Skip to main content
Article thumbnail
Location of Repository

On the observational equivalence of continuous-time deterministic and indeterministic descriptions

By Charlotte Werndl

Abstract

This paper presents and philosophically assesses three types of results on the observational equivalence of continuous-time measure-theoretic deterministic and indeterministic descriptions. The first results establish observational equivalence to abstract mathematical descriptions. The second results are stronger because they show observational equivalence between deterministic and indeterministic descriptions found in science. Here I also discuss Kolmogorov’s contribution. For the third results I introduce two new meanings of ‘observational equivalence at every observation level’. Then I show the even stronger result of observational equivalence at every (and not just some) observation level between deterministic and indeterministic descriptions found in science. These results imply the following. Suppose one wants to find out whether a phenomenon is best modeled as deterministic or indeterministic. Then one cannot appeal to differences in the probability distributions of deterministic and indeterministic descriptions found in science to argue that one of the descriptions is preferable because there is no such difference. Finally, I criticise the extant claims of philosophers and mathematicians on observational equivalence

Topics: Q Science (General)
Publisher: Springer
Year: 2011
DOI identifier: 10.1007/s13194-010-0011-5
OAI identifier: oai:eprints.lse.ac.uk:31093
Provided by: LSE Research Online

Suggested articles

Citations

  1. (1982). A Special Family of Ergodic Flows and Their d-Limits", doi
  2. (1971). Bernoulli Flows With In Entropy",
  3. (1974). Billiards and Bernoulli Schemes", doi
  4. Charlotte 2009a, \Are Deterministic Descriptions and Indeterministic Descriptions Observationally Equivalent?", doi
  5. Charlotte 2009b, \What Are the New Implications of Chaos for Unpredictability?",
  6. (2007). Compendium to the Foundations of Classical Statistical Physics", doi
  7. (2005). Determinism and Indeterminism",
  8. (1998). Deterministic Chaos and The Nature of Chance",
  9. (1963). Deterministic Nonperiodic Flow", doi
  10. (1985). Ergodic Theory of Chaos and Strange Attractors", doi
  11. (1982). Ergodic Theory, doi
  12. (1983). Ergodic Theory, Cambridge: doi
  13. (1974). Ergodic Theory, Randomness, and Dynamical Systems, doi
  14. Ian Melbourne and Frederic Paccaut 2005, \The Lorenz Attractor Is Mixing", doi
  15. (1970). Imbedding Bernoulli Shifts in Flows",
  16. (1944). In General a Measure-preserving Transformation is Mixing", doi
  17. (1989). Kolmogorov's Work on Ergodic Theory", doi
  18. (1949). Measurable transformations", doi
  19. N andor 2003, \Proof of the Boltzmann-Sinai Ergodic Hypothesis for Typical Hard Disk Systems", doi
  20. (1994). Nonlinear Dynamics and Chaos, doi
  21. (2011). On Choosing Between Deterministic and Indeterministic Models: Underdetermination and Indirect Evidence". Forthcoming in: doi
  22. (1970). On Entropy and Generators of Measure-preserving Transformations", doi
  23. (1996). Photons, Billiards and Chaos", doi
  24. (1932). Proof of Gibbs' Hypothesis on the Tendency Toward Statistical Equilibrium", doi
  25. (2005). Randomness Is Unpredictability", doi
  26. Roman Frigg and Fred Kronz 2006, \The Ergodic Hierarchy, Randomness and Hamiltonian Chaos", doi
  27. (1999). Semi-Markov Models and Applications, Dotrecht: doi
  28. (1991). Statistical Properties of Chaotic Systems", doi
  29. (1953). Stochastic Processes, doi
  30. (1999). The Noninvariance of Deterministic Causal Models",

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.