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The British Journal for the Philosophy of Science Advance Access originally published online on January 19, 2009
The British Journal for the Philosophy of Science 2009 60(1):195-220; doi:10.1093/bjps/axn053
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© The Author (2009). Published by Oxford University Press on behalf of British Society for the Philosophy of Science. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

What Are the New Implications of Chaos for Unpredictability?

Charlotte Werndl

Faculty of Philosophy, University of Cambridge Sidgwick Avenue, Cambridge, CB3 9DA, UK

csw39{at}cam.ac.uk


  Abstract

From the beginning of chaos research until today, the unpredictability of chaos has been a central theme. It is widely believed and claimed by philosophers, mathematicians and physicists alike that chaos has a new implication for unpredictability, meaning that chaotic systems are unpredictable in a way that other deterministic systems are not. Hence, one might expect that the question ‘What are the new implications of chaos for unpredictability?’ has already been answered in a satisfactory way. However, this is not the case. I will critically evaluate the existing answers and argue that they do not fit the bill. Then I will approach this question by showing that chaos can be defined via mixing, which has never before been explicitly argued for. Based on this insight, I will propose that the sought-after new implication of chaos for unpredictability is the following: for predicting any event, all sufficiently past events are approximately probabilistically irrelevant.

  1. Introduction
  2. Dynamical Systems and Unpredictability
    2.1 Dynamical systems
    2.2 Natural invariant measures
    2.3 Unpredictability

  3. Chaos
    3.1 Defining chaos
    3.2 Defining chaos via mixing

  4. Criticism of Answers in the Literature
    4.1 Asymptotic unpredictability?
    4.2 Unpredictability due to rapid or exponential divergence?
    4.3 Macro-predictability and Micro-unpredictability?

  5. A General New Implication of Chaos for Unpredictability
    5.1 Approximate probabilistic irrelevance
    5.2 Sufficiently past events are approximately probabilistically irrelevant for predictions

  6. Conclusion


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