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    Absence of proof of superpolynomial lower bounds is not e... — Carmelics
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    Challenges→The failure of polynomial boundedness has not been proven for most familiar proof systems

    Absence of proof of superpolynomial lower bounds is not equivalent to absence of superpolynomial lower bounds in those systems.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
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    • 1.Proof limitations reflect current mathematical tools, not reality. Gödel showed formal systems can't prove all true statements within them.
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    • 2.Complexity theory distinguishes between existence of phenomena and our epistemic access to them. Bounds may exist but remain formally unprovable.
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    • 3.Historical precedent: negative results about algebraic methods (Razborov-Rudich) show certain proof techniques fundamentally cannot establish superpolynomial bounds.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.In mathematics, 'existence' claims require construction or proof. Without evidence, asserting hidden bounds is unfalsifiable speculation, not justified belief.
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    • 2.The claim conflates epistemology with ontology illegitimately. Absence of proof may genuinely indicate absence of fact in formal systems designed precisely to capture computability.
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    Related

    Complexity theory distinguishes between existence of phenomena and our epistemic...Historical precedent: negative results about algebraic methods (Razborov-Rudich)...In mathematics, 'existence' claims require construction or proof. Without eviden...Proof limitations reflect current mathematical tools, not reality. Gödel showed ...
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    The claim conflates epistemology with ontology illegitimately. Absence of proof ...The failure of polynomial boundedness has not been proven for most familiar proo...

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