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    Fully analytical models could in principle achieve an exa... — Carmelics
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    Home/Modality & Possibility
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    Fully analytical models could in principle achieve an exact match between model states and target system states

    Modality & PossibilityTruth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
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    • 1.Analytical models are not constrained by discretization
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    • 2.An exact correspondence between the number of possible model states and target system states is achievable without discretization
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Chaotic systems exhibit sensitive dependence on initial conditions, meaning any finite specification of initial state—however precise—diverges exponentially from the true trajectory.
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    • 2.Even analytically exact equations require exact initial condition inputs, which are unavailable in principle given quantum indeterminacy and Heisenberg's uncertainty relations.
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    • 3.Therefore 'exact match between model states and target system states' is nomologically impossible regardless of whether discretization is eliminated.
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    Reason against 2 of 2
    ?
    • 1.Analytical models presuppose mathematical structures (real numbers, differential equations) that are human constructs, not ontological mirrors of physical systems.
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    • 2.The assumption that continuous mathematics maps exactly onto physical reality commits a category error identified by Hartry Field and structural realists: mathematical representation is not identity with the target domain.
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    Related

    An exact correspondence between the number of possible model states and target s...Analytical models are not constrained by discretizationAnalytical models presuppose mathematical structures (real numbers, differential...Chaotic systems exhibit sensitive dependence on initial conditions, meaning any ...
    +3 moreShow less
    Even analytically exact equations require exact initial condition inputs, which ...The assumption that continuous mathematics maps exactly onto physical reality co...Therefore 'exact match between model states and target system states' is nomolog...

    Similar

    An exact correspondence between the number of possible model states an...81%There will always be many more target system states than model states ...79%Assuming the model is perfect, there are too many states indistinguish...74%No matter how fine-grained the model state space is made, many differe...73%

    Source

    AI-extracted1/3 agreementValid
    SEP: chaos
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    Of course, we do not have perfect models. But even if we did, they are unlikely to live up to our intuitions about them (Judd and Smith 2001; Judd and Smith 2004). For example, no matter how many observations of a system are made, there still will be a set of trajectories in the model state space that are indistinguishable from the actual trajectory of the target system. Indeed, even for infinite past observations, we cannot eliminate the uncertainty in the epistemic states given some unknown on
    Extraction notes

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

    Details

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