CONTENTS.

BOOK I.
FORMAL LOGIC, DEDUCTIVE AND INDUCTIVE.
CHAPTER I.
INTRODUCTION.
SECTION
PAGE
1.
 Introduction
2.
 The Powers of Mind concerned in the Creation of Science
3.
 Laws of Identity and Difference
4.
 The Nature of the Laws of Identity and Difference
5.
 The Process of Inference
6.
 Deduction and Induction
7.
 Symbolic Expression of Logical Inference
8.
 Expression of Identity and Difference
9.
 General Formula of Logical Inference
10.
 The Propagating Power of Similarity
11.
 Anticipations of the Principle of Substitution
12.
 The Logic of Relatives
CHAPTER II.
TERMS.
1.
 Terms
2.
 Twofold meaning of General Names
3.
 Abstract Terms
4.
 Substantial Terms
5.
 Collective Terms
6.
 Synthesis of Terms
7.
 Symbolic Expression of the Law of Contradiction
8.
 Certain Special Conditions of Logical Symbols
CHAPTER III.
PROPOSITIONS.
1.
 Propositions
2.
 Simple Identities
3.
 Partial Identities
4.
 Limited Identities
5.
 Negative Propositions
6.
 Conversion of Propositions
7.
 Twofold Interpretation of Propositions
CHAPTER IV.
DEDUCTIVE REASONING.
1.
 Deductive Reasoning
2.
 Immediate Inference
3.
 Inference with Two Simple Identities
4.
 Inference with a Simple and a Partial Identity
5.
 Inference of a Partial from Two Partial Identities
6.
 On the Ellipsis of Terms in Partial Identities
7.
 Inference of a Simple from Two Partial Identities
8.
 Inference of a Limited from Two Partial Identities
9.
 Miscellaneous Forms of Deductive Inference
10.
 Fallacies
CHAPTER V.
DISJUNCTIVE PROPOSITIONS.
1.
 Disjunctive Propositions
2.
 Expression of the Alternative Relation
3.
 Nature of the Alternative Relation
4.
 Laws of the Disjunctive Relation
5.
 Symbolic Expression of the Law of Duality
6.
 Various Forms of the Disjunctive Proposition
7.
 Inference by Disjunctive Propositions
CHAPTER VI.
THE INDIRECT METHOD OF INFERENCE.
1.
 The Indirect Method of Inference
2.
 Simple Illustrations
3.
 Employment of the Contrapositive Proposition
4.
 Contrapositive of a Simple Identity
5.
 Miscellaneous Examples of the Method
6.
 Mr. Venn’s Problem
7.
 Abbreviation of the Process
8.
 The Logical Alphabet
9.
 The Logical Slate
10.
 Abstraction of Indifferent Circumstances
11.
 Illustrations of the Indirect Method
12.
 Second Example
13.
 Third Example
14.
 Fourth Example
15.
 Fifth Example
16.
 Fallacies Analysed by the Indirect Method
17.
 The Logical Abacus
18.
 The Logical Machine
19.
 The Order of Premises
20.
 The Equivalence of Propositions
21.
 The Nature of Inference
CHAPTER VII.
INDUCTION.
1.
 Induction
2.
 Induction an Inverse Operation
3.
 Inductive Problems for Solution by the Reader
4.
 Induction of Simple Identities
5.
 Induction of Partial Identities
6.
 Solution of the Inverse or Inductive Problem, involving Two Classes
7.
 The Inverse Logical Problem, involving Three Classes
8.
 Professor Clifford on the Types of Compound Statement involving Four Classes
9.
 Distinction between Perfect and Imperfect Induction
10.
 Transition from Perfect to Imperfect Induction
BOOK II.
NUMBER, VARIETY, AND PROBABILITY.
CHAPTER VIII.
PRINCIPLES OF NUMBER.
1.
 Principles of Number
2.
 The Nature of Numbe
3.
 Of Numerical Abstraction
4.
 Concrete and Abstract Number
5.
 Analogy of Logical and Numerical Terms
6.
 Principle of Mathematical Inference
7.
