- 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

The topic of probability in quantum mechanics is rather vast. In this chapter it is discussed from the perspective of whether and in what sense quantum mechanics requires a generalization of the usual (Kolmogorovian) concept of probability. The focus is on the case of finite-dimensional quantum mechanics (which is analogous to that of discrete probability spaces), partly for simplicity and partly for ease of generalization. While the main emphasis is on formal aspects of quantum probability (in particular the non-existence of joint distributions for incompatible observables), the discussion relates also to notorious issues in the interpretation of quantum mechanics. Indeed, whether quantum probability can or cannot be ultimately reduced to classical probability connects rather nicely to the question of 'hidden variables' in quantum mechanics.

Keywords: quantum mechanics, generalized probability, effect algebra, orthoalgebra, joint distribution, hidden variable

Guido Bacciagaluppi, Department of Philosophy, University of Aberdeen

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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