arithmetical Triangle and the Logical Alphabet	[189]
6.	Possible Variety of Nature and Art	[190]
7.	Higher Orders of Variety	[192]
CHAPTER X.
THEORY OF PROBABILITY.
1.	Theory of Probability	[197]
2.	Fundamental Principles of the Theory	[200]
3.	Rules for the Calculation of Probabilities	[203]
4.	The Logical Alphabet in questions of Probability	[205]
5.	Comparison of the Theory with Experience	[206]
6.	Probable Deductive Arguments	[209]
7.	Difficulties of the Theory	[213]
CHAPTER XI.
PHILOSOPHY OF INDUCTIVE INFERENCE.
1.	Philosophy of Inductive Inference	[218]
2.	Various Classes of Inductive Truths	[219]
3.	The Relation of Cause and Effect	[220]
4.	Fallacious Use of the Term Cause	[221]
5.	Confusion of Two Questions	[222]
6.	Definition of the Term Cause	[224]
7.	Distinction of Inductive and Deductive Results	[226]
8.	The Grounds of Inductive Inference	[228]
9.	Illustrations of the Inductive Process	[229]
10.	Geometrical Reasoning	[233]
11.	Discrimination of Certainty and Probability	[235]
CHAPTER XII.
THE INDUCTIVE OR INVERSE APPLICATION OF THE THEORY OF PROBABILITY.
1.	The Inductive or Inverse Application of the Theory	[240]
2.	Principle of the Inverse Method	[242]
3.	Simple Applications of the Inverse Method	[244]
4.	The Theory of Probability in Astronomy	[247]
5.	The General Inverse Problem	[250]
6.	Simple Illustration of the Inverse Problem	[253]
7.	General Solution of the Inverse Problem	[255]
8.	Rules of the Inverse Method	[257]
9.	Fortuitous Coincidences	[261]
10.	Summary of the Theory of Inductive Inference	[265]
BOOK III.
METHODS OF MEASUREMENT.
CHAPTER XIII.
THE EXACT MEASUREMENT OF PHENOMENA.
1.	The Exact Measurement of Phenomena	[270]
2.	Division of the Subject	[274]
3.	Continuous quantity	[274]
4.	The Fallacious Indications of the Senses	[276]
5.	Complexity of Quantitative Questions	[278]
6.	The Methods of Accurate Measurement	[282]
7.	Conditions of Accurate Measurement	[282]
8.	Measuring Instruments	[284]
9.	The Method of Repetition	[288]
10.	Measurements by Natural Coincidence	[292]
11.	Modes of Indirect Measurement	[296]
12.	Comparative Use of Measuring Instruments	[299]
13.	Systematic Performance of Measurements	[300]
14.	The Pendulum	[302]
15.	Attainable Accuracy of Measurement	[303]
CHAPTER XIV.
UNITS AND STANDARDS OF MEASUREMENT.
1.	Units and Standards of Measurement	[305]
2.	Standard Unit of Time	[307]
3.	The Unit of Space and the Bar Standard	[312]
4.	The Terrestrial Standard	[314]
5.	The Pendulum Standard	[315]
6.	Unit of Density	[316]
7.	Unit of Mass	[317]
8.	Natural System of Standards	[319]
9.	Subsidiary Units	[320]
10.	Derived Units	[321]
11.	Provisional Units	[323]
12.	Theory of Dimensions	[325]
13.	Natural Constants	[328]
14.	Mathematical Constants	[330]
15.	Physical Constants	[331]
16.	Astronomical Constants	[332]
17.	Terrestrial Numbers	[333]
18.	Organic Numbers	[333]
19.	Social Numbers	[334]
CHAPTER XV.
ANALYSIS OF QUANTITATIVE PHENOMENA.
1.	Analysis of Quantitative Phenomena	[335]
2.	Illustrations of the Complication of Effects	[336]
3.	Methods of Eliminating Error	[339]
4.	Method of Avoidance of Error	[340]
5.	Differential Method	[344]
6.	Method of Correction	[346]
7.	Method of Compensation	[350]
8.	Method of Reversal	[354]
CHAPTER XVI.
THE METHOD OF MEANS.
1.	The Method of Means	[357]
2.	Several Uses of the Mean Result	[359]
3.	The Mean and the Average	[360]
4.	On the Average or Fictitious Mean	[363]
5.	The Precise Mean Result	[365]
6.	Determination of the Zero Point	[368]
7.	Determination of Maximum Points	[371]
CHAPTER XVII.
THE LAW OF ERROR.
1.	The Law of Error	[374]
2.	Establishment of the Law of Error	[375]
3.	Herschel’s Geometrical Proof	[377]
4.	Laplace’s and Quetelet’s Proof of the Law	[378]
5.	Logical Origin of the Law of Error	[383]
6.	Verification of the Law of Error	[383]
7.	The Probable Mean Result	[385]
8.	The Probable Error of Results	[386]
9.	Rejection of the Mean Result	[389]
10.	Method of Least Squares	[393]
11.	Works upon the Theory of Probability	[394]
12.	Detection of Constant Errors	[396]
BOOK IV.