 Reasoning by Inequalities
8.
 Arithmetical Reasoning
9.
 Numerically Definite Reasoning
10.
 Numerical meaning of Logical Conditions
CHAPTER IX.
THE VARIETY OF NATURE, OR THE DOCTRINE OF COMBINATIONS AND PERMUTATIONS.
1.
 The Variety of Nature
2.
 Distinction of Combinations and Permutations
3.
 Calculation of Number of Combinations
4.
 The Arithmetical Triangle
5.
 Connexion between the Arithmetical Triangle and the Logical Alphabet
6.
 Possible Variety of Nature and Art
7.
 Higher Orders of Variety
CHAPTER X.
THEORY OF PROBABILITY.
1.
 Theory of Probability
2.
 Fundamental Principles of the Theory
3.
 Rules for the Calculation of Probabilities
4.
 The Logical Alphabet in questions of Probability
5.
 Comparison of the Theory with Experience
6.
 Probable Deductive Arguments
7.
 Difficulties of the Theory
CHAPTER XI.
PHILOSOPHY OF INDUCTIVE INFERENCE.
1.
 Philosophy of Inductive Inference
2.
 Various Classes of Inductive Truths
3.
 The Relation of Cause and Effect
4.
 Fallacious Use of the Term Cause
5.
 Confusion of Two Questions
6.
 Definition of the Term Cause
7.
 Distinction of Inductive and Deductive Results
8.
 The Grounds of Inductive Inference
9.
 Illustrations of the Inductive Process
10.
 Geometrical Reasoning
11.
 Discrimination of Certainty and Probability
CHAPTER XII.
THE INDUCTIVE OR INVERSE APPLICATION OF THE THEORY OF PROBABILITY.
1.
 The Inductive or Inverse Application of the Theory
2.
 Principle of the Inverse Method
3.
 Simple Applications of the Inverse Method
4.
 The Theory of Probability in Astronomy
5.
 The General Inverse Problem
6.
 Simple Illustration of the Inverse Problem
7.
 General Solution of the Inverse Problem
8.
 Rules of the Inverse Method
9.
 Fortuitous Coincidences
10.
 Summary of the Theory of Inductive Inference
BOOK III.
METHODS OF MEASUREMENT.
CHAPTER XIII.
THE EXACT MEASUREMENT OF PHENOMENA.
1.
 The Exact Measurement of Phenomena
2.
 Division of the Subject
3.
 Continuous quantity
4.
 The Fallacious Indications of the Senses
5.
 Complexity of Quantitative Questions
6.
 The Methods of Accurate Measurement
7.
 Conditions of Accurate Measurement
8.
 Measuring Instruments
9.
 The Method of Repetition
10.
 Measurements by Natural Coincidence
11.
 Modes of Indirect Measurement
12.
 Comparative Use of Measuring Instruments
13.
 Systematic Performance of Measurements
14.
 The Pendulum
15.
 Attainable Accuracy of Measurement
CHAPTER XIV.
UNITS AND STANDARDS OF MEASUREMENT.
1.
 Units and Standards of Measurement
2.
 Standard Unit of Time
3.
 The Unit of Space and the Bar Standard
4.
 The Terrestrial Standard
5.
 The Pendulum Standard
6.
 Unit of Density
7.
 Unit of Mass
8.
 Natural System of Standards
9.
 Subsidiary Units
10.
 Derived Units
11.
 Provisional Units
12.
 Theory of Dimensions
13.
 Natural Constants
14.
 Mathematical Constants
15.
 Physical Constants
16.
 Astronomical Constants
17.
 Terrestrial Numbers
18.
 Organic Numbers
19.
 Social Numbers
CHAPTER XV.
ANALYSIS OF QUANTITATIVE PHENOMENA.
1.
 Analysis of Quantitative Phenomena
2.
 Illustrations of the Complication of Effects
3.
 Methods of Eliminating Error
4.
 Method of Avoidance of Error
5.
 Differential Method
6.
 Method of Correction
7.
 Method of Compensation
8.
