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    There will always be many more target system states than ... — Carmelics
    Home/Skepticism
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    There will always be many more target system states than model states for any computational model

    Modality & Possibility
    ?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.The faithful model assumption implies the nonlinear model state space is a faithful representation of the possibilities in the physical space of the target system
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    • 2.No matter how fine-grained the model state space is made, many different ontological states of the target system will map into the same epistemic state of the model
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    • 3.Computational models require discretization of equations, which further limits the number of representable model states
      ?

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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Digital physics frameworks (Wolfram, Fredkin) propose that physical reality itself is fundamentally discrete and computational at the Planck scale.
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    • 2.If the target system's state space is itself finite and discrete, a sufficiently fine-grained computational model can achieve a bijective mapping with physical states.
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    • 3.The claim's force depends on assuming continuous physical state spaces, which is a substantive metaphysical commitment, not an established fact.
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    Reason against 2 of 2
    ?
    • 1.The argument conflates ontological states with physically distinguishable states, but quantum mechanics imposes fundamental limits on state distinguishability via the uncertainty principle.
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    • 2.If no physical process can distinguish between two target system states, they constitute one physical state for all scientific purposes, potentially equalizing model and target cardinalities.
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    Topics

    SkepticismModality & Possibility

    Connections

    2 topics

    Truth & Knowledge3 linkedPhilosophy of Language1 linked

    Related

    Computational models require discretization of equations, which further limits t...Digital physics frameworks (Wolfram, Fredkin) propose that physical reality itse...If no physical process can distinguish between two target system states, they co...If the target system's state space is itself finite and discrete, a sufficiently...
    +4 moreShow less
    No matter how fine-grained the model state space is made, many different ontolog...The argument conflates ontological states with physically distinguishable states...The claim's force depends on assuming continuous physical state spaces, which is...

    Similar

    An exact correspondence between the number of possible model states an...80%Fully analytical models could in principle achieve an exact match betw...79%No matter how fine-grained the model state space is made, many differe...77%Assuming the model is perfect, there are too many states indistinguish...77%

    Source

    AI-extracted1/3 agreementValid
    SEP: chaos
    View source passageHide passage
    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

    The faithful model assumption implies the nonlinear model state space is a faith...
    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit