Abstract
Chaos-related obstructions to predictability have been used to challenge accounts of theory validation based on the agreement between theoretical predictions and experimental data (Rueger & Sharp, 1996. The British Journal for the Philosophy of Science, 47, 93–112; Koperski, 1998. Philosophy of Science, 40, 194–212). These challenges are incomplete in two respects: (a) they do not show that chaotic regimes are unpredictable in principle (i.e., with unbounded resources) and, as a result, that there is something conceptually wrong with idealized expectations of correct predictions from acceptable theories, and (b) they do not explore whether chaos-induced predictive failures of deterministic models can be remedied by stochastic modeling. In this paper we appeal to an asymptotic analysis of state space trajectories and their numerical approximations to show that chaotic regimes are deterministically unpredictable even with unbounded resources. Additionally, we explain why stochastic models of chaotic systems, while predictively successful in some cases, are in general predictively as limited as deterministic ones. We conclude by suggesting that the way in which scientists deal with such principled obstructions to predictability calls for a more comprehensive approach to theory validation, on which experimental testing is augmented by a multifaceted mathematical analysis of theoretical models, capable of identifying chaos-related predictive failures as due to principled limitations which the world itself imposes on any less-than-omniscient epistemic access to some natural systems.
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We give special thanks to two anonymous reviewers for their helpful comments that have substantially contributed to the final version of this paper
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Batitsky, V., Domotor, Z. When good theories make bad predictions. Synthese 157, 79–103 (2007). https://doi.org/10.1007/s11229-006-9033-0
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DOI: https://doi.org/10.1007/s11229-006-9033-0