INDUCTIVE INVESTIGATION.
CHAPTER XVIII.
OBSERVATION.
1.	Observation	[399]
2.	Distinction of Observation and Experiment	[400]
3.	Mental Conditions of Correct Observation	[402]
4.	Instrumental and Sensual Conditions of Correct Observation	[404]
5.	External Conditions of Correct Observation	[407]
6.	Apparent Sequence of Events	[409]
7.	Negative Arguments from Non-Observation	[411]
CHAPTER XIX.
EXPERIMENT.
1.	Experiment	[416]
2.	Exclusion of Indifferent Circumstances	[419]
3.	Simplification of Experiments	[422]
4.	Failure in the Simplification of Experiments	[424]
5.	Removal of Usual Conditions	[426]
6.	Interference of Unsuspected Conditions	[428]
7.	Blind or Test Experiments	[433]
8.	Negative Results of Experiment	[434]
9.	Limits of Experiment	[437]
CHAPTER XX.
METHOD OF VARIATIONS.
1.	Method of Variations	[439]
2.	The Variable and the Variant	[440]
3.	Measurement of the Variable	[441]
4.	Maintenance of Similar Conditions	[443]
5.	Collective Experiments	[445]
6.	Periodic Variations	[447]
7.	Combined Periodic Changes	[450]
8.	Principle of Forced Vibrations	[451]
9.	Integrated Variations	[452]
CHAPTER XXI.
THEORY OF APPROXIMATION.
1.	Theory of Approximation	[456]
2.	Substitution of Simple Hypotheses	[458]
3.	Approximation to Exact Laws	[462]
4.	Successive Approximations to Natural Conditions	[465]
5.	Discovery of Hypothetically Simple Laws	[470]
6.	Mathematical Principles of Approximation	[471]
7.	Approximate Independence of Small Effects	[475]
8.	Four Meanings of Equality	[479]
9.	Arithmetic of Approximate Quantities	[481]
CHAPTER XXII.
QUANTITATIVE INDUCTION.
1.	Quantitative Induction	[483]
2.	Probable Connexion of Varying Quantities	[484]
3.	Empirical Mathematical Laws	[487]
4.	Discovery of Rational Formulæ	[489]
5.	The Graphical Method	[492]
6.	Interpolation and Extrapolation	[495]
7.	Illustrations of Empirical Quantitative Laws	[499]
8.	Simple Proportional Variation	[501]
CHAPTER XXIII.
THE USE OF HYPOTHESIS.
1.	The Use of Hypothesis	[504]
2.	Requisites of a good Hypothesis	[510]
3.	Possibility of Deductive Reasoning	[511]
4.	Consistency with the Laws of Nature	[514]
5.	Conformity with Facts	[516]
6.	Experimentum Crucis	[518]
7.	Descriptive Hypotheses	[522]
CHAPTER XXIV.
EMPIRICAL KNOWLEDGE, EXPLANATION AND PREDICTION.
1.	Empirical Knowledge, Explanation and Prediction	[525]
2.	Empirical Knowledge	[526]
3.	Accidental Discovery	[529]
4.	Empirical Observations subsequently Explained	[532]
5.	Overlooked Results of Theory	[534]
6.	Predicted Discoveries	[536]
7.	Predictions in the Science of Light	[538]
8.	Predictions from the Theory of Undulations	[540]
9.	Prediction in other Sciences	[542]
10.	Prediction by Inversion of Cause and Effect	[545]
11.	Facts known only by Theory	[547]
CHAPTER XXV.
ACCORDANCE OF QUANTITATIVE THEORIES.
1.	Accordance of Quantitative Theories	[551]
2.	Empirical Measurements	[552]
3.	Quantities indicated by Theory, but Empirically Measured	[553]
4.	Explained Results of Measurement	[554]
5.	Quantities determined by Theory and verified by Measurement	[555]
6.	Quantities determined by Theory and not verified	[556]
7.	Discordance of Theory and Experiment	[558]
8.	Accordance of Measurements of Astronomical Distances	[560]
9.	Selection of the best Mode of Measurement	[563]
10.	Agreement of Distinct Modes of Measurement	[564]
11.	Residual Phenomena	[569]
CHAPTER XXVI.
CHARACTER OF THE EXPERIMENTALIST.
1.	Character of the Experimentalist	[574]
2.	Error of the Baconian Method	[576]
3.	Freedom of Theorising	[577]
4.	The Newtonian Method, the True Organum	[581]
5.	Candour and Courage of the Philosophic Mind	[586]
6.	The Philosophic Character of Faraday	[587]
7.	Reservation of Judgment	[592]
BOOK V.
