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    Confirmation of chaotic models is problematic even under ... — Carmelics
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    Confirmation of chaotic models is problematic even under the assumption of a perfect model

    Skepticism
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Assuming the model is perfect, there are too many states indistinguishable from the actual state of the system
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    • 2.These indistinguishable states yield empirically indistinguishable trajectories in the model state space
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    • 3.If multiple distinct states produce empirically indistinguishable trajectories, confirmation cannot uniquely identify the actual state
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Confirmation is holistic and probabilistic: Bayesian updating over trajectory bundles raises posterior probability of model classes, not point states.
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    • 2.Van Fraassen's constructive empiricism holds that empirical adequacy across observable trajectories suffices for confirmation, making state-underdetermination epistemically irrelevant.
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    • 3.The indistinguishability of states is itself a structural prediction of the chaotic model, and observing it constitutes confirmatory evidence for that model.
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    Reason against 2 of 2
    ?
    • 1.Duhem-Quine holism shows that confirmation targets theoretical frameworks, not individual state attributions, so trajectory-bundle coherence confirms the model as a whole.
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    • 2.Chaotic models generate statistical invariants—SRB measures and Lyapunov spectra—that are robustly measurable and distinguish correct models from incorrect ones empirically.
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    Related

    Assuming the model is perfect, there are too many states indistinguishable from ...Chaotic models generate statistical invariants—SRB measures and Lyapunov spectra...Confirmation is holistic and probabilistic: Bayesian updating over trajectory bu...Duhem-Quine holism shows that confirmation targets theoretical frameworks, not i...
    +4 moreShow less
    If multiple distinct states produce empirically indistinguishable trajectories, ...The indistinguishability of states is itself a structural prediction of the chao...These indistinguishable states yield empirically indistinguishable trajectories ...Van Fraassen's constructive empiricism holds that empirical adequacy across obse...

    Similar

    Detailed predictions of individual trajectories fail rapidly for chaot...77%Many global behaviors of chaotic models can be precisely predicted, su...76%Formal definitions seek to fully characterize chaotic behavior in math...74%Γ implies C only if C is satisfied by every model in MΓ rather than ev...73%

    Source

    AI-extracted1/3 agreementValid
    SEP: chaos
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    Recall that SD—exponential divergence of neighboring trajectories—is taken by many to be a necessary condition for chaos. As we saw in §3, it is not straightforward to confirm when we have a model serving as a good explanation because, for instance, the slightest refinement of initial conditions can lead to wildly differing behavior. So on many standard approaches to confirmation and models, it would be difficult to say when we had a good explanation. Even if we push the faithful model assumpt
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit