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    A theorem whose premises invoke physically unrealizable m... — Carmelics
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    Challenges→NP is a proper subset of NEXP

    A theorem whose premises invoke physically unrealizable models yields conclusions whose modal force is limited to mathematical, not computational, necessity.

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    1 reason for
    1 reason against

    Reasons For

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    Reason for
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    • 1.Physically unrealizable models (e.g., infinite memory, zero noise) lack empirical grounding, so their theorems cannot guarantee real-world computational behavior.
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    • 2.Mathematical necessity concerns logical possibility; computational necessity requires physical instantiation. These are distinct modal categories with different scopes.
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    • 3.Theorems from idealized models (Turing machines, frictionless planes) traditionally yield only bounded claims about actual systems, not absolute guarantees.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Unrealizable premises can still yield conclusions with computational force if they abstract stable properties shared by all physically realizable implementations.
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    • 2.The distinction between mathematical and computational necessity may be artificial—computation just *is* mathematics applied to physical substrates, not a separate modality.
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    • 3.Many productive theorems (P vs NP, halting problem) use idealized models yet restrict computational claims appropriately without invoking the unrealizability objection.
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    Truth & Knowledge1 linkedModality & Possibility1 linked

    Related

    Many productive theorems (P vs NP, halting problem) use idealized models yet res...Mathematical necessity concerns logical possibility; computational necessity req...NP is a proper subset of NEXPPhysically unrealizable models (e.g., infinite memory, zero noise) lack empirica...
    +3 moreShow less
    The distinction between mathematical and computational necessity may be artifici...Theorems from idealized models (Turing machines, frictionless planes) traditiona...Unrealizable premises can still yield conclusions with computational force if th...

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    2 (1 for, 1 against)
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