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