A Treatise on Probability

Part I Fundamental ideas

CHAPTER I The Meaning of Probability
CHAPTER II Probability in Relation to the Theory of Knowledge
CHAPTER III The Measurement of Probabilities
CHAPTER IV The Principle of Indifference
CHAPTER V Other Methods of Determining Probabilities
CHAPTER VI The Weight of Arguments
CHAPTER VII Historical Retrospect
CHAPTER VIII The Frequency Theory of Probability
CHAPTER IX The Constructive Theory of Part I. Summarized

PART II Fundamental Theorems

CHAPTER X Introductory
CHAPTER XI The Theory of Groups, with special reference to Logical Consistence, Inference, and Logical Priority.
CHAPTER XII The Definitions and Axioms of Inference and Probability
CHAPTER XIII The Fundamental Theorems of Necessary Inference
CHAPTER XIV The Fundamental Theorems of Probable Inference
CHAPTER XV Numerical Measurement and Approximation of Probabilities
CHAPTER XVI Observations on the Theorems of Chapter XIV. and their Developments, including Testimony
CHAPTER XVII Some Problems in Inverse Probability, including Averages

PART III

Induction and Analogy

CHAPTER XVIII Introduction
CHAPTER XIX The Nature of Argument by Analogy
CHAPTER XX The Value of Multiplication of Instances, or Pure Induction
CHAPTER XXI The Nature of Inductive Argument Continued
CHAPTER XXII The Justification of these Methods
CHAPTER XXIII Some Historical Notes on Induction

PART IV

Some Philosophical Applications of Probability

CHAPTER XXIV The Meanings of Objective Chance, and of Randomness
CHAPTER XXV Some Problems arising out of the Discussion of Chance
CHAPTER XXVI The Application of Probability to Conduct

PART V

The Foundations of Statistical Inference

CHAPTER XXVII The Nature of Statistical Inference
CHAPTER XXVIII The Law of Great Numbers
CHAPTER XXIX The Use of à priori Probabilities for the Prediction of Statistical Frequency-the Theorems of Bernoulli, Poisson, and Tchebycheff
CHAPTER XXX The Mathematical use of Statistical Frequencies for the Determination of Probability à posteriori-the Methods of Laplace
CHAPTER XXXI The Inversion of Bernoulli's Theorem
CHAPTER XXXII The Inductive use of Statistical Frequencies for the Determination of Probability à posteriori-the Methods of Lexis CHAPTER XXXIII Outline of a Constructive Theory