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    The BGS oracle argument presupposes that a valid P≠NP pro... — Carmelics
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    Challenges→Diagonalization cannot be used to separate P and NP.

    The BGS oracle argument presupposes that a valid P≠NP proof must be syntactically relativizable, but this is a methodological assumption, not a logical necessity.

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    1 reason for
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    Reasons For

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    Reason for
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    • 1.Relativization is a proof technique, not a logical requirement. Non-relativizing arguments exist validly in other domains of mathematics.
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    • 2.The BGS oracle construction shows relativizing proofs have limits, but doesn't prove all valid proofs must be relativizing.
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    • 3.Confusing methodological constraints (what we've successfully used) with logical necessities is a common category error in mathematics.
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    Reasons Against

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    Reason against
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    • 1.Any P≠NP proof must explain why NP machines gain computational power over P machines. Oracles test whether a proof mechanism is robust to this variation.
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    • 2.Non-relativizing proofs would require new mathematical insights not yet developed. Dismissing relativization risks ignoring legitimate structural barriers.
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    • 3.The distinction between 'methodological assumption' and 'logical necessity' breaks down when the assumption reflects deep problem structure.
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    Related

    Any P≠NP proof must explain why NP machines gain computational power over P mach...Confusing methodological constraints (what we've successfully used) with logical...Diagonalization cannot be used to separate P and NP.Non-relativizing proofs would require new mathematical insights not yet develope...
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    Relativization is a proof technique, not a logical requirement. Non-relativizing...The BGS oracle construction shows relativizing proofs have limits, but doesn't p...The distinction between 'methodological assumption' and 'logical necessity' brea...

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