Evidence for the Deterministic or the Indeterministic Description? A Critique of the Literature About Classical Dynamical Systems
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It can be shown that certain kinds of classical deterministic and indeterministic descriptions are observationally equivalent. Then the question arises: which description is preferable relative to evidence? This paper looks at the main argument in the literature for the deterministic description by Winnie (The cosmos of science—essays of exploration. Pittsburgh University Press, Pittsburgh, pp 299–324, 1998). It is shown that this argument yields the desired conclusion relative to in principle possible observations where there are no limits, in principle, on observational accuracy. Yet relative to the currently possible observations (of relevance in practice), relative to the actual observations, or relative to in principle observations where there are limits, in principle, on observational accuracy the argument fails. Then Winnie’s analogy between his argument for the deterministic description and his argument against the prevalence of Bernoulli randomness in deterministic descriptions is considered. It is argued that while the arguments are indeed analogous, it is also important to see they are disanalogous in another sense.
KeywordsDeterminism Indeterminism Observational equivalence Randomness Underdetermination
- Berkovitz, J., Frigg, R., & Kronz, F. (2006). The ergodic hierarchy, randomness and chaos. Studies in History and Philosophy of Modern Physics, 37, 661–691.Google Scholar
- Bishop, R. (2008). Chaos. In E. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Fall 2009 Edition). URL = http://plato.stanford.edu/archives/fall2009/entries/chaos/.
- Chernov, N., & Markarian, R. (2006). Chaotic billiards. Providence: American Mathematical Society.Google Scholar
- Frigg, R. (2008). A field guide to recent work on the foundations of statistical mechanics. In D. Rickles (Ed.) The Ashgate companion to contemporary philosophy of physics (pp. 99–196). London: Ashgate.Google Scholar
- Judd, K., & Smith, L. A. (2004). Indistinguishable states II: Imperfect model scenario. Physica D, 196, 224–242.Google Scholar
- Suppes, P., & de Barros, A. (1996). Photons, billiards and chaos. In P. Weingartner, & G. Schurz (Eds.) Law and prediction in the light of chaos research (pp. 190–201). Berlin: Springer.Google Scholar
- Werndl, C. (2009c). Philosophical aspects of chaos: Definitions in mathematics, unpredictability and the observational equivalence of deterministic and indeterministic descriptions. Ph.D. thesis. University of Cambridge.Google Scholar
- Winnie, J. (1998). Deterministic chaos and the nature of chance. In Earman J., & Norton J. (Eds.). The cosmos of science—essays of exploration (pp. 299–324). Pittsburgh: Pittsburgh University Press.Google Scholar