 Method of Reversal
CHAPTER XVI.
THE METHOD OF MEANS.
1.
 The Method of Means
2.
 Several Uses of the Mean Result
3.
 The Mean and the Average
4.
 On the Average or Fictitious Mean
5.
 The Precise Mean Result
6.
 Determination of the Zero Point
7.
 Determination of Maximum Points
CHAPTER XVII.
THE LAW OF ERROR.
1.
 The Law of Error
2.
 Establishment of the Law of Error
3.
 Herschel’s Geometrical Proof
4.
 Laplace’s and Quetelet’s Proof of the Law
5.
 Logical Origin of the Law of Error
6.
 Verification of the Law of Error
7.
 The Probable Mean Result
8.
 The Probable Error of Results
9.
 Rejection of the Mean Result
10.
 Method of Least Squares
11.
 Works upon the Theory of Probability
12.
 Detection of Constant Errors
BOOK IV.
INDUCTIVE INVESTIGATION.
CHAPTER XVIII.
OBSERVATION.
1.
 Observation
2.
 Distinction of Observation and Experiment
3.
 Mental Conditions of Correct Observation
4.
 Instrumental and Sensual Conditions of Correct Observation
5.
 External Conditions of Correct Observation
6.
 Apparent Sequence of Events
7.
 Negative Arguments from Non-Observation
CHAPTER XIX.
EXPERIMENT.
1.
 Experiment
2.
 Exclusion of Indifferent Circumstances
3.
 Simplification of Experiments
4.
 Failure in the Simplification of Experiments
5.
 Removal of Usual Conditions
6.
 Interference of Unsuspected Conditions
7.
 Blind or Test Experiments
8.
 Negative Results of Experiment
9.
 Limits of Experiment
CHAPTER XX.
METHOD OF VARIATIONS.
1.
 Method of Variations
2.
 The Variable and the Variant
3.
 Measurement of the Variable
4.
 Maintenance of Similar Conditions
5.
 Collective Experiments
6.
 Periodic Variations
7.
 Combined Periodic Changes
8.
 Principle of Forced Vibrations
9.
 Integrated Variations
CHAPTER XXI.
THEORY OF APPROXIMATION.
1.
 Theory of Approximation
2.
 Substitution of Simple Hypotheses
3.
 Approximation to Exact Laws
4.
 Successive Approximations to Natural Conditions
5.
 Discovery of Hypothetically Simple Laws
6.
 Mathematical Principles of Approximation
7.
 Approximate Independence of Small Effects
8.
 Four Meanings of Equality
9.
 Arithmetic of Approximate Quantities
CHAPTER XXII.
QUANTITATIVE INDUCTION.
1.
 Quantitative Induction
2.
 Probable Connexion of Varying Quantities
3.
 Empirical Mathematical Laws
4.
 Discovery of Rational Formulæ
5.
 The Graphical Method
6.
 Interpolation and Extrapolation
7.
 Illustrations of Empirical Quantitative Laws
8.
 Simple Proportional Variation
CHAPTER XXIII.
THE USE OF HYPOTHESIS.
1.
 The Use of Hypothesis
2.
 Requisites of a good Hypothesis
3.
 Possibility of Deductive Reasoning
4.
 Consistency with the Laws of Nature
5.
 Conformity with Facts
6.
 Experimentum Crucis
7.
 Descriptive Hypotheses
CHAPTER XXIV.
EMPIRICAL KNOWLEDGE, EXPLANATION AND PREDICTION.
1.
 Empirical Knowledge, Explanation and Prediction
2.
 Empirical Knowledge
3.
 Accidental Discovery
4.
 Empirical Observations subsequently Explained
5.
 Overlooked Results of Theory
6.
 Predicted Discoveries
7.
 Predictions in the Science of Light
8.
 Predictions from the Theory of Undulations
9.
 Prediction in other Sciences
10.
 Prediction by Inversion of Cause and Effect
11.
 Facts known only by Theory
CHAPTER XXV.
ACCORDANCE OF QUANTITATIVE THEORIES.
1.
