- The Oxford Handbook of Probability and Philosophy
- List of Contributors
- Introduction
- Probability for Everyone—Even Philosophers
- Pre-history of Probability
- Probability in 17th- and 18th-century Continental Europe from the Perspective of Jacob Bernoulli’s <i>Art of Conjecturing</i>
- Probability and Its Application in Britain during the 17th and 18th Centuries
- A Brief History of Probability Theory from 1810 to 1940
- The Origins of Modern Statistics: The English Statistical School
- The Origins of Probabilistic Epistemology: Some Leading 20th-century Philosophers of Probability
- Kolmogorov’s Axiomatization and Its Discontents
- Conditional Probability
- The Bayesian Network Story
- Mathematical Alternatives to Standard Probability that Provide Selectable Degrees of Precision
- Probability and Nonclassical Logic
- A Logic of Comparative Support: Qualitative Conditional Probability Relations Representable by Popper Functions
- Imprecise and Indeterminate Probabilities
- Symmetry Arguments in Probability
- Frequentism
- Subjectivism
- Bayesianism vs. Frequentism in Statistical Inference
- The Propensity Interpretation
- Best System Approaches to Chance
- Probability and Randomness
- Chance and Determinism
- Human Understandings of Probability
- Probability Elicitation
- Probabilistic Opinion Pooling
- Quantum Probability: An Introduction
- Probabilities in Statistical Mechanics
- Probability in Biology: The Case of Fitness
- Probability in Epistemology
- Confirmation Theory
- Self-Locating Credences
- Probability in Logic
- Probability in Ethics
- Probability and the Philosophy of Religion
- Probability in Philosophy of Language
- Decision Theory
- Probabilistic Causation
- Name Index
- Subject Index

## Abstract and Keywords

In the 18th and 19th centuries, probability was a part of moral and natural sciences, rather than of mathematics. Still, since Laplace’s 1812 Théorie analytique des probabilités, specific analytic methods of probability aroused the interest of mathematicians, and probability began to develop a purely mathematical quality. In the 20th century the mathematical essence reached full autonomy and constituted “modern” probability. Significant in this development was the gradual introduction of a measure theoretic framework. In this way, the main subfields of modern probability, as axiomatics, weak and strong limit theorems, sequences of non-independent random variables, and stochastic processes, could be integrated into a well-connected complex until World War II.

Keywords: Laplace, error theory, kinetic theory of gases, sum of random variables, weak limit theorem, law of large numbers, non-independent random variable, stochastic process, axiomatics, measure theory

David Bellhouse, Department of Actuarial and Statistical Science, University of Western Ontario

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- The Oxford Handbook of Probability and Philosophy
- List of Contributors
- Introduction
- Probability for Everyone—Even Philosophers
- Pre-history of Probability
- Probability in 17th- and 18th-century Continental Europe from the Perspective of Jacob Bernoulli’s <i>Art of Conjecturing</i>
- Probability and Its Application in Britain during the 17th and 18th Centuries
- A Brief History of Probability Theory from 1810 to 1940
- The Origins of Modern Statistics: The English Statistical School
- The Origins of Probabilistic Epistemology: Some Leading 20th-century Philosophers of Probability
- Kolmogorov’s Axiomatization and Its Discontents
- Conditional Probability
- The Bayesian Network Story
- Mathematical Alternatives to Standard Probability that Provide Selectable Degrees of Precision
- Probability and Nonclassical Logic
- A Logic of Comparative Support: Qualitative Conditional Probability Relations Representable by Popper Functions
- Imprecise and Indeterminate Probabilities
- Symmetry Arguments in Probability
- Frequentism
- Subjectivism
- Bayesianism vs. Frequentism in Statistical Inference
- The Propensity Interpretation
- Best System Approaches to Chance
- Probability and Randomness
- Chance and Determinism
- Human Understandings of Probability
- Probability Elicitation
- Probabilistic Opinion Pooling
- Quantum Probability: An Introduction
- Probabilities in Statistical Mechanics
- Probability in Biology: The Case of Fitness
- Probability in Epistemology
- Confirmation Theory
- Self-Locating Credences
- Probability in Logic
- Probability in Ethics
- Probability and the Philosophy of Religion
- Probability in Philosophy of Language
- Decision Theory
- Probabilistic Causation
- Name Index
- Subject Index