Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-06T09:57:19.279Z Has data issue: false hasContentIssue false
  • English
  • Français

Probability and Determinism

Published online by Cambridge University Press:  01 April 2022

Jan Von Plato
Jan Von Plato*
Affiliation:
Department of Philosophy University of Helsinki
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper discusses different interpretations of probability in relation to determinism. It is argued that both objective and subjective views on probability can be compatible with deterministic as well as indeterministic situations. The possibility of a conceptual independence between probability and determinism is argued to hold on a general level. The subsequent philosophical analysis of recent advances in classical statistical mechanics (ergodic theory) is of independent interest, but also adds weight to the claim that it is possible to justify an objective interpretation of probabilities in a theory having as a basis the paradigmatically deterministic theory of classical mechanics.

Type
Research Article
Information
Philosophy of Science , Volume 49 , Issue 1 , March 1982 , pp. 51 - 66
Copyright
Copyright © The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bell, J. S. (1966), “On the Problem of Hidden Variables in Quantum Mechanics”, Reviews of Modern Physics, vol. 38: pp. 447–452.CrossRefGoogle Scholar
Billingsley, P. (1965), Ergodic Theory and Information. New York: Wiley.Google Scholar
Carnap, R. (1977), Two Essays on Entropy. Berkeley: University of California Press.CrossRefGoogle Scholar
de Finetti, B. (1974–5), Theory of Probability. New York: Wiley.Google Scholar
Ford, J. (1975), “The Statistical Mechanics of Classical Analytic Dynamics”, in Cohen, E. G. D. (ed.) Fundamental Problems in Statistical Mechanics, vol. 3. Amsterdam: North-Holland.Google Scholar
Friedman, K. S. (1976), “A Partial Vindication of Ergodic Theory”, Philosophy of Science, vol. 43: pp. 151–162.CrossRefGoogle Scholar
Giere, R. (1973), “Objective Single-Case Probabilities and the Foundations of Statistics”, in Suppes, Henkin, Moisil, Joja (eds.) Logic, Methodology and Philosophy of Science IV, pp. 467–483, Amsterdam: North-Holland.Google Scholar
Gillies, D. A. (1973), An Objective Theory of Probability. London: Methuen.Google Scholar
Hopf, E. (1934), “On Causality, Statistics and Probability”, Journal of Mathematics and Physics, vol. 17: pp. 51–102.CrossRefGoogle Scholar
Jammer, M. (1974), The Philosophy of Quantum Mechanics. New York: Wiley.Google Scholar
Khinchin (Chintschin), A. I. (1954), “Die Methode der willkürlichen Funktionen und der Kampf gegen den Idealismus in der Wahrscheinlichkeitsrechnung”, Sowjetwissenschaft-Naturwissenschaftliche Abteilung, 7 Jhrg.: pp. 261–273.Google Scholar
Koopman, B. and Neumann, J. von (1932), “Dynamical Systems of Continuous Spectra”, National Academy of Sciences Proceedings 18: pp. 70–82. Also von Neumann, Collected Works, vol. II: pp. 278–286.Google Scholar
Malament, D. and Zabell, S. (1980), “Why Gibbs Phase Averages Work—the Role of Ergodic Theory”, Philosophy of Science, vol. 47: pp. 349–359.CrossRefGoogle Scholar
Margenau, H. and Park, J. L. (1967), “Objectivity in Quantum Mechanics”, in Bunge, (ed.) Delaware Seminar on the Foundations of Physics. Berlin: Springer.Google Scholar
Martin-Löf, P. (1966), “The Definition of Random Sequences”, Information and Control, vol. 9: pp. 602–619.CrossRefGoogle Scholar
Moser, J. (ed.) (1975), Dynamical Systems, Theory and Applications, Lecture Notes in Physics 38. Berlin: Springer.CrossRefGoogle Scholar
Nagel, E. (1939), Principles of the Theory of Probability. Chicago: University of Chicago Press.Google Scholar
Ornstein, D. S. (1974), Ergodic Theory, Randomness and Dynamical Systems. New Haven and London: Yale University Press.Google Scholar
Ornstein, D. S. (1975), “What Does it Mean for a Mechanical System to be Isomorphic to a Bernoulli Flow?” in Moser, J. (ed.) Dynamical Systems, Theory and Applications, Lecture Notes in Physics 38. Berlin: Springer.Google Scholar
Popper, K. R. (1962), “The Propensity Interpretation of the Calculus of Probability, and the Quantum Theory”, in Körner, S. (ed.) Observation and Interpretation in the Philosophy of Physics, pp. 65–70, New York: Dover.Google Scholar
Reichenbach, H. (1935), Wahrscheinlichkeitslehre. Leiden: A. W. Sijthoff's.Google Scholar
Scheibe, E. (1973), The Logical Analysis of Quantum Mechanics. Oxford: Pergamon.Google Scholar
Shimony, A. (1966), “Basic Axioms of Microphysics”, Physics Today, vol. 19, no. 9: pp. 85–91.Google Scholar
Shimony, A. (1977), “Carnap on Entropy”, in Hintikka, (ed.) Rudolf Carnap, Logical Empiricist, pp. 381–395, Dordrecht: D. Reidel. Also in Carnap (1977).Google Scholar
Sinai, Ya. (1973), “Ergodic Theory”, in Cohen, E. G. D. and Thirring, W. (eds.) The Boltzmann Equation, Wien-New York: Springer-Verlag. (=Acta Physica Austriaca, Supplementum X) pp. 575–608.CrossRefGoogle Scholar
Sinai, Ya. (1976), Introduction to Ergodic Theory. Princeton: Princeton University Press.Google Scholar
Stegmüller, W. (1973), Probleme und Resultate der Wissenschaftstheorie und Analytischen Philosophie, Band IV, Personelle und Statistische Wahrscheinlichkeit, 1. Berlin: Halbband, Springer-Verlag.Google Scholar
Struik, D. J. (1934), “On the Foundations of the Theory of Probabilities”, Philosophy of Science, vol. 1: pp. 50–70.CrossRefGoogle Scholar
von Plato, J. (1981), “Reductive Relations in Interpretations of Probability”, Synthese, vol. 48: pp. 61–75.CrossRefGoogle Scholar
von Plato, J. (forthcoming), “The Method of Arbitrary Functions” in The British Journal for the Philosophy of Science.Google Scholar