 Accordance of Quantitative Theories
2.
 Empirical Measurements
3.
 Quantities indicated by Theory, but Empirically Measured
4.
 Explained Results of Measurement
5.
 Quantities determined by Theory and verified by Measurement
6.
 Quantities determined by Theory and not verified
7.
 Discordance of Theory and Experiment
8.
 Accordance of Measurements of Astronomical Distances
9.
 Selection of the best Mode of Measurement
10.
 Agreement of Distinct Modes of Measurement
11.
 Residual Phenomena
CHAPTER XXVI.
CHARACTER OF THE EXPERIMENTALIST.
1.
 Character of the Experimentalist
2.
 Error of the Baconian Method
3.
 Freedom of Theorising
4.
 The Newtonian Method, the True Organum
5.
 Candour and Courage of the Philosophic Mind
6.
 The Philosophic Character of Faraday
7.
 Reservation of Judgment
BOOK V.
GENERALISATION, ANALOGY, AND CLASSIFICATION.
CHAPTER XXVII.
GENERALISATION.
1.
 Generalisation
2.
 Distinction of Generalisation and Analogy
3.
 Two Meanings of Generalisation
4.
 Value of Generalisation
5.
 Comparative Generality of Properties
6.
 Uniform Properties of all Matter
7.
 Variable Properties of Matter
8.
 Extreme Instances of Properties
9.
 The Detection of Continuity
10.
 The Law of Continuity
11.
 Failure of the Law of Continuity
12.
 Negative Arguments on the Principle of Continuity
13.
 Tendency to Hasty Generalisation
CHAPTER XXVIII.
ANALOGY.
1.
 Analogy
2.
 Analogy as a Guide in Discovery
3.
 Analogy in the Mathematical Sciences
4.
 Analogy in the Theory of Undulations
5.
 Analogy in Astronomy
6.
 Failures of Analogy
CHAPTER XXIX.
EXCEPTIONAL PHENOMENA.
1.
 Exceptional Phenomena
2.
 Imaginary or False Exceptions
3.
 Apparent but Congruent Exceptions
4.
 Singular Exceptions
5.
 Divergent Exceptions
6.
 Accidental Exceptions
7.
 Novel and Unexplained Exceptions
8.
 Limiting Exceptions
9.
 Real Exceptions to Supposed Laws
10.
 Unclassed Exceptions
CHAPTER XXX.
CLASSIFICATION.
1.
 Classification
2.
 Classification involving Induction
3.
 Multiplicity of Modes of Classification
4.
 Natural and Artificial Systems of Classification
5.
 Correlation of Properties
6.
 Classification in Crystallography
7.
 Classification an Inverse and Tentative Operation
8.
 Symbolic Statement of the Theory of Classification
9.
 Bifurcate Classification
10.
 The Five Predicates
11.
 Summum Genus and Infima Species
12.
 The Tree of Porphyry
13.
 Does Abstraction imply Generalisation?
14.
 Discovery of Marks or Characteristics
15.
 Diagnostic Systems of Classification
16.
 Index Classifications
17.
 Classification in the Biological Sciences
18.
 Classification by Types
19.
 Natural Genera and Species
20.
 Unique or Exceptional Objects
21.
 Limits of Classification
BOOK VI.
CHAPTER XXXI.
REFLECTIONS ON THE RESULTS AND LIMITS OF SCIENTIFIC METHOD.
1.
 Reflections on the Results and Limits of Scientific Method
2.
 The Meaning of Natural Law
3.
 Infiniteness of the Universe
4.
 The Indeterminate Problem of Creation
5.
 Hierarchy of Natural Laws
6.
 The Ambiguous Expression—“Uniformity of Nature”
7.
 Possible States of the Universe
8.
 Speculations on the Reconcentration of Energy
9.
 The Divergent Scope for New Discovery
10.
 Infinite Incompleteness of the Mathematical Sciences
11.
 The Reign of Law in Mental and Social Phenomena
12.
 The Theory of Evolution
13.
 Possibility of Divine Interference
14.
 Conclusion
INDEX 773