Advertisement

Statistical Mechanics and the Propensity Interpretation of Probability

  • Peter J. Clark
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 574)

Abstract

One of the most fascinating problems for the philosopher posed by the corpus of statistical physics is the issue of the consistency problem which arises in both the classical and the quantum contexts. It arises starkly in classical statistical physics, there it is the issue of precisely how it is possible to add probabilistic assumptions to treat of an aggregate motion, the component submotions of which, being governed by the laws of mechanics, are entirely deterministic. Essentially the problem occurs because one of the two theories we want to employ viz. mechanics is a completely general theory, that is it ought to give a complete description of any physical situation to which it applies, hence if we put them together the suspicion must be that they will overdetermine the history of the physical system under consideration and inconsistency will result.1

Keywords

Classical Statistical Mechanic Admissible Sequence Deterministic Theory Objective Interpretation Canonical Hamiltonian Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J.C. Maxwell: ‘Illustrations of the Dynamical theory of gases’. In: The Scientific papers of James Clerk Maxwell, ed. W.D. Niven (Dover Publications, New York 1965) pp. 377–409Google Scholar
  2. 2.
    L. Boltzmann: ‘Weitere Studien über das Wärmegleichgewicht unter Gasmolek ülen’ Wien.Ber. 66, 275 (1872)Google Scholar
  3. 3.
    L. Sklar: Physics and Chance (Cambridge University Press, Cambridge 1993)CrossRefGoogle Scholar
  4. 4.
    K.R. Popper: The Logic of Scientific Discovery, sixth revised impression of the 1959 English translation (Hutchinson, London 1972)Google Scholar
  5. 5.
    K.R. Popper: ‘The Propensity interpretation of the Calculus of probability, and the Quantum theory’. In: Observation and Interpretation, Proceedings of the Ninth Colston Research Society, (University of Bristol, Bristol1957) pp. 65–70,88-9.Google Scholar
  6. 6.
    K.R. Popper: ‘The Propensity Interpretation of Probability, British Journal for the Philosophy of Science. 10, 25–42 (1959)CrossRefADSGoogle Scholar
  7. 7.
    K.R. Popper: The Quantum theory and the Schism in Physics (Hutchinson, London 1982)Google Scholar
  8. 8.
    K.R. Popper: Realism and the Aim of Science (Hutchinson, London 1983)Google Scholar
  9. 9.
    K.R. Popper: A World of Propensities (Thoemmes press, Bristol 1990)Google Scholar
  10. 10.
    D. Miller: Critical Rationalism: A Restatement and Defence (Open Court, Chicago and Lasalle 1994)Google Scholar
  11. 11.
    D. Miller: ‘Propensities and Indeterminism’. In: Karl Popper: Philosophy and Problems, ed. by A. O’Hear (Cambridge University Press, Cambridge 1996) pp. 121–47Google Scholar
  12. 12.
    M. Redhead: ‘Popper and the Quantum theory’ In: Karl Popper: Philosophy and Problems, ed. by A. O’Hear (Cambridge University Press, Cambridge 1996) pp. 163–176Google Scholar
  13. 13.
    R. Von Mises: Probability Statistics and Truth, 2nd English edn. (George and Alan Unwin, London 1961)Google Scholar
  14. 14.
    D. Gillies: ‘Varieties of Propensity’ British Journal for the Philosophy of Science. 52 (2000)Google Scholar
  15. 15.
    A.N. Kolmogorov: Foundations of the Theory of Probability, 2nd English edn. (Chelsea, New York 1956)zbMATHGoogle Scholar
  16. 16.
    K.R. Popper: The Open Universe: An argument for Indeterminism (Hutchinson, London 1982)Google Scholar
  17. 17.
    A.N. Kolmogorov: ‘Über die analytischen Methoden in der Wahrscheinlichkeitsrechnung’ Mathematische Annalen 104, 415–458 (1931)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    W.C. Salmon: Causality and Explanation (Oxford University Press, Oxford and New York 1998)CrossRefGoogle Scholar
  19. 19.
    R.C. Montague: ‘Deterministic Theories’. In: Formal Philosophy, Selected Papers ed. by R.H. Thomason (Yale University press, New Haven 1974), pp. 303–359Google Scholar
  20. 20.
    J. Earman: A Primer on Determinism (D. Reidel, Dordrecht 1986)Google Scholar
  21. 21.
    W.C. Salmon: ‘Propensities a Discussion Review’ Erkenntnis. 14, 183–216 (1979)CrossRefGoogle Scholar
  22. 22.
    P. Humphreys: ‘Why Propensities Cannot Be Probabilities’ Philosophical Review. 94, 557–70 (1985)CrossRefMathSciNetGoogle Scholar
  23. 23.
    D. Miller: ‘Single-Case Probabilities’ Foundations of Physics. 21, 1501–16 (1991)CrossRefADSMathSciNetGoogle Scholar
  24. 24.
    C.S.I. McCurdy: ‘Humphreys Paradox’ Synthese. 108, 105–125 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    P. Milne: ‘Can there be a Realist single Case Interpretation of Probability?’ Erkenntnis. 25, 129–32 (1986)CrossRefGoogle Scholar
  26. 26.
    D. Gillies: ‘Popper’s Contribution to the Theory of Probability’ In: Karl Popper: Philosophy and Problems, ed. by A. O’Hear (Cambridge University Press, Cambridge 1996) pp. 103–120.Google Scholar
  27. 27.
    P. Milne: ‘A Note on Popper, Propensities and the Two Slit experiment’ British Journal for the Philosophy of Science. 36, 66–70 (1987)CrossRefGoogle Scholar
  28. 28.
    L. Boltzmann: ‘Bemerkungen über einige Probleme der mechanischen Wärmetheorie’ Wien.Ber. 75, 62 (1877)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Peter J. Clark
    • 1
  1. 1.Dept of Logic and MetaphysicsThe University of St AndrewsFife ScotlandUK

Personalised recommendations