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    In nonlinear systems, the whole cannot be reduced to the ... — Carmelics
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    Home/Modality & Possibility
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    In nonlinear systems, the whole cannot be reduced to the sum of its parts.

    CausationModality & 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.Hamiltonians for nonlinear systems are never separable.
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    • 2.Nonseparable Hamiltonians cannot be decomposed into individual independent subsystems.
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    • 3.The interactions in a nonseparable system cannot be transformed away, so subsystems cannot be treated as independent.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Nonseparability of Hamiltonians is a mathematical feature of the formalism, not a metaphysical fact about ontological parts and wholes.
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    • 2.Causey, Nagel, and classical reductionists distinguish formal intractability from ontological irreducibility: epistemic limits do not entail compositional failure.
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    • 3.A system whose behavior cannot be computed from parts independently may still be fully constituted by those parts and their intrinsic properties.
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    Reason against 2 of 2
    ?
    • 1.Oppenheim and Putnam's unity-of-science framework allows reduction through bridge laws even when subsystem dynamics are coupled and nonlinear.
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    • 2.The supporting argument conflates dynamical inseparability with mereological non-summation, but classical mereology permits wholes fully grounded in parts even under strong interaction.
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    Modality & PossibilityCausation

    Related

    A system whose behavior cannot be computed from parts independently may still be...Causey, Nagel, and classical reductionists distinguish formal intractability fro...Hamiltonians for nonlinear systems are never separable.Nonseparability of Hamiltonians is a mathematical feature of the formalism, not ...
    +4 moreShow less
    Nonseparable Hamiltonians cannot be decomposed into individual independent subsy...Oppenheim and Putnam's unity-of-science framework allows reduction through bridg...The interactions in a nonseparable system cannot be transformed away, so subsyst...The supporting argument conflates dynamical inseparability with mereological non...

    Similar

    For nonlinear systems, Hamiltonians are never separable.80%Hamiltonians for nonlinear systems are never separable.80%Chaos only exists in nonlinear systems (for classical macroscopic syst...74%Chaos is impossible for linear systems with separable Hamiltonians.74%

    Source

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    SEP: chaos
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    As discussed in Section 1.2.2, linear systems always obey the principle of linear superposition. This implies that the Hamiltonians for such systems are always separable. A separable Hamiltonian can always be transformed into a sum of separate Hamiltonians with one element in the sum corresponding to each subsystem. In effect, a separable system is one where the interactions among subsystems can be transformed away leaving the subsystems independent of each other. The whole is the sum of the par
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    Validity: Extracted via Max plan + API grounding/validity checks

    Details

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