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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
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    Perspectives
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    Home/Original/inverse
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    Inverse View

    It is not the case that The polynomial/exponential boundary in complexity theory is a formal, machine-model-relative result dependent on Church-Turing thesis assumptions that strict finitists explicitly rejected.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    1 perspective
    Reason for
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    • 1.P/NP polynomial boundary holds across all standard Turing-equivalent models regardless of philosophical beliefs about finiteness or infinity.
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    • 2.Strict finitism's rejection of Church-Turing doesn't invalidate it; one can accept computational results while denying their philosophical interpretation.
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    • 3.Complexity classes measure worst-case feasibility for concrete inputs, not abstract infinite processes, grounding them in finitist-compatible terms.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Church-Turing thesis is unprovable foundational assumption, not theorem, so complexity boundaries rest on non-logical philosophical commitments.
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    • 2.Strict finitists reject infinite sets and unbounded computation; P/NP distinction presupposes Turing machines operating on arbitrarily large inputs.
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    • 3.Different computational models (quantum, analog, hypercomputation) yield different complexity classes, showing boundaries are model-dependent conventions.
      ?

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