GENERALISATION, ANALOGY, AND CLASSIFICATION.
CHAPTER XXVII.
GENERALISATION.
1.	Generalisation	[594]
2.	Distinction of Generalisation and Analogy	[596]
3.	Two Meanings of Generalisation	[597]
4.	Value of Generalisation	[599]
5.	Comparative Generality of Properties	[600]
6.	Uniform Properties of all Matter	[603]
7.	Variable Properties of Matter	[606]
8.	Extreme Instances of Properties	[607]
9.	The Detection of Continuity	[610]
10.	The Law of Continuity	[615]
11.	Failure of the Law of Continuity	[619]
12.	Negative Arguments on the Principle of Continuity	[621]
13.	Tendency to Hasty Generalisation	[623]
CHAPTER XXVIII.
ANALOGY.
1.	Analogy	[627]
2.	Analogy as a Guide in Discovery	[629]
3.	Analogy in the Mathematical Sciences	[631]
4.	Analogy in the Theory of Undulations	[635]
5.	Analogy in Astronomy	[638]
6.	Failures of Analogy	[641]
CHAPTER XXIX.
EXCEPTIONAL PHENOMENA.
1.	Exceptional Phenomena	[644]
2.	Imaginary or False Exceptions	[647]
3.	Apparent but Congruent Exceptions	[649]
4.	Singular Exceptions	[652]
5.	Divergent Exceptions	[655]
6.	Accidental Exceptions	[658]
7.	Novel and Unexplained Exceptions	[661]
8.	Limiting Exceptions	[663]
9.	Real Exceptions to Supposed Laws	[666]
10.	Unclassed Exceptions	[668]
CHAPTER XXX.
CLASSIFICATION.
1.	Classification	[673]
2.	Classification involving Induction	[675]
3.	Multiplicity of Modes of Classification	[677]
4.	Natural and Artificial Systems of Classification	[679]
5.	Correlation of Properties	[681]
6.	Classification in Crystallography	[685]
7.	Classification an Inverse and Tentative Operation	[689]
8.	Symbolic Statement of the Theory of Classification	[692]
9.	Bifurcate Classification	[694]
10.	The Five Predicates	[698]
11.	Summum Genus and Infima Species	[701]
12.	The Tree of Porphyry	[702]
13.	Does Abstraction imply Generalisation?	[704]
14.	Discovery of Marks or Characteristics	[708]
15.	Diagnostic Systems of Classification	[710]
16.	Index Classifications	[714]
17.	Classification in the Biological Sciences	[718]
18.	Classification by Types	[722]
19.	Natural Genera and Species	[724]
20.	Unique or Exceptional Objects	[728]
21.	Limits of Classification	[730]
BOOK VI.
CHAPTER XXXI.
REFLECTIONS ON THE RESULTS AND LIMITS OF SCIENTIFIC METHOD.
1.	Reflections on the Results and Limits of Scientific Method	[735]
2.	The Meaning of Natural Law	[737]
3.	Infiniteness of the Universe	[738]
4.	The Indeterminate Problem of Creation	[740]
5.	Hierarchy of Natural Laws	[742]
6.	The Ambiguous Expression—“Uniformity of Nature”	[745]
7.	Possible States of the Universe	[749]
8.	Speculations on the Reconcentration of Energy	[751]
9.	The Divergent Scope for New Discovery	[752]
10.	Infinite Incompleteness of the Mathematical Sciences	[754]
11.	The Reign of Law in Mental and Social Phenomena	[759]
12.	The Theory of Evolution	[761]
13.	Possibility of Divine Interference	[765]
14.	Conclusion	[766]
INDEX		[773]

THE PRINCIPLES OF SCIENCE.

CHAPTER I.
INTRODUCTION.

Science arises from the discovery of Identity amidst Diversity. The process may be described in different words, but our language must always imply the presence of one common and necessary element. In every act of inference or scientific method we are engaged about a certain identity, sameness, similarity, likeness, resemblance, analogy, equivalence or equality apparent between two objects. It is doubtful whether an entirely isolated phenomenon could present itself to our notice, since there must always be some points of similarity between object and object. But in any case an isolated phenomenon could be studied to no useful purpose. The whole value of science consists in the power which it confers upon us of applying to one object the knowledge acquired from like objects; and it is only so far, therefore, as we can discover and register resemblances that we can turn our observations to account.

Nature is a spectacle continually exhibited to our senses, in which phenomena are mingled in combinations of endless variety and novelty. Wonder fixes the mind’s attention; memory stores up a record of each distinct impression; the powers of association bring forth the record when the like is felt again. By the higher faculties of judgment and reasoning the mind compares the new with the old, recognises essential identity, even when disguised by diverse circumstances, and expects to find again what was before experienced. It must be the ground of all reasoning and inference that what is true of one thing will be true of its equivalent, and that under carefully ascertained conditions Nature repeats herself.